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dissertation entitled

Predicting the Path of Grain Prices With Limited
Data: A Case Study From Mall

presented by

Kimberly M. Aldridge

has been accepted towards fulﬁllment

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PREDICTING THE PATH OF GRAIN PRICES WITH LIMITED DATA:
A CASE STUDY FROM MALI

By

Kimberly M. Aldridge

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1999

ABSTRACT
PREDICTING THE PATH OF GRAIN PRICES WITH LIMITED DATA:
A CASE STUDY FROM MALI
By

Kimberly M. Aldridge

The late 19803 witnessed a surge of agricultural market reform efforts in the
developing world, including Africa. Many of these efforts were accompanied by the
implementation of market news services, which sought to encourage the competitive
growth of the private sector by improving market transparency. One result of market
reform in Mali has been the increased demand for improved outlook information on the
likely evolution of grain prices. Such information is essential for making, inter alia, better
marketing store/sell decisions.

This purpose of this research is twofold. The ﬁrst is methodological in nature and
focuses on developing and evaluating alternative methods of forecasting short-term
agricultural prices with limited data, using the grain markets from Mali as a case study. In
ﬁscally austere environments, publicly-funded market information systems must
continually Show evidence of their social/economic value, thus, the second objective is to
demonstrate that investing scarce resources in improved forecasting methods can be
economically valuable.

Monthly grain price data from the Malian market information system, from
September 1982 to September 1998, are used to build univariate and multi-variate time-

series models of rice, sorghum and maize prices. The models which have errors that

approximate a white noise process, a necessary condition for emcient forecasting, are
entered into a forecast competition and out—of-sample forecasts are generated for 1, 2 and
3-steps ahead. The forecast contenders are statistically evaluated and scored using root
mean squared error and turning point error criteria. The competitor with the lowest score
emerged as the winner. For sorghum, the results of the forecasting competition indicated
that the ARIMA with second-order harmonic speciﬁcation of seasonality was the most
accurate for forecasting sorghum price changes 2, and 3 months ahead, while the vector
error correction model had the lowest root mean squared error for predicting 1 month
ahead.

To demonstrate the value of investing in improved price forecasting techniques,
model-generated store/sell strategies of a sorghum producer in the Zangasso region of
Mali, were compared to marketing Strategies generated from a random walk model. The
criteria used to evaluate the models included mean net price received (net of storage cost)
and percentage of correct decisions. The model with the highest mean net price and
highest percentage of correct decisions was declared the winner. The results indicate that
relative to the random walk, marketing strategies based on improved forecast models,
generate a higher mean net price received, thus, without accounting for risk preferences

and capacity to respond, such models can indeed be economically valuable.

Cepyright by
Kimberly M. Aldridge

1999

DEDICATION

for my Imani

ACKNOWLEDGMENTS

The completion of this dissertation is a product of ﬁerce determination and a
staunch belief in myself. I can make that claim because despite the fact that dissertations
assume lives of their own, the cycle of our own life does continue. The challenge lies in
striking an appropriate balance between investing time in theories of time-varying volatility
and a 3 year old’s dance recital. Although, the path has been long and often painful, my
growth academically, professionally and personally indicate that it is well worth the
struggle.

I had help. Many thanks to my guidance committee: To John Staatz, my major
professor and thesis coordinator, who skillfully, but gently nudged me along, yet again.
Since completing my masters program under your guidance, my profound gratitude to you
has only deepened. Your continued support and standard of excellence was the impetus
that encouraged me to work harder and to not succumb to the trials and tribulations of
just living life. Somehow, if you could believe, then I could as well. I look forward to
years of collaboration and ﬁ‘iendship. To Bob Myers from whom I gleaned the intricacies
of time-series econometrics (well, I tried anywayl). Dr. Myers patiently (usually) spent
many hours trying to convince me that “it’s not rocket science”! Fortunately, “it” turned
out okay, althoughl remain skeptical about its unrocketscienceness! To Torn Reardon,
your energy and enthusiasm during our initial brainstorming sessions made conceptualizing
enjoyable and the potential exciting. To John Strauss, many thanks for your support over

the years. And ﬁnally, to Al Schmid who insists that high exclusion cost and non-

appropriability both add up to the marginal cost of an additional user being zero! Al, I
only wish I had time to learn more.

I must also thank Nango Dembele and Jim Teﬂt, both who work or have worked
at the market information system in Mali, for sending data and helping me to understand
the stories behind the numbers.

Financial support for this research was critical to its completion and was provided
by the Food Security H Cooperative Agreement between USAID and Michigan State
University, Department of Agricultural Economics, for which I am most grateful I would
also like to thank the food security project and the Department for its institutional and
infra structural support, including Chris, Carol and Elizabeth of computer services, Janet
and Josie of the business ofﬁce, Roxie Damer, and the folks in the reference room, and
many others. I would also like to express my gratitude to the Minority Competitive
Doctoral Fellowship program and the ALAN A fellowship program which both provided
support during the early years of my doctoral studies.

To my family, and the many friends and colleagues whom I’ve met along this
journey and who in numerous ways contributed to its successful completion, thank you all
for your unwavering support and belief in me. Special thanks go to my mom, Cheryl
Danley and Raymond F amilusi. Finally, thanks to my daughter, Imani, my faith, my peace,

for enduring the many hours at the babysitter so Dr. mommy could ﬁnish her big book!

TABLE OF CONTENTS

INTRODUCTION AND RESEARCH CONTEXT ............................ 1
1.0 Introduction .............................................. 1
1.1 Problem Statement and Research Objectives ...................... 3
1.2 Malian Grain Markets ....................................... S
1.3 Organization of Dissertation ................................ 15

ECONOMIC FORECASTING IN AGRICULTURE FOR

DEVELOPING COUNTRIES ........................................... 16
2.0 Introduction ............................................. 16
2.1 Conceptual Issues ......................................... 17
2.2 Qualitative Forecasting Techniques ............................ 18
2.3 Structural Models for Forecasting ............................. 19
2.4 Noncausal Forecasting Techniques ............................ 22

2.4.1 Trends and Exponential Smoothing Methods .............. 23

2.4.2 Time-series Models .................................. 24

2.4.2.1 ARIMA Models .............................. 26

2.5 Vector Autoregression Models ............................... 33
2.6 Measuring Forecast Accuracy ................................ 34

PRELIMINARY ANALYSIS OF PRICE LEVEL DATA ..................... 37
3.0 Introduction ............................................. 37
3.1 Data ................................................... 37
3 .2 Missing Data ............................................ 39
3.3 Inﬂation ................................................ 40
3.4 Seasonal Analysis & Price Trends ............................. 42
3.5 Marketing Margins ........................................ 51
3.6 Characteristic Time Series Properties of Commodity Price Data ...... 51

3.6.1 Stochastic trends .................................... 52
3.6.2 Time-varying Volatility and Excess Kurtosis ............... 58
3 .7 Implications for Forecasting ................................. 60

SPECIFICATION AND ESTIMATION OF ALTERNATIVE PRICE MODELS . . . . 61

4.0
4.1

4.2

Introduction ............................................. 61
Smoothing Models ........................................ 62
4.1.1 Smoothing Procedures for Sorghum and Maize ............. 63
4.1.2 Smoothing Model for Rice ............................ 66
ARIMA Models .......................................... 68
4.2.1 ARIMA Models for Sorghum .......................... 72

4.2.1.1 Speciﬁcation Search for Seasonality in Sorghum Prices 74

viii

4.2.2 ARIMA Models for Maize Prices ....................... 79

4.2.3 ARIMA Models for Rice .............................. 86
4.2.4 ARIMA Models for Sorghum Producer Prices ............. 90
VECTOR AUTOREGRESSIONS AND COMMODITY PRICE MODELS ........ 94
5.0 Introduction ............................................. 94
5.1 Conceptual Framework .................................... 95
5.2 VAR Methodology: Some Practical Issues ...................... 97
5.2.1 Co-integration ...................................... 99
5.2.1.1 Co-integration Tests .......................... 100
5.3 Granger Causality in Grain Prices ............................ 105
5.4 VEC and Forecasting ..................................... 110
5.5 Forecast Error Variance Decomposition ....................... 112
5.6 VEC for Producer Prices in Zangasso ......................... 1 14
STATISTICAL EVALUATION OF THE FORECAST COMPETITORS ......... 120
6.0 Introduction ............................................ 120
6.1 Forecast Evaluation Criteria ................................ 121
6.1.1 Forecasting Consistency: Updating Procedure ............. 124
6.2 Predicting Retail Sorghum Prices ............................ 125
6.3 Predicting Retail Maize Prices .............................. 127
6.4 Predictions for Retail Rice ................................. 129
6.5 Predicting Sorghum Producer Prices .......................... 131
6.6 Summary of the Forecast Competition Results .................. 132
ECONOMIC EVALUATION OF PRICE FORECAST MODELS .............. 135
7.0 Introduction ............................................ 135
7.1 Conceptual Considerations and Decision Criteria ................ 136
7.2 Storage Rules ........................................... 141
7.3 Marketing Strategies and Storage Costs: Some Stylized Facts ...... 143
7.4 Decision Framework ..................................... 145
7.5 Economic Evaluation of Forecast Models for Sorghum
Producer Prices ......................................... 146
SUMMARY AND IMPLICATIONS ..................................... 155
8.0 Introduction ............................................ 155
8.1 Research Methods ....................................... 157
8.2 General Results ......................................... 160
8.3 Complements and Extensions to Information ................... 163
8.4 Implications ............................................ 164
8.5 Further Research ........................................ 164
REFERENCES ...................................................... 166

ix

LIST OF TABLES

Table 1.1: Evolution of Grain Production ................................... 5
Table 3.1: Annual Percentage Change in National CPI ........................ 41
Table 3.2: Summary Statistics for Niono ................................... 49
Table 3.3: Summary Statistics for Sorghum in Zangasso ....................... 49
Table 3.4: Summary Statistics for Maize in Zangasso .......................... 49
Table 3.5: Summary Statistics for Consumer Prices in Bamako .................. 49
Table 4.1: Forecasts from Holt-Winters Smoothing Procedures .................. 65
Table 4.2: Forecasts ﬁ'om Holt-Winters Smoothing for Rice .................... 67
Table 4.3: Results of Unit Root Tests ..................................... 70
Table 4.4: ARIMA Models for Sorghum ................................... 76
Table 4.5: Chow Forecast Tests .......................................... 78
Table 4.6: ARIMA Models for Maize ..................................... 83
Table 4.7: ARCH(q) Lagrange Multiplier Statistics .......................... 84
Table 4.8: ARIMA with GARCH errors ................................... 85
Table 4.9: ARIMA Models for Rice ....................................... 89
Table 4.10: Moving Average with GARCH errors ............................ 89
Table 4.11: ARIMA Processes for Sorghum Producer Prices .................... 93
Table 5.1: Co-integration Tests ......................................... 103
Table 5.2: Normalized Co-integrating Equation ............................. 104
Table 5.3: Test Statistics for Order Selection ............................... 107
Table 5.4: Results of Causality Tests ..................................... 109
Table 5.5: VEC(2) for log Cereals ...................................... 112
Table 5.6: Variance Decomposition ...................................... 113
Table 5.7: Pairwise Granger Causality Tests ............................... 116
Table 5.8: VEC(4) for Producer Prices in Zangasso .......................... 117
Table 5.9: Variance Decomposition for Producer Prices ....................... 118
Table 6.1: Summary of Retail Sorghum Models ............................. 126
Table 6.2: Forecast Evaluation Statistics for Sorghum ........................ 126
Table 6.3: Summary of Retail Maize Models ............................... 128
Table 6.4: Forecast Evaluation Statistics for Maize .......................... 128
Table 6.5: Summary of Retail Rice Models ................................ 130
Table 6.6: Forecast Evaluation Statistics for Rice ............................ 130
Table 6.7: Summary of Sorghum Producer Price Models ...................... 131
Table 6.8: Forecast Evaluation Statistics for Sorghum Producer Prices ........... 132
Table 7.1: Post-Harvest Marketing Strategies .............................. 147
Table 7.2: Economic Results of Post-Harvest Marketing Strategies-Season 1 ...... 150
Table 7.3: Economic Results of Post-Harvest Marketing Strategies-Season 2 ...... 151
Table 7.4: Correctness of Decision ...................................... 152

LIST OF FIGURES

Figure 1.1: Principales zones of culture du Mali ............................... 7
Figure 1.2: Production cerealiere ......................................... 8
Figure 3.3: Correlogram of Sorghum Prices ................................. 44
Figure 3.4: Correlogram of Maize Prices ................................... 45
Figure 3.5: Correlogram of Rice Prices .................................... 46
Figure 4.1: Nominal Prices logged ....................................... 64
Figure 4.2: Logged Rice Prices .......................................... 66
Figure 4.3: Percentage change in Sorghum Prices ............................ 72
Figure 4.4: Correlogram of the Percent Change in Sorghum Prices ............... 73
Figure 4.5: Percent Change in Maize Prices ................................. 80
Figure 4.6: Correlogram of the Percent Change in Maize Prices ................. 81
Figure 4.7: Volatility in Maize Prices ...................................... 84
Figure 4.8: First Differences of logged Rice Prices ............................ 86
Figure 4.10: Correlogram of the Percent Change in Rice Prices .................. 87
Figure 4.12: Correlogram of Sorghum Producer Prices ........................ 91
Figure 5.1: Evolution of Commodity Prices ................................ 105
Figure 5.2: Evolution of Producer Prices in Zangasso ........................ 115

CHAPTER 1

INTRODUCTION AND RESEARCH CONTEXT

1.0 Introduction

The future is uncertain, and thus the ﬁll] impact of decisions taken today is oﬁen
not realized until later. To reduce some of this uncertainty and improve the efﬁciency of
the decision making process, many economic decisions require forecasts of the future
behavior of key economic variables. The more accurate the predictions, the better able are
decision makers to make accurate and timely decisions (Holden 1990).

Agricultural management decisions in a market-oriented economy involve
considerable uncertainty. Indeed, the special position of food production in a nation’s
security, coupled with the public-good characteristics of information, have led most
developed countries to institute national statistical and armlytical organizations which
regularly disseminate market news and outlook information on the agricultural sector.
Forecast information is used to inform policy decisions such as the provision of market
support to producers, as well as provides private decision makers information with which
to plan and strategize. These projections are typically made with conventional
econometric methods, with time-series approaches occupying minor roles (Allen 1994).

The late 1980s witnessed a surge of agricultural market reform efforts in the
developing world, including Aﬁica. Many of these efforts were accompanied by the
implementation of market news services, which sought to encourage the competitive

growth of the private sector by improving market transparency. As expected,

2

liberalization altered the operating and decision environments facing economic agents.
One result has been the increased demand for improved outlook information on the likely
evolution of cereals and related markets. Such information is essential for making better
storage/sales decisions, for production planning and acquiring stock for processing, as
well as for planning trade operations and for better public policy decisions.

To the degree that they are undertaken systematically in newly hberalizing
economies, forecasts of key economic decision variables are largely subjective, i.e., based
on guesses, experience or intuition without an explicit structure or method for processing
information'. And the forecasts that are derived from explicit or model-based procedures
(formal relationships between variables) are usually based on simple smoothing or trend
extrapolation methods. Because these methods often fail to capture turning point errors
(Tomek & Robinson, 1990), more sophisticated models that account for such turning
point errors can theoretically ameliorate forecast accuracy and increase the value of
outlook information to the economic agent and society as a whole.

Most market information systems M85) in the developing world are primarily
price reporting services which are publicly supported with substantial reliance on
external/donor ﬁnancing. However, as donor support is increasingly withdrawn, the
sustainability of market information systems is challenged as they are forced to survive on
very fragile governmental budgets. The value of market information and information

services is often poorly understood by policymakers, making market information systems

 

ISubjective forecasting techniques are not necessarily less accurate than model-based
forecasting, but these methods usually preclude any quantitative measure of conﬁdence in
the resulting forecasts.

3

prime candidates for budget cuts and possible elimination. Indeed, despite the well known
public good arguments of non-appropriability and high exclusion costs, even the
developed world debates the necessity of public investment in market news servicesz.
Nonetheless, these services in industrial countries continue to receive public support by
delivering information products that are in demand ﬁ'om the business, policy-making and
research sectors. Analogously, market information systems in the developing world are
under pressure to demonstrate that they are a worthwhile public investment by creating a
constituency to lobby for political support by strengthening and adding value to their
current product proﬁle. Meeting the demand for improved outlook information such as
Short-run forecasts on the future path of prices, is one such effort to induce constituents to

contribute ﬁnancially to maintaining market information systems.

1.1 Problem Statement and Research Objectives

The cereals market information system in Mali, known until recently as the SIM,
has regularly disseminated price information on various grains in various markets
throughout the country Since 1989’. Currently the SIM is ﬁghting to sustain itself
ﬁnancially by inter alia meeting the revealed demand for price outlook information. Using
the SIM price data, this research develops and evaluates statistically and economically

short-term price forecasting models. The Speciﬁc objectives are to:

 

2For instance, see Bonnen 1977, 1996.

3In late 1998, the SIM was restructured (broadening its mandate) and renamed the
Observatoire des Marches Agricoles (OMA).

4

0 develop alternative models for sorghum, maize and rice prices in Mali that can be
used for Short-term forecasting in the context of sparse data.

0 evaluate the forecasting ability of the alternative price models based on statistical
criteria.
One way to improve outlook information is to develop “better” forecasting
models, where better implies an increase in value to an end-user and/or society‘. Once an
appropriate forecast model is developed, in the context of grain marketing strategies, the

value of improved price forecast information is analyzed. Towards this end, this research

0 evaluates the economic value of improved price forecast information to a group of
users by evaluating the utility of the alternative price models in a decision-making
context and;

0 draws lessons on which time-series models produce accurate and economically
useful forecasts with limited data.

In order to predict the future path of grain prices, it is ﬁrst necessary to develop an
understanding of the markets in which the prices are formed. The next section therefore
sets the research context by identifying important aspects of the sorghum, maize and rice
markets in Mali which are relevant for understanding and modeling grain price behavior.
It describes the salient characteristics of the these markets which inﬂuenced the formation

of grain prices during the January 1982 to September 1996 period.

 

4The terms “outlook” and “(short-run) forecasts” are used interchangeably.

1.2 Malian Grain Markets

Theoretically, commodity prices are determined by the interaction of supply and

demand, which in turn is conditioned by the institutional and climatic environment in

which the markets operate. Mali is a landlocked country where about 85% of the total

population derives its livelihood from agriculture and livestock. Millet, sorghum and

maize are rainfed while a large component of rice production is irrigated. Between the

1984/85 and 1996/97 production campaigns total cereal production increased by almost

50%, led by a signiﬁcant rise in rice production of 9.8% to 27.9% of total cereals

produced. See table 1.1.

 

 

 

 

 

 

 

 

 

 

 

 

Table 1.1: Evolution of Grain Production in metric tons
1984/85 1990/91 1995/96 1996/97
Sorghum 369,818 531,433 710,275 540,273
(33.2) (30.0) (21.3) (24.5)
Maize 101,440 196,579 264,457 289,761
(9.12) (11.0) (12.2) (13.2)
Rice 109,354 282,236 462,702 613,965
(9.83) (16.0) (21.3) (27.9)
Total 1,1 1 1,668 1,769,153 2,172,429 2,200,933
Source: Ministere du Developpement Rural et de L’Eau (March 1998). Recueil des
Statistigues du Secteur Rural Malien. (Percent of total cereals in parentheses)’

 

 

5Millet, fonio and wheat are included in the total.

 

6

Millet, sorghum, maize and rice are the staple crops produced and consumed in Mali.
Smallholders account for the bulk of grain production. Millet and sorghum comprise the
largest cultivated areas and are produced throughout the country, while maize is produced
in the higher rainfall areas. Irrigated rice is concentrated in the irrigated areas of the
Ofﬁce du Niger zone“. See map of the diﬂerent agricultural zones in ﬁgure 1.1. Mais
sorgo and riz are the French terms for maize, sorghum and rice respectively.

The structure of millet and sorghum production has changed little over the last
twenty years. The technological change that has occurred has come from the introduction
of shorter-cycle varieties, which has allowed farmers to manage climatic risk better but has
not led to dramatic increases in yield. Maize and rice on the hand have witnessed
technological change7 In general, only farmers engaged in cash crop production such as

cotton and rice have access to purchased inputs and labor-saving technologies”.

 

6The Oﬂice du Niger is a parastatal enterprise established in 1932 to provide
irrigation in the area surrounding Niono (Diarra 1994).

7Although animal traction has become common in the cotton zone of southern
Mali, most farmers continue to rely on the traditional hoe to cultivate. See Dirnithe
(1997), Boughton (1994) and Diarra (1994) for ﬁIrther discussion of technological
advances of grain crops in Mali.

uPaddy rice is produced both as a food and cash crop.

7

Figure 1.1

Principales zones de culture du MALI

D Provinces

 

 

 

 

 

8

Rainfall variability, which in the agricultural zones of central and southern Mali
ranges from an average of 700 mm tol300 mm. per year, is the major factor affecting the
productivity of smallholders. Grain production ﬂuctuates directly with the variability in
rainﬁalL In ﬁgure 1.2, ﬁ'om 1991 to 1998, sorghum production appears relatively stable
arormd 700 thousand tons, increasing towards 800 thousand tons in 1998. From 1987 to
1998, maize production, which is considerably less than both sorghum and rice, increased
slowly ﬁ-om about 200 thousand tons to 375 thousand tons. Rice appears to be the most
rapidly growing and highly variable grain, increasing ﬁom about 250 thousand tons in

1987/88 to almost 700 thousand tons in 1997/98 (FAO website, January 1999).

Figure 1.2

MALI
Production cdréalﬁn (mailers do tonnes)

 

 

 

1200 '

_Hiz
coo —Mi|
600 _ — s 5'

Autros
400

 

 

 

 

 

 

 

 

 

200
0% 8. (:7 m g. 8 8F! '1 g
h- ; a) 0" 0.) g") m "-
§ ,_ 5 g 3 g. .85 g g it; E3 OFAOISMAR

 

9

Cereals (millet, sorghum, maize and rice) account for 80% of total calorie intake in rural
diets and 70% of urban diets (Badiane et al., 1992 as reported in Dembele 1994). Rural
consmners produce most of their grain needs; consequently only about 15% of total grain
production reaches the market. Like most developing countries in Aﬁica, the pattern of
domestic consumption in Mali has evolved with urbanization, with rice, which is easier and
faster to prepare, being the preferred urban grain. Urban consumers devote about 51% of
their total expenditures to food, and cereals comprise 48% of household food
expenditures (reported in Diarra 1994). Grain prices therefore strongly inﬂuence the real
incomes of urban consumers.

The coarse grain markets are thin, with maize being the lowest in volume. Rice
beneﬁts from the stabilizing effects of irrigation and imports, and thus rice prices appear
more stable relative to coarse grains. Variations in marketed surplus are determined
largely by variations in climatic conditions. During good rainfall years a higher proportion
of total production reaches the market, while during bad years rmrketed surplus drops
Sharply. The level of production inﬂuences inter-annual variability in marketed surphrs,
while the marketing strategies of producers determine the seasonal distribution of
marketed surplus within years. Another factor that contributes to the volatility of the
market is that many farmers go from being net sellers in good years to net buyers in bad
years. Hence, both the supply curve and the demand curve are shifting in ways that
accentuate price movements.

Furthermore, cash-crop producers store most of their cereals at harvest and spread

sales over the season, while the rmjority of noncash crop producers tend to sell more at

10

harvest (when prices are low) to meet ﬁnancial obligations (Dione 1994). In general,
marketed surplus, which takes place through a network of rural collectors, assemblers,
wholesalers and retailers, peaks during harvest and declines progressively over the months,
consequently shifting the storage function from producers to traders and/or farmer
cooperatives (Mehta 1989; Dembele 1994). It should be noted that some farmer
cooperatives support farm prices at harvest by buying and storing grain for sale when
prices rise later in the season.

AS mentioned above, domestic grain production in a given year is largely
determined by the level of rainfall, such that shortfalls in rainfall translate into shortfalls in
production. To satisfy the growing demand for cereals, Mali uses cereal imports and
food aid to oﬂSet the instability in domestic production and stabilize domestic
consumption. Thus, when domestic production is low, imports including food aid are high,
and when domestic production is high, imports are low and exports rise. Rice and wheat
constitute the bulk of imports and food aid. Moreover, Since the 1994 devaluation, export
demand has increased sharply, as Mali has become more competitive within the CF A zone
vis a vis non-ﬁanc zone suppliers.

In addition to food aid and imports, the national grain board maintains and
manages a national food security stock (N SS) to guard against severe food deﬁcits. At
58,500 tons, the N88 is comprised primarily of millet and sorghum. The replenishment of
the NSS creates an additional demand for traders and thus is very politicized. Indeed,
under political pressure OPAM distributes its demand across all agricultural zones by way

of quotas instead of pursuing more cost effective strategies such as procuring solely ﬁ'om

11
surplus zones’. According to Dembele (1994), these quotas inﬂate prices in deﬁcit zones,
later creating pressure for food aid distribution.

The polices governing the grain subsector have varied almost as much as the
weather”. Nonetheless, govemmental policy has consistently stressed self-sufﬁciency in
cereals as a major policy objective. While this goal has remained largely unchanged, the
policies used to achieve self-sufﬁciency have varied. In 1981, the Malian govemment, in
collaboration with several donors, began the process of reforming the grain markets under
the Cereals Market Reorganization Project, known by its French acronym, PRMC. The
previous agricultural policies which included sanctioning the national grain board (OPAM)
as a legal monopoly in cereals marketing and oﬁcial price ﬁxing, were unproductive,
ineﬂicient and ﬁnancially unsustainable (Steﬂ‘en 1992). During the early years of the
PRMC, when the country faced severe food deﬁcits, the objectives of the PRMC were to:

- legalize and increase the role of the private sector in the grain trade;

0 reduce marketing costs through increased competition and better

management of OPAM; and

0 transfer resources to farmers to enable them to invest in productivity-

increasing technologies.
Food aid receipts were used to stabilize and increase market prices for cereals, and the
national grain board was assigned a market stabilization role to support ofﬁcial producer

and consumer prices (Dembele 1994).

 

9Procurement is ﬁ'om local production during surplus years and from imports and
food aid during periods of poor harvests.

10For a historical perspective of the policies governing the Malian grain markets
see Dembele (1994) or Steﬁ‘en (1992).

12

These policy instruments were effective until 1986, when the return of normal
rainfall patterns resulted in two successive surplus years, making it ﬁnancially difﬁcult for
OPAM to stabilize producer prices through the management of a buffer stock”. Grain
marketing policies were adjusted in1987; speciﬁcally, OPAM’S role was reduced to the
distribution of food aid, the management of the national security stock, and the collection
and diffusion of market information. The determirmtion of producer and consumer prices
was left to market forces and instead supported indirectly by credit and export assistance
programs. These marketing-facilitating services were ﬁnanced by the sale of food aid.

Although the process of h'beralization began in 1981/82, the above policy
adjustments led to the eﬂ‘ective lrberalimtion of the coarse grain markets in 1987.
However, the paddy rice market, which is more concentrated, strategic and politically
sensitive, liberalized at a much Slower pace. Indeed, in 1987, the rice marketing parastatal
for the main irrigated rice production area, Oﬂice du Niger, continued to set a ﬂoor price
for paddy rice (Diarra 1994). Moreover, relative to the coarse grains, imports and thus
import policies play an important role in the rice market. In 1981, as part of the initial
reform process and to encourage imports, the government eliminated nearly all rice import
duties and taxes. Improved eﬁciencies in the irrigated rice sector, coupled with good
rains, led to signiﬁcant increases in domestic paddy rice production in the mid-19805,

leading the government to increase import duties ﬁom 5 to 32 percent of the border price

 

”In 1984/85 the country experienced a drought, and consequently market prices
were higher than OPAM’S prices. But in 1985/86 and 1986/87 rains were abundant and
OPAM’S guaranteed producer prices were higher than the market prices, so most
merchants attempted to sell to OPAM.

13

in 1986 (Diarra 1994) in order to protect domestic producers. In 1987, ﬁrrther attempts
to protect domestic rice production witnessed the introduction of “twinning”, in which
private traders wishing to import rice were forced to purchase an equal quantity ﬁom the
Oﬁce du Niger. A low world price and accumulating domestic stocks led the government
in October1987 to completely ban all rice imports.

The ban on rice imports resulted in high grain prices until June 1988, when the ban
was relaxed. In 1989, “twinning” was abandoned as part of an import reform program
imposed by the IMF. In 1990, another import ban was imposed which produced similar
results until the ban was lifted in the later part of 1990. From March 1991 to March
1992, the transitional government, in need of ﬁnancial resources, encouraged rice imports
by reducing import tariff rates if importers agreed to pay the import tax in advance of
actually importing the rice. This caused rice prices to decline in 1992/1993. More recent
import policies include a variable levy. The increased protection for the domestic rice
subsector starting in the early 19805 represented an implicit compensation for the
increasingly over-valued CFA ﬁ'anc, which hurt the competitiveness of Malian rice. In
January 1994, the CFAF, the Malian currency, was devalued by 100 percent, making rice
imports and fertilizer more expensive, but making domestic rice production more
competitive”.

As a result of near stagnant production technology for sorghum and millet,

uncertain rainfall, relatively low demand for maize, variable sectoral and tariff policies

 

12Prior to devaluation in 1994, rice could be obtained more cheaply on the
international markets.

14

which affect rice, the sorghum, maize and rice markets can be largely characterized as thin,
low-volume markets. Capturing the dynamic behavior of prices that result from such

uncertain markets and making Short-term forecasts is the focus of this research and is

conceptualized as follows:
Basic conditions
Inter-annual variation Intra-annual variation
Production Seasonality
Rainfall Storage
Policies Marketing strategies

The variation in grain prices is examined under two broad categories: inter-annual
variation, where the forces explaining the difference in prices ﬁ'om one year to the next are
examined; and intra-annual variation, where determinants of month-to-month variation are
identiﬁed. In a ﬁrst-best world, the factors speciﬁed above could be measured and
quantiﬁed and described in an econometric model designed to capture the price
determination process and then used to forecast the ﬁxture path of prices. However,
historical data bases in many developing countries are limited, and Mali is no exception
The challenge is to develop reasonably accurate forecast models with limited data on

variables other than price.

15

1.3 Organization of Dissertation

The dissertation is organized into eight chapters. Chapter 2 reviews the
forecasting literature and identiﬁes relevant forecast modeling techniques for countries
with sparse data sets (i.e., limited in length, quality and number of available measured
variables). Having identiﬁed a set of forecasting procedures, chapter 3 discusses and
analyzes the grain price data for Mali, while chapters 4 and 5 develop univariate and
mulitvariate price models, respectively. In chapter 6, the alternative price forecasting
models for sorghum, maize and rice are evaluated statistically for forecasting and the
“best” models for each commodity are identiﬁed. In an effort to analyze the value of
improved price forecast information, chapter 7 uses the forecast-decision-support
literature and the storage literature to economically evaluate forecasts models of producer
prices. Chapter 8 summarizes the study and draws major conclusions for policies and for

future research.

CHAPTER 2
ECONOMIC FORECASTING IN AGRICULTURE
FOR DEVELOPING COUNTRIES
2.0 Introduction

The nature of agricultural production and the historical relations among diﬁ‘erent
groups of participants in agriculture make agriculture different ﬁ'om most economic
activity. Both nature and governmental policy can have a major impact on agricultural
production, prices and proﬁts, making agriculture forecasting very difﬁcult. In fact,
empirical research has found that the large structural econometric models often do poorly
or do no better than simple naive models at forecasting agricultural production and prices.
The most likely reason, according to Allen (1994), is the inﬂuence of random Shocks or
unpredictable events such as droughts, ﬂoods, and pest attacks. Nonetheless, forecasts of
future events must be incorporated into the decision-making process to manage better the
impact of these events.

The purpose of this chapter is to discuss the various forecasting techniques and
terminology that have been applied to agriculture as well as to justify and outline the
methods that are used in this study. It begins by reviewing the conceptual tools that are
used throughout the paper, with the majority of this chapter dedicated to the theoretical

models and forecast functions upon which the models in chapters 4 and 5 are grounded.

17

2.1 Conceptual Issues

A forecast is deﬁned as a qualitative or quantitative estimate or set of estimates
about the likelihood of future events based on current and past information (Pindyck and
Rubenfeld 1991; Holden 1990). In the forecasting literature a distinction is made between
short, medium and long-term forecasts. Short-term forecasts, or outlook, generally refer
to the next few months to a year. With Short-term forecasts, it is usually assumed that
there will be little change in recent patterns of behavior, and that the market structure and
policy environment will remain the same over the forecast horizon. Medium-term forecasts
can range ﬁom one to three years, while a forecast horizon of three years or longer is
considered as long-term since the economic environment can change dramatically after
three years (Holden 1990).

Forecasting can be done ex ante or ex post. With ex-post forecasting techniques,
observations on both the endogenous and exogenous variables are known with certainty
during the forecast period. This type of forecasting provides a means of evaluating a
forecasting model because the forecast can be checked against existing data. Ex ante or
out-of-sample forecasting predicts values of the dependent variable beyond the period of
estimation and is considered to be a true test of a model’s forecasting ability.

Forecasting techniques are classiﬁed into two broad categories: qualitative
(subjective or implicit) and quantitative (model-based or explicit). Subjective or implicit
forecasts are based on guesses, experience or intuition without an explicit structure or
method for processing inforrmuion. Explicit or model-based forecasting techniques are

based on formal relationships between variables of interest. Explicit model building forces

18

one to think clearly about, and account for, all the important interrelationships involved in
a problem, whereas reliance solely on intuition can cause one to ignore or improperly use
important relationships. In addition to the forecast itself; a measure of forecast accuracy
gives more information to the user with which to plan. Subjective forecasting techniques
usually preclude any quantitative measure of conﬁdence in the resulting forecasts. Rather,
with qualitative forecasting it is difﬁcult to analyze why a particular forecast is good or
bad or learn ﬁ‘om past forecast errors.

In practice, most forecasting systems employ both qualitative and quantitative
forecasting techniques - the results of explicit forecasting are modiﬁed based on qualitative
information known by the analyst. In general, quantitative methods are used when the
existing data pattern is expected to persist, while qualitative methods are useful when the
existing data pattern is expected to change. Moreover, forecasts generated by quantitative
methods are subjectively evaluated by the forecast user and may be revised accordingly.
Because qualitative forecasting techniques can be very important when historical data is
sparse or of dubious quality, the next section discusses a common qualitative forecasting
technique. The remainder of this chapter discusses quantitative forecasting techniques,

with a focus on the methods employed in this study.

2.2 Qualitative Forecasting Techniques
In practice, qualitative forecasting methods generally use the opinions of experts to
subjectively predict the future. Subjective forecasts are formed and based on the

experience, intuition and judgement of the forecaster. The goal is to pull expert opinion

19

ﬁ'om those who have insights about a particular future event. The Delphi technique,
developed by the RAND Corporation, is a common qualitative forecasting technique. In
this method, experts are surveyed independently to forecast a particular event over a
speciﬁed time period. The results are collected and discussed by the experts. Those with
the highest and lowest forecast are asked to justify their opinion, and after further
discussion the experts are surveyed again, results are again discussed and this process
continues until a consensus forecast emerges. The discussion may take place in a round-
table format or in written or computer form where the experts never physically meet.
Combining the opinion of several experts who must justify their forecasts and then
iterating until a consensus is reached is considered to be the main advantage of the Delphi
method. It is assumd that the consensus forecast will be more accurate than any outlier.
The major disadvantage is that experts may be inﬂuenced by the opinion and personalities
of other experts if anonymity is not preserved. In addition, the Delphi method can be
costly to implement and it is possible to end up with a forecast that none of the experts
strongly believe in. Moreover, the deﬁnition of an “expert” must be agreed upon as well
as how much information should be passed on in the iterative stages. According to
Holden (1990), the Delphi method is most appropriate for longer-term forecasting and

where historical data may be misleading.

2.3 Structural Models for Forecasting
The rest of this chapter discusses quantitative forecasting methods, which are

techniques that focus on the analysis of historical data to predict ﬁrture values. There are

20

two groups of quantitative forecasting methods: causal and noncausal models. This
section discusses causal or structural models in which the focus is on explaining the
behavior of a variable and using that explanation to predict the future behavior of that
variable. According to Holden (1990), the best method for forecasting the future values
of a given variable, ceteris paribus, is to build a structural (causal) econometric model
using time-series data. Once the correct economic theory is employed and a model is
speciﬁed, the parameters can be estimated ﬁom a data base, and by extrapolating the
model beyond the estimation period, forecasts of future values of the variable of interest
can be made. Single and multi-equation regression models and multi-equation
simultaneous models are common structural models used for forecasting.

To illustrate, a simple linear single-equation in which x explains the movement of y

is described below:

y,=a+l3x,+e, (1)

The equation is estimated and if it is found acceptable in a statistical sense, then the
estirmted parameters are used to forecast future values of y conditional on x. Since the
model is causal, ﬁrture values of exogenous or explanatory variables will need to be
projected forward or taken ﬁ'om another source. In this model, the forecast information is
embodied in a single—equation structural model The forecast function for a number of

periods can be obtained as a series of one-step-ahead forecasts as in equation 2. The

yr+1:&+l§xr+| (2)

21

simple linear model can be expanded and modiﬁed to include other regressors, equations
or different ﬁmctional forms if the theory and data availability warrant.

In multi-equation simulation modeling, the variable may be a ftmction of several
explanatory variables which are related to each other, as well as to the variable under
study through a set of equations. If assumptions are made about the future behavior of
explanatory variables, then the model is simulated into the future to obtain forecasts for
each of the variables in the model. AS simulation models presume to explain individual
relationships and interactions among all the relationships of the process under study, the
data requirements as well as the time and money for such models can be quite large.
These models can provide insight and thus greater understanding of the relationships
between variables, which can improve forecast precision.

The major steps involved in constructing a structural model and using it to forecast
include: selecting the appropriate endogenous and exogenous variables according to
economic theory; writing the theory as an equation or series of equations linking together
variables with an appropriate ftmctional form; ﬁnding data on the variables; estimating
parameters using appropriate econometric techniques; and conditional on the estimated
equation parameters, generating predictions of the future value of the exogenous variables
to forecast the endogenous variables.

Causal models are useful in that they allow decision mkers to evaluate the impact
of various alternative policies once the relationship between variables is identiﬁed. While
structural models attempt to explain behavior by identifying the links between variables,

they are complex and diﬂicult to develop. They require more data and time and thus are

22

more costly than non-causal models. Often reliable data is unavailable on the relevant
variables that economic theory suggests Should be included in the structural model. In
other cases, it is not clear wlmt constitutes the appropriate economic theory. As a
consequence of the foregoing points, the costs of constructing and estimating a structural
model may be greater than the perceived beneﬁts, so a cheaper forecasting technique may
be required. But if the costs are justiﬁed, structural models by design give more accurate

long-term forecasts than noncausal techniques.

2.4 Noncausal Forecasting Techniques

Unlike structural models, noncausal models presume to know nothing about the
causal relationships that affect the variable of interest. That is, noncausal modeling
techniques focus on identifying a statistical method for projecting br extrapolating the
historical data into the ﬁrture. Smoothing, trend extrapolation and Box-Jenkins or
ARIMA models are common classes of univariate noncausal models used for short-term
forecasting and are discussed below. Each class of model involves a different degree of
complexity and presumes a different level of comprehension about the underlying
processes that are being modeled. Smoothing and trend extrapolation are simple
forecasting tools which are discussed in the next section, followed by a discussion of the
Box-Jenkins method, also referred to as ARIMA or time-series models. Vector
autoregression (VAR) is a common mulitvariate noncausal forecasting technique which is

also discussed.

23

2.4.1 Trends and Exponential Smoothing Methods

One class of extrapolation methods is based on trends or the general movement of
a time series in a particular direction. In trend extrapolation, the type of trend (linear or
nonlinear) observed in past values of a series is identiﬁed and then projected into the
future. Various polynomial ﬁmctions of time can be estimated using regression methods
or by forming moving averages of the time series. Some common trend extrapolation
models include the linear trend, exponential growth curve, the quadratic, autoregressive
and logarithmic curves". Trend regression models relate the dependent variable y, to
functions of time and are useful when the parameters describing a time series remain
constant over time. The model formulation depends on the forecaster’s beliefs about the
future growth of the variable of interest. According to the literature, these simple trend
models often have larger standard errors than some other models and are better used as a
quick and inexpensive way of formulating initial forecasts.

Exponential smoothing is a forecasting method that weights the observed time
series values unequally, with more weight given to more recent observations. The
weighting scheme is determined by using one or more smoothing constants that are
determined by smoothing equations. Simple exponential smoothing methods are most
eﬁ‘ective when the time series has no discernable trend and the parameters change Slowly
over time. Double-exponential smoothing methods are useful when the time series

displays a Slowly changing linear trend. Other smoothing methods incorporate

 

‘H‘hesemodelswillnotbeusedinthisstudyandthusarenot describedindetail
here. See any forecasting textbook for examples.

24

adjustments for changing trends and seasonal factors”. Exponential smoothing methods

work well in situations that call for one-step ahead forecast in successive time periods.

2.4.2 Time-series Models

Time-series econometrics is based on the theory of linear stochastic difference
equations, where a diﬁ'erence equation expresses the value of a variable as a function of its
own lagged values, exogenous variables and a disturbance term (Enders 1995). It is
based on two ﬁmdamental notions: the idea of unobserved components, and a more
probabilistic theory based on parametric models (Nerlove 1995). Time-series analysis can
be used to identify the properties of and decompose a series into a trend, a seasonal and an
irregular component to forecast the time path of a variable. These predictable components
of the series are then extrapolated into the ﬁrture, uncovering the dynamic path allowed
for more accurate forecast. The basic idea is that past patterns in the data series will be
repeated in the future and thus predictions about future values can be made by
extrapolating ﬁ'om past and current information. For example, since the trend component
changes the mean of the series and the seasonal component imparts a regular cyclical
pattern, predictions concerning the ﬁrture path of the variable would include such
information.

The challenge is to develop grain price models that capture the essence of the true

data generating process, as it is difﬁcult to completely characterize the probability

 

" Holt-Wmters two-parameter double exponential smoothing and Winters’method
for forecasting seasonal data are common methods and are described in most forecasting
books.

25

distributions for prices. A univariate reduced-form difference equation is expressed solely
as a function of its own lags and disturbance terms, and is particularly useful for
forecasting because predictions can be made solely on its own current and past
observations. For instance, the naive model is a simple deterministic model that predicts

future values of a variable to be its current value.

y,:y;_1 (3)

However, if y, is not thought to be perfectly predictable (i.e., deterministic), then the naive

model can be modiﬁed by adding a random term, becoming the random walk model:

yr:yr-l+€r ' (4)

The random walk accounts for the probabilistic nature of a time series by including a
stochastic term, 6,, such that the change in y is random. The model says that the value in
time t is a function of the value in time t-I plus some random error, where the random
error term is assumed to meet the standard requirements (i.e., is white noise).

A one-period ahead forecast of a random walk process is given by:
)373] :yT+E(€T+|) :yT (5)
where E(eT,,)=0. The best prediction of y, is its previous value. If upon visual inspection

of a time series an upward or downward trend is detected, then a drift parameter, (a), can

be used to capture the trend, and the random walk becomes a random walk with drift.

yrzyr-l ”he; (6)

26

The I-period ahead forecast is given by:

in: =J’r + Id (7)

The major advantage of the random walk model is the minimal data requirements,
that is, the only information needed is the current value of y,. Additionally, because the
random walk model is stochastic, a standard error of forecast can be computed, which
allows forecast conﬁdence intervals to be constructed. Decision makers often need to
know the margin of error associated with a particular point forecast, thus conﬁdence

intervals are important, useful plarming tools.

2.4.2.1 ARIMA Models

In this section, several different types of stochastic processes that are useful in
modeling time series are discussed. The random walk model described above is a simple
example of a stochastic time-series model. This section discusses a more general class of
stochastic time-series models that explain the movement of a time series by relating it to
its own past values and/or to a weighted sum of current and lagged random disturbances.
models. A linear difference equation is essentially an auto-regressive process and can be
described by the following:

9
P, =00 + 2 aiPH +x, (8)

I=1

27

Equation (8) is a pm-order linear difference equation, equation (9) is a moving average

x1: 2‘3: EH (9)

r=0

process of order q and equation (10) is an ARMA(p,q) model for P, The autoregressive

part of the model is the difference equation. The white noise process is the basic building

9 (I
P: :a0 + zaIPr-i + Elite“. (10)
i=1 i=0

block of stochastic time series models and is a necessary condition for forecasting. A
sequence {6,} is a white noise process ifeach value in the sequence has a mean ofzero, a
constant variance, and is serially uncorrelated; E(e,)=E(c,,l)= ...0; E(cf)=E(ef_,)= 01; and
for all j, E(e, e,,,)=E(€,,j e,,-_,)=0 for all 3.

Linear forms of the autoregressive (AR), moving average (MA), autoregressive
moving average (ARMA) and the autoregressive integrated moving average (ARIMA)
time-series models were popularized by Box and Jenkins (1976), and are known as Box-
Jenkins models. Like all the non-causal models, the Box-Jenkins forecasting techniques
assume that past observations can be used to predict future values. These models have
been found to give good forecasts in a wide variety of situations and thus are cormnonly

used.

28

Because of its generality, the Box-Jenkins method is one of the most widely used
approaches for the analysis of time-series data. The Box-Jenkins method consists of four
stages: 1) identiﬁcation, 2) estimating the coefﬁcients, 3) checking the adequacy of the
ﬁtted model, and 4) using it for forecasting. Identiﬁcation consists of examining the
autocorrelation and partial autocorrelation functions to determine the appropriate order of
the AR and MA components. In a time series, adjacent values are often highly correlated
and autocorrelation coeﬂicients are used to examine the strength of the relationship among
the values at different lags. The autocorrelations are graphed against T/4 lags, where T is
the number of observations". For example, a large value of the autocorrelation at the
second lag indicates that values two time points away are closely related. The researcher
may thus consider including an AR(2) or MA(2) term in the model. The partial
autocorrelation coeﬂicients are the result of eliminating (controlling for or netting out) the
effect of intervening values. In this way, the pattern of autocorrelations is used for
selecting the ARIMA model. There are, however, no clear-cut rules for this identiﬁcation
process, and in fact, some have called it more of an art than a science.

Estimation of these models is commonly accomplished with maximum likelihood
methods, which are standard in most time-series software packages. The Akaike
information criterion (AIC) and the Schwartz-Bayesian criterion (SBC) are cormnonly

used diagnostic measures to check the goodness of ﬁt of a tentative model to the data.

 

l‘T/4 is standard for determining how many lags to examine (Enders 1995).

29

The lower the AlC/SBC, the better the ﬁt”. Because the marginal cost of adding
regressors is greater with the SBC than the AIC, the SBC selects a more parsimonious
model than the AIC. A necessary condition for forecasting with ARIMA models is that
the residuals approximate white noise; therefore, as part of the diagnostic tests, the
residuals are examined for serial correlation. The Box-Pierce Q and the Ljung—Box Q' are
the commonly used statistics for testing for serial correlation. The Q°-statistic is more
appropriate for small samples and is used in this study (Enders 1995). If the model is
ﬁtted appropriately, then Q has an asymptotic x2 with m-p-q degrees of freedom, where p
and q are, respectively, the orders of the AR and MA components”. Once an appropriate
model is identiﬁed, estimated and checked, it can then be used for forecasting.

In the autoregressive process (AR), the current observation is assumed to have

been generated by a weighted average of its past observations:

y125+¢1yr-1+¢2V1—2 +6: (11)

The above equation describes an AR(2) process in that y, is described by a weighted
average of past observations going back two periods, a constant term, 6, and a random

disturbance in the current period, 6,. An AR(p) of order p is given by:

 

'6 AIC(p) = n log 0:, +2p, where 6: =RSS/(n -p)and p is the total number of
parameters estimated. SBC is the same except instead of adding 2p, pln(n) is added. RSS
is the residual sum of squares.

'7 It Should be noted that Maddala (1992) argues that the Q-tests have low power
because of the autoregressive components and that a Lagrange-Multiplier (LM) test
described in Maddala (p.541) is more appropriate, i.e., has higher power. However, since
most software packages do not compute the LM-statistic, the Q-tests continued to be
widely used.

30

yt:6+¢lyt—l +¢2y:—2+”'¢er—p+€r (12)

If the time series is assumed to have been generated by a weighted average of
random disturbances going back q periods, the process is described as a moving average
of order q, MA(q). An MA(q) model is Simply a linear combination of white noise error

terms.

yt=u+€,-Ol€,_l-9€ -...-06 (13)

2 r—2 q t-q

However, many random processes have characteristics of both autoregressive and
moving average and thus are modeled as an ARMA of order (p,q). Rather, the time series

is expressed as a function of its lagged values and lagged residuals:

yrzd)IyI-l +“' +¢pyt-p +5 +er-eler-l -"' —eq€t-q (14)

The AR, MA, and ARMA models described above assume that the underlying
random process that generated the time series is invariant with respect to time. That is,
the characteristics of the stochastic process remain stationary over time. This is
particularly important for forecasting because if the random process is stationary, it can be
modeled with an equation with ﬁxed coeﬂicients which can be estimated ﬁ'om past data
and used for forecasting future values of the dependent variable. However, in practice
rmny economic time series are nonstationary and the underlying characteristics do change
over time. Fortunately, nonstationary processes can be made stationary by differencing

the time series and the differenced series is then modeled as a stationary time series. If the

31
differenced series (Ay, =yt-yt,,) is modeled as an ARMA(p,q), then the original series y, is
said to be an integrated ARMA or ARIMA(p,d,q) where d is the number of times the
original series must be diﬂ‘erenced to become stationary”. Note that the differencing
operation used to achieve stationarity involves a loss of potential information about long-
nm movements. Differencing can remove trends, and seasonal differencing removes
seasonal trends.

One of the most difﬁcult aspects of time-series modeling is determining the correct
lag length for model speciﬁcation and indeed can require considerable trial and error. The
properties of the sample autocorrelation function (ACF) and partial autocorrelation
function (PACF) are used to identify the underlying data-generating process of a time
series including the order of the ARIMA process. The ACF indicates how much
correlation (interdependency) there is between neighboring data points in a series, where
the size of the autocorrelation represents the strength of the pattern between past values of
the variables. An analysis of the ACF can help determine the order of the moving average
component and for moving average models of order q, the autocorrelation should be close
to zero for lags greater than q. Similarly, the PACF, which indicates the partial or extra
effect of adding another lagged variable when one lag is already included, is used to
determine the order of the autoregressive component.

Once a time-series model has been estimated and checked, it can be used for

forecasting. ARIMA models are cormnonly used in empirical work Since many economic

 

'8 There are several methods available for testing the stationarity of a time series,
such as the unit root test. The procedures are discussed in most time series econometric
books and are examined in greater detail in chapter 3.

32

time series are generated by nonstationary processes. Equation (16) describes how

computation of a forecast is accomplished. Let w represent a differenced series
(w=Ayr=yr'yr-l)°

W,=¢1W,_1+-~+¢,,W,-p+€,’6.€,-."we e _ +6 (15)

‘1"!

A one-period ahead forecast involves modifying the above equation by one period:

Wm:¢rwr+“-+¢pWT-p+r+€r+1’61€1"'-eqer-q+1 +5 (16)

The forecast is calculated by taking the conditional expected value of WT, ,:

197(1) =E(wm|w7,...) =¢le+... +tl>pr_p,l -BléT-... -6qéT,q,l +6 (17)

é, and é“ are observed residuals and the expected value of Em =0.
Once the diﬂ‘erenced series has been forecasted, a forecast of the original series can be
obtained by summing the differenced series d times. An I-period ahead forecast for y

when d==l is given by:

97(1) =yr W10) +visa) + - . 97(1) (18)

Because they account for the dynamic structure of the time series, Box-Jenkins
models (univariate ARIMA) can often forecast quite well compared to econometric or
structural models. However, once the temporal structure of the data is accounted for,
structural models can perform well. One of the major theoretical limitations of ARIMA

models is that they assume linearity and cannot accommodate nonlinear data generating

33

processes. Moreover, this class of models assumes that the underlying structure that
generated the time series remains constant. But if structural change does occur, then the
ARIMA model estimated and used for forecasting under the old structure may give
misleading and even incorrect forecasts for the new structure. It can also be difﬁcult to
obtain sufﬁcient observations to identify/ specify an appropriate ARIMA model, therefore
parameter estimates Should be frequently updated as new observations become available
(Holden 1990). If the time series exhibits seasonality, then it can be removed by
seasonally differencing the time series and specifying a seasonal ARIMA.

In summary, the major advantage of non-causal modeling techniques is that they
are cheap and relatively simple, while the major disadvantage is that they assume the
future will be like the past and are unable to explain behavior. However, Shift variables
(e.g., dummies) can be added to ARIMA models to capture structural and other

exogenous changes greatly improving the utility of non-causal modeling techniques.

2.5 Vector Autoregression Models

The above methods focus on the time-series analysis of a single time series. The
Box-Jenkins methodology can be extended to the Simultaneous study of two or more time
series. The vector autoregression (VAR) is essentially a multiple-time series or vector
generalization of the autoregression model which focuses on the interrelationship between
different time series and is a popular forecasting tool. Equations (19) and (20) describe a

simple 2-equation system:

yrr=5+¢nyu4 +¢12y2J—1 +51: (19)

34

In VAR models, the euterms are called impulses.

, y2: = a “Eryn-1 + ¢22yzm + 52: (20)

VAR models are nonstructural models where the data speciﬁes the dynamic
structure of the models instead of economic theory and thus puts minimal demands on the
structure of a model. Indeed, one need only specify the set of variables that are assumed
to interact with each other, decide the number of lags needed to capture most of the
eﬂ‘ects the variables have on each other. However, a major weakness of VAR modeling is
over-paramterization: the tradeoﬂ‘ between having a sufﬁcient number of lags to capture
the dynamics of the system with having a sufﬁcient number of he parameters or degrees
of ﬁeedom. VAR modeling techniques often make good short-term forecasting models
because they are simple, and can be estimated using OLS procedures; they avoid some of
the restrictiveness of structural model, and the multi-variate representation allows them to

overcome some of the limitations of the univariate models.

2.6 Measuring Forecast Accuracy

Regardless of the forecasting technique employed, a forecast is a prediction of an
outcome and thus is subject to a certain amount of forecast error. Given that different
economic agents have different needs, the amount of acceptable forecast error to a
particular user diﬁ‘ers. For example, decision makers who are less risk averse may be

willing to rely on a forecast that has a wider conﬁdence interval than agents who are more

35

risk averse because the economic decisions that are based on those forecasts embody a
wider margin of error. Various measures are available for assessing the predictive
accuracy of forecasting models. Most .-. ’1?- designed to evaluate ex post forecasts, that is,
forecasts for which the exogenous variables do not have to be forecast. Forecasts based
on models made before the values of the exogenous variables are known are called an ex
ante forecasts and are the true test of a models predictive accuracy.

There are three types of forecasts: point forecasts, prediction intervals of a forecast
and forecasts with probability distributions attached. A point forecast is a single number
representing the best guess of the variable being forecasted, whereas a prediction interval
forecast is a range of numbers calculated such that one is e.g., 95% conﬁdent that the
actual value is contained in the interval. The third type calculates a probability for each
possible point forecast such that there is a 60% chance that the actual value will be x.

If the forecasting technique is appropriate, the forecast errors Should be purely

random. Mean squared error (MSE) is a common measure of forecast error:

MSE = 2: (y, —y‘,)2/n (21)
r=l

which penalizes a forecasting technique more for larger errors than smaller errors. This is
also known as a quadratic loss function, which is simply a summary of how concerned the
user is if the forecast is oﬁ‘ by a particular amount (Hamilton 1994). The forecast is
chosen to minimize the MSE and will be used in this study to assess the performance of

alternative price forecasting model.

36

Choosing an appropriate forecasting method involves consideration of the user’s
needs in regard to form; for instance, will a point forecast suﬁice or is an interval
prediction required? Further, what is an acceptable margin of error? In some cases, a
10% margin of error is acceptable whereas in other cases it might be disastrous. The
length of the forecast horizon can also inﬂuence the forecasting technique. In general, the
longer the time frame (longer than two years), the more diﬂicult it is to make accurate
forecasts with quantitative models, and qualitative techniques become more useful as the
forecast horizon lengthens. Data availability is a major factor in deciding which
forecasting methods are plausible.

In Mali, developing large structural models for forecasting is not feasible because
the current data base cannot support their construction. Structural models also require
that large amounts of data be stored. The complexity and operation of the forecasting
technique inﬂuences the cost of forecasting and must be considered when choosing a
forecasting technique. The method should be Simple enough to operate and understand
for decision-makers to have conﬁdence in the predictions. A balance of cost, complexity
and desired accuracy is needed. For these reasons, this study builds forecasting models
using time series methods. The next chapter presents the results of the preliminary
analysis of the data and discusses the conceptual issues necessary for modeling commodity

price series.

CHAPTER 3

PRELIMINARY ANALYSIS OF PRICE LEVEL DATA

3.0 Introduction

Using time-series methods, this study develops and estimates alternative price
models for rice, sorghum and maize which can be employed to produce reliable Short-term
forecasts in representative grain markets in Mali. This chapter will discuss the data,
perform some preliminary analysis including Statistical descriptives and real price trends,
and end with a discussion of the stochastic properties of the time series relevant for

modeling commodity prices.

3.1 Data

As in my studies of this nature, the choice of cereals and markets is partly driven
by the availability, continuity and quality of data. The cereals price data used in this study
were constructed from three sources: the PRMC/OPAM (1982-1984), the MSU/Mali
Food Security Project from 1985 to 1989, and the market information system (SIM) Item
1989 to September 1998”. By design, the SIM data set is considerably more
comprehensive and complete than the MSU project data. For example, the SIM reports
average weekly cereals prices for 52 markets across the country including Six different
qualities of rice at various levels in the marketing chain Since price information was not

the primary focus of the MSU project, it collected monthly (and some weekly) average

 

“The market information system is known by its French acronym, SIM. It ﬁrst
came into being in 1989, in part as an outgrowth of the MSU/Mali Food Security Project.

38

prices for key cereals in fewer markets and thus is much more limited in scope.

The analysis undertaken here uses monthly data Spanning ﬁ'om January 1982 to
September 1998. The last twenty-four observations were excluded from the modeling
process to check the accuracy and consistency of the alternative forecasting models. To
obtain a complete monthly price series for each cereal, Simple averages of the weekly SIM
data were computed to obtain monthly observations and then merged with the MSU
data”. The different levels of aggregation and reporting in the two data sets required that
careful consideration be given to ensuring that the variables in the two data sets were
consistent. Speciﬁcally, the MSU data report an average monthly price for rice in
Bamako while the SIM reports an average weekly price for Six different qualities of rice in
various markets across Bamako. Determining what quaﬁty of rice and what market in
Barmko the MSU rice price referred was not a trivial task. Based on discussions with
MSU project people and given that RM40 (40% broken) is the most commonly consumed
and marketed quality of rice in Mali, and Niarela is the most heavily traded market in
Bamako, it is assumed here that the MSU rice price referred to RM40 in the Niarela
market.

The producer prices were taken ﬁom the most actively traded markets for each
grain in each region. Consideration was also given to data availability, as an effort was
rmde to construct the longest monthly time series possrble. Since the SIM did not become

operational until April 1989, the markets covered by the MSU project dictated which

 

2"The SIM enumerators were trained by the MSU project and hence the sampling
methodologies are consistent.

39

rmrkets were actually studied“. All urban retail prices are studied at the Bamako-Niarela
market, resulting in a monthly time series ranging from January 1982 to September 1998.
Rural retail and producer prices for rice are studied in the markets of the Oﬁice du Niger
zone and cover the period ﬁ'om February 1988 to May 1997, while the coarse grains are
ﬁom the region of Sikasso and cover the period from October 1985 to September 1998.

Refer to ﬁgure 1.1 in chapter 1 for map of the agricultural zones.

3.2 Missing Data

From January 1982 to September 1998 there are 201 months of potential price
observations for urban markets. In the urban retail market (Niarela), the price series for
sorghum and maize are complete, with 201 observations each. The price series for rice
(RM40), however, has 9 missing values”. One common way to deal with missing data is
to simply replace the missing values with the series mean or the mean of the values
surrounding the missing observations. Close examination and comparison of plots of the
actual series with the missing observations and the series completed with the means
revealed that these methods appear to seriously under- predict the actual series.

Riz DP, another quality of rice for which data was available in the Niarela market,
is a close substitute in consumption to RM40. Correlation analysis revealed that prices for

the two varieties were, as expected, highly correlated (correlation coefﬁcient of 0.93).

 

2|The SIT, transitory information system, actually began in April 1989, while the
permanent market information system (SIM) began in October 1989.

22Missing February 1995-May 1995 and February 96-June 1996.

40

Since RM40 and riz DP are closely related, simple linear regressions speciﬁed with and
without a time trend were estimated to predict RM40 prices conditional on riz DP prices.
The mean squared error (MSE) was computed and used to determine which speciﬁcation
best ﬁt the data. This resulted in replacing the 9 missing values for the RM40 series with
the predicted values conditional on riz DP and a time trend.

Also at issue is why the observations for RM40 are missing. The SIM deﬁnes
Rm40 to be imported 35% broken rice or rice produced domestically (riz DP). According
to SIM technicians, imported rice was not competitive with local rice during those
periods, nor were the industrial mills producing very much, which resulted in literally no
RM40 on the market. Rather, the observations are missing because RM40 was truly
absent on the market. This study made an effort to work with as long a series as possible
and rather than work with 9 less observations, particularly since the correlation between

the series was high, it was decided that completing the series was justiﬁed.

3.3 Inflation

Inﬂation plays an important role in understanding price movements. For most of
the study period the average rate of inﬂation remained relatively low and constant. In fact,
between 1982 and 1993 inﬂation as measured by the GDP deﬂator was an average 2.4% .
In 1994, the CFA ﬁanc was devalued, and inﬂation as measured by the annual percentage
change in the national consumer price index increased to 32% (Teﬂt et a1. 1997). Prices

began to stabilize in 1995, and, as indicated in table 3.1, continue to fall towards their pre-

41

devaluation levels”. '

 

Table 3.1: Annual percentage change in national consumer price index

 

1994 32
1995 9.2
1996 2.8
1997 3.1

 

Source: Tefft et al. 1997

 

 

 

If price movements are a ﬁrnction of inﬂation, then deﬂating the price series by an
appropriate measure of inﬂation theoretically removes the inﬂationary eﬂect, making it
easier to identify other components like seasonality, cycles and trends. Choosing an
appropriate measure of inﬂation, however, is not a trivial task and often depends on data
availability". Ideally, the measure of inﬂation should reﬂect the decision environment and
opportunity sets within which decision agents operate.

Food products represent the largest weights in the consumer price indices in the
CF A countries, including Mali, with cereals representing a large component of the food
subgroup (Teﬂt et al. 1997). Therefore, increases in grain prices directly inﬂuence the
rate of inﬂation, which in price analysis can bias coefﬁcient estimates or lead to Spurious
inferences. It is not uncommon in extension work to use nominal prices to develop

models which are created explicitly for the purpose of forecasting. Since the level of

 

’3 For a speciﬁc analysis of the effect of devaluation on cereals prices, see Teﬂt et
a1. (1997).

24See price study by Jayne et al. (1996).

42

inﬂation in Mali has been relatively low, and because cereals comprise such as large

component of the food subgroup, this study seems justiﬁed in using nominal prices.

3.4 Seasonal Analysis & Price Trends

The seasonal nature of grain production and market supply in Sub-Saharan Africa,
including Mali, suggests that the price series Should be investigated for seasonal patterns.
In time series, adjacent values are often highly correlated. Autocorrelation coeﬁcients are
used to examine the strength of the relationship among the values at different lags.
Inspection of the correlogram, which is a graph of the auto and partial autocorrelation
ﬁrnctions, of the sorghum and maize series revealed that these series exhibit signiﬁcant
spikes (i.e., correlation coefﬁcients that fall outside the two standard error band) at or near
seasonal lags, consistent with a priori expectations of rainfed crops. For instance, the
partial ACFS in ﬁgures 3.3 and 3.4 have spikes at near lags (12-14) which are considered
seasonal in monthly data, and the ACFS Show an oscillating pattern consistent with
theoretical seasonal patterns. That is, prices peak during the hungry season (June-
August) and are at their lowest when harvest is complete (November-January). The intra-
annual variation of when peaks and troughs occur is inﬂuenced by rainfall and the
marketing strategies of net sellers.

In ﬁgure 3.5, the correlogram of the rice series, it is more diﬂicult to ascertain
whether seasonal patterns exist in the rice series because of its imported and food aid
components. With the exception of the ﬁrst lag, the partial autocorrelation coefﬁcients are

not statistically diﬂ‘erent ﬁ'om zero. Close inspection of the time series revealed that in

43
some years, a clear seasonal pattern approximating the peaks and troughs in the coarse
grain series exist, whereas in other years no discernible pattern emerges or one contrary to
expectations”. The ﬂuidity of the import laws and other macro exogenous shocks may

help to explain this phenomenon.

 

2’ For instance, import policies might explain the price peak in December/January
in 1989/90, and the low price in June and April, while substantial food aid arrivals in 1988
might explain why the peak price was in July and the low price in January.

44

Figure 3.3: Correlogram of Sorghum Prices
LN PS

 

1.0

 

0.0 I

 

 

-.5 d

 

 

 

7"va t" wTvvvf' wr- '

 

1.0

.5‘

 

0.0 I

Confidence lelts

 

 

Partial ACF

 

'1 — - w t- — iv ' rivw — v -

159131721252933
3711151923273135

ACF

Partld ACF

45

Figure 3.4: Correlogram for Maize

 

 

 

 

 

 

 

 

 

 

 

 

LNPZ
1.0
.51
0.01
.51
Conﬁdencelelts
-11) ________________ Mont
159131721252933
3711151923273135
LagNumber
LNPZ
1.0
.5‘
0.04
IIJIII _
._51
ConfidenceLImlts
'1-°_,f-___-,~---tvf~- W
15913172125833

37111510232731”

Lag Number

ACF

Partial ACF

46

Figure 3.5: Correlogram for Rice

 

 

 

 

 

 

 

 

 

 

 

LNPR
1.0
.5'
0,, llllllllllllllllll
.5:
ConﬁdemeUmlts
.1,o __________________ W
1 5 9 13 17 21 25 29 33
3 711151923273135
LagNumber
LNPR
1.0
.5'1
0.01
._51
Confidencelelts
-10 _________________ “Coefﬁclem

 

47

Many economic time series trend over time, and if the underlying data generating
process is stationary (i.e., mean reverting), then the series can be broadly characterized by
the polynomial trend models discussed in chapter two. The plots of the nominal sorghum
and mize series in ﬁgure 3.1 were suggestive of a slight trend during the post devaluation
period, while the upward trend in the rice series is readily apparent. Simple linear time
trends (P, = [to + [3] Time + 6,) were ﬁtted to all three series using OLS regression
procedures. To examine the effect of the devaluation on prices, two trend lines, pre and
post devaluation, were ﬁtted to each series. Tables 3.2-3.5 present several summary
statistics for consumer and producer prices in the Bamako-Niarela market and two other
important trading markets, Niono and Zangasso.

Note that the CPI is based on an urban consumption basket purchased in Bamako
and has a base year of July 1986 to June 1987. Due to the unavailability of a consistent
and sufﬁciently long CPI series for the rural areas, the urban-Bamako CPI was also used
to deﬂate rural prices, which can often lead to misleading results and spurious inferences.
For example, urban consumption baskets in developing countries tend to have a higher
import content than rural consumption baskets, thus devaluation would have a greater
impact on the urban basket than it would the rural basket. Therefore, deﬂating rural prices
by an urban CPI may suggest that real prices in rural areas are ﬁlling more than they are,
hence the real prices in the Niono and Zangasso markets should be interpreted with
caution.

Nonetheless a few observations: In the Niono market, a major rice producing

zone, before devaluation nominal consumer and producer prices declined ﬁom 1988 to

48

December 1993, while post devaluation nominal consumer and producer prices have
increased 1.5 CFAF/kg and 1.3 CFAF/kg per month respectively. In this same market real
prices rice declined both before and after devaluation. The coefﬁcient of variation
indicates that producer rice prices in Niono have been more unstable than consmner
prices.

In Zangasso, a high rainﬁll area and major coarse grain producing zone, real
producer prices for both maize and sorghum increased both prior to and after the
devaluation. The magnitude of the monthly price increase is larger after the devaluation.
Relative to rice prices in Niono, maize and sorghum prices in Zangasso are more than
twice as volatile. This is consistent with knowledge of the grain markets, as mentioned
earlier. Rice is more heavily traded than either sorghum or maize and so the rmrkets are
not as thin. Also rice beneﬁts ﬁom the potential Stabilizing effects of imports and food
aid. In the Bamako-Niarela market, a rmjor consuming area, real maize and sorghum
prices increased ﬁom 1986 to 1997 both during and after devaluation. Nominal prices of
these cereals were on a downward trend before devaluation and increased post
devaluation. Real rice prices, on the other hand, decreased before and after devaluation,
while nominal prices increased 1.76 CFAF/per kg per month after the devaluation.
Sorghum prices in the Bamako-Niarela market have been the most volatile, while rice is

the most stable.

49

 

Table 3.2: Summary Statistics for Niono Consumer and Producer Rice Prices -
February 1988 to May 1997

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable T Max Min 02 P trend CV S.E.
t1 = pre
t2 = post
Nominal 112 280 157.2 1246 208 II = -0.68* 0.17 17.3
Consumer 12 = 150“
Real Consumer 112 207 150 169 171 t1 = -0.32* 0.08 11.4
12 = -O.54*
Real Producer 112 166 88.9 210 127 t1 = -0.31"‘ 0.11 13.4
12 = -0.31*
Nominal 112 240. 90.8 1106 156 11 = -0.58* 0.21 20.5
Producer 12 = 1.28“
Table 3.3: Summary Statistics for Sorghum Producer Prices in Zangasso -
October 1985 to September 1998
Variable T Max Min 62 13 trend CV S.E.
t1 = pre
t2 = post
Nominal 156 136.2 24.15 648.2 56.41 t1 = 0.11" 0.45 20.1
Producer ‘2 = 1'02.
Rea] Producer 132 95.7 23 289 44.5 t1 = 0.16” 0.38 16.2
t2 = 0.56"

 

 

 

 

 

 

 

 

 

 

Table 3.4: Summary Statistics for Maize Producer Prices in Zangasso - October

 

 

 

 

1985 to September 1998
Variable T Max Min 62 13 trend CV S.E.
t1 = pre
t2 = post
Nominal 156 118.8 17.3 492.4 47.3 t1 = 0.07 0.47 15.9
Producer 0 =0-98“
Real 132 77 17 18.1 36.6 tl= 014* 0.37 12.2
produce, t2 = 065*

 

 

 

 

 

 

 

 

 

 

 

 

50

 

Table 3.5: Summary Statistics for Consumer Grain Prices in Bamako-Niarela-
January 1982 to September 1998

 

 

 

 

 

 

 

Variable T Max Min 02 P trend CV S.E.
t1 = pre
t2 = post

Nom-ﬁce 201 288 157.2 1306 198.6 11 = -0.06 0.18 21.2
12 = L76"

Nominal. 201 186.3 57 966.6 97.53 11 = -0.12"‘ 0.32 27

sorghum t2 =0.73"‘

Nominal-main 201 175 52.9 700 91.2 11 =-0.09* 0.29 20.7
t2 =0.86"

Real-rice 132 207 150 148.8 171 t1 = -0.09"' 0.07 1 1.8
t2 = —0.48*

Real.sorghmn 132 123 46.8 351.2 74.75 11 = 0.13“ 0.25 18.1
t2 = 0.65“

Real-maize 132 110 47.7 219 71.2 t1 = 0.09"l 0.21 14.1
12 = 0.61 "‘

 

 

 

 

 

 

 

 

 

 

 

where:
o: = variance of the price series
P = mean price

Trend = the coefﬁcient of the trend variable in the regression: t1=pre-devaluation and t2=
post-devaluation

T = number of observations

CV = coeﬂicient of variation

S.E. = standard error of the regression equation
* = signiﬁcant at the 5% level

** = signiﬁcant at the 6% level
Max = maximum value of the series
Min = minimum value of the series

51

3.5 Marketing Margins

Real marketing margins for coarse grains between Zangasso and Bamako declined
slightly between 1986 and 1997. Simple regressions of real marketing margins, deﬁned as
the difference between retail prices in Bamako-Niarela and producer prices in Zangasso,
on pre and post-devaluation time trends, revealed that relative to 1986/1987, real margins
for both sorghum and maize declined signiﬁcantly before and alter the devaluation.
Speciﬁcally, real sorghum margins fell -0.07 (-2.91) CFAF/kg per month before the
devaluation and fell -0.18 (-2.62) after the devaluation“, while real maize prices fell -0.07
(~2.46) CFAF/kg per month before devaluation and -0.22 (-2.84) during the post
devaluation period. Unlike the coarse grains, trends in the real rice marketing margins
between Niono and Bamako before the devaluation, were not statistically signiﬁcant. The
post-devaluation margins however, fell by -0.24 (-2.07) CFAF/kg per month.

As mentioned above, the rice market was much Slower to h'beralize than the coarse
grain markets, which could help explain why margins in the rice market did not ﬁll prior
to devaluation. Moreover, rice is internationally traded, so domestic prices are linked,
albeit imperfectly, to world prices. Historically, sorghum and maize have been largely

nontraded goods for Mali, especially in the pre-devaluation era.

3.6 Characteristic Time Series Properties of Commodity Price Data
As reviewed in chapter two, time-series models can be quite useful in capturing

information about past patterns in price behavior to generate Short-term forecasts. The

 

2"The t-statistics are in parentheses.

52

challenge is to develop models that capture the essence of the true data generating
mechanism In addition to seasonality, there are several characteristic time-series
properties which many cormnodity price series seem to share, speciﬁcally stochastic
trends, excess kurtosis and time-varying volatility in the error term (Myers 1994). In this
section, the stochastic properties of the historical price data are examined in the context of
the commodity price literature. The discussion serves as the conceptual ﬁ'amework for

modeling the underlying data generating mechanism of each grain price.

3.6.1 Stochastic trends

Since time-series analysis focuses on regressing current values on past values,
there is a possibility that the resulting forecasts could be divergent (or unstable), causing
the forecast error to become larger over time (Ferris, class notes). To minimize this,
ARIMA modeling techniques, which focus on analyzing the stochastic properties of
economic time series, require that the underlying data generating processes be
(covariance) stationary, i.e., not contain stochastic trends or writ roots”. Simply put, a
time-series is covariance stationary if its mean and all autocovariances are unaﬁ'ected by a
change of time origin, i.e., are time invariant. In a Simple example, suppose a price, P1 is

described by equation (22) and a price, P} is described in equation (23):

P.‘ = u + e. (22)

 

27 Stochastic trend, nonstationarity and unit root are all synonyms and used
interchangeably throughout the paper.

53

P,’ :0: +e, (23)

Also suppose that 6, is a Gaussian white noise process, such that E(6,) =0. Then the mean
in equation (22) is given by E(PD = p+E(€,) = ,u; analogously the mean of equation (23)
is given by E(P2,) = ﬂ. Given the deﬁnition of stationarity, the process described in
equation (22) is stationary, while that described in equation (23) is not, because the mean,
ﬁr, is a function of time.

If the series is stationary, then the theoretical mean, variance and autocorrelations
of the time series, which are unknown to the researcher, can be approximated by the
sample mean, variance and autocorrelations. The sample descriptives can then be used to
estimate the parameters of the underlying data generating process. Moreover, stationarity
is also required if the usual asymptotic results are to apply (Enders 1995; Hamilton 1994;
Myers 1994; Pindyck 1991).

Many economic time series do trend upward over time, potentially violating the
stationarity assumption. Indeed, several empirical studies of commodity prices ﬁnd strong
evidence of stochastic trends (Baille 1997; Enders 1995; Myers 1994). Moreover, Phillips
(1988) argues that a unit root is a theoretical implication of models which postulate the
rational use of information available to economic agents, suggesting that we Should expect
unit roots. The important point is to evaluate the nature of the trend, that is, diagnose
whether it is deterministic or stochastic as the type of trend affects long-term forecasts. If
stationarity tests revealed that the underlying data generating process of the trending time

series was stationary, then the trend is considered to be deterministic and can be captured

54

with a polynomial time trend like the process described above in equation (23). Such a
data generating process is often referred to as trend-stationary because it is made
stationary by subtracting out the trend. A stochastic trend, on the other hand, is made
stationary by differencing and hence, is sometimes called a difference-stationary process.
The random walk with drift, i.e., ( P, =P,_l + u +e,), which Shows no particular tendency
to increase or decrease over time, is the classic example of a stochastic trend.

It is important to model the trend correctly because deterministic and stochastic
trends have diﬂermg impacts on long-term forecasts. A deterministic trend has a
permanent effect on the time series; since the irregular component is stationary (i.e., mean
reverting) shocks to this component have a tendency to die out, while the trending
elements remain in the long-term forecasts. But if the trend is stochastic, then Shocks to
the irregular component accumulate (i.e., do not die out), imparting a permanent, albeit
random change in the conditional mean. To forecast a trend-stationary process, the
known deterministic component is simply added to the forecast of the stationary stochastic
component. The forecast of process with a stochastic trend, like the random walk, is
given by: PM,’ =su +P,, such that P, is expected to grow at the constant rate of a per
period ﬁ'om whatever its current value P, happens to be, where s is the step-ahead horizon.

In summary, the forecasts in both speciﬁcations converge to a linear ﬁmction of
the forecast horizon, s, with slope B or u. The key difference is that the trend-stationary
process converges to a line whose intercept is the same regardless of the value of P,, while
the intercept of the limiting forecast for a diﬁ‘erence stationary or unit root process is

continually changing with each new observation on P. The two processes also diﬂ‘er in

55

their implications for the variance of the forecast error. The mean squared error (MSE)
increases with the forecasting horizon if the trend is deterministic, but as the horizon gets
larger, the added uncertainty from forecasting over a longer horizon becomes negligible.
That is, the MSE reaches a ﬁnite bound as the forecast horizon becomes larger. In
contrast, for a unit root process, the MSE also gets larger as the forecast horizon increases
but eventually grows linearly with the forecast horizon, not reaching a ﬁnite bound.

There are several tests available to test the hypothesis of a stochastic trend and
evaluate the nature of the nonstationarity, particularly in determining whether the trend is
stochastic through the presence of a unit root, or deterministic through the presence of a
polynomial time trend (Phillips 1988). These include the Dickey-Fuller (DF), the
Augmented Dickey-Fuller (ADF) and the Phillips-Perron (PP) tests. The tests differ in
their Speciﬁcation of the data generating process, i.e., some include a constant, implying a
non-zero drift, while others include a time trend and/or autoregressive terms. The ADF
test corrects for serially correlated errors, but is unable to eliminate autocorrehtion in
residuals if the error term has moving average components. The Phillips-Perron tests can
be more robust to autocorrelation and hetereogeneity in the distribution of residuals than
the Dickey-Fuller tests (Myers 1994). In these standard tests, the stochastic trend is the
null hypothesis. It is argued that these tests in general are not very robust and have low
power to discriminate between unit root and near unit root processes (Enders 1995). It is
important to include the appropriate regressors in the test equations. Because of the low
power of all the tests, there is no clear advantage of preferring one test over another. The

ADFtestisthemostcommonprocedureandisusedinthispaper.

56

Before beginning, it is common practice in price analysis to transform the series
into natural logs to eliminate some of the variability inherent in time series. Inspection of
the autocorrelation and partial autocorrelation flmctions is the ﬁrst indicator of whether a
unit root is present. A slowly decaying ACF is indicative of a nonstationary process. AS
shown above, the ACF S for the sorghum and maize series are indicative of seasonality,
while the rice series decays more Slowly. The test procedure for sorghum and maize
included estimating a ﬁrst equation with seasonal dummies, then using the residuals from
these equations to essentially deseasonalize the series. The stationarity tests for sorghum
and maize are performed on the deseasonalized series. The test equations for rice includes
a time trend.

Determining lag length is also an important consideration for testing
nonstationarity. Including too many lags ﬁrrther reduces the power of the test to reject a
unit root, since the an increased number of lags requires estimating additional parameters,
and a loss of degrees of ﬁ'eedom. On the other hand, too few lags will ﬁll to capture the
actual error process. Enders (1995) suggests starting with a relatively long lag length and
paring down the model by the usual t-test and/or F-test. For example, the ADF equation
is estimated using a lag length of 11*. If the t-statistic on lag n“ is insigniﬁcant at some
speciﬁed critical value, then the model is re-estimated using a lag length of n"‘-l . This
process is repeated until the lag is signiﬁcantly different ﬁom zero. In a pure
autoregressive case, if the initial choice of lag length includes the true length, such a
procedure will yield the true lag length with an asymptotic probability of unity (Enders

1995,p.227)

57

If the data exhrhit seasonality, the procedure is modiﬁed with the intent to employ
a lag length long enough to capture the seasonal pattern. For example, with monthly data,
one could start with 3 years of lags (n=36). If the t-statistic on lag 36 is insigniﬁcant, and
an F—test indicates that lags 25-36 are insigniﬁcant then one reduces n to 24 and repeats
the process until a reasonable lag length has been determined. Once a tentative lag length
is found, diagnostic checking of the residuals Should reveal them to approximate a white
noise process.

This study followed these procedures, and the natural log of all three series were
subjected to various speciﬁcations of the Dickey-Fuller tests. Equation (24) below
assumes there is no serial correlation while equations (25) and (26) correct for serial
correlation. Preliminary analyses of the coarse grain data revealed that the errors were
indeed serially correlated and therefore the augmented Dickey-Fuller tests were
perfornwd. Speciﬁcally, the following random walk processes with and without a time

trend were ﬁtted by OLS regression to the monthly data and H0: 6=0 was tested

API=6PH+et (24)

API:“+5P1-1+BlAP1-1+pzt+€1 (25)

APt=a+5Pr—l+plApt-l+et (26)

58

where P refers to the natural log of the individual price series.

The software package used (EVIEWS) computes the Dickey-Fuller t-statistic,
which is compared to the asymptotic critical values for unit root tests calculated in
Davidson and McKinney (1993). A series that is found to be nonstationary is made
stationary by differencing. The remainder of this chapter discusses the other time series

properties characteristic of commodity price data.

3.6.2 Time-varying Volatility and Excess Kurtosis

In addition to not having a constant mean, many economic time series exhibit
phases of relative tranquility followed by periods of high volatility. ARIMA modeling
techniques generally assume that e, is i.i.d. with mean zero and variance 0’. However,
empirical research (Myers 1994; Wang 1996) on commodity prices has Shown that time-
varying volatility and excess kurtosis (i.e., ﬁt tails) are inherent in commodity price data.
Particularly, studies Show that while a series of price changes is uncorrelated and thus
linearly independent, often in high frequency data, the moments of the price distributions
are correlated, implying that the price changes are nonlinearly dependent”. That is, the
volatility of price changes tends to vary over time, in that large (small) price changes tend
to be followed by other larger (smaller) changes.

Temporal instability in the variance of cormnodity prices leads to autocorrelation

patterns in the conditional variance of the price errors, where the variance is conditional

 

2’ Annual data is considered as low frequency and daily data is considered to be
high ﬁequency. Since monthly data ﬁlls in between it can possess characteristics of both
low and high ﬁ'equency data

59

on an information set available at the time the forecasts are being made. This is known as
conditional heteroskedasticity, after Engle (1982) who developed the autoregressive
conditional heteroskedasticity (ARCH) model to capture such effects. The ARCH model
was later generalized by Bollerslev (1986).

Econometric work which ignores conditional heteroskedasticity leads to
hypothesis tests which are not asymptotically valid, and/or biased estimates of standard
errors. Thus, the models developed in chapter 4 are examined for ARCH effects. The
conventional test statistic is: TR’ ~ X2 (q) where T is the number of observations, q is the
number of lags and degrees of ﬁeedom, and R2 is the coeﬂicient of determination ﬁom the

following OLS regression:

.2 _ 2 2 .2
c, — a0 + a,é,_, +012é,_2 + ...aqe,_q (27)

and {1%,} are the residuals ﬁ'om the price model. The null hypothesis is that the errors are
normally distributed with mean zero and constant variance 02.

In addition to conditional heteroskedasticity, research on empirical distributions of
commodity prices indicates that the tails of such distributions are ﬁtter than the generally
assumed standard normal distribution, suggesting excess kurtosis in commodity price
changes (Myers 1994). The price models are tested for excess kurtosis relative to the
standard normal. A kurtosis greater than three indicates excess kurtosis. Most computer

software packages compute kurtosis as a descriptive statistic.

60

3.7 Implications for Forecasting

If nonstationarity is not properly accounted for, then forecasts based on models
which assume stationarity when in ﬁct the series is nonstationary are of dubious value. In
ﬁct, there are important differences between stationary and nonstationary time series.
Shocks to a stationary time series are necessarily temporary. That is, over time the effects
of shocks will dissipate and the series will revert to its long-run mean. As such, long-term
forecasts of a stationary series will converge to the unconditional mean of the series
(Enders 1995).

On the other hand, the presence of a stochastic trend implies that ﬂuctuations in a
time series are the result of shocks not only to the transitory or cyclical component but
alsotothetrendcomponent ofthetime series. Thatis,themeanand/orvariancearetime
dependent, and thus shocks to such time series will permanently alter their level (Gujariti
1995). Moreover, a variance that changes over time Ins implications for the validity and
efﬁciency of statistical inferences about the parameters that describe the dynamics of the
price level. Changes in variances can also be very important in understanding price
movements. Using the standard ARIMA modeling techniques, chapter 4, uses the results
of the unit root and ARCH tests, the autocorrelation and partial autocorrelation functions,
and the Q-tests to identify price models for each commodity. The best models are then

identiﬁed as forecast competitors and evaluated in chapters 6.

CHAPTER 4

SPECIFICATION AND ESTIMATION OF ALTERNATIVE PRICE MODELS

4.0 Introduction

In this chapter alternative stochastic models for rice, sorghum and maize prices are
speciﬁed and estimated for the sample period of January 1982 to September 1996.
Because there are insufﬁcient data to build structural models, the price models developed
in this chapter use a time-series approach, modeling statistical properties such as serial
correlation and temporal dependence of the univariate time series. Information on
exogenous forces hypothesized to affect price movements, such as rainfall, are
incorporated in the modeling process when data are available. The tentative models are
evaluated with standard statistical selection criteria for time-series models, such as the Q-
statistic, the Akaike information criterion, the Schwartz-Bayesian criterion, parsimony and
tests for conditional heteroskedasticity. The most appropriate models for each commodity
are then put forward as forecast competitors and evaluated further for forecasting ability
using statistical and economic criteria in chapters 6and 7, respectively.

Due to their simplicity, broad availability in software packages, as well as their
limited success in forecasting (Makridakis 1993), exponential smoothing models are
examined in section 4.1. Furthermore, since part of this research seeks to identify the
beneﬁts of improved price forecasts, the forecasts ﬁ'om the smoothing models are included
in the forecast competition, along with the results generated ﬁ'om random walk (naive)
models. The interdependent behavior of different grain prices suggests that modeling the

commodities as a system, such as a vector autoregression (VAR), might improve the

62

forecasts of the individual grain prices. Therefore, a simple VAR is also developed and

evaluated for forecasting in chapter 5.

4.1 Smoothing Models

Exponential smoothing is a method of forecasting which is not based on any formal
statistical model or economic theory. It is a simple method of adaptive forecasting in
which the forecasts adjust based on past forecast errors (e.g. PM =P, + are) where a is an
adjustment or smoothing parameter, and e is the forecast error in period t. The past
forecast error is used to correct the next forecast in a direction opposite to that of the
error (Makridakis 1978). Smoothing methods require only a minimal amount of data and
are most effective when the parameters describing the time series change slowly over time
(Bowerman 1993).

There are several different smoothing procedures available. Single exponential
smoothing is appropriate for a series that moves randomly above and below a constant
mean with no trend or seasonal pattern (EViews users guide 1997). However, if the
series displays a slowly clunging linear trend, then double exponential smoothing which
produces forecasts that grow along a trend is more appropriate. And if the trend is
nonlinear, then the smoothing model is modiﬁed to handle nonlinear trends. Indeed, most
statistical packages allow for nonlinear trends such as the exponential (rate ﬁster than a
straight line) and damped (rate slower than a straight line).

If the time series has a seasonal pattern and a linear trend, then Holt-Winters is a

more appropriate exponential smoothing procedure. The Holt-Wmters forecasting

63

procedure can accommodate increasing (multiplicative) seasonal variation, i.e., seasonal
eﬂeas whose magnitudes grow along with the series and constant (additive) seasonal
variation. Short-term forecasts for sorghum, maize and rice are produced using the

smoothing procedures in EViews.

4.1.1 Smoothing Procedures for Sorghum and Maize

The choice of smoothing procedure is a ﬁrnction of the underlying pattern
observed in the time series. The plots of the evolution of logged. nominal sorghum and
maize retail prices ﬁ'om January 1982 to September 1996 are shown in ﬁgure 4.1. The
results in chapter 3 indicated that sorghum and maize prices exhrhited seasonal patterns
and possessed signiﬁcant downward trends prior to devaluation, and signiﬁcant upward
trends after devaluation. Therefore, the observed time series were assumed to trend with
temporal dependence occurring at or near seasonal lags. Smoothing procedures which
capture seasonality and trends were examined.

Holt-Winters is a common exponential smoothing method for forecasting seasonal
time series and is standard in most time series software packages. Holt-Winters requires
that the seasonal pattern in a time series be identiﬁed as either increasing or constant over
time. If it is increasing over time, the seasonal pattern is assumed to exhibit increasing
seasonal variation and the smoothing equation is multiplicative. If the seasonal pattern is

independent of time, it is modeled as additive.

Figure 4.1

5.2 5.4
—- ncmlnd ma'ze prices logged 5 2 ‘ — nominal sorghum prices logged

 

 

5.0-
4.84
4.69
4.41

4.2-1

 

 

 

 

4'0 T V V I I Y ﬂ Y ﬁr T V l I I
82 84 06 88 90 92 94 96

 

 

 

As there is no apriori reason to believe that the seasonality is increasing in the coarse
grain series, it is assumed to be constant and modeled as additive. The smoothed series
P,of P, is computed recursively by: P = a + bk +c,,k where P is the nominal price in
levels, a is the permanent component or intercept, b is the trend, c, is the constant seasonal
ﬁctor and k is the forecast horizon The coeﬂicients a, b and c are given by equations
(28)-(30) and are computed recursively in EViews. a, [3, and y are damping ﬁctors which

ﬁllbetweenOand 1,andsistheseasonalﬁ‘equency, 12inthiscase.

at =0r(P, —cr-s) +(l —a)at—l +br—l (28)

bi : B(at -01—1) + (1 -p)br-l (29)

6, =Y(P, -a,) + (1 -r)c,-, (30)

The smaller the smoothing parameter the smoother the series. The Holt-Winters

procedures in EViews estimates initial values for the damping factors by minimizing the

sum of squared errors. Forecasts are given by: 131+ k =a, + b,K + c

The results of the

r+k-r'

smoothing procedures (forecasts) for October 1996 to September 1998, starting ﬁom the

September 1996 prices for sorghum and maize, are reported in table 4.1.

 

 

 

 

 

 

Table 4.1: Forecasts from Holt-Winters Smoothing Procedures
Period Ahead Sorghum Actual Sorghum Maize Actual Maize
a=l; 0=y=0 “=1; l3=Y=0
Oct. 1996 7 176.6 170 150.1 144.4
Dec. 1996 159.4 110 141.6 109
Feb. 1997 160.7 122.5 145.1 122.5
June. 1997 174.2 125 152.3 125
Aug. 1997 181.9 121.3 160.5 121.3
Oct. 1997 178.3 102.5 152.6 102.5
Dec. 1997 161.1 106.7 143.8 105
Mar. 1998 164.8 115 150.2 115
June 1998 175.9 144 154.8 134
Sep. 1998 183.4 177 161.7 152

 

The mean, a,, is computed as 168.8 and 148.2 for sorghum and maize respectively,

while the trend, b, is 0.14 and 0.21. The seasonal factors for sorghum range ﬁom -3.8 to

12.1, with the negative ﬁctors occurring in November through May. The results are

similar for maize prices, which range from 1.69 to 10, with the negative ﬁctors occurring

 

66

in the same months as for sorghum. The zero values for B and y in the table imply that the
trend and seasonal components are estimated as ﬁxed and not changing. That is, ﬁxed

nonzero trend and seasonal ﬁctors are included in the forecasts.

4.1.2 Smoothing Model for Rice

Figure 4.2 Shows that the rice series to be trending upward over time, particularly
Since the January 1994 devaluation of the CF AF . Furthermore, the autocorrelation
function does not indicate signiﬁcant seasonaﬁty in the rice series. These characteristics
are consistent with rice’s role as an imported and food aid commodity. Nonetheless,

various Speciﬁcations with and without seasonality were examined and compared on the

Figure 4.2

 

5.7
— l edrice rices
5.6 _ 099 P

5.5 —

5.3 a

5.2 —

 

 

5.0 r I I I l I I I I r I I
82 84 86 88 90 92 94 96

 

67

basis of the root mean squared errors (RMSES). The trend in the rice series was best
described as linear. The model with the lowest root mean squared error was the Holt-

Winters with additive seasonality and is described below in table 4.2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4:2: Forecasts from Holt-Winters Smoothing Procedures for Rice
Period Ahead Rice w/o seasonality Rice w/ seasonality Actual Rice
a=0.99; [i=0 01=0.96; B=y=0
Oct. 1996 265 265.5 268
Dec. 1996 265.1 264.7 233
Feb. 1997 265.2 266.1 240
June. 1997 265.3 269.2 257.5
Aug. 1997 265.3 271 252.5
Oct. 1997 265.5 272.8 235
Dec. 1997 265.5 272.1 240
Mar. 1998 265.6 271 .1 246
June 1998 265.6 276.5 257
Sep. 1998 265.7 279.8 288
RMSE 7.47 7.33

 

Smoothing methods assume that the parameters describing the time series are

changing slowly over time. However, the estimates of the damping parameter, a, which

minimized the sum ofthe squared residuals, is equal to one in both the coarse grain

models and nearly one (0.99 and 0.96) in the rice models. This indicates that the

parameters are not changing Slowly. In ﬁct, the large value of the smoothing constant

suggests that the series are essentially random walks in which case the best forecast gives

 

68

high weight (in this case 100%), to the most recent observation and little weight to past
observations. Bowerman (1993) suggest that if the smoothing parameter that minimizes
the sum of the squared errors is greater than 0.3, then smoothing is probably not the best
forecast method.

In summary, although smoothing procedures are Simple and inexpensive, the
results of the smoothing procedures for each of the commodity prices generates
smoothing constants considerably greater than 0.3. This indicates that forecasting
performance may be improved with other forecasting techniques. Structural analysis in
which prices are related to other variables such as quantity produced can lead to improved
forecasts. But since data is limited in the Malian case, time-series modeling techniques are
used to forecast the commodity prices. In section 4.2, the price series are ﬁtted with

various univariate ARIMA models.

4.2 ARIMA Models

Recall that a univariate ARIMA (p,d,q) model is a stochastic or probabilistic
description of the outcome of a process operating through time (Enders 1995). AS
discussed in chapter 3, ARIMA models describe time series where the statistical properties
are independent of time, i.e., are covariance or weakly stationary. If the time series is
stationary, then the sample mean, variance and autocorrelations can be used to estimate
the parameters of the underlying data generating process. And if the process can be
described with a stationary statistical model, the model can be used to predict the time

path of prices. Therefore, the starting point for building ARIMA models is to test for

69

stationarity to determine whether ﬁrst-differencing is needed to achieve stationarity or if
the models Should be developed using levels.

The results of the preliminary analyses in chapter 3 suggested that each series had
a tendency to trend upwards after the devaluation. Structural change can complicate the
unit root test by making an otherwise stationary series appear nonstationary. Since the
Dickey-Fuller tests are biased towards the nonrejection of a unit root in the presence of
structural change, Perron (1989) developed a formal procedure to test for unit roots in

this context and is descrlhed below in equation (31):

I:
Pt:ao+02t+pZDL+§BlA'Pt-t+€r (31)

where P, is logged price, t is a deterministic time trend, and D, is similar to the devaluation
dummy variable described above, equal to 0 before devaluation and 1 after the
devaluation. Since the autocorrelation functions indicated that sorghum and maize price
series had strong seasonal patterns, 11 seasonal dummies were added to equation (31).
The augmented form is used to correct for serial correlation. The model is estimated and
Ho: a,=1 is tested and compared to the critical values in Perron (1989)”.

It should be noted that there is a substantial literature concerning the

appropriateness of the various Dickey-Fuller and Perron test statistics, where it is argued

 

29The distribution of a, depends on the proportion of observations occurring prior
to the break, which in this case is 0.82 (A=144/177). The critical values are identical to
the Dickey-Fuller statistics when A=0 or 1. Note that Perron’s critical values do not
account for seasonal dummies. This is believed not to have a signiﬁcant effect on the
results.

70

that these tests have low power to distinguish between unit roots and near unit root
processes. However, for forecasting, borderline cases have nearly identical forecasting
performance and one-step ahead forecasts ﬁ'om a differenced model are usually superior
to forecasts ﬁ'om a stationary model (Enders 1995). Furthermore, the tests are
confounded by the presence of deterministic regressors like trends, intercepts and seasonal
dummies. Too army or too few deterministic regressors reduce the power of the tests.
Nonetheless, each of the price series was subjected to the unit root test described by
equation (31) and each were found to have unit roots. So the models are built on the ﬁrst
diﬂ‘erences of the logged prices multiplied by 100, thus in effect modeling the percent
clmnge in prices. Table 4.3 reports the t-statistics. Further tests indicated that the ﬁrst-

differenced series were indeed stationary.

 

Table 4.3: Results of Unit Root tests - T-statistics for Ho: a,=1

 

Sorghum Maize Rice Critical value @ 5%

 

-0.54 -0.67 -l .33 -3.5

 

 

 

 

 

 

Using the Box-Jenkins methodology outlined above in chapter 2, this section
further examines the time-series properties of the ﬁrst-differences of each series to identify
tentative models of the underlying data generating processes. The focus is not identifying
precisely the forces that actually determine prices, but to develop models that capture the

essence of the true data generating process. The models are estimated by OLS in EViews

71

using White’s covariance estimator instead of the standard OLS formula”. White’s
heteroskedasticity-consistent covariance corrects estimates of the coefﬁcient covariance
when the form of the heteroskedasticity is unknown. This is used because many economic
series exhibit time-varying volatility ( a time dependent variance). The models are
estimated for January 1982 to September 1996 and include 177 monthly observations.
The speciﬁcation search proceeds as follows: beginning with sorghum, followed by
maize and then rice, the correlogram of the percentage change of each price is plotted and
the sample autocorrelation and partial autocorrelation coemcients are used to identify
tentative models. The correlogram of the model residuals is then casually investigated for
serial correlation and formally tested using the Ljung-Box Q-Statistic. The correlogram of
the squared residuals is examined and formally tested for conditional heteroskedasticity.
The speciﬁcation search continues until the model residuals approximate a white noise
process. Further validation is accomplished with the Akaike Information Criterion and the
Schwartz-Bayesian Criterion. The models that emerge from the diagnostic tests as
statistically adequate representations of the true data generating process are put forward
as forecast competitors. In chapter 5, vector autoregression representations of the price
series are developed and evaluated. The predictive performance of the univariate and
mulitvariate forecast competitors is further evaluated using statistical criteria, such as root
mean squared error and turning point errors in chapter 6, and economically evaluated in

chapter 7.

 

3"The White covariance matrix is given by: SW = —l—L(X’X)"(}3 11,2xric,l)(}t”21’)‘l ,
where T is the number of observations, k is the number ofiegressors, and u, is the least
squares residual.

72

4.2.1 ARIMA MODELS FOR SORGHUM
Figure 4.3 is a graph of the percentage change in sorghum prices, which clearly

ﬂuctuates around a constant mean of zero, and is indeed stationary.

 

 

 

 

 

Figure4.3
40
percentmechmgeinscruunprices

20 -1

a. W
.20 _
~40 _
-60 e T

82 84 88 88 90 92 94 96

Figure 4.4 graphs the autocorrelation and partial autocorrelation functions of the series
depicted in ﬁgure 4.3. Consistent with a priori expectations of rainfed crops in Mali, the
correlogram for 36 lags displayed in ﬁgure 4.4 reveals a cyclical pattern and indicates that

at a 5% level of signiﬁcance there is signiﬁcant autocorrelation at or near seasonal lags.

73

Figure 4.4: Correlogram of the Percent Change in Sorghum Prices

percent change in sorghum

 

 

 

 

 

 

 

 

 

 

 

1.0
.51
0.0-
-.5-1
ConﬁdenceLimits
u.
2 —1.0 __________________ nCoefficient
1 5 9 13 17 21 25 29 33
3 7 11 15 19 23 27 31 35
Lag Number
percent change in sorghum
1.0
.51
0.01
LL -.5:I
2 Confidence Limits
3 _
E
g_ -1.0 ECoefficient

 

 

Lag Number

74

The Q-8tatistic at lag 36 is 135 and with a p-value of 0.0 rejects the null hypothesis of zero
serial correlation.

In general, there are two major ways of handling seasonality in a time series using
ARIMA models: deseasonalize/seasonally adjust the time series, or model the seasonality.
Recent literature on time series econometrics argues against deseasonalizing, maintaining
that seasonal and ARMA coefﬁcients are best identiﬁed and estimated jointly (Enders
1995; Davidson & Mckinnon 1993). Therefore, this study models the seasonal pattern in
the time series using typical methods, such as seasonal dummy variables, harmonic
functions and seasonal ARIMAS. The next section discusses the results of the
alternative representations of seasonal pattern ﬁtted to various ARIMA structures of the

sorghum price series.

4.2.1.1 Speciﬁcation Search for Seasonality in Sorghum Prices

Harmonic functions and seasonal dummy variables are common methods of
describing deterministic seasonality in a time series. Seasonality is deﬁned as any cyclical
or periodic ﬂuctuation in a time series that recurs at the same phase of the cycle or period.
Due to their ﬂexibility in capturing periodic ﬂuctuations, harmonic functions have been
successful in describing the deterministic seasonal component of a time series and are
examined here. When the seasonal variation is believed to be constant over time, seasonal
dummy variables can also be an effective means of capturing seasonal patterns. A priori
expectations coupled with visual examination of the correlogram in ﬁgure 4.4, and the plot

of the nominal series did not indicate that the seasonal pattern in the sorghum series was

75

increasing or decreasing over time. Hence, the seasonal variation is assumed to be
constant. Excluding December from the analysis, the seasonal dummies equal one for the
current month and zero otherwise. The seasonal parameters are interpreted relative to the
harvest month of December. There are two Signiﬁcant spikes in the PACF in ﬁgure 4.4,
one at lag 1 and the other at lag 20. Several low-order ARIMA models with seasonal
dummies or harmonic ﬁ'equencies with ﬁrst and second order seasonaﬁty were estimated
and evaluated. The results of the most statistically adequate models are presented in table
4.4.

Beginning with the seasonal dummy speciﬁcation of the seasonality, the true
process that generated the sorghum realizations could be characterized as an ARIMA
(1,1,1). The ARIMA structure was Signiﬁcant at the conventional level. The seasonal
dummies were all signiﬁcant at the 5% level except for October and November. All the
seasonal dummies were positive, except November. The negative Sign on November is
valid if abundant rainﬁll leads to an early harvest. The parameter estimates indicate that in
the Bamako-Niarela market, the average percentage increase in sorghum prices is greatest
in June (13%) and smallest in October (3.1%). This is consistent with knowledge of the
sorghum market. The constant is Signiﬁcant and negative. The Q-tests for lags 1-12 and
1-36 indicates that the residuals are not serially correlated, and Q-tests of the squared

residuals indicates that there are also no ARCH (i.e., the variance is constant).

 

Dependent variable: percent change in sorghum prices

Table 4.4: ARIMA Models for Sorghum with Seasonal Dummies and Harmonic Functions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARIMA(1,1,1) ARIMA(1,1,(1,13)) ARIMA
w/seasonal dummies harmonic ((1 ,24),1,(1,24))

Constant —6.1 (3.5) 0.06 (0.31) 0.68 (0.50)

January 6.3 (2.7)

February 8.7 (4.2)

March 8.4 (3.7)

April 6.8 (3.1)

May 10.8 Q18)

June 13.1 (5.1)

July 12.9 (4.8)

August 8.5 (2.9)

September 5.2 (2.4)

October 3.1 (1.4)

November -5.3 (-l.3)

Sin (21tt/12) 2.0 (2.4) -0.09 (-4.76)

Cos (21tt/12) -5.6 (-6.9) -0.07 (-3.55)
. Sin (21tt/6) 3.1 (3.0) 0.01 (2.05)

CosQ‘ltt/6) -0.03 (-0.03) -0.03 (-2.96)

AR(l) 0.78 (3.7) 0.74 (8.6) 1.05 (26.34)

AR(24) 0.68 (13.7)

MA(lL -0.70 (-2.6) -0.71 (-10.5) 0.20 (3.3)

MA(13) -0.25 (~38)

MA(24) -0.62 (4164.8)
Log Likelihood -605.6 ~604.3 -534.5

AIC/SBC 7.08 / 7.33 6.99 / 7.14 7.09 / 7.16

Q(12) / Q(36) 0.48 / 0.47 0.24 / 0.59 0.65 / .18

Q2(12) / Q’(36) 0.60 / 0.16 0.86 / 0.23 0.90 / 0.15

 

 

T-statistics are in wentheses and the 00 statistics are the probability values

 

77

The sorghum series was also ﬁtted as an ARIMA (l,l,(1,l3) with 2"d -order
harmonic seasonality Similar to the model in Yang & Brorsen (1992). The letter “t ” in the
sine and cosine functions refers to the month and the denominator represents the length of
the cycle. The diagnostic statistics presented in table 4.4 column three indicates that this is
also a statistically adequate representation of the data The moving average coefﬁcient at
lag 13 indicates that values every 13 months away are closely related, which suggests that
the harmonic functions are not capturing correlations at near seasonal lags. Both the AIC
and the SBC criteria select the harmonic speciﬁcation over the seasonal dummy model.

In addition to using seasonal dummies and harmonic functions, seasonality can be
captured directly with the ARIMA structure by incorporating seasonal correlations into
the model. Identiﬁcation of seasonal ARIMA structures is accomplished through
inspection of the seasonal lags of the auto and partial auto-correlation flmctions but is
complicated by the ﬁct that the seasonal pattern often interacts with the nonseasonal
pattern in the data. That is, the correlogram for a combined seasonal/nonseasonal process
will reﬂect both elements. The model in the fourth colurrm in table 4.4 is the result of the
speciﬁcation search and includes both autoregressive and moving average coeﬂicients at
lag 24, as well as an MA(l) term. The model diagnostics indicate that the model is
adequate. The AIC and SBC statistics select that the harmonic speciﬁcation over the
other 3 models. These models are further evaluated for forecasting ability in chapter 6.

In addition to the seasonality in sorghum marketing, other exogenous ﬁctors
hypothesized to affect the evolution of sorghum prices were examined in the ARIMA

framework. Speciﬁcally, rainﬁll levels, the January 1994 devaluation of the currency, the

78
exchange rate between the CF AF and US. dollar and world price of rice (Thailand) dollar

were examined. Results indicate that none of these ﬁctors contribute Signiﬁcantly to
explaining the variation in sorghum prices. The insigniﬁcance of rainfall, deﬁned as the
monthly level of rainﬁll in Koutiala, a major sorghum producing area, is contrary to
expectation Since other studies have shown that coarse grain production is largely
determined by the variation in weather ( Boughton 1994; Dione 1989; D’Agostino 1988).
Several alternative speciﬁcations for rainfall were also examined, including diﬁ'erent lag
lengths and using the sum of rainﬁll ﬁ'om June through September (major rainﬁll months)
as the monthly observation. Rainﬁll was consistently insigniﬁcant. It does suggest that
the variation in production levels may not be directly transmitted to market prices.

The ARIMA models were formally investigated for structural change at the point
of devaluation using the Chow forecast test. The model was re-estimated for a sub-
sample comprising observations ﬁ'om January 1982 to December 1993 and used to predict
the percent change in sorghum prices for January 1994 through the end of the sample,
September 1996. A large difference between the actual and predicted values is indicative
of parameter instability or structural change. For the Chow forecast test, EViews reports
two test statistics: an F statistic and a log likelihood ratio statistic. The statistics for the

ARIMA with the seasonal dummies are presented below in table 4.5.

 

Table 4.5: Chow Forecast Tests - Ho: No structural change

 

Break lF-statistic (p-value) LR statistic (p-value)

 

 

 

 

 

January 1994 I 0.81 (0.76) 33.14 (0.46)

79

From table 4.5, it is clear that the null hypothesis of no structural change for the
devaluation cannot be rejected with either test statistic, and therefore the devaluation
dummy variable is not included in the analysis of the sorghum prices.

In summary, the models of sorghum prices presented in this section are all
statistically adequate representations of the conditional mean. The correlogram, Q-tests of
the squared residuals for each model and Lagrange multiplier test for ARCH effects all
suggest that the conditional variance is homoskedastic. The Chow Forecast tests for
structural changes indicates that there is none with both the LR and F -statistics ﬁiling to
reject the null of no structural change at 5% leveL Therefore, the ARIMA model with the
seasonal dummies, the ARIMA with the harmonic speciﬁcation, and the seasonal ARIMA
are put forward as forecast competitors. These models are further investigated for
forecasting performance relative to the random walk model in chapter six. Following the
same procedure as the sorghum models, the remainder of this chapter presents the forecast

competitors for the maize and rice prices.

4.2.2 ARIMA Models for Maize Prices
Figure 4.5 depicts the evolution of the percentage change in maize prices and

correlogram is shown below in ﬁgure 4.6.

80

 

 

Figure 4.5
30
percent change in maize prices
20 _
1O _ l
0 _

-10 .4
-20 q
-3) T
40 T 4

 

 

 

The dip in late 1988 corresponds to higher tlﬁn average rainﬁll for the critical months of
June through September, whereas it is less clear what is driving the dip in late 1991. At
913 mm, rainﬁll was abundant in 1990, but was slightly less than average in 1991 at 695
mm. One explanation is that producers and traders released large amounts of inventory
accumulated in 1990 in 1991.

In ﬁgure 4.6, the ACF has the typical seasonal pattern as does the PACF. There
are signiﬁcant spikes (exceeds the 2 Standard error band) at lags 1, 12, 20, 24 and 36,

clearly indicative of seasonality.

81

Figure 4.6: Correlogram of the Percent Change in Maize Prices

percent change in maize prices
1.0

 

.5‘

 

 

 

 

 

 

 

 

<54
ConﬁdenceLimits
L1.
2 -1.0 __________________ ﬂCcefﬁcient
15 9131721252933
3 711151923273135
Lag Number
percent change in maize prices
1.0
.51
0.01
U- -.5(
2 Conﬁdence Limits
2"; _
E
a -1.0 ﬂooerﬁcient

 

 

 

Lag Number

82

Table 4.6 presents feasible ARIMA representations of the stochastic process that
generated the maize data using seasonal dummies, harmonic functions, and seasonal lags
to capture the deterministic seasonal component. The maize harvest takes place in
October and thus the coefﬁcients on the seasonal dummies are interpreted relative to the
harvest month of October. With the exception of November, all the seasonal dummies are
positive and signiﬁcant at the 5% level. Relative to October, the largest percentage
increase (13.5%) occurs in July, with the smallest percentage increase (5.3%) occurring in
September. Although not signiﬁcant, the negative Sign on the November coeﬁcient is
consistent if harvest occurs in November.

The ARIMA model with the harmonic functions is signiﬁcant and has residuals
that approximate white noise, according to the Q-statistic. The seasonal lag model is a
higher-order pure moving average model with coefﬁcients at seasonal lags 24 and 36. The
MA(l) and MA(20) terms capture the signiﬁcant Spike at lag l and lag 20 in the PACF.

It is not clear what is consistently occurring every 20 months. It could be anything ﬁom
rainﬁll effects to the marketing strategies of producers. All the models were validated
statistically. However, the correlogram of the squared residuals suggest potential low-
order ARCH effects in the seasonal dummy and harmonic models, and higher-order
ARCH effects in the seasonal lag model. This was tested formally with the Lagrange

multiplier tests. The results are reported in table 4.7.

83

 

Table 4.6: ARIMA Models for the Percent Change in Maize Prices

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Models seasonal dummy harmonic seasonal lag
Constant -7. l4 (~2.68) 0.39 (0.73) 0.60 (0.82)
January 8.28 (2.35)

February 11.5 (3.42)

March 9.78 (3.39)

April 7.81 (2.63)

May 8.56 (2.79)

June 11.1 (3.42)

July 13.5 (3.89)

August 10.3 (2.97)

September 5.29 (1.78)

November -3.92 (-l.25)

December 7.37 (2.39)

Sin(21tt/12) 2.84 (3.84)

Cos(21tt/12) -3.7 (-4.83)

Sin(21tt/6) 4.62 (5.6)

Cos(21tt/6) 0.32 0 (0.47)

AR(l) 0.22 (2.44) 0.18 (1.97)

AM”)

AR(13) -0.22 (-2.70)

MA( 1) 0.17 (2.83)
MA(12)

MA(IS) -0.19 (-2.68)

MA(20) -0.20 (-2.83)
MA(24) 0.18 (3.05)
MA(36) 0.32 (4.19)
Log likelihood -578.8 -544.9 -598.4
AIC/SBC 6.77 / 7.02 6.77 / 6.91 6.86 / 6.94
Q(12)/Q(36) 0.39 / 0.27 0.41 / 0.25 0.11 / 0.13
Q’(12)/Q2(36) 0.48 / 0.26 0.30 / 0.23 0.33 / 0.02

 

 

84

 

 

 

 

 

 

 

Table 4.7: ARCH(q) Lagrange Multiplier Statistics: TR2(q)

Order seasonal dummies harmonic seasonal lags
First 4.4 (0.04) 6.14 (0.01) 2.2 (0.14)
Second 4.5 (0.10) 6.75 (0.03) 3.5 (0.17)
Twelve 9.9 (0.62) 1 1.8 (0.47) 9.2 (0.68)
Thirty-six 34.6 (0.54) 37.0 (0.42) 31 .8 (0.67)

 

 

 

 

 

The Lagrange multiplier tests indicate that there exists low-order ARCH effects in the
harmonic speciﬁcation and marginally in the seasonal dummy model, while there are no
ARCH effects in the seasonal lag model. The p-values are in parentheses.

The volatility in maize prices is hypothesized to be inﬂuenced by, ceteris paribus,
seasonality in marketing and weather. The plot of the squared logged differences of rmize
prices in ﬁgure 4.7 is used to identify patterns in the conditional variance. Two large
peaks occur in late 1988 and late 1991, while the rest ofthe volatility appears to exhibit
periodic peaks. The conditional variance of the hamronic speciﬁcation was ﬁtted as a

GARCH(1,1) model, which was investigated for seasonality and rainﬁll.

Figure 4.7

0.12

 

Vdﬂllw in mdze prices
0.10 _

0.08 .. ~

0.“ -1

0.04 -
0.“)
S

 

 

 

 

 

81
2
8
8
8
i
8

 

85

The results are presented in table 4.8.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.8: ARIMA with Harmonic Seasonality and GARCH (1,1) Errors
Constant 0.19 (0.43)
Sin(21tt/12) 3.19 (6.37)
Cos(21tt/12) -3.76 (-7.06)
Sin(21tt/6) 5.34 (8.17)
Cos(21tt/6) 1.31 (2.24)
AR(l) 0.15 (2.04)
AR(13) -0.28 (-5.08)
AR(29) 0.16 (2.70)
Conditional Variance
Constant 0.72 (1.19)
ARCH( 1) -0.05 (-1 . 14)
GARCH( 1) 1 .03 (28.7)
Log likelihood -478.7
AIC/SBC 6.66 / 6.89
Q(12) / Q(36) 0.46 / 0.35
Q(12) / Q2(36) 0.32 / 0.02

 

 

 

All the parameters in the conditional mean equation are signiﬁcant at the 5% level. Rainfall
was not signiﬁcant in the conditional variance equation, while seasonality described by a
ﬁrst-order harmonic speciﬁcation was signiﬁcant. However, the correlo gram revealed
serial correlated residuals at all lags in the conditional variance equation when the
lmrmonic functions were included. The model described in table 4.7 is an adequate ﬁt of

the data. The ARCH term is not signiﬁcant at conventional levels, but the GARCH term

86

is signiﬁcant at the 0.0% level. ARCH tests on lag 36 indicate that there are no remaining
ARCH effects. In summary, 4 models are put forward as forecast contenders, the ARIMA
with the seasonal dummies, the ARIMA with the harmonic speciﬁcation, the seasonal

ARIMA model, and ﬁnally, the ARIMA with the GARCH(] ,1) errors.

4.2.3 ARIMA Models for Rice
The plot of the ﬁrst diﬁ‘erenced rice series is shown below in ﬁgure 4.8 and the
correlogram is displayed in ﬁgure 4.10. Figure 4.8 appears to have a constant mean with

periods of high volatility, particularly during the devaluation and post-devaluation periods.

Figure 4.8
0.15

 

0.10 -

0.05 .1 ‘ '
0.00 a
-0.05 .. ‘ _

-0.1O _.

 

 

‘0‘15 '1 ﬁrst differences of logged nce

 

 

 

 

'0' 20 I T v I I I v v v I 1 ﬁ I 1
82 84 86 88 90 92 94 96

87

Figure 4.10: Correlogram of the Percent Change in Rice Prices

percent change in rice prices

 

 

 

 

 

 

 

 

 

 

 

1.0
.51
0.0!W
-.5I
ConﬁdenceLimits
35
< -1.0 __________________ .Coefﬁcient
1 5 9 13 17 21 25 29 33
3 7 11 15 19 23 27 31 35
Leg Number
percent change in rice prices
1.0
.5!
QMW
“- -.5l
‘3 Conﬁdence Limits
313
1'5
0. -1-0 __________________ .Coefficient

 

 

Lag Number

88

A binary variable was used to capture the effect of the devaluation. The binary
variable equals zero before January 1994, one through December 1994 and zero ﬁ'om
January 1995 to the end of the sample, September 1996. A Gauss program for computing
the log likelihoods for each month following the devaluation was designed to determine
the cutoff point of the impact of the devaluation. December 1994 generated the highest
log likelihood. This result is consistent with other studies on the impact of devaluation in
Mali. (See Teﬂt et al.1997). It was concluded that devaluation was a temporary Shock
to the system that caused retail rice prices to shoot up ﬁom January 1994 to December
1994. F omral tests for structural change are examined below.

The autocorrelation and partial autocorrelations functions in ﬁgure 4.10 do not
exhibit any seasonal pattern or signiﬁcant Spikes, with the exception of lag 17. In ﬁct,
the underlying process appears to be a Simple random walk. Nonetheless, during the
speciﬁcation search sonre low-order ARIMA models were examined. The results are
reported in table 4.9. The ﬁrst model is a random walk with a dummy variable for
devaluation, and the second model is an ARIMA ( 1,1,1) with a moving average term at
lag 17. The diagnostic tests indicate that both models are adequate representations of the
conditional mean, but Q-tests on the squared residuals in both models are suggestive of
conditional heteroskedasticity. Indeed, ARCH(q) tests for lags greater than 12 reject the

null of no ARCH effects in both models.

89

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.9: ARIMA Models for Rice

p=0; d=l; q=0 p=1; d=l; q=1,17
Constant -0.00 {-0.02)
Devaluation 3.37 (2.87) 3.23 (2.53)
AR(l) -0.52 (3.01)
MA(I) 0.53 (3.22)
MA(17) -0.28 (-2.46)
Log Likelihood -459.9 0.11 / -451.7
AIC / SBC 5.23 /5.26 5.22 / 5.31
Q(12) / Q(36) 0.18 / 0.08 0.22 /0.71
Q2(12) / Q2(36) 0.01 /0.29 0.00 / 0.42

 

To capture the time-varying volatility in the underlying process, the conditional

variance of a moving average model (MA(17)) with devaluation was ﬁtted as a GARCH

(1,1) model with ﬁrst-order harmonic speciﬁcation for seasonality in the variance. The

parameter estimates and model diagnostics are presented in table 4.10

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.10: Moving Average with GARCH (1,1) errors
MA(17) I -0.20 (-2.66) Model Diagnostics
Devaluation l 2.93 (3.25)

Conditional Variance Log Likelihood = .435'0
Constant 1.36 (1.87) AIC = 5.02 / SBC = 5.15
ARCH(” 0°13 (2'02) Q(12) / Q(36) = 0.54 / 0.52
GARCH(I) 075 (7.00)
Sin(21tt/12) 1.66 (2.31) Q2(12) / Q2(36) = 0.77 / 0.77
Cos(21tt/12) 1.73 (4.51)

 

 

 

90

The GARCH parameters are signiﬁcant at the conventional levels and the Qz-statistics
indicate that the residuals are white noise and that the model does a good job

characterizing the conditional heteroskedasticity in the data

4.2.4 ARIMA Models for Sorghum Producer Prices

The models developed thus ﬁr have been used consumer prices from the Bamako-
Niarela market. This section uses producer prices, speciﬁcally sorghum producer prices
from Zangasso, to develop producer price models. The data span ﬁom October 1985 to
September 1996. Observations for October 1996 to September 1998 were set aside to
validate the out-of-sample forecasting performance of the models. Identiﬁcation efforts
followed the same procedures outlined above. Unit root tests indicate that like the retail
price series, the producer price series is also nonstationary (t=-2.22 with a critical value of
-3.44). The analysis is therefore performed on the ﬁrst differences. Figure 4.11 shows
the evolution of the percent change in sorghum producer prices in Zangasso and ﬁgure

4.12 depicts the correlogram.

91

Figure 4.12: Correlogram of Sorghum Producer Prices in Zangasso

percent change in producer prices

1.0

 

 

 

 

 

 

 

 

 

 

-.54
Conﬁdence Limits
LL
2 -1.0 T' _f_jjt_ _ _ _ __ _ ___ ”Coefﬁcient
15 9 31721252933
3 711151923273135
Lag Number
percent change in producer prices
1.0
.54
0.0.
I
LL .51 '"“'
2 Confidence Limits
.7“
E
(L -1.0 _ 1 i t _ - mCoefﬁcient

 

 

 

— — w w t'ﬁ

5 911 17 2125 29 33
3 711151923273135

.7

Lag Number

92

The graphs show that there is a 75% drop in producer prices in late 1988 which
corresponds to a good rainﬁll year, and that the ACF and the PACF are both indicative of
seasonality. August and September are important months for producers because they tend
to release stocks during those months if rains are better than average, and store if rains are
lower than average. Therefore, a market dummy variable was designed to capture the
impact of the ﬂurry of activity in August and September; it equals one in August and
September and zero otherwise. An integrated moving average model with second-order
harmonic functions and the market dummy variable lagged once, ﬁt the data well, as did a
second-order seasonal lag model with the market dummy variable lagged twice. The
parameter estimates and diagnostic statistics are reported in table 4.11. All the
coefﬁcients are signiﬁcant at the 5% level and the residuals approximate white noise.

The correlogram of the squared residuals from the harmonic model was suggestive
of low-order ARCH effects. Indeed, the Lagrange multiplier tests revealed ARCH effects
for lags 1 and 2 (6.2 (p-value of 0.01) and 7.8 (p-value of 0.02) respectively). The ﬁnal
model in table 4.11 is the integrated moving average models with ARCH(2) errors. The
Q-tests indicates that there are no remaining ARCH eﬂ‘ects. The 3 models are put forward
as forecast competitors in chapter 6.

The purpose of this chapter was to identify a set of alternative univariate
forecasting models for each commodity. Mulitvariate models are identiﬁed in chapter 5.
The models developed in chapters 4 and 5 are summarized and further evaluated for

forecasting in chapter 6.

 

Table 4.11: ARIMA Processes for Sorghum Producer Prices

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

harmonic seasonallag ARCH(2)
Constant -1.63 (—1.10) 4.08 (4.78) -2.16 (-l.73)
Sin(21rt/12) 11.2 (5.23) 10.5 (5.31)
Cos(21tt/12) -6.93 (-5.97) -8.38 (-7.59)
Sin(21tt/6) 9.52 (4.58) 8.66 (5.96)
Cos(21tt/6) 7.28 (4.19) 5.75 (3.51)
Market(-1) 14.92 (2.36) 15.8 (2.29)
Market(-2) -19.9 (-5.85)
AR(l)
AR(24) 0.46 (7.37)
MA(13) -0.23 (-255) -0.24 (3.72)
MA(24) -0.78 (-3978.3)
MA(29) 0.21 (2.21)
MA(36) 0.32 (4.78)
Constant“ 113.9 (6.02)
ARCH(1)* 0.26 (1.25)
ARCH (2)* -0.08 (-200)
Log likelihood -5075 410.2 -501.9
AIC/SBC 7.87 / 8.05 7.74 / 7.84 7.83 / 8.07
Q(12)/Q(36) 0.23 / 0.22 0.91 /0.08 0.27 / 0.05
Q2(12)/Q2(36) 0.08 / 0.31 0.28 / 0.09 0.67 / 0.62

 

 

* conditiorml variance equation

 

 

CHAPTER 5

VECTOR AUTOREGRESSIONS AND COMMODITY PRICE MODELS

5.0 Introduction

In addition to the single equation ARIMA mdq) models examined above, several
transfer ﬁrnctions were also examined. Transfer functions generalize the univariate
methodology by allowing the time path of the dependent variable to be inﬂuenced by the
time path of an independent or exogenous variable. In the absence of feedback eﬁ’ects,
transfer functions can be an effective tool for forecasting (Enders 1995). For example, a

transfer function for maize prices is described below in equation (1):

1m, =a, +A(L)Pz,_, + C(LllnPs, +B(L)e. (32)

where A(L), C(L) and B(L) are polynomials in the lag operator L, and 11er and lnPS are
logarithrrric rmize and sorghum prices respectively. “6th a parameter estimate of 0.77,
OLS results indicate that sorghum prices are highly signiﬁcant (t-statistic is 20.27) in
explaining the evolution of maize prices.

Transfer function analysis assumes that sorghum prices evolve independently of
maize prices and that the maize innovations (i.e., disturbances in VAR language) have no
effect on sorghum prices. The critical assumption is that there be no feedback ﬁom maize
to sorghum. However, reversing the position of maize and sorghum prices in equation (1)
and re-estimating, we ﬁnd that maize is highly signiﬁcant (t-statistic of 21 .22) in explaining
the time path of sorghum prices, violating the no-feedback (reverse causality) assumption.

Since transfer ﬁmction analysis cannot capture the true relationship in the presence of

95

feedback, the question of whether the commodity prices are jointly determined is raised,
and if modeling the prices as a system of equations would improve forecasting
performance. Towards this end, this chapter develops vector autoregression models for
forecasting the grain prices. VARS can be useful when there is a paucity of data and
knowledge of the underlying system is uncertain. Section 5.1 discusses the conceptual
framework for VAR amlysis, while methodological issues regarding VARS, including co-
irrtegration, are discussed in section 5.2. Granger causality is discussed in section 5.3,
while section 5.4 descrrhes the VAR model for the retail prices and section 5.5 discusses
the forecast error variance decomposition. The ﬁnal section, 5.6 presents and discusses the
results of a VAR model for sorghum and maize producer prices. The results of the

forecast generated ﬁom the VAR models are evaluated for forecast accuracy in chapter 6.

5.1 Conceptual Framework

Structural models are often used to determine the relationship between variables in

an economic system. Consider a generalized structural model for the endogenous variable
Y1:

y, =BX, +6, (33)

where y, is a vector of endogenous variables, 0 is a matrix of structural parameters, X , is a
vector of pre-determined variables hypothesized to effect y,, and e, is a vector of structural
error terms. In addition to requiring large amounts of data, structural equations suffer

from problems of identiﬁcation in that there is often insufﬁcient information to

96

econometrically recover (identify) the structural parameters. In practice, restrictions
derived ﬁ'om economic theory are imposed on the system of equations to achieve
identiﬁcation.

The sometimes subjective imposition of restrictions on system equations was the
major criticism of structural models outlined in Sims’ (1980) seminal paper on vector
autoregressions (VAR) (Charemeza 1997; Enders 1995; Gujariti 1995; Hamilton 1994).
VAR models were developed to address some of these concerns. Speciﬁcally, a VAR
representation of a process makes no a priori distinction between endogenous and
exogenous variables, and thus identifying restrictions are not necessary. Since there are no
exogenous variables in the system, a VAR model is essentially an a-theoretic (non-
structural) summary of the dynamics of a group of variables. It is a statistical description
of the dynamic interrelations (i.e., correlations) between different variables in a vector, and
this summary description of historical data can be extrapolated into useful forecasts.

Formally, the VAR model expresses a variable as a linear function of the past, or
lagged values of that variable and all others variables in the system. The standard VAR

reduced-from equation iS described as:

y,=A,yH +.... +Apy,_p+Bx,+r-:, (34)

where y, is a vector of k variables, and p-lagged values of y, appear in each of the k
equations. x, is a vector of deterministic variables, such as intercept terms, deterministic
trends and seasonal dummy variables, etc.,. A , and B are unrestricted matrices of

coefﬁcients to be estimated, and e, is a vector of individually serially uncorrelated

97

innovations with zero means and constant variances.

Restricted VARS have been used in policy analysis and in the evaluation of
commodity price relationships in developing countries (Donovan 1996; Sims 1986), while
unrestricted VARS have traditionally been used for forecasting systems of interrelated
variables. In many cases the forecasts obtained from VARS are better than the forecasts
derived ﬁom more complex structural models. Allen’s (1994) study of economic
forecasting in agriculture found the VAR method to be the single best forecast method. In
addition to reducing the identiﬁcation problem, the VAR approach is relatively simple and
less costly than structural systems, and is particularly useful when data are limited and/or
knowledge of the underlying economic structure is uncertain. The fourteen years of
monthly grain price data used in this study are inﬂuenced by uncertain policy and weather
effects. This uncertainty coupled with data limitations makes the grain prices good

candidates for the VAR approach to forecasting.

5.2 VAR Methodology: Some Practical Issues

In practice, it is not possible to avoid imposing some prior restrictions on a vector
autoregression. In ﬁct, the forecasting performance of unrestricted VARS can often be
improved by imposing some restrictions (Engle and Y00 1997; Charemeza 1997). Using
mean squared error (MSE) as a performance measure, Engle and Y00 (1987) found that
unrestricted VARS only forecast well in the very Short run (i.e., four periods or less), and
that forecast accuracy indeed improved when restrictions were imposed on the VAR. The

literature discusses alternative approaches to imposing restrictions on VARS, including

98

exclusion restrictions in structural VARS already discussed above, Bayesian priors and co-
integration".

In a VAR, the standard errors for inference can be large because so many
parameters are estinmted. However, the estimates can be improved if the analyst has any
information about the parameters beyond that contained in the sample. For example, it is
possible to allow for time-varying elements by formulating the VAR model recursively and
imposing a priori knowledge by assuming Bayesian priors. The essence behind Bayesian
priors in VAR analyses is Simply that prior information that improves the estirmtes of the
VAR be included/imposed on the model. In an important paper on Bayesian priors in
VARS, Litterman (1986) suggested that the representation of the prior information be
based on the belief that the change in an economic time series is impossible to forecast,
due to inter alia, speculative and arbitrage behavior. The low explanatory power of some
of the ARIMA models suggest that the grain prices could be unpredictable in Litterman’s
ﬁamework; particularly since there appears to be considerable uncertainty in the grain
rmrkets. However, the literature indicates that this ﬁ'amework is not appropriate for
seasonal data or co-integrated systems and thus is not investigated further in this study.

If the series are nonstationary, then another method of imposing restrictions on a

VAR to improve forecast accuracy is to impose co-integrating restrictions. In a univariate

 

3'In a structural VAR, exclusion restrictions are imposed on the matrix of
structural coefﬁcients and identiﬁcation is recursive and the innovations are
orthogonalized, where orthogonalized innovations refer to the transformation of the model
such that the error terms are no longer contemporaneously correlated. For example,
Donovan (1996) used a recursive VAR structure to investigate the eﬂ‘ects of monetized
food aid on maize prices in Mozambique after exogeneity tests showed that rmize prices
were signiﬁcant in predicting food aid deliveries.

99

model, a stochastic trend can be removed by diﬁ'erencing. In a multi-variate context,
stationarity can be achieved if a linear combination of integrated variables is stationary;
such variables are said to co-integrated (Engle and Granger 1987). The unit root tests in
chapter 4 indicated that all the price series were nonstationary, therefore, the ﬁrst step in

identifying a VAR is to test for co-integration.

5.2.1 Co-integration

Similar to testing for stationarity in univariate analysis, the ﬁrst step in mulitvariate
or VAR modeling is to determine whether the nonstationary price series are co-integrated
or share common stochastic trends. Formally, nonstationary variables are said to be co-
integrated if there exist a linear combination of the integrated variables that is stationary
(Charemeza 1997, Enders 1995 and Hamilton 1994). That is, co-integration will occur
whenever the trend in one variable can be expressed as a linear combination of the trends
in the other variables. Such a linear combination is called the co-integrating or long-run
equilibrium relation”. A key feature of co-integrated variables is that their time paths are
inﬂuenced by the extent of any deviation ﬁ'om long-run equilibrium, such that short-run
dynamics are inﬂuenced by deviations from the long-run relationship. If the system is to
return to long-run equilibrium then the movements of at least some of the variables must

respond to the magnitude of the disequilibrium. Such a response is called error correction.

 

3’2 The econometric use of the term equilibrium refers to any long-run relationship
among nonstationary variables. The equilibrium relationship may be causal, behavioral, or
simply a reduced-form relationship among Similarly trending variable (Engle and Granger
1987).

100

Vector error-correction (V EC) models are restricted VARS that have co-
integration restrictions built into the speciﬁcation. In particular, the VEC restricts the
long-run behavior of the endogenous variables to converge to their co-integrated
relationship, while allowing for a wide range of Short-run dynamics (EViews 1997). If co-
integration tests reveal that the price variables are indeed co-integrated, then there exist an
error correction representation such that the differences respond to the previous period’s
deviation ﬁ'om long-run equih’brium”. If such an error representation exist, then
estimating the nonstationary prices as a VAR in ﬁrst differences is inappropriate and
entails a misspeciﬁcation error. In ﬁct, according to Hamilton (1994), a VAR in
diﬁerences is a poor approximation of a co-integrated system because the levels contain
information useful for forecasting beyond that contained in lagged changes. The
important point is if nonstationary series are co-integrated, then the VAR should be
speciﬁed with error correction terms to eliminate any deviation ﬁom long-run equih'brium,
and estimated as a vector error correction (VEC) model. If the series are not co-

integrated, then the system of nonstationary variables is run in ﬁrst diﬁ'erences.

5.2.1.1 Co-integration Tests
There are two major ways to test for co-integration: the Engle-Granger
methodology which seeks to determine whether the residuals of the equilibrium

relationship are stationary; and Johansen’s method. Johansen’s method is essentially a

 

33Granger’s representation theorem states that for any set of I( 1) variables, error
correction and co-integration are equivalent expressions (Charemeza 1997; Enders 1995).

101

mulitvariate generalization of the Dickey-Fuller tests, which focuses on determining the
rank of a matrix, which equals the number of co-integrating relations in a system. Since
the statistical properties of Johansen’s procedure are generally better and the power of the
co-integration tests higher, this study uses Johansen’s method to test for co-integration
between the sorghum, maize and rice series (EnderS 1995).

Note that testing for co-integration when using seasoml data is still under
development. The scant literature that is available suggests seasonally adjusting the data
before applying standard co-integration tests. However, Hallrnan (1989) and others argue
that the use of seasonally adjusted data to estimate the long run model (i.e., the co-
integrating equation) may give rise to inconsistent estimates of the long run parameters.
The approach followed in this study is the one suggested by Charemeza (1997) who
asserts that the most practical procedure is to assume that stochastic seasonality can be
approximated by deterministic seasonal durmny variables or harmonic functions.

Johansen’s test for co-integration begins with a determination of lag length using a
VAR in levels. The procedure is essentially a mulitvariate generalization of the procedure
discussed above for determining lag length in the Dickey-Fuller tests. Lag- length tests
using the log likelihood statistic indicated that 2 lags were sufﬁcient for the test VAR

which is described below in equation (35).

P, :AIPr-l +A2Pr—2 +er +6: (35)

where P, is a vector containing the logarithm of the three nonstationary time series, x, is a

vector including deterministic seasonality, an intercept and a dummy variable representing

102

devaluation, A ,- for i=1,2 and B are matrices of coefﬁcients, and E, is a vector of error

terms or innovations in VAR language. The estimated form of the test equation is

rewritten as:
p-l
AP, =IIPH + 2 I‘lAPH +th + e, (36)
i=1
where
p p
II=EA,-I, I‘i=- 2A. (37)

and I is the identify matrix. H reﬂects the impact of lagged PS on AP, and represents the
dynamic adjustment of ﬁrst differences of variables to levels. The test involves estimating
the 11 matrix in an unrestricted form and then using the likelihood ratio statistic for testing
whether the restrictions implied by the reduced rank of II can be rejected (Hamilton 1994;
Charemeza 1997; EViews 1997).

Before proceeding with the co-integration tests, assumptions about the intercept
and the deterministic trend component in the co-integrating equation had to be made,
because the asymptotic distribution of the likelihood ratio (LR) statistic depends on the
assumption made with respect to the deterministic trend. The test was carried out in

EVIEWS which uses the critical values given by Osterwald-Lenum (1992):“. Consistent

 

34Note that the critical values do not account for deterministic regressors such as
seasonality and devaluation. The test VAR was therefore Speciﬁed with and without the
exogenous regressors. The results were the same.

103

with Johansen’s 1995 paper, EVIEWS allows for ﬁve alternative Speciﬁcations of
intercept and trend with diﬁerent combinations of rank. Without any a priori information
concerning the long term relationship between the grain prices, the co-integration test was
performed using all ﬁve speciﬁcations. The Akaike information criterion (AIC) and the
Schwartz criterion (SBC) were used to choose the most appropriate ﬁt of the data. A

summary of the results are reported in table 5.1”.

 

 

 

 

 

 

 

Table 5.1: Co-integration Tests and Deterministic Trend Assumptions

Data trend: None None Linear Linear Quadratic
Co-integrating No intercept Intercept Intercept Intercept Intercept
Equation No trend No trend No trend trend trend
Rank = 1

AIC -9.41 -9.44 -9.42 -9.41 -9.39
SBC -8.97 -8.98 -8.93 -8.90 -8.85

 

 

 

 

 

 

 

The bold represents the smallest values. Preliminary results of the co-integration tests
resulting ﬁ'om the trend speciﬁcation tests indicate that the rank is one. The AIC and SBC
information criteria select the speciﬁcation without a deterministic trend in the time series.
The test was re-speciﬁed assuming that there was no deterministic trend in the
series and includes an intercept in the co-integrating relation. The null hypothesis of zero
co-integrating equations is rejected at the 5% level of signiﬁcance. The test ﬁnds one co-

integrating equation (rank=1) in the three variable (price) system regardless of the

 

3’The statistics in table 5.1 include seasonal terms and devaluation.

104

assumptions made about the deterministic trend component. The resultant co-integration
relation or long-run equilibrium is described below in table 5.2”. Eviews reports the
asymptotic standard errors; the t-statistics were computed and are in parentheses. The
estimated long-run relationship between the sorghum, maize and rice prices suggests that
in the long run relative to sorghum prices, maize prices grow at a Slower rate (-1 .24) and

rice prices at a ﬁster rate (0.38).

 

 

 

Table 5.2: Normalized Co—integrating Equation
Log(sorghum) Log(maize) Log(rice) Constant
1.00 -1.24 0.38 -1.02
(-26.7) (5.25) (-2.96)
Log likelihood 846.1

 

 

The ﬁrst step in specifying a VAR for the price series found that the series were
co-integrated; therefore the prices are modeled as a VEC. Seasonality and devaluation
are modeled as short-run phenomena and are not included in the co-integrating equation,
which represents the long-run relationship between the variables. The next steps involve
determining the speciﬁcation of the VEC using Granger causality tests and order selection

tests.

 

3"The co-integrating equation is not identiﬁed unless some type of normalization
procedure is undertaken. Eviews adopts a normalization such that the ﬁrst series in the
vector of endogenous variables, in this case sorghum, is normalized to the identity matrix.

105

5.3 Granger Causality in Grain Prices

Granger causality tests developed by Granger (1969) are used to determine
whether one scalar y can help forecast another scalar x. Ifit cannot, then we say that y
does not Granger cause x. Figure 5.1 depicts an overwhelming co-movement between
sorghum and maize in the Bamako-Niarela market, such that lagged sorghum prices could

be a good predictor of maize prices, and vice versa.

Figure 5.1

6.0

 

Evolution of Commoditiy Prices in CFAF/KG

beralzelcn
5-0 - ff 4') devulretlcn M

 

 

 

 

41,. ‘ .3 "‘. 1‘ 1.11.1994
l, J‘ ‘\{7b’\l‘ j‘i‘ /
4.5 — ,sz Viv-gr " - r
'1' “\”r/ U \ “4% j I‘
T” ‘W’ ‘Vf ‘ ‘ ﬂV/r/ .3591; \V’T"
4.0 —1 I u "H “mm",
ccerseo‘elns W
061.1985 1991/92
3.5 T T T T T T T T T T T T T T
82 84 86 88 90 92 94 96
[ —-- nee ------- sorghum ————— malze ]

 

Indeed, all the commodity prices appear to be evolving more or less in tandem. Block
causality, a mulitvariate generalization of the Granger causality test, is used to formally
investigate whether to incorporate a particular variable(s) into a VAR/VEC system. For
example, if a forecast of maize prices is more accurate (lower RMSE) when current and
lagged values of sorghum prices are included in the model, then sorghum is said to

“Granger cause” maize and the two could be modeled as a VAR system (Enders 1995;

1 06
Hamilton 1994)”.

Using a trivariate VAR, causality tests were performed in EViews by estimating a
VAR using the ﬁill information maximum likelihood (F IML) estimator with the
Marquandt algorithm and testing for zero restrictions on the VAR coefﬁcients. The block
causality test restricts all lags of sorghum prices in the maize and rice equations to be zero,
and tests these cross-equation restrictions using a log likelihood ratio test with a chi-
squared distribution. The restricted regression excludes lags of one or more of the
variables, while the unrestricted regression allows the coeﬁcients on those lags to be
nonzero (Hamilton 1994). In summary, Granger causality measures precedence and
information content and is a useful tool for testing hypotheses that can be ﬁ‘amed as
statements about the predictability of a particular series. The issue is to determine
whether lags of one variable help to predict any other variables in the system.

Before testing for causality, the order of the VAR was determined by using
likelihood ratio tests and the AIC and SBC information criteria to test lag lengths ﬁom l
to 4. The test regressions include 173 observations to accommodate the fourth-order
speciﬁcation as well as harmonic functions describing ﬁrst and second order deterministic

seasonality. The intercept term was excluded since it was statistically insigniﬁcant in all

 

3 If E,(PZ,+,|PZ,) =E,(PZM|PZ,,PS,), the only additional information contained in PS, are
the past values of {em}. However, such values do not affect PZ, and thus cannot improve
on the forecasting performance of the Pl, sequence. Thus {PS,} does not Granger cause
{PZ,}. If the coefﬁcient on the moving average term for PS, is not equal to zero, {PZ,} is
not exogenous to {P8,} and pure shocks to PSM (i.e., 6P3“) affect the value of PZM even
though the {PS,} sequence does not Granger cause the {PZ,} sequence (Enders 1995,

p.3 16).

107

three equations”. For a trivariate VAR, the number of zero restrictions required to move

ﬁ'om a VAR(2) to a VAR(1) is nine (3x3)39. The results are reported in table 5 .3

 

 

 

 

 

 

 

Table 5.3: Test Statistics for Order Selection of VAR/VEC
Order Likelihood Ratio x2(m=9)/( p-value) AIC SBC
1 829.5 (0.00) -9.34 -8.96
2 19.4 (0.02) -9.35 -8.81
3 12.0 (0.21) -9.32 -8.61
4 6.6 (0.68) -9.25 -8.38

 

 

 

 

The null hypothesis states that the restriction is valid and at conventional levels of
signiﬁcance, the LR tests cannot be rejected at lags 3 and 4, indicating that restricting the
order to two lags is a valid restriction. The AIC also selects two lags, whereas the more
parsimonious SBC criterion selects one lag”. The goal is to include as many lags as are
necessary to capture system dynamics, and since the theory behind Granger causality is
couched in terms of the relevance of all past information, the hg length is chosen to

correspond to reasonable beliefs about the longest time over which one of the variables

 

’8 A likelihood ratio test for ﬁrst versus second order deterministic seasonality
selected the second order speciﬁcation with a likelihood ratio statistic of 34.2 and p-value
of 0.00. The order selection results were the same with and without the deterministic

seasonality components.

3"From Hamilton (1994. P.297), restrictions determined by n2(p,-po) where n is the
number of equations and p, and po refer to the higher and lower lags respectively.

‘0 Recall tlmt with the AIC and SBC criteria, the lowest value is selected. The SBC
selects a more parsimonious speciﬁcation by imposing a larger penalty for additional
coeﬁcients.

 

108

could help predict the other. Granger causality is thus investigated using two lags and
reported in table 5.4.

The large probability values (all greater than 85%) in the rice equations indicate
that none of the null hypotheses can be rejected at any conventional level of signiﬁcance.
Therefore, including sorghum and maize prices in the rice equation does not contribute
any additional information for predicting the time path of rice prices and thus will not
improve the forecast of rice prices. As rainfed crops, sorghum and maize face diﬂ'erent
production and demand environments than irrigated, tradeable, urban—preferred, politically
charged rice. Moreover, past sorghum and maize prices may not contribute signiﬁcantly
to predicting rice prices because the marketed surplus of coarse grains which is a ﬁmction
of inter alia, home consumption needs, storage capacity and liquidity constraints, may be
low. Thus, this ﬁnding seems consistent with knowledge of the cereals markets in that
information about past sorghmn and maize prices is not expected to contribute

signiﬁcantly to predicting the future path of rice prices.

109

 

 

 

 

Table 5:4: Results of Causality Tests on the Cereals Prices

Null hypothesis LR~ x2 p-value
Maize and Rice prices do not help predict Sorghum prices 46.66 0.00
Rice prices do not help predict Sorghum prices 8.44 0.01
Maize prices do not help predict Sorghum prices 30.44 0.00
Sorghum and Rice prices do not help predict Maize prices 28.66 0.00
Rice prices do not help predict Maize prices 25.26 0.00
Sorghum prices do not help predict Maize prices 12.46 0.00
Sorghum and Maize prices do help predict Rice prices 1.04 0.90
Sorghum prices do not help to predict Rice prices 0.24 0.88
Maize prices do not help to predict Rice prices 0.18 0.91

 

 

 

On other hand, the results do suggest that rice prices will help predict both
sorghum and maize prices. The Granger causality between rice and the coarse grains is
due primarily to the fact that the grains are substitutes in consumption. Another
explanation posits that since rice is more marketed or tradeable than both maize and
sorghum, that when maize and sorghum do enter the market rice is a good predictor of
market dynamics. For example, in dire need of revenue, the transitional government in
1991/2 reduced the import tariﬂ' to encourage rice imports and increase the collection of
tariﬂ‘ revenue. In the absence of storage and/or speculative behavior, this rice entered the
market and ceteris paribus led to falling rice prices and consequently, induced a decline in

the price of coarse grains. Therefore, due to the substitutability in consumption,

110

particularly in urban areas like Bamako-Niarela, information contained in past rice prices
could indeed help to predict the ﬁrture path of sorghum prices.

Further examination of the results in table 5.4 indicate that the coarse grains are
highly signiﬁcant in helping to forecast each other, i.e., the null hypotheses of zero
coemcients are all rejected at even the 1% level. Although sorghum prices are slightly
higher, it is clear in ﬁgure 5.1 that maize and sorghum prices have evolved in tandem over
the last fourteen years and that information contained in the past prices of one could
indeed be a good predictor of the other. Moreover, because the production, demand and
marketing environments are similar, when maize prices fall, ceteris paribus, sorghum
prices are expected to fall. In summary, the results of the causality tests demonstrate that
sorghum, maize and rice prices are indeed dynamically related and could be described and

forecast with a restricted vector autoregression model.

5.4 VEC and Forecasting

The results of the above tests indicate that a three-variable VEC of order two
might yield superior forecasting properties than the univariate models developed in chapter
4. The additional information gleaned from modeling sorghum and maize prices as a
system should lead to “better” forecasts. The forecast properties of the rice equation are
not expected to dominate those derived ﬁom the univariate models because sorghum and
maize prices fail to contribute any additional information useﬁrl for forecasting rice prices.
As a practical question, rice could therefore be excluded from the system, but since rice

prices do Granger cause sorghum and maize prices, it is retained in the VEC.

111

The following VEC(2) was estimated:

AP, = a,(PS,_, - 1331’qu +0.38PRH —2.83)+y,AP,_, +y,AP,_, +ax,+e, (33)

where P is the vector of logged sorghum (PS), maize (PZ) and rice (PR) prices, 7, and )9,
B are matrices of coefﬁcients to be estimated, 1:, is a vector of deterministic variables
containing second-order seasonal harmonic functions and a dummy variable representing
the devaluation. a, is the coefﬁcient on the error correction term, referred to as the
adjustment parameter. i refers to the equation for each endogenous variable and e is a
vector of innovations assumed to be contemporaneously correlated but not
autocorrelated". The term in parenthesis is the error correction term ﬁ'om table 5.2. The
parameter estimates and t-statistics are reported in tables 5.5.

As expected, neither sorghum nor maize are signiﬁcant in explaining rice prices
over time and in fact, devaluation is the only signiﬁcant variable in the rice equation. Past
rice prices 1 and 2 months back are also not signiﬁcant in explaining the dynamics of the
percent change in rice prices. In contrast, past changes of sorghum and maize prices and
the ﬁrst lag ofrice are signiﬁcant inthe sorghumequation, asarethemost ofthe seasonal
terms. Consistent with the univariate analyses, devaluation is not signiﬁcant in either the
sorghum or maize equations. Finally, maize prices are largely inﬂuenced by its own lags

and one lag of sorghum prices (at the 10% level) and seasonality.

 

"According to Charemeza (1997), the assumption of no serial correlation is not
restrictive because any autocorrelation can be absorbed by adding more lagged InP ’s.

112

 

 

 

 

 

Table 5.5: VEC(2) for Log Cereals Prices with Deterministic Components

ASorghum AMaize ARice
Co-integration term -0.01 (-0.12) 0.33 (3.52) -0.00 (-0. 16)
ASorghum(-l) -O.27 (-2. l l) -0. 12 (-l.09) -0.01 (-0.22)
ASorghum (-2) -0.28 (-2.41) -0. 17 (-1.64) 0.03 (0.58)
AMaize(-l) 0.49 (3.47) 0.34 (2.67) -0.01 (-0.18)
AMaize(-2) 0.32 (2.41) 0.23 (1.89) 0.05 (0.91)
ARice (-1) 0.36 (1.99) 0.07 (0.43) -0.05 (-0.62)
ARice(-2) O. 18 (0.98) 0.03 (0.20) -0.09 (-l .08)
Sin (2m/12) 0.01 (1.50) 0.03 (3.61) -0.00 (.059)
Cos (2111/12) -0.05 (-4.58) -0.04 (-4.01) -0.00 (-0.98)
Sin (21rt/6) 0.02 (2.31) 0.04 (4.49) 0.00 (0.72)
Cos (21rt/6) 0.02 (1.70) 0.01 (1.29) 0.01 (1.75)
Devaluation -0.02 (-0.75) 0.00 (0.09) 0.04 (3.71)
Log likelihood 205.8 226.2 352.5
AIC/SBC -2.23/ -2.01 -2.46 / -2.24 -3.91 / -3.69
Q(12) / Q(36) 0.28 / 0.11 0.70 / 0.11 0.29 / 0.35
Model Statistics Log likelihood = 860.3; AIC/SBC = -9.43 / -8.70

 

 

Q-tests of the residuals from each equation at lags 12 and 36 indicate that the VEC (2) is a
statistically adequate representation of the data generating mechanisms. The

decomposition of the forecast error variance is discussed in the next section.

5.5 Forecast Error Variance Decomposition
In VAR analysis the decomposition of the variance can be used to ascertain the

importance of the interaction between series. Variance decomposition calculates the

113

percentage of the variance in forecast errors attributed to the different shocks over the
forecast horizon. Table 5.6 reports the variance decomposition results for the 24'11 period
of model one, while Appendix A presents the variance decompositions for each period of

the 24 month forecast sample for each price.

 

 

 

 

 

 

 

 

 

 

Table 5.6: Variance Decomposition Percentage of 24-month Error Variance
% of forecast error Typical shocks in

variance in Sorghum Maize Rice
Sorghum 92.8 85.19 7.82

Maize 1.16 4.15 0.38

Rice 6.09 10.66 91.79

 

 

As expected, most price series explain the preponderance of their own past values; by
period 24, sorghum explains over 92% of its own forecast error variance, while rice
explains nearly 92% of its own forecast error variance. However, at just over 4%, rmize
seem to explain very little of its past values, with most (85.2%) of the forecast error
variance attributable to sorghum prices. This suggests that shocks to sorghum prices have
a larger impact on nmize prices than own price shocks. One explanation is that as maize
markets are considerably thinner than sorghum markets, when maize does enter the
market, it takes its cues ﬁom sorghum.

Further analyses of the variance decomposition reveals that as the forecast horizon
gets larger, rice prices have a small but growing inﬂuence on the forecast error variance of

sorghum (from 1% to 6%) prices, whereas maize’s inﬂuence is the opposite, declining

114

ﬁ'om 6% to 1%. Again perhaps because maize is not a highly marketed commodity in
Mali, and rice is, maize explains about ‘/2 a percent on average of the forecast error
variance in rice prices. Together, less than 10% of the forecast error variance in the rice
series is attributable to sorghum and maize prices. In summary, the variance
decomposition analysis underscores the importance of sorghum shocks in predicting maize
prices as well emphasized how unimportant sorghum and maize are in predicting rice
prices. Along side the univariate models, the VEC(2) is solved and put forward as a
forecast competitor. The results are presented and evaluated for forecast accuracy in
chapter 6.

The ﬁnal section of this chapter reports the results of the VEC (4) for rural
sorghum and maize prices, covering the period from October 1985 to September 1996.
The procedure for developing the model is similar to that described above for the retail
price model. Rice is not produced in the Zangasso zone and so producer prices for rice

are not included in the VAR analysis for producer prices.

5.6 VEC for Producer Prices in Zangasso

Figure 5.2 illustrates the strong co-movement between sorghum and maize
producer prices such that the producer prices could be jointly determined, hence
investigation in a VAR framework is justiﬁed. Unit root tests revealed that the producer

price series for sorghum and maize were nonstationary in levels, but stationary in ﬁrst

115

differences". Therefore, co-integration tests were performed.

 

 

Figure 5.2
5.0
evoluﬁonotproducerpricesinhngaaso *.\ /
/\ / ‘1 J
4.5 1 r“ ’,\ I , r l
'1 ( y’ ‘ 1 a". '.
-3 1 ’1 I 1 4'
,l r i 1: 1 , '
4.0 F ‘ .I i! I" f ‘l I“ ,1
' .1 n\ I I ' \ ’
”I ' IV ‘l‘s - J ‘4’ \ ‘l
3.5 — \1 r ' i1 _ i v 'w-j i, r .r
‘\ / x! ‘5
3.0 _
LOG_ZMZE ------ LOG_ZSORG
2.5

 

 

 

The results of the co-integration tests were highly sensitive to the assumptions
made regarding the mean and trend in the data and the co-integrating equation. Using lags
lengths ﬁ'om l to 12, the number of co-integrating relations was anywhere between 0 and
2, with the later being the maximum number. Because of the upward trend in ﬁgure 5.2,
the speciﬁcations that included the linear trend in the data were examined in depth. Tests
for lag length found that the residuals approximated white noise in the maize equation at
lag 4, but 9 lags were required to approximate white noise in the sorghum equation. The
ﬁnal co-integration test was investigated using 9 lags and a linear trend in the data and the

co-integrating (long-run) equation, and exogenous regressors for seasonality and a market

 

42The t-statistic for maize after adjustment for seasonality and a trend is ~2.64 with
a critical value of -3.44. The sorghum results are discussed in chapter 4.

116

dummy variable”. The LR test (8.57 with critical value of 12.25) indicates that there is
one co-integrating equation at the 5% level of signiﬁcance. Therefore, the nonstationary
producer price series are speciﬁed as a vector error correction model.

Granger causality tests between sorghum and maize producer prices at 4 and 9 lags
indicate that maize prices Granger cause sorghum, but that sorghum prices do not Granger
cause maize. (See table 5.7). Since maize producer prices do help to predict sorghum

producer prices, modeling the prices as a system can be justiﬁed.

 

Table 5.7: Pairwise Granger Causality Tests with 4 and 9 lags

 

 

 

 

Null Hypothesis: F-statistic (p—values):4 lags F-statistic (p-value): 9 lags
Ho: Maize prices do help 13.98 (2.2E-09) 6.53 (2.5E-07)

predict sorghum prices

Ho: Sorghum prices do not 0.551 (0.699) 0.60 (0.79)

help predict maize prices

 

 

 

 

Both a VEC(4) and a VEC(9) were estimated. A likelihood ratio test (23.88 with
a p-value of 0.24) selected the VEC(4) over the VEC(9) as did the AIC and SBC
statistics. Therefore, the ﬁnal model was estimated as a VEC(4). The parameter

estimates, the co-integrating relation and t-statistics are reported below in table 5.8.

 

”The results were the same with and without the exogenous regressors. This is
important as the critical values were tabulated without accounting for the exogenous
regressors.

ll7

 

 

Table 5.8: VEC(4) for Producer Prices in Zangasso

ASorghum AMaize
Co-integration term -0.07 (-0.52) 0.40 (2.89)
ASorghum(-l) -0.33 (-2.15) -o.12 (.077)
ASorghum (-2) -0. l 3 (-0.88) 0.09 (0.59)
ASorghum(-3) 0.08 (0.61) 0.01 (0.05)
ASorghum (-4) 0.08 (0.68) -0.05 (0.40)
AMaize(-l) 0.52 (3.47) 0.24 (1.47)
AMaize(-2) 0.22 (1.44) -002 (.014)
AMaize(-3) 0.03 (0.21) 0.04 (0.27)
AMaize(-4) -0.13 (-1.01) 0.01 (0.09)
Constant 0.02 (1.72) -0.00 (-0.26)
Sin (2nt/12) ~0.01 (-0.26) 0.12 (4.22)
Cos (ert/ 12) -0.05 (-1.98) ~0.05 (-l.83)
Sin (21tt/6) 0.04 (1.86) 0.08 (3.36)
Cos (21:06) 0.02 (0.73) 0.09 (3.37)
Market -0.12 (-2.24) 0.04 (0.63)
Log likelihood 100.2 91.69
AIC/SBC -1.34/ -l.01 -1.21 /-0.87
Q(12) / Q(36) 0.78 / 0.01 0.17 / 0.49
Model Statistics: Log likelihood = 241.2; AIC/SBC = -3.28/ -2.54

 

 

 

The co-integrating vector is:

AZP, = rx,.(ZPSH -1.56ZPZH+0.00Trend+0.16)+ypAZP,_p+BX,+e, (39)

where ZP, is a vector including the sorghum and maize producer prices in Zangasso, i

represents each equation, ZPS and ZPZ are the sorghum and maize producer prices

118

respectively, p is the number of lags, which in this case are from 1-4 and ﬂ is the matrix of
parameters for the exogenous regressors in X. All the parameters are signiﬁcant at the
5% level in the co-integrating equation.

However, in addition to the exogenous regressors, only the ﬁrst lags of sorghum
and maize are signiﬁcant at the 5% level. The estimated maize equation indicates that
seasonality, and not lagged prices, explains most of the variation in the percent change in
maize prices. The market variable, which recall is a dummy variable describing the ﬂurry
of market activities that occurs in August and September in producing markets, is
signiﬁcant in the sorghum equation but not the maize equation. This is consistent with
knowledge of the producing markets, since maize is not as commercialized as sorghum.

The ﬁnal table (5.9) describes the variance decomposition of the forecast error in
the producer prices. Similar to the results of variance decomposition of the forecast error
for the retail prices, sorghum explains 97.8% of its own forecast error variance, while also
explaining almost 95% of the error variance in maize prices. From close inspection of the
variance decomposition table in appendix B, we note that the ability of maize producer
prices to explain own error variance decreases with time, speciﬁcally falling ﬁ'om ahnost

46% in period one to less than 6% in period 24.

 

Table 5.9: Variance Decomposition Percentage of 24-month Error Variance

 

 

 

 

 

% of forecast error variance Typical shocks in

in: Zangasso Sorghum Zangasso Maize
Zangasso Sorghum 97.8 94.7

Zangasso Maize 2.20 5.28

 

 

 

 

119

This chapter discussed the development of, and presented the results of VAR
models for the retail grain prices in the Bamako-Niarela market, as well as a VAR for
sorghum and maize producer prices in the Zangasso market. The results of the co-
integration tests, which is analogous to test for stationarity in the univariate case, found
one co-integrating relation in each of the VAR systems; therefore the VARS were
speciﬁed and estimated as vector error correction models. Inspection of the model
residuals indicated that the models were statistically adequate representations of the
underlying data generating mechanisms for the grain prices. The VEC models are put
forward as forecasting competitors along with the univariate models presented in chapter

4, and evaluated further in chapter 6 for forecasting accuracy.

CHAPTER 6

STATISTICAL EVALUATION OF THE FORECAST COMPETITORS

6.0 Introduction

In an extensive review of forecast competitions in agriculture, Allen (1994)
compared several time-series forecasting techniques for their ability to make post-sample
forecasts using criteria such as root mean squared error and turning point measures. He
found that the VAR and the ARIMA models were “markedly better” than naive
forecasting methods, which performed better than other mulitvariate methods. The VEC
out-performed the other methods in terms of capturing turning points. This chapter
summarizes and compares the results of the univariate models and the VECs and produces
and evaluates short-term out-of-sample forecasts. Speciﬁcally, I, 2 and 3 month ahead
dynamic forecasts for each commodity are produced, and the forecasting ability of each
forecast competitor is statistically evaluated. Conclusions regarding the “best” forecast
method are made. The results in this chapter are consistent with Allen’s ﬁnding,
particularly with regards to the VARs ability to predict turning point errors.

Note that the forecasts are made assuming that the pattern identiﬁed in the time
series and described by the model parameters will continue into the future. During the
data sample period the grain markets were hberalized and the currency was devalued,
raising the question of potential parameter instability. The results of the unit root tests in
the presence of structural change indicated that the series were nonstationary; therefore,
the series were modeled as difference-stationary processes. A dummy variable

representing devaluation was signiﬁcant in explaining the evolution of the percentage

121

change in rice prices and is retained in the rice models. Alternatively, the rice series could
have been modeled as two distinct series, one pre-devaluation and one post- devaluation.
Since the number of postdevaluation observations is limited and recent research (Teﬂt et
a1. 1997) on the impact of devaluation on prices in Mali indicated that its impact was
temporary, this alternative is not pursued here.

In summary, the forecasts are made assuming that the parameters are stable. The
ﬁrst section discusses the evaluation criteria which are used in this study, while the
remainder of the chapter presents and discusses the evaluation statistics for sorghum,

followed by maize and then rice.

6.1 Forecast Evaluation Criteria

In ex ante forecasting with time-series models, residual uncertainty is the major
source of prediction error, hence many of the statistical forecast evaluation criteria focus
on evaluating the sum of the squared residuals. Residual uncertainty exists because the
disturbances from the equation, which are unknown in the forecast period, are replaced by
their expected value of zero, while the actual values are nonzero. The larger the variation
in the individual errors, the greater the overall error in the forecasts. Moreover, in
dynamic forecasts, residual uncertainty is compounded by the fact that lagged dependent
variables and ARMA terms depend on lagged disturbances.

Relatedly, other parts of the forecast evaluation literature assess the utility and
reliability of a forecasting technique in terms of a loss ﬁmction indicating how concerned

the user is if the forecast is oﬂ~ by a particular amount. This study assumes that the

122

forecast users are in some sense risk averse and hence require loss functions which impose
severe penalties on errors. The quadratic loss function penalizes errors heavily and is a
convenient and common measure of forecast accuracy. The forecast is chosen to minimize

the mean square prediction error (MSE) and in general is described as:

MSE = 2013-1592/11 (40)
t= l

where P, and 13, are actual and forecasted price, and n is the length of forecast sample. It
should be noted that the MSE imposes identical penalties on both positive and negative
errors. Regardless of whether the predicted value is 50 points higher or 50 points lower
than the actual value, the mean square prediction error is the same. In cases where there is
an asymmetric cost to being either too high or too low, then another forecast evaluation
criterion might be more appropriate.

There exists a plethora of related forecast error statistics in the literature, including
root mean squared error (RMSE), mean absolute error, (MAE), mean absolute percentage
error (MAPE), Theil’s inequality coeﬂicient (TIC) and others“. The RMSE and the MAE
depend on the scale of the dependent variable and can be used as relative measures to
compare forecasts for the same series across alternative models. The decision rule states
that the smaller the RMSE, the MAE, or the MAPE, the better or more accurate the

forecasting ability of the model. Theil’s U-statistic will be 0 when the forecast are exact,

 

“Algebraic expressions for each of the error statistics can be found in most
statistics books and are not repeated here.

123

and equal to 1 if the forecasting technique being evaluated is no better than a naive
method of forecasting". Unlike the ﬁrst two statistics, the MAPE and the TIC are scale
invariant, expressing accuracy in relative terms. The RMSE and MAPE are used in this
study, with RMSE deﬁned as the square root of equation (40) and MAPE deﬁned below

in equation (41 ).

24
MAPE=[Z[(P,-P)/P,]*100]/24 (4r)
i=1

The above evaluation measures reﬂect the statistical accuracy of a forecast model.
Turning point error (TPE) is an additional evaluation measure which reﬂects how well a
forecast model predicts changes in direction and is also a common evaluation tool. If the
forecast user is most concerned with predicting the direction of prices, then TPE is a
useful measure. This study evaluates the forecast competitors ability to make 1, 2 and 3-
step ahead forecasts using the root mean squared error, mean absolute percentage error
and turning point error measures. Before beginning the analysis, it should be noted that an
effort was made to evaluate carefully the forecast competitors. Often a forecast method
may forecast one observation poorly yet forecast another observation quite accurately. To
minimize this sampling error and assure a consistent test of forecast accuracy, the next

section describes the procedure used to ensure more consistent results.

 

45Theil’s U-statistic allows for a relative comparison of formal forecasting methods
with naive approaches. A U<1 implies that the forecast competitor is better than the naive
method. The smaller the U-statistic, the better the forecasting techniques is relative to the
naive method. A U>1 implies that the naive method will produce better results

(Makridakis 1978).

124

6.1.1 Forecasting Consistency: Updating Procedure

Twenty-four observations excluded from the speciﬁcation search were used for
assessing the predictive power of the alternative models. For instance, a seasonal ARIMA
model of sorghum prices developed in September 1996 is used to generate a forecast of
sorghum prices in October 1996. The squared error is computed (P-Pf)2 and the forecast
sample is updated, and a one-period ahead forecast made in October 1996 is generated for
November 1996. Again, the squared error is computed and the forecast sample is
updated and a one-period ahead forecast made in November 1996 is generated for
December 1996, and its squared error computed. This process is repeated for all twenty-
four observations in the forecast sample. The mean of the 24 squared errors is computed
and the square root is taken of the mean. This procedure is performed for each model and
each 1,2 and 3-step ahead forecast horizon for each commodity. The computation of the
MAPE [(P-P,)/P* 100] follows a similar procedure. The RMSEs and MAPBs are
compared across models. A model with a smaller RMSE, or MAPE is considered to
forecast consistently better than an alternative speciﬁcation with a higher RMSE or
MAPE.

Turning point errors are also calculated for each step-ahead forecast over the 24
period sample. Total possible turning points for the l, 2 and 3-step ahead horizon are 24,
23 and 22 respectively. Updating in this way allows a sample size of 24 for the forecast
evaluation. Beginning with sorghum, the remainder of this chapter presents a summary of
the forecast competitors for each commodity, as well as the forecast evaluation statistics.

The “best”, deﬁned as the most accurate , forecast model for each grain price is then

1 2 5
identiﬁed.

6.2 Predicting Retail Sorghum Prices
The univariate and mulitvariate forecast competitors for the retail sorghum series
are summarized below in table 6.1, where the random walk model is included as a point of

reference. Forecasts generated ﬁ‘om the random walk model are deﬁned by equation (39):

PM =P. +5031) (42)

These speciﬁcations illustrate alternative representations of the strong seasonal patten
present in the sorghum series as well as varying autoregessive and moving average
processes. 'The analyses in chapter 5 indicated that the gain prices were dynamically
interrelated, which led to the construction of a VEC. All equations with the exception of
the random walk model have white noise residuals, a necessary condition for efﬁcient
forecasting. Models (1)-(5) were used for predicting sorghum prices one, two and three

months ahead.

126

 

Table 6.1: Summary of Fitted Retail Sorghum Models

 

 

Model 01302) Qu,(36) T

1. Random Walk 0.00 0.00 176

2. ARIMA (1,1,1) with seasonal dummies 0.48 0.47 175

3. ARIMA (1,1,(1,13)) with 2'"I -order harmonic 0.24 0.59 175
ﬁmctions

4. ARIMA ((1,24)1,(1,24)) seasonal lag model 0.65 0.18 152

5 VEC(2) with 2""-order harmonic & devaluation 0.28 0.11 174

 

 

Note: Q1300 is the probability value of the Ljung-Box Q-statistic and is a test for white noise at
lag (k). T is the number of observations used in estimation.

 

 

Table 6.2: Forecast Evaluation Statistics of Sorghum Retail Price Models

 

 

 

Model 1 Model 2 Model 3 Mode14 VEC
random seasonal harmonic seasonal lag
walk dummies

RMSE l-step 13.89 11.23 11.05 12.75 10.82
RMSE 2-step 23.23 17.66 16.51 21.35 17.46
RMSE 3-step 28.33 20.29 18.98 25.86 21.05
MAPE l-step 7.32 7.01 6.66 7.03 7.12
MAPE 2-step 13.14 11.29 10.67 12.29 11.8
MAPE 3-step 16.57 13.97 12.51 16.19 14.86

TPE l-step 10/24 =42% 8/24=33% 8/24=33% 9/24=38% 7/24=29-/.
TPE 2-step 15/23=65% 10/23=43% ll/23=48% 11/23=48% 9/23'—'39'/o
TPE 3-step 12/22=55% 8/22=36% 10/22=45% 10/22=45% 10/22=45%

 

Table 6.2 presents the results of alternative forecast evaluation statistics for

 

 

127

predicting sorghum price clmnges 1,2, and 3 months ahead using the 24 period forecast
sample. The ﬁgures in bold indicate the lowest value in the row, i.e., across models. The
VEC has the lowest RMSE for predicting sorghum prices 1 month ahead, followed by the
ARIMA with the harmonic speciﬁcation of seasonality. The random walk has the highest
RMSE l-step ahead. Model 3, the ARIMA with the harmonic speciﬁcation, has the
lowest RMSE and the lowest MAPE for predicting 2 and 3-steps ahead, with the VEC
coming in second. The VEC does the best job predicting turning points 1 and 2-steps
ahead, while the seasonal dummy model does the best job predicting turning points 3-steps
ahead. In terms of accuracy and predicting turning points, the random walk is clearly
dominated by the competitors. The seasonal dummy model appears to be more accurate
than the seasonal lag model, but not as accurate as the harmonic or VEC models for
making short-term predictions about sorghum price changes. Model 3, the ARIMA with

the harmonic speciﬁcation of seasonality, emerges as the consistent winner.

6.3 Predicting Retail Maize Prices
The presentation of the results of the maize forecast competition follow the same

format as that of sorghum The forecast competitors for maize retail prices are

summarized in table 6.3, followed by the evaluation statistics in tables 6.4

128

 

Table 6.3: Summary of Fitted Retail Maize Models

Model
1. Random Walk
ARIMA (1,1,15) w/ seasonal dummies

ARIMA (0,1,(1,20,24,36)) seasonal lag

mews»

devaluation

ARIMA ((1,13),1,0) w/2"d -order harmonic functions

VEC(2) with 2"“-order harmonic functions &

0.1.02)
0.00
0.39
0.41
0.1 1
0.70

Qu(36) T

0.00 176
0.27 175
0.25 163
0.13 176
0.1 l 174

 

Note: QLB(k) is the probability value of the Ljung-Box Q-statistic and is a test for

white noise at lag (k). T is the number of observations.

 

Table 6.4: Forecast Evaluation Statistics of Maize Retail Price Models

 

 

 

Model 1 Model 2 Model 3 Model 4 VEC
random walk seasonal harmonic seasonal
dummies lag

RMSE l-step 11.49 9.47 9.02 9.87 9.66
RMSE 2-step 17.31 12.48 11.83 14.75 13.57
RMSE 3-step 20.83 12.87 12.58 16.61 15.67
MAPE 1-step 6.85 6.10 5.59 6.39 6.20
MAPE 2-step 10.34 8.56 7.93 9.69 8.86
MAPE 3-step 13.29 8.69 . 8.22 10.52 11.22
TPE l-step 13/24=54% 10/24=42% l0/24=42% 12/24=50% Ill/24:427.
TPE 2-step 12/23=52% 11/23=48% 10f23=43% 13/23=57% l l/23=48%
TPE 3-step 12l22=55% 8/22=36% 9/22=41% 14/22=64% 9/22=41%

 

Similar to the sorghum price models, the ARIMA with the harmonic speciﬁcation

 

129

also emerges as the most accurate method for forecasting short-term maize prices,
followed by the seasonal dummy model. The random walk formulation does not capture
the strong seasonal pattern present in the maize series and thus is out-performed by all
other speciﬁcations. The seasonal dummy model, the harmonic speciﬁcation and the
VEC tie for ﬁrst place in terms of predicting turning points 1 month ahead, while the
harmonic commits the smallest number of turning point errors 2 months ahead. The
seasonal dummy speciﬁcation does the best job predicting turning points 3-steps ahead.
One implication of these results is that a representative farmer who formulates
maize price expectations based on a random walk can improve her forecast accuracy by
employing any other model in table 6.4. The harmonic speciﬁcation with the
GARCH(],I) errors was not included in the forecast competition because as the forecast
sample was updated, the standard errors of the forecasts exploded. The model was

therefore considered unstable.

6.4 Predictions for Retail Rice Prices

The models that were ﬁtted to the monthly rice retail price changes in chapter 4
are summarized below in tables 6.5, and the evaluation statistics are given in table 6.6.
Model 4, with the GARCH errors, was an attempt to capture the time varying volatility in
the series and has the most lowest RMSE for forecasting 1 and 2-steps ahead. The VEC

has the lowest RMSE for predicting rice retail price changes 3-steps ahead.

 

130

 

Table 6.5: Summary of Fitted Rice Models

 

 

Model 01.1.02) Qu,(36) T

1. Random Walk 0.35 0.49 176
2. ARIMA (0,1,0) with devaluation 0.18 0.08 176
3. ARIMA (1,1,(1,17)) with devaluation 0.22 0.71 175
4. ARIMA (0,1,17) with GARCH(1,1) errors w/harmonic 0.54 0.52 176
5 VEC(2) with 2nd-order harmonic functions & devaluation 0.29 0.35 174

 

Note: Qw(k) is the probability value of the Ljung-Box Q-statistic and is a test for white

noise at lag (k). T is the number of observations.

 

 

Table 6.6: Forecast Evaluation Statistics of Rice Price Models

 

 

 

Model 1 Model 2 Model 3 Model 4 VEC
random walk random ARIMA MA(17)
walk (1, 1,(1,17)) w/deval &
w/deval deval GARCH
RMSE 1-step 9.93 9.93 10.09 9.52 9.69
RMSE 2-step 15.01 15.01 14.05 14.03 14.09
RMSE 3-step 18.73 18.73 17.70 17.59 17.55
MAPE l-step 2.74 2.74 2.81 2.69 2.86
MAPE 2-step 4.75 4.75 4.16 4.33 4.38
MAPE 3-step 6.10 6.10 5.29 5.44 5.84
TPE 1-step 11/24=46% 11/24=46% 12/24=50% 6f24=25'/o 10/24=42%
TPE 2-step 15/23=65% 15/23=65% 11l23=48% 12l23=52% l3/23=57%
TPE 3-step l4/22=64% 14/22=64% 12l22=55% 12l22=55% 12l22=55%

 

 

 

131

The GARCH model commits the smallest number of turning point errors for 1-step
ahead, while model 3 cormnits the smallest number for predicting 2-steps ahead, and ties
with the GARCH model and the VEC model for predicting TPEs 3-steps ahead. The
random walk models are more accurate at forecasting 1-step ahead than the ARIMA

(1,1,(1,17)) model.

6.5 Predicting Sorghum Producer Prices
The univariate and mulitvariate models that were ﬁtted to the monthly sorghum

producer price changes in the Zangasso market are sunnnarized below in table 6.7, and the

forecast evaluation statistics are given in table 6.8.

 

Table 6.7 : Summary of Fitted Sorghum Producer Price Models

 

 

Model Q1302) Qu(36) T
1. Random Walk 0.00 0.00 131
2. ARIMA (0,1,(13,29)) harmonic w/market 0.23 0.22 131
3. ARIMA (24,1 ,24) seasonal lag w/market variable 0.91 0.08 107
4. ARIMA (0,1,(13,36)) harmonic and ARCH(2)errors 0.67 0.62 131
5 VEC(4) w/harmonic functions and market 0.78 0.00 127

 

Note: QLB(k) is the probability value of the Ljung-Box Q-statistic and is a test for white
noise at lag (k). T is the number of observations.

 

 

 

132

 

 

 

 

Table 6.8: Forecast Evaluation Statistics of Sorghum Producer Price Models
Model 1 Model 2 Model 3 Model 4 VEC
random harmonic seasonal ARCH

walk lag

RMSE 1-step 11.23 8.71 9.78 7.56 9.74

RMSE 2-step 18.92 13.30 14.90 12.17 14.38

RMSE 3-step 21.44 15.02 16.54 14.49 17.53

MAPE l-step 10.40 9.33 10.43 8.35 8.78

MAPE 2-step 19.26 14.79 16.25 14.00 15.62

MAPE 3-step 22.86 17.05 19.32 16.72 18.56

TPE l-step 6/24=25% 7/24=29% 11/24=46% 9/24=38% 7/24=29%

TPE 2-step 10/23=43% 10/23=43% 12/23=52% 9/23=39% 8/23=35%

TPE 3-step 9/22=41% 9/22=41% 10/22=45% 8/22=36% 8/22=36°/o

 

 

In the forecast competition for sorghum producer prices, model 4, the ARCH model,
emerges as the most accurate across all 3 forecast horizons, followed by the harmonic
model. The random walk model commits the smallest number of turning point errors for
predicting producer prices 1 month ahead. The seasonal lag model errs the most in terms

of predicting turning points for all 3 horizons.

6.6 Summary of the Forecast Competition Results

The most consistently accmate models, as deﬁned by the lowest RMSE and the
lowest MAPE, for predicting short-term changes in sorghum and maize retail prices are
the ARIMA models with the harmonic speciﬁcation of seasonality. However, the VEC

has a lower RMSE for forecasting sorghum price changes one month ahead. The

133

harmonic speciﬁcation of seasonality out-performed both the seasonal dummy and
seasonal lag models. The integated moving average model with devaluation and the
GARCH(1,1) errors with harmonic functions is the most accurate at predicting changes in
rice prices 1 and 2 months ahead; however, the ARIMA without the GARCH errors has a
lower MAPE for forecasting 2 and 3 months ahead. The VEC model is more accurate at
forecasting rice retail price changes 3 months ahead. For the sorghum producer prices,
the ARCH model emerges as the most consistently accurate method for forecasting short-
term price changes.

In terms of turning points errors, the VEC is more accurate at capturing turning
points in the retail and producer price sorghum models, although the seasonal dummy
model is more accurate at capturing turning points 3 months ahead. The GARCH model
is considerably more accurate than the VEC (75% versus 58%) at capturing turning points
1 month ahead in the rice retail price changes. For horizon 2 and 3, the results are mixed,
with the ARIMA model committing the smallest number of turning point errors 2 months
ahead, and the VEC, the ARIMA and the GARCH models all tied for ﬁrst for predicting
turning points 3 months ahead. The results of the turning point predictions for maize are
alsomixed,withtheVEC, seasonaldummyandtheharmonicalltyingforﬁrstplace for 1
month ahead; with the harmonic coming in ﬁrst for 2 months ahead and the seasonal
dummy model for 3 months ahead.

In summary, the GARCH and ARCH models emerged as the most consistently
accurate forecast methods for the retail rice and sorghum producer price series, while the

ARIMA models with the harmonic speciﬁcation of seasonality were the most accurate at

134

predicting short-term price changes in the seasonal retail sorghum and maize series. After
the random walk model, the seasonal lag models turned out to be the least accurate
method of making short-term forecast of the changes in gain prices in Mali. Consistent
with Allen’s (1994) forecast competition, the VEC models, which capture the dynamic
interrelatedness of the gain price changes, on average are better at predicting turning
points than the univariate models. Because the choice of most accurate forecast model
depends on the objective of the forecaster and the end-user, chapter 7 evaluates forecast

methods in a decision support framework

CHAPTER 7

ECONOMIC EVALUATION OF PRICE FORECAST MODELS

7.0 Introduction

The uncertainty of future prices makes agricultural market strategy and investment
planning difﬁcult. Forecasts of commodity price changes given speciﬁed market
conditions provide information necessary to carry out the marketing or investment
planning process. The gain price forecasting models developed in this study are intended
to aid ﬁrmers, traders and policymakers forge more eﬂicient production, marketing,
investment planning and policy decisions. The premise is that improved forecast models
augment the agent’s ability to make proﬁt-enhancing decisions. The results in chapter 6
indicated that the developed models were statistically more accurate in making out-of-
sample forecasts than the naive model of price expectations. This type of evaluation
implicitly assumes that statistical criteria, like root mean squared error, are consistent with,
and optimal for, the subsequent use of the forecast in a decision ﬁamework.

However, several researchers (Gerlow 1993; Parks et a1. 1989; Wright et al. 1986;
Brandt and Bessler 1983) argue that although system linearity and normal random
disturbances are assumed in most statistical forecasting methods, linear decision rules and
quadratic cost functions are rarely met in business applications. Hence, decisions based
solely on a statistical evaluation method, such as root mean squared error, will in general,
not be optimal. Therefore, the true test of a forecast model’s economic performance is to

ascertain what impact, if any, the model has on a forecast user’s ability to make more

136

efﬁcient or proﬁtable decisions.

This chapter evaluates alternative forecast models in a decision-support ﬁamework
and tests whether the improved price forecast information leads to more proﬁtable
decisions. The results indicate that relative to naive generated forecasts, the improved
models do indeed lead to more proﬁtable decisions/actions. This is an important result for
Malian policymakers, as the role of government in providing market facilitating services
such as price information in a ﬁscally austere environment is continuously being called into
question

The ﬁrst part of this chapter discusses the salient concepts for evaluating forecast
models in a economic ﬁamework, while the remainder of the chapter discusses and
analyzes an economic decision. A model is considered to exhibit economic value if it can
lead to more efﬁcient and potentially income-enhancing decisions. The decision problem
used to test the economic value of the price forecast models centers on a storage decision
for a producer in the Zangasso region in Mali. The optimal commodity storage literature

and the importance of storage in the Malian context is also discussed.

7.] Conceptual Considerations and Decision Criteria

The germane question is: which competing forecast method produces the “best”
set of forecasts for a given set of decision makers? Most models are generally chosen
according to their ability to minimize a statistical loss function. A srmll body of the
commodity price forecast evaluation literature discusses the need to evaluate the

performance of alternative models as a function of their end use, rather than the magnitude

137

of their forecast errors (e.g., Gerlow 1993; Leitch and Tanner 1991; Park et. a1 1989; and
Wright et. al 1986; Brandt and Bessler 1983). The concern is that the statistical criteria
may not fully account for the inﬂuence of forecasting errors on the resulting decisions and
returns. This literature asserts that while improved decisions are the objective of forecast
users, the evaluation of forecast accuracy is often not performed in a decision ﬁamework.
The utility of a forecast model depends on how well it performs in a decision context.
For instance, does a forecasting system based on model A enable the user to make better
decisions than using a forecast based on model B, where ‘better’ is deﬁned by the end-
user.

Cornrnon measures for economically evaluating forecasts of commodity prices
include investigating the effects of decision rules derived ﬁom alternative forecasting
systems on proﬁt or returns, market timing ability or correctness of decisions. A typical
ﬁ'amework involves analyzing buy and sell signals generated ﬁ'om a decision rule that is
based on forecasts derived ﬁom the alternative forecasting models. The proﬁts and losses
resulting ﬁom the buy and sell signals are then calculated and compared. To illustrate,
Gerlow (1993) developed the following decision rule to guide futures trading strategies of

a hog producer:

S. =1 if HPF. >HPC.-. (43)

S. =-1 if HPF},sHPC,_, (44)

I!

138

Equation (43) says to buy if the forecast price (here a forecast of the seven market average
cash price for model i and time period t) in time t is higher than the hog price (the seven
market average hog price) in time t—I, whereas equation (44) generates a sell signal if the
forecast price from model i is less than or equal to the hog price in time t-I .

The returns resulting ﬁ'om the buy and sell signals are calculated as the change in
futures prices over the holding period. Thus, the percentage goss, R“, from following a

buy or sell signal for model i and time t is:

R, = S, [InFPm - lnFPm] * 100 (45)

FF, and FP,,, refer to ﬁltures prices of live hogs on the ﬁst and ﬁrst day of time, t,
respectively. S, is deﬁned by equations (43) and (44). The model that generates the
highestmeanpercentagereturnsisrevealedasthe ‘best’ modeLbutnotnecessarilythe
most statistically accurate. By examining mean returns, the eﬁ'ect of the forecasting
errors on economic variables is incorporated into the evaluation process (Gerlow 1993,
p.390).

Parks et a1. (1989) suggest further that speciﬁc information about the user’s
decision processes and preferences are necessary to identify the “best” forecast model for
the end user. In the above example, the trading strategies for the hog producers could
have been modiﬁed to incorporate risk preferences for the presence of risk in retln'ns
(Gerlow 1993; Park et al. 1989). Some studies use the expected utility model as a

ﬁamework to examme risk-adjusted mean returns, stochastic dominance or mean-variance

139

in regard to various aspects of the distribution of returns. These studies employ risk
eﬁciency criteria to permit an ordering of outcomes for individuals whose preferences
conform to certain restrictions.

Following Merton (1981), some studies focus speciﬁcally on the accuracy or
“correctness” of decisions made based on the forecast model, and not on the accuracy of
the forecast model. Merton (cited in Gerlow (1993)) contends that forecasts have positive
value only if they cause rational decision makers to alter their expectations about the
future. Rather, if knowledge of the forecast does not cause economic agents to alter their
expectations, then the information embodied in the forecast has already been assimilated
into the rmrket and the forecast has no positive value. To test this, Merton (1981)
developed a directional accuracy statistic which is based on the number of times that price
is correctly forecast to increase, decrease or remain constant. He called this the test for
market timing ability, where market timing implies an ability to accurately forecast
direction of price movement.

In a related study by Wright et al. (1986), “correctness of decision” as a forecast
evaluation criterion was investigated by examining the actions of a trader engaged in the
forward exchange market. To speculate proﬁtably, the trader must correctly predict the
direction of the forward rate error. The decision rule stated that if the forecast of the
ﬁlture spot rate is geater than the forward rate, the trader buys foreign exchange forward,
and if it is lower, then the trader sells foreign exchange forward. A forecast is considered
“correct” ifboth the actual spot rate and the forecast spot rate are on the same side ofthe

forward rate. In another example, Spreen and Arnade in Parks et. a1 (1989) evaluated an '

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applied agicultural situation where a producer had to decide whether to overwinter cattle.
The decision rule was based on calculating a breakeven price. If the model-generated
forecast is geater than or equal to the breakeven price, cattle are fed over the winter and
sold in the spring. In this case, an effective forecasting model is one that can consistently
predict whether the subsequent price is above or below the breakeven price. The results
of their study found that the forecasting methods that exhibited high mean squared errors
provided better forecast support when judged by the proportion of correct decisions and
proﬁt generated.

These studies suggest that the forecasting method that is the most accurate in
terms of statistical criteria is not necessarily the “best” in term of planning and decision
support. Indeed, an accurate forecast may result in a poor decision and an inaccurate
forecasts may result in a good decision. Comparing an ARIMA and an econometric
model of hog prices, Gerlow (1993) found that the econometric model outperformed the
ARIMA model in terms of the economic criteria (mean returns in this study) but scored
poorly in terms of statistical criteria. Other studies ﬁnd a near one-to-one relationship
between the results of the statistical and economic forecast criteria. For example, in their
study of ﬁrtures trading of the hog market, Brandt and Bessler in Park (1989) found that
two of the most statistically accurate forecast techniques were associated with the highest
mean price, while their variances were also high relative to other forecast methods.

Leitch and Tanner (1991) took a slightly diﬂ‘erent approached and examined the
question of why proﬁt-maximizing ﬁrms purchase economic forecasts when most

statistical criteria rarely reveal major differences between professional forecasting services

141

and a simple naive approach of no change in the variable being forecast. In empirical tests
of interest rate forecasts, they found that the conventional forecast evaluation criteria lmd
no systematic relationship to proﬁts. They did ﬁnd that directional accuracy was related
to proﬁts and thus could be used as an evaluation criterion if proﬁts were unobservable.
They argue that economists generally assume that ﬁrms use forecasts because they add to
proﬁts and thus a more accurate test of forecast accuracy is proﬁtability and not the size
of the forecast error or its squared value.

In summary, several studies have found that, in some cases, the most statistically
accurate forecast models are not the most accurate or “best” models in the context of
economic evaluation. Towards this end, this chapter further investigates the forecasting
perforrmnce of the alternative gain price models in a decision support ﬁ'amework. The
model-generated price forecasts are used to guide the post-harvest marketing strategies of
a sorghum producer. The forecast models are evaluated using root mean squared error
(RMSE), mean price received and percent correctness of decision. Section 7.2 discusses
brieﬂy the relevant concepts ﬁom the storage literature and outlines the decision

ﬁamework while section 7.3 discusses the simulations and results.

7.2 Storage Rules

A fundamental decision facing most farmers in Mali who produce storable
commodities such as cereal gains is the question ofhow much and when in the post-
harvest marketing season their marketed surplus should be sold. This question constitutes

the foundation of the vast literature on (optimal) storage rules, which studies everything

142

from public policies that manage buffer stocks of agricultural commodities, to the
inventory strategies of private speculators (Fackler 1995; Williams and Wright 1991;
Newbery and Stiglitz 1981; Gislason 1960 and Gustafson 1958). A storage rule is broadly
deﬁned as a statistical decision function, which stipulates the level of storage under a given
set of relevant economic conditions. Further, a storage rule is considered “optimal” when
its derivation is based on a speciﬁc objective function, such as consumption smoothing,
price stabilization or maximizing the sum of discounted proﬁts for a given period.

The typical approach for determining the level of harvest to stockpile in a given
period uses dynamic progamming procedures to derive a storage rule conditional on,
inter alia, supply and demand factors, storage costs and capacity constraints (Myers
1996). The result is an optimal decision rule as a function of the above parameters. It is
characterized by the condition that storage today continues until current price per unit plus
per unit storage cost is driven up to equality with the present discormted value of the
expected future price. If current prices are high, then stocks are sold until the price plus
the storage costs are driven down to this level, or until stocks are exhausted (Newbery &
Stiglitz 1981; Gilbert 1990). Similarly, Fackler (1995) discusses an optimal stopping
problem for producers with on-site storage ﬁcilities in which the optimal sales rule is a
simple condition on current price. The strategy is to sell everything when current piice is
high, otherwise store everything into the next period. The next section describes a few

stylized facts about the marketing strategies and storage environment in Mali.

143

7.3 Marketing Strategies and Storage Costs: Some Stylized Facts

In Mali, the level of marketed surplus depends to a large extent on the level of
production at the ﬁrm household level, while the post-harvest marketing strategies of
producers reﬂect their cash needs. For instance, sorghum farmers who also produce cash
crops (e.g., cotton) store most of their marketed surplus at harvest and spread sales over
the nine-to-ten month marketing season. Noncash croppers, on the other hand, are forced
to sell a geater portion of their surplus at harvest. Indeed, studies reveal that cash
croppers in the Zangasso region market on average 15% of their sales at harvest, while
noncash croppers market an average 58% at harvest (Dembele 1994)“. However, if
rainfall is good and the harvest is larger than average, then cash croppers sell only a small
proportion (studies say 8%) of their harvest. This is presumably because their cash needs
are being met from the cash crops which also beneﬁt ﬁom good rains. Analogously, cash
croppers increase their harvest sales if rainfall is lower than average to wet cash needs
and noncash croppers tend to sell a larger proportion at harvest if rains are goods, and
reduce sales when rains are lower than average.

Later in the marketing season, when prices begin to rise, marketed surplus is
inﬂuenced by producer expectations of rainﬁll (Dembele 1994). That is, once the rainfall
pattern for the current agicultural production campaign is established, the producer
decides to release stocks in August/September if the rains are good. The expectation is

that yields will be high and prices will be low. However, if the rains are bad, or less than

 

“According to Dembele (1994), this practice has changed in recent years because
cotton payments to ﬁrmers have been delayed so cash croppers have been forced to sell
more at harvest.

144
average, the producer continues to store in anticipation of supply shortages and higher
prices.

The gain stocks will be determined by expected future prices relative to the
current price, taking into account the interest and other costs of storage. The sorghum
producer stores on-site in mud-clay ganaries and the gain is rarely stored for longer than
a year. Storage losses are assumed to be low, as is the physical cost of storage. However,
the opportunity cost of foregoing sales when the crop is harvested ranges from 12% to
30%"7 (Dembele 1994). Producers face cash ﬂow problems during the marketing season
which force them to release the crop at various non-optimal times of the year. The
investigation therefore, focuses on evaluating post-harvest marketing strategies on the
residual marketable surplus (after cash needs at harvest have been met).

The results of empirical research in Mali (Dione 1989) suggests that the objective
of the sorghum producer’s marketing strategy is to spread marketed surplus over the post-
harvest season to meet cash needs. However, in the later part of the marketing season,
due to the uncertainty surrounding the next harvest, the producer is more concerned with
meeting household consumption needs. Conditional on good rains, a post-harvest
marketing strategy for a cash cropper in Zangasso for January through September might
entail marketing:

0% of the marketed surplus in January;
10% in February and March;

40% in April, June and July; and
50% in May, August and September

 

"Theinterestonaloanintheformalsectoris12%whiletheinterestcanbeas
highas 30% inthe informal sector.

145

Such a marketing rule is desigled to meet cash needs during the marketing season and to
take advantage of seasonal increases. The low percentage marketed in January-March is
to avoid marketing large quantities during times of low-prices. 40% of the residual
marketable surplus is allocated to April, June and July to take advantage of rising prices.
Most of the surplus is sold in May, August and September. May is planting time for the
new crop season, while July and August are historically peak price months. If the rainfall
pattern for the upcoming harvest is revealed to be less than average, then to reduce the
risk of a poor harvest and protect consumption needs, the proportion marketed in August
and September decreases to zero (Dione 1989, Dembele 1994). The optimal storage
literature and knowledge of the sorghum market were used to develop a practical storage
rule or marketing strategy for the ﬁrmer. The decision framework for the evaluation of
the alternative forecast models for sorghum producer prices is discussed in the next

wamn

7.4 Decision Framework

Consider a sorghum producer with marketed surplus in the Zangasso region in
southern Mali evaluating post-harvest marketing strategies. Speciﬁcally, the producer
uses a model-generated forecast of spot prices to guide her decisions to make one—step
ahead sell or store decisions over the marketing season, which spans ﬁ'om January to
September.

The post-harvest marketing strategy for the producer is patterned after the

optimal stopping problem described in Fackler (1995), which consists of a simple

146

condition on current price. The marketing strategy is to sell everything for that month

when the current spot price is geater than the forecasted spot price, otherwise store

everything into the next period.

Sell when P, > Pflmw; store otherwise (46)

For example, in the month of January the producer will store the 5% apportioned for
February if the forecast of February prices is geater than the current price in January. If
the January price is geater than the forecast of February prices, then the producer sells the
5% in January. The decision is made every month through September for the forecast
competitors. Since there are 24 observations in the forecast sample, two 9 month
marketing seasons are evaluated. The performance of each forecast model is evaluated by
examining the mean price received per kilogam and the percentage of correct decisions

generated for each marketing strategy.

7.5 Economic Evaluation of Forecast Models for Sorghum Producer Prices

In chapter 6, the statistical evaluation of the 5 sorghum producer price models
revealed that the ARIMA model with the 2”“-order harmonic functions and ARCH(2)
errors was the most accurate at forecasting short-term price changes. Accuracy was
deﬁned as the lowest RMSE and/or MAPE. The VEC(4) model with seasonality and a
market dummy variable was the most accurate (lowest TPEs) at capturing turning points.

The forecasts generated from the 5 models were used to rmke market/store decisions and

147

are further evaluated for forecasting performance using economic criteria. The marketing
strategies for the 2 marketing seasons that were generated ﬁ'om the forecast models using
the decision rule in equation (46) are presented in tables 7.1. Season 1 covers January
1997 to September 1997, while season 2 covers January 1998 to September 1998. If no

sell signals are generated by August, then everything is sold in September.

 

 

 

 

Table 7.1: Post-harvest Marketing Strategies Generated from Forecast Models
strategy Forecast Model Action-sell: season 1 Action-sell: season 2
1 Random walk all 9 months ' (9) all 9 months (9)
2 ARIMA w/harmonic April, July, Aug (6) September (9)
3 ARIMA: seasonal lag January, May (7) Jan, September (7)
4 ARIMA w/ lﬁrmonic February, July, September (9)
and ARCH errors August (6)
5 VEC w/harmonic and February, March, July, August (7)
July, August (5)

 

 

The numbers in parentheses indicate the months of storage. The strategy that emerged
ﬁom the naive random walk model is to sell in each period in both post-harvest seasons.
The ARIMA model with the harmonic functions generated sell siglals for April July and
August in season 1, and since no sell siglals were generated byAugust inseason 2, the
strategy is to sell everything ill September. The seasonal lag model generates sell signals
inDecember inboth season 1 and season 2, which is sold inJanuary. For season 1, the
ARCH model has the producer selling in February, July and August, and only in

September in season 2. Finally, alter the random walk model, the VEC model generated

148

the most sell siglals in season one. In season 2, most of the models indicate that sorghum
should be stored until August/September. Marketing strategies based on the random walk
and the models that store until September incur the most amount of storage cost, while
those based on the VEC model incurs the least amount of storage cost.

Historical analysis (1986-1998) of the percent returns to storage, deﬁned as the
post-harvest price in each month less the price prevailing at harvest, divided by the post-
harvest price multiplied by 100, revealed July (64.8%) and August (64.2%) to be the
months with the highest average goss margins (Goetz 1986)“. January is the lowest
with an average 9.93%, followed by November at 11.3%. After November, the average
goss margins gadually rise slightly in December, ﬁll in January and rise again each
month throughout the post-harvest marketing season, peaking in July. The strategies
generated ﬁom the forecast models appear consistent with the information embodied in
the historical goss margins analysis in that sell signals are generated in July/August, the
high price months. It is encouraging that the forecast models recogrize and are able to
capture this market phenomena.

The criteria used to economically evaluate the alternative forecast models are the
mean price received and the mean net price received assuming storage costs are constant
at 3 ‘CFAF/kg/mo" Additionally, since information is not available on storage costs, the

ﬁnal column in table 7.2 reports average percent returns to storage, which is compared to

 

“Selected results of the goss margin analysis are included in the discussion

149

the opportunity cost of capital”. The informal credit rate of 30% in Mali is used as the
opportunity cost of capital (Dembele 1994). In season 1, if the producer incorporates the
marketing strategy derived ﬁ'om the random walk model and sells in each period, then the
mean price received per kilogam for the marketing season is 74.3, which is the same as
the VEC model despite the fact that sales occur only in 4 of the months compared to 9 in
the random walk model. The VEC is selling in more proﬁtable months. If positive
storage costs are assumed, in this case 3 CFAF/kg/mo., then strategy number ﬁve based
on the VEC model becomes more proﬁtable than strategy number one, because the mean
net price is lower in the random walk model due to the 9 months of storage. The VEC
followed by the ARIMA with harmonic seasonality, followed by the ARIMA with the
ARCH errors yield the geatest mean net prices. The random walk followed by the

ARIMA with the seasonal lags yield the lowest mean net prices received.

 

4”Percent returns are calculated by subtracting the lmrvest price of 63.25 CFAF/kg
ﬁ'om the mean price received and dividing by the harvest price and multiplying by 100.

150

 

 

 

 

 

Table 7.2: Season 1: Economic Results of Post-harvest Marketing Strategies with
and w/o positive storage cost
Forecast Model Mean Price Mean Net Average %
CFAF/kg Price Returns
CFAF/kg to storage
1. Random walk 74.3 47.3 17.5*
2. ARIMA with harmonic 73.2 55.2 15.73
3. ARIMA seasonal lag 70.8 49.8 11.9
4. ARIMA with ARCH 72.4 54.4 14.4
5. VEC with harmonic 74.3 59.3 17.5
" Compared to selling at harvest during December 1997

 

 

The percentage rate of return to storage is often used when physical storage costs are
minimal and where a large portion of storage costs are due to the opportunity cost of
money tied up in the stored commodity (Goetz 1986). If the opportunity cost of money
to the sorghum producer is based on the 12% formal credit lending rate, all strategies
except number 3 become proﬁtable. However, if the opportunity cost of capital is based
on the informal lending rate of 30%, then none of the strategies become proﬁtable.

The results for season 2 are presented below in table 7.3. Recall that three of the
models generated marketing strategies where most of the crop was stored for 9 months
and sold in September. The ﬁrst thing to notice is that mean prices in the second season
(1998) are higher than the ﬁrst season (1997) prices. The random walk is dominated by
all other strategies in terms of mean price received and average percent returns. The
ARIMA with the harmonic speciﬁcation yields the highest mean price and the same

returns to storage as the ARIMA with the ARCH errors. The VEC model generates the

151

highest mean net price.

 

 

 

 

 

Table 7.3: Season 2: Economic Results of Post-harvest Marketing Strategies with
and w/o positive storage cost
Forecast Model Mean Price Mean Net Average %
CFAF/kg Price Returns
CFAF/kg to storage
1. Random walk 90.8 63.8 39.0“
2. ARIMA with harmonic 126 99.0 93.3
3. ARIMA seasonal lag 94.6 73.6 45.2
4. ARIMA with ARCH 126 99.0 93.3
5. VEC with harmonic 121.7 100.7 86.8
* Compared to selling at harvest during December 1999

 

 

The average mean percentage returns to storage is above 30% in all 5 strategies in
season 2, with models 2 and 4 generating-the highest rates of return. Because the prices
are higher in season 2, unlike season 1, it is proﬁtable for the producer to store using a
30% opportunity cost. If the producer follows strategy number 2 and sells a portion of
her harvest in April to meet cash needs at planting time, and spreads the rest of her sales
over July and August, she can earn 63.3% above her opportunity cost of capital. And if
the producer’s objective is to smooth liquidity over the entire marketing season, she can
still earn 9% by following strategy number 1 by spreading sales equally over the post-
harvest marketing season. However, the results of the historical goss margin analysis
indicate that the producer would need to store at least until May to barely break even

(31 .82%-30%), earning an average 1.82%.

152

Table 7.4 presents a ﬁnal criterion for economically evaluating the performance of
the forecasts models. Based on the decision rule to sell if the current price is geater than
the forecast, correctness of decision describes the number of times the forecaster made the
right decision to sell or store for each period. For example, the ARIMA model with the
harmonic functions in January 1997 forecasted the price of sorghum in February 1997 to
be higher than the current price in January. Therefore, the signal was to store in January.
The actual price in February was indeed geater than the January price and thus the correct

decision was to store. This analysis was done for each model for each decision period.

 

 

 

 

Table 7.4: Correctness of Decision

Forecast Model Season 1 Season 2 Average
1. Random Walk" 55.5% 77.8% 66.7%
2. ARIMA with harmonic 88.9% 44.4% 66.7%
3. ARIMA seasonal lag 77.8% 33.3% 55.6%
4. ARIMA w/ ARCH 55.6% 44.4% 50%
5. VEC w/harmonic 77.8% 33.3% 55.6%
* generated forecast values that are equal to the current value

 

The random walk and the ARIMA with the harmonic speciﬁcation of seasonality
make the correct sell decision almost 67% of the time, while the ARCH model and the
VEC model make correct decisions 56% of the time. The ARCH model, which emerged

as the single best model using the root mean squared error criterion, does the poorest job

153

making decisions in this context. Moreover, the VEC model of the changes in sorghum
producer prices which was the best at capturing turning points, in terms of correctness of
decision, is dominated by the random walk and the ARIMA with the harmonic seasonality.
Forecast evaluation is commonly carried out by considering only statistical accuracy using
criteria like root mean squared error and in many applications this will be consistent with
the needs of the user. However, statistical evaluation may not be consistent with, or
optimal for the subsequent use of the forecasts in a decision ﬁ'amework. The concern is
that statistical criteria may not ﬁllly account for the inﬂuence of forecasting errors on
resulting decisions and returns. Therefore, evaluation based on economic criteria may
provide important additional information on the performance of the forecasting model.
Here mean price received, percent returns to storage and the correctness of
decision were applied to the out-of-sample forecasts of ﬁve sorghum producer price
forecasting models over 2 marketing seasons: January 1997 to September 1997, and
January 1998 to September 1998. Averaging the mean price received over the 2
marketing seasons, the ARIMA with the harmonic speciﬁcation of seasonality at 99.6
CFAF/kg is selected, followed by the ARCH model at 99.2 CFAF/kg. The VEC comes in
third at 98 CFAF/kg. In this case, the economic criteria selects a different model than the
root mean squared error and the turning point tests, which selected the ARCH and VEC
models respectively. Averaging over the 2 seasons, the random walk model is dominated
by all other models. The correctness of decision criterion also selects the ARIMA with
the harmonic speciﬁcation and the random walk Finally, these results demonstrate that,

ceteris paribus, investing in simple improved forecasting models can improve the decision

154

making ability of an average producer in devising proﬁt-enhancing post-harvest marketing

decisions in some years.

CHAPTER 8

SUMMARY AND IMPLICATIONS

8.0 Introduction

This research was directed toward two key questions. The ﬁrst was
methodological in nature and focused on developing and evaluating alternative methods of
forecasting short-term agicultural prices with limited data. The gain rmrkets in Mali are
used as an example. Since the process of gain market h'beralization began, the
importance of accurate price forecasting for decision makers has increased. One result has
been higher demand for improved outlook information on the likely evolution of gain
prices. Such information is essential for making, among other things, better marketing and
inventory decisions.

However, as is often the case in developing countries, the historical data base is
very limited in scope, constricting the capacity to construct structural econometric models
of supply and demand. Moreover, much of the forecasting literature argues that such
large-scale econometric models may ﬁt the data well, but often ﬁil to forecast well In
fact, many of the time-series models which focus on identifying the properties of a single
series or a vector containing interdependent series have been found to forecast short-term
prices just as well, and in many cases better, than some structural models.

The second goal of this study was to investigate whether investing in improved
forecasting methods is indeed a worthwhile endeavor. In ﬁscally austere environments,
publicly-funded market information systems must continually show evidence of their

worth, lest ﬁnd themselves possibly eliminated. The Malian market information system,

156
the SIM, which regularly disseminates information on weekly gain prices in key trading
markets throughout the country, has been so plagued by ﬁnancial crises that at one point it
was inoperable. To create a constituent base to lobby for political support and sustain
itself ﬁnancially, the SIM seeks to add value to its product portfolio by meeting the
revealed demand for price outlook information and demonstrating that the information has
economic value.

The speciﬁc objectives of the study were to:

0 develop alternative price models, using limited data, for sorghum, maize and rice
prices in Mali that can be used for short-term forecasting;

O evaluate the forecasting ability of alternative price models based on statistical

criteria;

0 evaluate the economic value of improved price forecast information to a group of
users by evaluating the utility of the alternative price models in a decision making
ﬁ'amework; and

O draw lessons on which time-series models produce the most accurate and

economically useful forecasts with limited data.

Mali is used as a caSe study, however many developing countries face similar conditions in
that the product proﬁle of their market information systems is limited in scope and the
value of continuing to publicly collect price information is poorly understood. Moreover,
historical data bases are limited, as often is analytical capacity. Therefore, the results of

this study have implications broader than the Malian context.

157

8.1 Research Methods

Using monthly price data ﬁ'om the SIM ﬁom January 1982 to September 1998,
consumer sorghum, maize and rice prices from the Bamako-Niarela market and sorghum
producer prices for the Zangasso market (for the period October 1985-September 1998)
were analyzed using time-series techniques. The last 24 observations covering October
1996 to September 1998 were excluded ﬁom the speciﬁcation search process and used to
check the out-of-sample forecasting properties of the alternative models. The time-series
techniques employed here follow the Box-Jenkins methodology of ﬁrst identifying any
pattern in the data such as seasonality and time trends, by examining the plots and the
correlogams. Stationarity was tested for using the augnented Dickey-Fuller (ADF) tests
and the Philips-Perron test for testing for unit roots in the presence of structural change.
The results of the unit root tests indicated that the data generating process of each series
had a unit root, thus the series were modeled in ﬁrst differences.

Investigation of the autocorrelation and partial autocorrelation functions were used
to identify tentative ARIMA models, which were estimated using OLS procedures. The
tentative models were validated using various diagnostic tests such as the Ljung-Box Q-
statistic, and the AIC and SBC information criteria. Lagange multiplier or ARCH tests of
the squared residuals were used to investigate whether the variance was homoskedastic or
heteroskedastic. A necessary condition for efﬁcient forecasting is that the errors
approximate the white noise process; thus all the ﬁnal models included in the forecasting
competition met this criterion.

Many agicultural commodities CXhibit seasonal patterns, as did the sorghum and

158

maize price changes. Seasonality was modeled using ﬁrst and second-order harmonic
ﬁlnctions, seasonal dummy variables and by directly including seasonal or near seasonal
correlations in the ARIMA model. Various other exogenous factors were examined,
including alternative speciﬁcations of monthly rainfall, world prices as captured in
Thailand rice prices, the exchange rate between the US. dollar and the CF AF . Two
dummy variables were also included in the analysis, one for the 100% devaluation of the
CFAF in January 1994, and the other a nﬁrket variable designed to capture the ﬂurry of
market activity that regularly occurs in the producing markets in the months of August and
September.

In addition to the single equation ARIMA models, several transfer ﬁmctions
where, for example, sorghum price changes were included as an explanatory variable in
the maize equation of price changes, were also examined. Transfer ﬁlnction analysis
assumes that sorghum prices evolve independently of maize prices and that the maize
disturbances have no effect on sorghum prices. The critical assumption is that there be no
feedback ﬁom maize to sorghum. Further analysis indicated that the no feedback
assumption was indeed violated and that the interdependent relationships between the
prices were best captured in a VAR ﬁamework. Therefore, the 3 price series are
modeled as a VAR with seasonal components and a dummy variable representing
devaluation. Further investigation of the VAR for co-integation indicated that the series
were best described as a VEC. The VEC models were validated in much the same way as
the univariate models and the best models were put forward as forecast competitors.

The valid univariate and multivariate models for each commodity were entered into

159

a forecasting competition, which takes place in chapter 6. Three evaluation criteria, the
root mean squared error, the mean absolute percentage error and percentage of turning
point errors were used to score the competitors for their ability to make predictions 1, 2
and 3 months ahead. The competitor with the lowest score emerged as the winner.

To demonstrate the value of investing in improved price forecasting techniques,
model-generated marketing strategies of a sorghum producer in the Zangasso region of
Mali were compared to marketing strategies generated ﬁom a naive, random-walk model.
The optimal storage literature and knowledge of the sorghum market were used to
develop a practical storage rule or marketing strategy for the producer based on the price
forecasts generated ﬁom the alternative models. After being statistically evaluated in the
forecasting competition in chapter 6, the same producer price models were used to
generate store/sell signals for 2 marketing seasons. The economic criteria used to evaluate
the models included mean price received, mean net price received and the percentage of
correct decisions. The model with the highest mean price and highest percentage of
correct decisions was declared the winner. The exercise is desigled for illustrative
purposes and abstracts away ﬁom risk preferences, marketing responsiveness, etc., Some
of these issues are discussed below. The results of the statistical evaluation of the

producer price models in chapter 6, and the economic evaluation in clmpter 7, were then

compared.

160

8.2 General Results

The sorghum and maize price series exhibited strong seasonal patterns which were
investigated using harmonic functions, seasonal dummies and seasonal ARIMAS. None of
the exogenous regessors were signiﬁcant at the 5% level in explaining the evolution of
sorghum price changes for the period of study. In particular, the rainfall variable, which
was based on various speciﬁcations and lag lengths of monme rainﬁll from Koutiala, was
not signiﬁcant. This is in stark contrast to empirical studies of coarse gain production in
Mali (Dione 1989) which found rainfall to be the single most important variable in
explaining variations in production. Even though the coarse gains are substitutes ill
consumption for rice, the devaluation, which made rice imports more costly and hence
increased domestic rice prices, was not sigliﬁcant in explaining the evolution of sorghum
price changes. Therefore, the univariate forecast models for sorghum were largely
ARIMA models with seasonal components. The VEC models also include seasonal
components.

The results of the forecasting competition indicated that the ARIMA with the
second-order harmonic speciﬁcation of seasonality was the most accurate model for
forecasting sorghum price changes 2, and 3 months ahead, while the VEC had the lowest
root mean squared error for predicting 1 month ahead. Much of the forecasting literature
indicates that VARS are considerably better at capturing turning points. This is evident in
the sorghum series, where the VAR emerges at the most accurate model at predicting
turning points 1 and 2 steps ahead, while the seasonal dummy speciﬁcation actually is

better at predicting turning points in the sorghum series 3 months ahead.

161

Relative to the sorghum series, modeling procedures suggested that the maize
series might be more volatile. Indeed, some of the identiﬁed models suggested that the
maize price series had time-varying volatility or a heteroskedastic conditional variance,
thus implying that periods of low (high) volatility in the maize series are followed by other
periods of low (high) volatility. The maize markets have traditionally been thinner than
either the sorghum or rice markets, which could lead to uncertain market volume and
hence more volatile prices. Nonetheless, the ARIMA with the harmonic speciﬁcation of
seasonality emerged as the consistent winner for most accurately predicting maize price
changes 1,2 and 3 months ahead. The results of the turning point tests are less consistent,
and depend on the forecast horizon The VAR, the harmonic and the seasonal dummy
model all tie for ﬁrst in predicting turning points 1 month ahead.

The results of the forecast competition for rice are not as consistent as were the
competition results for the coarse gain models. Rice was not modeled as a seasonal
series since the autocorrelation and partial autocorrelation ﬁlnctions did not indicate that
the conditional mean exhibited a seasonal pattern The tests for conditional
heteroskedasticity indicated that the conditional variance exhibited time-varying volatility.
Indeed, the most accurate model for predicting changes in rice prices 1 and 2 months
ahead in the Bamako-Niarela market, is the GARCH model. Even though the conditional
mean did not exhibit seasonality, the conditional variance of the rice series did, and
therefore, the conditional variance equation included seasonal terms which were
signiﬁcant at the 5% level. At 75%, the GARCH model was by ﬁr the most accurate at

capturing turning points in the rice series, followed by 58% in the VEC.

162

Of the 5 models in the sorghum producer price competition, the ARCH model was
unambiguously the winner for most accurately predicting short-term price changes in the
Zangasso market. The VEC was the Wilmer for capturing turning points 1, 2 and 3
months ahead. The results ﬁom the statistical forecasting competition for sorghum
producer prices were compared to the results from the economic evaluation. The ARIMA
with the harmonic speciﬁcation of seasonality emerged as the clear winner in terms of
highest mean price received and percentage of correct decisions, followed by the ARCH
and then the VEC models. These results suggest that the intended use of the forecast
inﬂuences the type of model selected to generate the forecast and the criteria used to
evaluate the forecasting technique. The objective of avoiding extremely large forecast
errors might suggest a forecast approach diﬂerent from that associated with the goal of
predicting price turning points in the market. Similarly, short-term marketing strategies
would require a diﬁerent set of predictions than long-term investment planning.

Using the Zangasso sorghum producer as an example, if the concern was to avoid
extremely large forecast errors, then the ARIMA with the harmonic speciﬁcation of
seasonality and the ARCH(2) errors would be the best model for that objective. However,
ifthe producer is more concerned with capturing the direction ofprice changes in the
market, then modeling the prices as a VEC model would yield the best results. And
ﬁnally, if the producer is basing her post-harvest marketing decisions on strategies
generated ﬁom the alternative forecast models, then using the ARIMA model with the

harmonic speciﬁcation without the ARCH errors would yield the highest return.

163

8.3 Complements and Extensions to Information

This study assumes that the producer or forecast user can improve her ability to
make economic decisions with a better forecast of ﬁlture prices. However, information is
but one constraint to improved decision making in the Malian context. Several empirical
studies (e.g., Dirnithes 1997; Boughton 1994; Dembele 1994; Dione 1989; d’Agostino
1989) on Mali have cited access to credit as one of the major constraints to increasing
marketing responsiveness. Research has shown that non-cash croppers are often forced
to sell their harvest at non-optimal times in order to meet immediate cash needs (e.g.,
taxes and school fees), selling when prices are low and re-entering the markets to buy
when prices are high. Evidence shows that cash croppers in the southern producing zone
in Mali are able to better spread their sales over the post-harvest marketing season, taking
advantage of seasonality in prices. Easier access to credit by the non-cash croppers would
improve their ability to proﬁt economically ﬁ'om seasonality in prices.

Marketing extension is another necessary condition for ﬁcilitating market
responsiveness amongst producers. The dissemination of extension services in Mali is
accomplished through the rural development organizations and more recently through
farmer/trader associations, where the more successful rural development institutions focus
on the production and marketing of cash crops like cotton and irrigated rice and much less
on the coarse gains. One goal of the agicultural extension progams in the U.S. is to
help ﬁrmers understand and interpret, among other things, market information Such an
extension progam would prove invaluable in the Malian setting where adult literacy rates

are less than 10%.

164

8.4 Implications

What does it mean for the various categories of economic agents in a country like
Mali to have broad access to improved price forecasting techniques? A food gain
producer with access to credit, storage facilities and an understanding of basic marketing
concepts can improve his household food security by pursuing better marketing strategies
and reduce some of the risk and uncertainty associated with holding gain stocks by
incorporating price forecasts into his information set.

Analogously, a policymaker charged with managing the national security stock can
use the forecasts of gain prices to determine better when and in which markets to release
gains. For example, a consistent forecast of high prices in a particular market might lead
the national stock manager to release gain in that market, causing prices to ﬁll, hence
easing the pressure on net buyers. Private traders and speculators with the appropriate
inﬁastructure (trucks, assemblers, etc.,) can perform spatial arbitrage by buying in low

price markets and selling in high price markets, increasing competition in those markets.

8.5 Further Research

This study is but a ﬁrst attempt to develop price forecasting models using the data
ﬁom the Malian market information system, and much more can be done. This research
focused on developing and evaluating alternative forecasting models in the context of the
limited available data The models can be easily updated as more observations become
available and/or as other ﬁctors hypothesized to inﬂuence price become available. Such

information can be incorporated into the models and further evaluated using statistical and

165

economic criteria.

The evaluation of the post-harvest marketing strategies assumed that producers
formulated their expectations about price using a simple random walk model. Future
research could include identiﬁcation and an empirical analysis of the way in which Malian
producers actually formulate their expectations about price. The method is likely to be
more sophisticated than the simple random walk. Future research could also include

information about risk preferences.

166

References

Allen, P. Geoffrey (1994). Economic Forecasting in Agricultural in Intmtipnal .102le
of Forecasting Volume 10. Elsevier Science. Pp.81-135.

Antonovitz, Frances and Terry Roe (1984). The Value of a Rational Expectations
Forecast in a Risky Market: A Theoretical and Empirical Approach. American Jopmﬂ pf

Agg'culturﬂ Economics, Volume 66, Number 5.

Bapna, 8L. and KR. Rao. (1987). Supply and Price Outlook for Crops: A Study Based
on Preharvest Market Information in Gujarat. Oxford & IBH Publishing Co. PVT. LTD.

New Delhi.

Brandt Jon and David Bessler (1983). Price Forecasting and Evaluation: An Application
in Agriculture. Joumaj of Forecasting, Vol. 2, 237-248.

Brorsen, B. Wade (1998). Can Preharvest Marketing Strategies Be Used to Increase
Income? Review of Agr_icultural Economics. Volume 20, Number 2, F all/Winter 1998.

Bowerman, Bruce and Richard O’Connell (1993). Fgrming gd Time Series: An
Applied Approach. Third Edition. The Duxbery Advanced Series in Statistics and
Decision Sciences, Duxbury Press, Belmont, California.

Carlson, John (1977). A Study of Price Forecasts in Ann_a_ls pf Economic Ed Social
Measurement. Volume 6.

Charemeza, Wojciech and Derek Deadman (1997). New Directions in Econometric
Practice: General to Speciﬁc Modelling, Cointeggation apd Vector Autoreggession.
Second Edition. Edward Elgar, Cheltenham, UK.

CILSS (1998). Food Security and Agp'cultural Subsectors in West Aﬁica: Futurp
Proppects and Key ISﬂJCS Four Years After the Devaluation of the CFA Franc. Policy
conference organized by CILSS November 30-December 2 1998. Dakar Senegal.
Permanent Interstate Committee for Drought Control in the Sahel. Institut du Sahel.

Danthine, J .P (1992). Information, Futures Prices, and Stabilizing Speculation in 111;
Theory of Futures Markets Edited by Paul Weller. Blackwell Publishers, Oxford, UK.

 

Davidson Russel and R James G. Mackinnon, Estimation and Inference in Econometrics.
Oxford University Press. New York. 1993.

167

Dembele, Niama Nango. (1994) Economic Analysis of Traders’ Response to Cerrlls
Mgket Reform; in Mil Ph.D. Dissertation, Department of Agricultural Economics,
Michigan State University.

Donovan, Cynthia (1996). Effects of Monetized Food Aid on Local Maize Prices in
Mozambique. Ph.D. Dissertation in Agricultural Economics, Michigan State University.

Enders Walters (1995). Applied Econometric Timp Series. John Wiley & Sons, INC. New
York.

EViews User’s Guide 1997. Quantitative Micro Software. Irvine, CA, USA.

Fackler Paul and Michael Livingston (1995). Optimal On-Farm Storage. Paper presented
at Michigan State University, Department of Agricultural Economics. Authors are from
the Department of Agricultural and Resource Economics, North Carolina State University,
Raleigh, North Carolina.

Ferris, John (1998). Agp'cultural Prices and Commodity Market Analysis. WCB/
McGraw-Hill, Boston, Massachusetts.

Gerlow, Mary, Scott Irwin and R-Re Liu (1993). Economic Evaluation of Commodity
Price Forecasting Models in International Journal of Forecasting. Volume 9, Elsevier
Science Publishers B.V. Amsterdam. Pp. 387-397.

Ghosh, 8.; CL. Gilbert and A.J. Hughes Hallett (1987). Stabilizing Speculative
Commodig Markets. Chapters 1 and 2. Clarendon Press, Oxford.

Gilbert, Christopher and Theodosios Palaskas (1990). Modelling Expectations Formation
in Primary Commodity Markets in Primagy Commodig Prices: Economic Models and
Polig. Eds. Winters and Sapsford. Center for Economic Policy Research, Cambridge
University Press, Cambridge.

Gislason, Conrad (1960). Grain Storage Rules, J oum_al of Farm Economics,Nolume 42,
pp.576—595.

Goetz Stephan and Michael Weber (1986). Fundamentals of Price Analysis in
Developing Countries Food Systems: A Training Manual to Accompany the
Microcomputer Software Program “MSTA T’. MSU International Development Papers.
Working Paper N. 29. Department of Agicultural Economics, Michigan State University.
East Lansing, Mi.

Goetz, Stephan. (1992). Household Marketing Strategies in A ﬁica in American Journal of
Agp'cultural Economics. Volume 74, Number 2.

168

Gujarati, Darnodar (1995). Basic Econometrics. Third Edition. McGraw-Hill, Inc. New
York.

Gustafson, Robert (1958). “Implications of Recent Research on Optimal Storage Rules”,
Journal of Farm EconomichVolume 40, pp.290-300.

Hayenga, Marvin, Aaron Johnson and Bruce Marion, Eds. (1978). Market Information
gd Price Reporting in the Food and Agg'cultural Sector. Proceedings of a Conference
Sponsored by North Central Regional Committee 117. Madison, Wis, May 24-25.

Helrnberger, Peter and Jean-Paul Chavas (1996). The Economigs of Agicultural Prices.
Prentice Hall, Upper Saddle River, New Jersey.

Holden, D., D.A. Peel and IL. Thompson (1985). Emtations: Theopy and Evidence. St.
Martin’s Press, New York.

Judge, George, W.E. Grifﬁths, R. Carter Hill, Helrnut Lutkepohl and Tsolmg-Chao Lee
(1985). The Theory a_nd Prpctice of Econometrics. Second Edition Wiley Series in
Probability and Mathematical Statistics. New York.

Leitch, Gordon and J. Ernest Tanner (1991). “Economic Forecast Evaluation: Proﬁts
versus the Conventional Error Measures, American Economic Review, Volume 81, Pp.
580-590.

Just, Richard and Gordon Rausser (1981). Commodity Price Forecasting with Large-
Scale Econometric Models and the Futures Market. American Journal of Agicultural
Economics, Volume 63, Number 2

Maddala, G.S. (1990).“Estimation of Dynamic Disequih’brium Models with Rational
Expectations: The Case of Commodity Markets”in ' Commo ' Prices: Economic
Models and Policy. Eds. Winters and Sapsford. Center for Economic Policy Research,
Cambridge University Press, Cambridge.

Makridakis Spyros and Steven Wheelwright (1978). Forecastmg' : Methods m
Applications. John Wiley & Sons, Santa Barbara, CA.

Mehta, Mona (1989). An A_n_aﬂsis of me Structure of the Wholesale Cereals Market in
_M_aﬁ. Unpublished Plan B Paper, Department of Agricultural Economics, Michigan State
University.

University of Minnesota, Department of Applied Economics (1997). Midwest Outlook
Conference. Papers.

 

169

Ministere du Developpement Rural et de L’Eau, Cellule de Planiﬁcation et de Statistique
(March 1998). Recueil des Statistiques du Secteur Rural Malien Republique du Mali.

Myers, Robert (1996). Notes on Dynamic Models in Agricultural and Resource
Economics: Chapter 6 Optimal Storage Rules. Dynamic Progamming Class Notes

Myers, Robert J. (1994). T ime-Series Econometrics and Commodity Price Analysis: A
Review. Review of Marketg' g and Agg'cultural Ecnornics. Vol. 62, no.2.

NCR—134 Conference on Applied Commodity Price was, Forecastu_1g' , and Market
Risk Mement (1990). Editor Marvin Hayenga. Chicago, Illinois, April 23-24.

NCR-134 Conference on Applied Commom' Price MSE, Forecasting, and Market
Risk Mement (1992). Editor Marvin Hayenga. Chicago, Illinois, April 20-21

Nelson CR and CI. Plosser (1982). Trends and random walks in macroeconomic time
series: some evidence and implications. Journpl of Mone_ta_ry Economics, Volume 10.

Nerlove, Marc; David M. Grether; and Jose L. Carvalho (1995). Myst of Economic
Time Serigs: A Sypthesis. Revised Edition Academic Press, San Diego. A volume in
Economic Theory, Econometrics, and Mathematical Economics.

Newbery, D.M.G. and J .E. Stiglitz (1992). “Futures Markets and Risk Reduction” in ILe
Theog of Futures Markets Edited by Paul Weller. Blackwell Publishers, Oxford, UK.

Newbery David and Joseph Stiglitz. The Theory of Commodig Price Stab1h_;a,t' ' ion: A
Study in the Ecommics of Risk. Clarendon University Press, Oxford. 1981

Ooms, Marius (1994). Empirical Vector Autgregpegive Modem . Springer-Verlag,
Berlin

Park Wayne; Philip Garcia and Raymond M. Leuthold (1989). “ Using a Decision Support
Framework to Evaluate Forecasts” in North Central Journal of A gricultural Economics.
Volume 11, Pp. 233-242.

Price D.H.R. and IA. Sharp. (1986). “A Comparison of the Performance of Diﬂ‘erent
Univariate Forecasting Methods in a Model of Capacity Acquisition in UK Electricity
Supply. International Journal of Forecasting. Volume 2, Elsevier Science Publishers B.V.
Amsterdam Pp. 333-348.

Rausser, Gordon (1982) Editor. New Directions in Econometric Modell_ng° and
Forecastgg' in U.S. Agg'culture. North Holland. New York.

170

Sims, Christopher (1986). Are Forecasting Models Useable for Policy Analysis. Federal
Reserve Bank of Minneapolis. Quarterly Review. Winter.

Steﬂ‘en, Philip Nathan (1995). The R__o_____les and Limits of the Grain Mar_ket m Assurm uring

Ho_use_hold Food Securi_ty in Northeastern Mali. Implications for Public Policy Vol I ,
Ph. D. Dissertation, Department of Agicultural Economics, Michigan State University.

 

Tefﬁ James, John Staatz and Josue Dione (1997). Impact of the CFA Devaluation on
Sustainable Growth for Poverty Alleviation: Preliminary Results. Comite Permanent
Interetats de Lutte Contre la Secheresse dans le Sahel. Institut du Sahel and PRISAS,
Bamako, Mali.

Theil, H. (1958). Economic Forecasts and Policy. North-Holland Publishing Company,
Amsterdam.

United States Department of Agiculture, ERS (1997). Rice: Situation and Outlook
Yearbook. Market and Trade Economics Division, Economic Research Services, U.S.
Department of Agiculture, December 1997, RCS-l997.

Williams, Jeﬂ‘rey and Brian Wright (1991). Stor_age and Commodm' Markets. Cambridge
University Press, Cambridge.

Winters L. Alan and David Sapsford (1990). Fri—m Commodﬂ' Prices: Economic
Models pn_d Poli_c_y. Eds. Winters and Sapsford. Center for Economic Policy Research,

Cambridge University Press, Cambridge.

Winters L. Alan and David Sapsford (1990). Primary Commodity Prices: An Introduction
to the Major Policy and Modelling Challenges in mum Comm Prices: Economic

Models and Policy. Eds. Winters and Sapsford. Center for Economic Policy Research,
Cambridge University Press, Cambridge.

Wisner Robert, E. Neal Blue and E. Dean (1998). Preharvest Marketing Strategies
Increase Net Returns for Corn and Soybean Growers in Review of Agg'cultural
Economics Volume 20, Number 2, Fall/Winter.

Wohlgenant, Michael K. (1985). “Competitive Storage, Rational Expectations, and Short-
run Food Price Determination”. American Journal of Agicultural Economics.

Wright, D.J.; G. Capon; R. Page; J.Quiroga; A.A.Taseen and F. Tomasini (1986).
“Evaluation of Forecasting Methods for Decision Support” in Ipternational Journal of
Fprecastmg' . Volume 2, Elsevier Science Publisher B.V., North Holland. Pp. 139-152.

171

Xiao, Jingyue (1991). A Food Security Study in Mali: Toward Hmonized Food Policy
for Rural Farm Households. Unpublished Master’s Thesis, Department of Agricultural
Economics, Michigan State University.

Yang, Seung—Ryong and B. Wade Brorsen (1992). Nonlinear Dynamics of Daily Cash
Prices. American Agicultural Economics Association. Volume 74, Number 3.

Zulauf, Carl and Scott Irwin (1998). Market Efﬁciency and Marketing to Enhance
Income of Crop Producers in Revi_ew of Agicultural Economics. Volume 20, Number 2,
Fall/Winter.

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