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thesis entitled

ForecastingAgriaflUn'alPrioesinanmierdevelopequenEwmy:
IheCaseofMaizeianlozaubique

presented by
Pedro Arlinio

has been accepted towards fulfillment
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6/01 cJCIRC/DateDuepss-p. 15

 

FORECASTING AGRICULTURAL PRICES IN AN UNDERDEVELOPED OPEN
ECONOMY:
THE CASE OF MAIZE IN MOZAMBIQUE
By

Pedro Arlindo

A THESIS

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

MASTER OF SCIENCE

Department of Agriwlmral Economics
2001

 

 

ABSTRACT

FORECASTING AGRICULTURAL PRICES IN AN UNDERDEVELOPED OPEN
ECONOMY: THE CASE OF MAIZE IN MOZAMBIQUE

By

Pedro Arlindo

Mozambique’s maize marketing system faces high levels of price uncertainty. Price
uncertainty can be reduced if future price are forecasted accurately and used along with
consistent policies. This research estimates alternative out-of-sample forecasting models
for maize prices in Mozambique and evaluates the statistical and economic forecasting
performance of the alternative models. The research uses an econometric time-series
approach through the estimation of univariate ARMA and ARIMA models and
multivariate VAR and VEC models for the northern and the central/southern regions of
the country. The data includes monthly retail maize prices, from November 1992 through
August 2000, and maize production data for 1992 - 2000. Preliminary tests indicate that
all price series are nonstationary and the series within each region are cointegrated. The
main conclusion is that the performance of the forecasting models is generally poor due to
significative differences in price path between the model estimation period and the
forecasting period. Nevertheless, statistical evaluation suggests that the estimated models
have a potential to improve random walk models’ forecasts, and economic evaluation
suggests that the estimated models tend to have better results than a ‘no-model’ strategy, .

especially in the center/south.

To my Parents.
To Telvio and Tunelga.

iii

ACKNOWLEDGMENTS

This research would have never been possible if many peOple had not given their time,
patience and support. I would like to thank all those who made possible the completion of
this thesis. My special thanks are for my committee members. Professor David L.
Tschirley, my major professor and thesis supervisor, was the author of the idea of time
series models for maize prices in Mozambique. His e-mails and phone conversations
helped me think about the importance of research on maize price modeling in
Mozambique. Professor Michael T. Weber was my major professor for most of my
Masters’ program, and was extremely important for my achievements. He helped me in
careful course selection leading me toward the skills needed for the kind of analysis that I
present in this thesis. His support and meticulous advice throughout the program was
critical to the completion of the research. Professor Robert J. Myers was also extremely
important for the completion of this thesis. By agreeing to examine and correct the
methods and models that I have used, he transmitted to me the confidence I needed to face
the challenge of the topic. Throughout the research, he patiently spent many hours
working with me. Finally, Professor Jefl’rey Wooldridge agreed to be a member of my
committee, and gave me important contributions. His comments on the thesis were very

important for corrections and improvements.

Many other maple and institutions made this research possible. Special thanks go to the

ATLAS Program for funding my Masters’ program, and to the Food Security Project in

iv

the Department of Agricultural Economics at Michigan State University for providing
technical assistance. On campus, three Mozambicans gave me special support. Initially
Dr. Paulo N. Mole, and later Rui Benfica and Marcia Jeremias-Benfica. Dr. Cynthia
Donovan also played a key role for the completion of this research. To them and to all the

fellow graduate students in the Department of Agricultural Economics, my great thanks.

In Mozambique, special friendship and support came from Perpétua, who agreed to stay
alone with our two very young children while I was studying. It was a very diflicult
decision. Thanks Perpétua. Thanks also for the pictures you always sent, for all the good
work towards a better life for our children, and for permanently updating me with our
kids’ health and our relatives’ lives. Many thanks. In all this, “Tio Lourenco” and “Tia

Graca” helped a lot. My sincere thanks to both.

Paula Santos and Anabela Mabota worked with me at SIMA in Maputo and helped me
understand that a good team always makes a good success. Higino Manule, Nita Dengo
and José I. Jeje were also there. With their experience in similar programs, they helped
me be confident and make the decision to “try” the experience. Thank you all.
Conceicao, Simao, Chico, Abel and Reginaldo did a great work in helping, each one in his
way. Danilo Abdula had timely and extremely helpful responses to my e-mails when I
needed additional data. To all of them and all other colleagues at SIMA in Maputo, my

sincere thanks.

To my extended family and friends, my deepest thanks. Special thanks go to 1050,
Moises, Anselmo, Lino, Jaime, Ermelinda and Dominica for helping me with everything
they did. To my grandparents, parents, Mana Teresa and Belalva, my gratefulness for all

the help.

TABLE OF CONTENTS

LIST OF TABLES ..................................................... x

LIST OF FIGURES ................................................... xi
Chapter 1

INTRODUCTION AND RESEARCH OBJECTIVES .................... 1

1.1 Introduction ................................................ 1

1.2 Problem Statement ........................................... 2

1.3 Modeling Maize Prices in Mozambique ........................... 4

1.4 Research Objectives and Thesis Organization ....................... 9
Chapter 2

STRUCTURE OF THE MAIZE SUBSECTOR IN MOZAMBIQUE ....... 10

2.1 Introduction ............................................... 10

2.2 Methodological Approach .................................... 11

2.3 Basic Conditions in Mozambique’s Maize Subsector ................ 12

2.4 Organization of the Subsector and Participants’ Characteristics and

Functions ................................................... 13

2.4.1 Marketing Channels in Northern Mozambique .............. 14

2.4.1.1 Farm producers .............................. 16

2.4.1.2 Assemblers .................................. 16

2.4.1.3 Large-scale grain wholesalers .................... 17

2.4.1.4 Grain Processors/Manufacturers .................. 17

2.4.2 Marketing Channels in Central/ Southern Mozambique ........ 18

2.4.2.1. Farm Producers .............................. 19

2.4.2.2 Small-Scale Assemblers/Wholesalers .............. 20

2.4.2.3 Grain Wholesalers ............................ 21

2.4.2.4 Grain Processors/Manufacturers ................. 21

2.4.2.6. Retailers ................................... 22

2.4.2.7. Maize Consumption .......................... 23

2.5 Coordination Problems ....................................... 24

2.5.1 High Cost of Marketing from North to South .............. 24

2.5.2 Instability of Returns and High Costs of Storage ............ 27

2.5.3 Uncertainty About Market Opportunities .................. 28

2.5.4. Limited Access to Working Capital ....................... 28

2.5.5. Low Farm Yields .................................... 28

2.5.6. Inefficiency in the Small-Scale Milling Industry .............. 29

2.6 Indicators of Performance in the Maize Subsector in Mozambique ...... 29

2.6.1 Index of Availability of Maize Grain and Maize Flour ........ 30

vii

2.6.2 Marketing Margin Between Price of Maize Grain and Maize

Flour ................................................ 31

2.6.3 Price coordination and stability ......................... 33

2.7. Conclusions ............................................... 34
Chapter 3

THEORETICAL FRAMEWORK AND METHODOLOGY .................... 35

3.1 Introduction ............................................... 35

3.2 Forecasting Techniques ...................................... 35

3.3 Univariate Models .......................................... 39

3.3.1 Naive and Random Walk Models ........................ 39

3 .3 .2 Trend Extrapolation Models ........................... 40

3.3.3 Exponential Smoothing Models ......................... 41

3.3.4 ARIMA Models ..................................... 42

3.3.4.1 Identifying ARIMA Models ..................... 44

3.4 Multivariate Models ......................................... 46

3.4.1 VAR Models ....................................... 46

3.4.2 VEC Models ....................................... 49

3.5 Methodology in Time Series Analysis ............................ 50

3.5.1 Unit Root Tests ..................................... 50

3.5.2 Testing for Trend Component .......................... 55

3.5.3 Checldng for Seasonality .............................. 56

3.5.4 Cointegration and Vector Error Correction (VEC) Models . . . . 58

3.5.4.1 The VEC Models ............................ 58

3.5.5 Testing for Autocorrelation in the Error Term .............. 60

3.6 Evaluation of Forecasting Accuracy ............................. 61

3.6.1 Statistical Criteria ................................... 61

3.6.2 Economic Criteria ................................... 64

3.7 The Models ............................................... 65

3.7.1 The ARIMA models for Nampula and Maputo .............. 66

3 .7 .2 VAR Model for Nampula .............................. 67

3.7.3 VAR Model for Maputo .............................. 68
Chapter 4

PRELIMINARY DATA ANALYSIS ............................... 70

4.1 Introduction ............................................... 70

4.2 The Data ................................................. 70

4.3 Missing Data .............................................. 75

4.4 Characteristic Time Series Properties of Commodity Prices ........... 76

4.4.1 Unit Root or Stochastic Trends ......................... 77

4.4.1.1 Unit Root Tests .............................. 78

4.4.2 High Volatility and Time-Varying Volatility ................ 79

4.5 Deterministic Time Trend and Seasonality ........................ 80

viii

4.6 Structural Shocks ........................................... 83

4.7 Marketing Margins .......................................... 86

4.8 Implications of the Characteristics of the Data ..................... 89
Chapter 5

ESTIMATION OF THE ALTERNATIVE FORECASTING MODELS ..... 91

5.1 Introduction ............................................... 91

5.2 ARIMA Model Specifications ................................. 92

5.2.1 ARIMA Specification for Northern Mozambique ............ 93

5.2.2 ARIMA Forecasting for Northern Mozambique ............. 98

5.2.3 ARMA Models for Northern Mozambique ................ 100

5.2.4 ARIMA Specification for Central/Southern Mozambique ..... 105

5.2.5 ARIMA Forecasting for Central/Southern Mozambique ...... 110

5.2.6 ARMA Models for Central/Southern Mozambique ......... 112

5.3 Multivariate Models ........................................ 116

5.3.1 Cointegration Models ............................... 117

5.3.2 VEC Specifications and Forecasting ..................... 120

5.3.2.1 Northern Mozambique ........................ 120

5.3.2.2 Central/Southern Mozambique ................. 125

5.3.3 VAR Specifications and Forecasting .................... 129

5.3.3.1 Northern Mozambique ....................... 129

5.3.3.2 Central/Southern Mozambique ................. 132

5.4 Conclusions ............................................... 136
Chapter 6

EVALUATION OF THE COMPETITIVE FORECASTING MODELS . . . . 137

6.1 Introduction .............................................. 137

6.2 Preliminary Data Search ..................................... 137

6.3 Statistical Evaluation ....................................... 140

6.3.1. Nampula Prices .................................... 140

6.3.2 Maputo Prices ..................................... 142

6.4 Economic Evaluation ....................................... 144

6.4.1 Sell-or-Store Signals ................................ 150

6.4.2 The Evaluation Criteria .............................. 152

6.5 Conclusions .............................................. 157
Chapter 7

CONCLUSIONS AND IMPLICATIONS ........................... 159

7.1 Introduction and Research Questions ........................... 159

7.2 Research Methods ......................................... 160

7.3 General Findings .......................................... 162

7.3.1 Organization of the Maize Subsector .................... 162

7.3.2 Characteristics of the Data ............................ 164

ix

7.3.3 Forecasting Models Results ........................... 164
7.4 Lessons and Further Research ................................ 166
References ................................................... 169

LIST OF TABLES

Table 2.1 Index of Availability of Product in Consumer Markets in Mozambique,

1992 - 1999 ................................................... 31
Table 2.2. Average Annual Real Prices of Maize Grain and Maize Flour in Selected

Retail Markets in Mozambique, 1993, 1996 and 1999 (May 1999 = 100) ...... 32
Table 4.1 Summary Statistics ........................................... 72
Table 4.2 Unit Root Tests for Maize Prices in Mozambique, with trend and seasonal

dummies ...................................................... 78
Table 4.3 Drift and Seasonality in First Difi’erences in Maize Prices in Mozambique . . 82
Table 5.1a ARIMA Models for Nampula Maize Prices ........................ 96
Table 5.1b Correlogram for the Nampula ARIMA Models ..................... 97
Table 5.2a ARMA Models for Nampula Maize Prices ........................ 101
Table 5.2b Correlogram for the Nampula ARMA Models ..................... 102
Table 5.3a ARIMA Models for Maputo Maize Prices ........................ 107
Table 5.3b Correlogram for the Maputo ARIMA Models ..................... 108
Table 5.4a ARMA Models for Maputo Maize Prices ......................... 113
Table 5.4b Correlogram for the Maputo ARMA Models ...................... 114
Table 5.5 Cointegrating Equations and Deterministic Trend Assumptions ......... 117
Table 5.6 Cointegration Tests for Mozambique Maize Prices .................. 119
Table 5.7 VEC (2,0) Model for Maize prices in Northern Mozambique ........... 123
Table 5.8 VEC (2,0) Model for Maize prices in Central/Southern Mozambique . . . . 127
Table 5.9 VAR (2,0) Model for Maize prices in Northern Mozambique .......... 130

Table 5.10 VAR (2,0) Model for Maize prices in Central/Southern Mozambique . . . 134
Table 6.1 Statistical Evaluation of the Price Forecasting Competitor Models for

Nampula ..................................................... 141
Table 6.2 Statistical Evaluation of the Price Forecasting Competitor Models for

Maputo ...................................................... 143
Table 6.3a Post-Harvest Marketing Strategies Generated from Forecasting Models in

Nampula ..................................................... 150
Table 6.3b Post-Harvest Marketing Strategies Generated from Forecasting Models in

Maputo ..................................................... 152
Table 6.4a Economic Results of Post-Harvest Marketing Strategies for Nampula . . . 153
Table 6.4b Economic Results of Post-Harvest Marketing Strategies for Maputo . . . . 154

LIST OF FIGURES

Figure 1.1 Map of Mozambique .......................................... 6
Figure 2.1 Maize Marketing Channels in Northern Mozambique ................. 15
Figure 2.2 Maize Marketing Channels in central/southern Mozambique ........... 19
Figure 4.1 Retail Maize Prices in Nampula and Mocuba, November 1992 - August

2000 ......................................................... 74
Figure 4.2 Maize Retail Prices in Maputo and Manica, November 1992 - August

2000 ......................................................... 75
Figure 4.3 Marketing Margin for Maize Prices, Nampula - Mocuba, Nov 1992 - Aug

2000 ......................................................... 87
Figure 4.4 Marketing Margins for Maize Prices, Maputo - Manica, Nov 1992 - Aug

2000 ......................................................... 89
Figure 5.1 Autocorrelation and Partial Autocorrelation Coefficients for Nampula

Prices ....................................................... 94
Figure 5.2 Out-of-Sample Forecasts for Nampula Prices, ARIMA Models, Sep 1999 -

Aug 2000 .................................................... 99
Figure 5.3 Out-of-Sample Forecasts for Nampula Prices, ARMA Models, Sep 1999 -

Aug 2000 .................................................... 104
Figure 5.4 Autocorrelation and Partial Autocorrelation Coefficients for Maputo

Prices ..................................................... 106
Figure 5.5 Out-of-Sample Forecasts for Maputo Prices, ARIMA Models, Sep 1999 -

Aug 2000 ................................................... 111
Figure 5.6 Out-of-Sample Forecasts for Maputo Prices, ARMA Models, Sep 1999 -

Aug 2000 ................................................... 1 15
Figure 5.7 Out-of-Sample Forecasts for Nampula, VEC Model, Sep 1999 - Aug

2000 ....................................................... 124
Figure 5.8 Out-of-Sample Forecasts for Maputo Prices, VEC Models, Sep 1999 -

Aug 2000 ................................................... 128
Figure 5.9 Out-of-Sample Forecasts for Nampula Prices, VAR Models, Sep 1999 -

Aug 2000 ................................................... 131
Figure 5.10 Out-of-Sample Forecasts for Maputo Prices, VAR Models, Sep 1999 -

Aug 2000 ................................................... 135
Figure 6.1 Maize Retail Prices in Nampula, November 1992 - August 2000 ....... 138
Figure 6.2 Maize Retail Prices in Maputo, November 1992 - August 2000 ........ 139

xii

Chapter 1

INTRODUCTION AND RESEARCH OBJECTIVES

1.1 Introduction

In the 1980s, several developing countries experienced profound transformations in their
economic policy, including the agricultural sector. Mozambique is not an exception.
After following a centrally planned economic policy since 1975, in 1987 the government
of Mozambique (GOM) adopted a structural adjustment program (SAP), firnded by the
World Bank and the International Monetary Fund that was aimed at reverting the
downward trend in economic growth rates. One important constituent of Mozambique’s

SAP was the liberalization of agricultural markets.

The agricultural sector plays a key role in Mozambique’s economy, employing
approximately 85% of the population and generating 35% of GDP. Maize is the most
important staple in the country, both in production and consumption, though cassava is
more important in some areas of the north. Maize production in Mozambique takes place
in all provinces, but production potential is greater in the northern and central regions of
the country. On the other hand, the most important consumption centers in the country
are the three major cities, namely Maputo in the south, Beira in the center and Nampula in
the north. Maputo, the capital city and the most important consumption center in the
country, and most southern areas, are net maize consumers. Due to these geographic

patterns, commercial linkages between southern and central Mozambique are considerable

and, as a result, retail prices in the south, especially in Maputo, are highly correlated with

prices in some of the most important producer areas in central Mozambique.

Linkages between southern and central Mozambique face several infrastructure
constraints, which leads to high transportation costs. AS a consequence, maize imports to
the south from South Afiica are notable and prices in the southern urban markets are
expected to be highly correlated with the expected production in South Africa. Transport
cost between northern and southern Mozambique are so high that maize trade between

these two regions occur very infi'equently.

In Mozambique, expected profits in the maize subsector, as well as in other food staples,
are generally low compared to the profits obtained fiom cash crop staples and non-
agricultural sectors. Farm production in the maize subsector is almost entirely performed
by smallholder households, and trade between surplus and deficit areas is basically
dominated by small scale informal traders, with little presence of large scale formal
traders. Also, there is a high level of uncertainty on quantity and prices in the maize
subsector, and producers and consumers assume individually the risk associated with the

quantity and quality of product they produce, sell, buy or consume.

1.2 Problem Statement and General Objective
One of the most important characteristics of agricultural commodities in Mozambique is

their price instability. Indeed, both short-term and long-term management decisions in the

agricultural sector involve uncertainty, which is greater the more the agricultural
production depends on climatic conditions. This is the case in Mozambique where, in
addition to the individual risk to participants in the food system in determining what, when
and how much to produce, store and sell, agriculture depends almost entirely on climate,
such as the timing and levels of rainfall. , This increases risk and uncertainty. High levels
of risk associated with price uncertainty can be reduced if consistent price forecasting
models are estimated and results are disseminated to all participants in the food system
throughout the country. Price forecasting models might help reduce uncertainty if used
judiciously in combination with knowledge about (i) patterns and levels of production in
the country, (ii) patterns and levels of production in the region, and (iii) policy initiatives
which might alter production levels and/or trade flows in the region. The general
objective of this research is to see if existing data and techniques will support the

development of models which might improve commodity price forecasts in Mozambique.

Mozambique has a consistent and regular data series on weekly maize prices from 1992 to
the present. Mozambique’s agricultural market information system (SIMA, fi'om its
acronym in Portuguese), with financial and technical assistance under the Food Security 11
project in Mozambique, has played a critical role in the development of a solid system of
price data collection and analysis in the Ministry of Agriculture and Rural Development of
Mozambique. However, like in many other developing countries, this data has been
primarily used for short-term market information reports, intended to allow quick,

appropriate decisions by producers, traders, consumers and the public sector.

Nonetheless, in addition to the importance of the short-term price reporting services, this
price data can be used for other purposes like price forecasting._This research estimates

and tests short-term forecasting models for maize prices in Mozambique.

1.3 Modeling Maize Prices in Mozambique

Modeling maize prices in Mozambique requires taking into consideration that
Mozambique has two regions with different characteristics in maize production, and
without commercial connections. On the one hand, southern Mozambique is a poor maize
producer, where most maize consumed is brought from central Mozambique. Except for
large-scale millers and animal feed producers, who import nearly all their maize fi'om
South Afiica due to better quality, large scale, and lower transportation costs, SIMA data
indicate that during the last decade, about 95 percent of the domestic maize traded in
informal retail and wholesaler markets in Maputo has been bought either in central
Mozambique or in the producer districts within southern Mozambique. Indeed, the most
important destination for maize produced in central Mozambique is southern
Mozambique. Between 1992 and 2000, about 64 percent of the informal wholesalers in
the area of Chimoio, central Mozambique, indicated that they would sell their product in
southern Mozambique. The remaining product has been supplied to the net consumer
areas within central Mozambique, among them Beira, where about 93 percent of the

maize has been acquired within the central region of Mozambique.

In Figure 1.1, the typical maize trade flows from Mocuba to Nampula, and from Manica to
Maputo are emphasized. By road, the distance between Mocuba and Nampula is

approximately 400 km, and that between Manica and Maputo is 1,135 km.

On the other hand, northern Mozambique is commercially isolated fi'om the center and
south, regardless of its high potential to produce maize, due to poor and expensive road

linkages, un-

Figure 1.1 Map of Mozambique With Principal Domestic Maize Trade Flows

   
    
 
  

CABO

NIASSA DELGADO

Pomba

        
    
  
 
 
     

. Lichinga

NAMPULA

“' ampuia

Ouelimano
O

0 Provincial Capital
- Provincial Boundaries
° DistrictTowns

7
inhambano

, I

. T Maputo

operational and ineficient maritime connections, and nonexistence of north-south railway
connections. Maize produced in the north is consumed within the region and exported to
neighboring countries, especially Malawi. Indeed, Malawi has been shown to be an
important destination of Mozambican maize when maize production drops in the southern
Afiican region. As an example, when maize production decreased 34 percent in Malawi in
the 1997/98 season, imports from Mozambique were an important resource to Malawian
traders. Total formal exports fi'om northern Mozambique to Malawi were about 42,000
metric tons that season, and estimated to be approximately 100,000 metric tons including

informal trade in the 1998/99 season (Santos and Tschirley, 1999).

These exports to Malawi had noteworthy efl‘ects on maize prices in northern Mozambique,
but little or no efi‘ect in the south. Maize retail price in northern Mozambique increased
between 13 percent in Nampula city and 21 percent in the rural district of Mocuba in
1997, and cash income earnings fi'om maize sales had a total increment of about 3.5
million US dollars in Nampula and Zambezia in the 1998/99 marketing season as a result
of trading to Malawi (Santos and Tschirley, 1999). No statistically significant price
increase effects were found in southern markets. Based on these characteristics of maize
production, trading and consumption in Mozambique, modeling maize prices in the
country might imply dividing the country into two regions with difi‘erent price generating

processes: southern-central Mozambique and northern Mozambique.‘

 

I
In Mombique’s political administrative division, northern Mozambique includes the provinces of
Niassa, Cabo Delgado and Nampula, central Mozambique is composed by Zambezia, Tete, Manica

7

This research divides Mozambique into these two geographic units, and the cities of
Nampula and Maputo are taken as the representative markets for the northern and the
central/southern regions respectively due to their importance in the respective regions.
Having this in mind, the research estimates and tests short-term forecasting models for
these two cities, using a time series approach. Time-series models are widely used for
forecasting purposes, do not require economic theory, have economical data requirements,
have been found to give good forecasts, and are easy to implement and interpret. This
research assumes that price forecasts in Mozambique are of interest primarily to producers
and traders. Producers in Mozambique face high levels of this uncertainty about prices
and earnings, thus accurate and well difi‘irsed forecasts might reduce uncertainty. For
traders, forecasts are important in that if accurate forecasts are available and timely
disseminated, it can improve plans of volumes to trade. The government is also interested

in forecasts because it needs to plan public investments and policies.

 

and Sofala provinces, and southern Mozambique includes the provinces of Inhambane, Gan and
Maputo. Agra-climatic characteristics and the pattern of agricultural trades, however, lead analysts
at SIMA in the Ministry of Agriculture and Rural Development (MADER, fi'om its acronym in
Portuguese) to include Zarnbezia in the north. In fact, there is a high commercial linkage between
northern Mozambique, especially Nampula province, and Zambezia. And maize prices seem to be
driven by the same data generating mechanism in northern Mozambique and Zambezia. For instance,
when northern Mozambique exported considerable quantities of maize to Malawi in 1997, prices in
Zarnbezia were afiected, but there was no statistical significance ofprice changes in central and
southern Mozambique (Santos and Tschirley, 1999). In addition, about 86% of the maize marketed
in informal markets of Nampula city between 1992 and 2000 has originated fiom northern Zambezia.
In this study, therefore, Zambezia is considered as part of northern Mozambique.

8 .

1.4 Specific Research Objectives and Thesis Organization

In developing forecasting models for maize retail prices in the cities of Nampula and
Maputo, this research is directed toward two specific objectives. First, to develop
alternative quantitative, short-term forecasting models for retail prices of maize in
northern and southern Mozambique. Second, to evaluate the forecasting ability of

alternative models using statistical and economic criteria.

The thesis is organized as follows. Chapter 2 discusses the characteristics and
organization of the maize subsector in Mozambique, with special emphasis on maize
marketing channels, subsector participant characteristics, and problems of the subsector.
Chapter 3 reviews the theoretical framework behind quantitative and qualitative
forecasting techniques, and outlines the methods followed in the research. Chapter 4
presents a discussion of the preliminary data analysis. Based on the methods discussed in
chapter 2 and findings from chapter 4, chapter 5 uses time-series econometric tools to
identify and estimate the comparative univariate and multivariate forecasting models.
Chapter 6 evaluates the alternative forecasting models, and chapter 7 presents the

conclusions and draws recommendations for further work.

Chapter 2

STRUCTURE OF THE MAIZE SUBSECT OR IN MOZAMBIQUE

2.1 Introduction

This research develops price modeling for maize subsector in Mozambique. A solid
understanding of the price data generating process is an important premise for a well-
formulated price analysis and a better understanding of the model results. A way to
understand the underlying price formulation mechanism in a given subsector is to examine
the structure and organization of the subsector through the analysis of the characteristics
of demand and supply. Particularly, by analyzing the structure and organization of the
maize subsector in Mozambique, this research seeks to examine how the subsector is I

organized in terms of the participating agents and their functions.

The chapter is organized as follows. Section 2.2 reviews the methodological approach
followed in this chapter, section 2.3 analyzes the basic conditions in Mozambique’s maize
subsector, section 2.4 presents a discussion on the maize supply chain and the
characteristics and functions of the participants. Section 2.5 reviews the most important
coordination problems. Section 2.6 discusses the indicators of performance in

Mozambique’s maize subsector, and section 2.7 has the major conclusions of the chapter.

10

2.2 Methodological Approach

In general, the organization and structure of a given subsector or food system can be
addressed in two ways: the subsector approach or the industrial organization approach.
Although these two approaches are similar in focusing on the performance of the
subsector, the former seems to be appropriate for the specific objectives of this research as
(i) it puts emphasis on aspects related to the transformation, value adding, and transactions
that take place at every stage of production, fi'om the stage of input supply to the stage of
consumption of the final output; (ii) it focuses on the vertical coordination of the firms that
add value to a product or related products; (iii) it analyzes how, through vertical
coordination, all the participants in the subsector have incentives to participate in
institutional arrangements that reduce fluctuations of the commodity supply and
consequently reduce excessive fluctuations of prices and; (iv) it is focused on the channel

coordination and specialization of all participants in the subsector.

As Shafl‘er et al (1983) and Holtzrnan (1986) argued, by focusing on such aspects, the
subsector approach leads to a better comprehension of the characteristics and problems in
the coordination of a food system. Through such an effort, the underlying price
formulation process can be understood, and the food system can move from levels in
which firms have low productivity, operate at a small scale, have poor levels of innovative
capacity, and operate at high costs with little specialization into systcttts in which firms
have higher levels of specialization and can explore economies of scale, minimize unit

costs, reduce excessive fluctuations of commodity supply and prices, and improve

11

producers and consumers’ welfare. This chapter uses the subsector approach to examine

the structure of the maize subsector in Mozambique.

2.3 Basic Conditions in Mozambique’s Maize Subsector

The most important basic conditions in the maize subsector in Mozambique are related to
agro-ecological conditions, technological development, and the characteristics of demand.
Agro-ecological conditions are determinant in the geographic pattern of maize production
in Mozambique. Maize supply depends on rainfall. There is a single rain season and a
single cropping season per year in most parts of the country. Furthermore, as Tschirley

( 1998) stated, areas north of the Zambezi river have a better potential of maize production

than south of it, determined by better reliability of rainfall and much better fertility of soils.

Agricultural technology is rudimentary in Mozambique. As a result, most maize is
cultivated with the use of rudimentary tools and few external inputs. A national survey by
the Ministry of Agriculture and Rural Development of Mozambique estimated that, in
1996, hoes were the most important tool in farm production for 99.5 percent of the
houSeholds. Only 3.2 percent used tractors and 1.2 percent used animal traction systems.
In addition, 55 percent of the seed used was retained from previous production, and only
16.7 percent was acquired through the commercial channel. Only 0.1 percent of the
households used fertilizer (Strasberg, 1997). Furthermore, although the National Institute

for Agronomic Research (INIA) has some experimental field stations for new and

12

improved varieties of maize seed in the country, most households use traditional varieties

of seed. This situation is likely to have changed little up to the present date.

Finally, due to production lags and the use of rudimentary tools, maize supply is inelastic
in the short-run. Due to both factors, households can barely adjust their levels of
production to changes in demand. Ifdemand decreases, households can hardly adjust in
the short-run because of the asset fixity that characterizes the use of land and other
production factors. Ifdemand increases, households cannot, either, easily adjust the levels
of production in the short run. Also, because maize is a basic component of the

consumption patterns in the country, it is demand inelastic.

2.4 Organization of the Subsector and Participants’ Characteristics and Functions
A comprehensive subsector analysis involves a review of the supply chain fiom the input
market stage to the stage of consumption of the final product. By reexamining the basic
characteristics of the supply chain and the organization, characteristics and functions of
the participants, such a review helps understand the mechanisms that influence prices.
This section reviews the characteristics of the difi‘erent stages of price formation in
Mozambique’s maize subsector. The analysis is conducted first for northern Mozambique
and then for central/southern Mozambique. In both cases, the stage of input supply is not
analyzed. Figures 2.1 and 2.2 present the structure and organization of the maize
marketing channels in the two regions and describe the linkages between the agents

participating in each marketing channel. From top to bottom, these Figures show the

13

different levels of transformation and transaction in the maize subsector and the
coOrdination processes within the channels. The remained of this section reviews the

marketing channels in the two regions.

2.4.1 Marketing Channels in Northern Mozambique

Nearly all maize consumed in northern Mozambique is produced within the region. As a
food staple, most families produce maize primarily for on-farm consumption, farmers
retain the majority of their production for on-farm consumption, and only the surplus is

marketed through the marketing channels.

As Figure 2.1 indicates, the most important marketing channel in northern Mozambique,
given by the thick arrows, involves domestic farm producers, large-scale wholesalers and
exports. In addition to this main channel, there are other channels by which difi‘erent
participants deliver product either to domestic consumers or for export. These channels
involve small scale assemblers, small-scale and large-scale millers, feed manufacturers,
meal wholesalers, retailers, and final consumers. The level of specialization of the
difl‘erent groups of participants in the subsector varies across the difi’erent levels of
production-transaction both in the vertical and in the horizontal coordination. This

performance depends on the institutional arrangements at each stage.

14

Figure 2.1 Maize Marketing Channels in Northern Mozambique

 

 

 

 

 

 

 

 

 

At the different stages of production-transaction in these channels, the transactions involve
difl‘erent types and levels of product processing. The different types of output obtained
from the different stages of transformation are: maize grain, refined maize meal milled in
the country, hand-processed refined maize meal, and whole maize meal. The remained of
this sub-section describes the linkages and firnctions of the participants in the maize

marketing channels in northern Mozambique.

15

2.4.1.1 Farm producers

In Mozambique, nearly all maize is produced by smallholder households. The nationally
representative rural household survey carried out by the Ministry of Agriculture and Rural
Development of Mozambique in 1996 indicated that 80 percent of rural households in the
country cultivated maize grain, but around 90 percent of the produced grain was
consumed on the farm, and only the remaining 10 percent was sold. This semi-subsistence
nature of the country’s agriculture is emphasized by the fact that average households
cultivate only 1.85 hectares, and average maize yield in the country is 717 kg per hectare
(Strasberg, 1997). In northern Mozambique, farm producers mainly sell their surplus to

large-scale wholesalers, but also sell to small-scale assemblers and large-scale millers.

2.4.1.2 Assemblers

In northern Mozambique, most of the grain sold by farm producers is bought by large-
scale wholesalers working through small-scale assemblers or directly fiom farm producers.
Compared to central/southern Mozambique, small-scale assemblers in northern
Mozambique have little importance in trading maize. An important characteristic of small-
scale assemblers in northern Mozambique is that they usually buy small quantities of
maize, and trade other agricultural commodities in addition to maize. There is an
emergent entry of large-scale wholesalers to the maize grain trading in northern
Mozambique, especially for export or to sell to donors and/or large-scale millers within
the country. This is contributing strongly to a recent and dynamic organimtion and

consolidation of the assembling function in the north.

16

2.4.1.3 Large-Scale Grain Wholesalers

Grain wholesalers in Mozambique can be divided into two groups: the large-scale and the
small-scale grain wholesalers. In northern Mozambique, basically there are only large-scale
wholesalers. Wholesaler traders have considerable experience and usually trade other
products in addition to agricultural commodities, taking advantage of profit opportunities
in the market. Also, they usually have access to credit and adequate access to working
capital. This sector of wholesale traders entered firmly into maize marketing in northern
Mozambique when opportunities to export grain to neighboring countries, especially into

Malawi, appeared (T schirley, 1998).

2.4.1.4 Grain Processors/Manufacturers

In Mozambique, maize processors can be divided into two groups. One is composed of
industrial millers, the most important of which are Companhia Industrial da Matola (CIM),
in the Maputo city area, and MOBEIRA in Beira, and the second is composed by small-

scale custom millers, who can be found throughout the country.

The structure of milling industry is changing in northern Mozambique. A new large-scale
miller was installed in July 2000 in Nampula city, with a processing capacity of 70 metric
tons per day, around 25 percent of the processing capacity of the large-scale milling
industry in the country (SIMA-Mozambique, 2000). CIMPAN, the name of this new
processing unit, expects to buy all its maize grain within northern Mozambique. Small-

scale custom millers, on the other hand, rather than buying maize grain and selling maize

17

meal, process grain belonging to small-scale wholesalers, informal retailers and consumers,

and receive a payment for the milling service.

2.4.2 Marketing Channels in Central/Southern Mozambique

Unlike in the north, maize supply in central/southern Mozambique does not depend solely
on domestic production. As Figure 2.2 indicates, there are two important maize
marketing channels in central/southern Mozambique. First, most maize marketed fiom
central Mozambique is channeled by small-scale assemblers/wholesalers and informal
retailers to domestic consumers, especially to the cities of Maputo and Beira. A small part
of it is exported by informal traders to neighboring countries. Second, the south, in
addition to receiving delivers from central Mozambique, imports maize grain and maize
meal fiom South Afiica, a connection made especially by large-scale millers and formal

retailers.

Such as in the north, participants involved in maize transformation and transaction at the
difl’erent stages of production-transaction in the marketing channels in central/southern
Mozambique have different levels of specialization. The characteristics and firnctions of

these participants are discussed next.

18

Figure 2.2 Maize Marketing Channels in Central/Southern Mozambique

 

 

 

 

 

2.4.2.1 Farm Producers

Maize production is lower in southern Mozambique than in the rest of the country. In
1996, the three provinces of southern Mozambique had an average maize yield of 400
kg/ha, ranging between 484 kg/ha in Gaza province and 296 kg/ha in Inhambane province.
In the same year, the average maize yield in central Mozambique was 758 kg/ha, and it
was 862 kg/ha in northern Mozambique. The poor performance in farm production in

southern Mozambique is likely to have worsened in considerable areas of this region and

19

some areas of central Mozambique after the February/March 2000 floods, which were

estimated to be the worst of the last 50 years.

2.4.2.2 Small-Scale Assemblers/Wholesalers

In opposition to northern Mozambique, there is a considerable consolidation of a group of
small-scale assemblers and wholesalers in central/southern Mozambique, with a visible
level of specialization. The major problem with this function is that, given that most maize
grain in Mozambique is produced by smallholder households, assemblers usually acquire
small quantities from many small farmers, thereby they need much time to accumulate
quantities up to a level that allows profitable transactions. Also, nearly all the small-scale
grain assemblers, generally from the major cities, perform this function, acting
simultaneously as wholesalers. The emergent entry of large-scale wholesalers to the maize
grain trading that is observed in the north has not been observed in central/southern
Mozambique up to date. The absence of this new dynamic in this regions implies that
maize assemblers will continue operating more actively only in the strategic areas of the
most important producer districts in the country, like the area of Chimoio, Manica, and
Sussundenga districts in Manica province, central Mozambique. From this area,
assemblers supply the product to wholesalers fi'om southern Mozambique and from the

central city of Beira.

In central/southern Mozambique, small-scale grain wholesalers either started or fortified

their activity in 1992, with the end of the civil war in Mozambique, or in 1994 after the

20

first multiparty elections and the establishment of a trustworthy environment of peace and
stability in the country. This group of wholesalers is composed of informal traders and is
responsible for the linkages between most surplus and deficit areas in central/southern
Mozambique, especially between the major rural producer areas in the center and the most

important urban markets in the south.

2.4.2.3 Grain Wholesalers

There is a strong, organized and dynamic group of small-scale wholesalers in
central/southern Mozambique. Also, contrary to northern Mozambique, there is not a
large-scale sector trading maize grain from the producer areas into the consumer centers
in central/southern Mozambique. CIM, the only large-scale milling industry in the south,
has experimented purchasing some maize grain form large-scale wholesalers fi'om northern

Mozambique, but continues to rely almost entirely on imports.

2.4.2.4 Grain Processors/Manufacturers

The most important and traditional large-scale maize processors in central/southern
Mozambique~ are MOBEIRA, which produces 40 percent of Mozambique’s refined maize
meal, and CIM, which processes about 35 percent. Maize meal processed by these two
industrial units is mostly oriented to domestic markets, especially urban markets. In
addition to these large-scale processing units, small-scale custom millers can be found

throughout central and southern Mozambique. While CIM buys most of its maize grain in

21

neighboring countries, especially in South Africa, MOBEIRA acquires most of its maize

grain within central Mozambique.

Such as in the north, small-scale custom millers, on the other hand, usually do not buy
grain. Instead, they process grain belonging to their customers, either small-scale
wholesalers, informal retailers or consumers, and receive a payment for the milling service

that they provide.

2.4.2.6 Retailers

In the maize marketing channel, both in northern and in central/southern Mozambique, the
maize retail sales function is performed both by formal and informal traders. Formal
traders are those who have a government licence to trade, and the group of informal
retailers includes all those retailers who sell maize grain or maize meal with no
governmental licence. In the past, during the colonial period in Mozambique, only formal
retailers could participate in agricultural commodity trading. This policy was maintained
after the country’s independence in 1975, and it only was replaced in 1987 when the
government started to liberalize agricultural markets. At present, food crops in
Mozambique are traded mostly by informal retailers. Nevertheless, financial problems

faced by these traders lead to high operational costs.

22

2.4.2.7 Maize Consumption

In Mozambique, there is a distinction between urban and rural consumers. On the one
hand, urban consumers usually acquire most of the maize grain or maize meal in the
markets. Urban consumers will buy maize grain and manually process it, instead of buying
flour, if they want a high quality flour but face financial problems to directly buy refined
flour. Alternatively, urban consumers might buy grain and take it to small-scale custom
millers and have non-refined flour, instead of buying flour from retailers, if the price
margin between grain and flour is much higher than the price paid for the milling service.
The margin of prices between grain and maize meal can be higher than the prices paid for
milling if there is no competition in maize flour marketing, and prices of flour are

artificially high.

In general, the percentage of household expenditures used to buy agricultural products,
maize included, are still low in Mozambique’s urban areas. For instance, Donovan (1996)
noted that only about 15 percent of the average monthly household expenditures in the
provincial capitals were in maize consumption in Mozambique in 1993. In the area of
Maputo city, the 20 percent poorest households spent 18 percent of their household
income in maize consumption (Donovan, 1996). On the other hand, although rural
households purchase grain especially during the planting season and in drought years,

most maize consumed by rural consumers is mostly own-produced by the households.

23

2.5 Coordination Problems

The analysis of the maize subsector in Mozambique suggests the existence of coordination
problems in the subsector. Coordination is one of the key concepts in subsector analysis.
Ifthe maize subsector faces few coordination problems, more clear functions of the

participants and high levels of specialization should be expected.

As Boughton et al ( 1995) pointed out, two consecutive production levels in the
production-distribution-consumption sequence are linked with a transaction, which must
be performed by a specialized group of agents. Ifthis does not happen or it happens with
deficiency, the marketing channel is facing coordination problems and there are not
enough incentives for individuals to perform transaction activities, which results in

negative consequences to the subsector.

Mozambique’s maize subsector faces several coordination problems, the most important
of which are: the high cost of marketing from north to south, instability of returns to
storage, uncertainty about market opportunities, dificult access to working capital, low

yields, and inefliciency in the small-scale custom milling industry.

2.5.1 High Cost of Marketing from North to South
High costs to trade fiom north to south directly affect primarily large and small-scale
wholesalers and consequently producers and consumers. Large-scale wholesalers are

affected because the high costs they face transporting maize grain fi'om northern or central

24

Mozambique to the south result in high price to consumers in the south. This situation is
currently overcome with the introduction of substitute products in Mozambique’s

southern markets, especially from South Afiica.

In fact, in southern Mozambique maize grain brought fi'om South Afiica is usually cheaper
than that brought fi'om northern Mozambique. In these conditions, Mozambican
producers and traders fi'om the north do not have a market in the south. However,
consumers in southern Mozambique are likely to face the higher prices of the maize grain
fi-om northern Mozambique when the southern Afiica region, particularly South Afiica,
faces a shortage in maize grain production. Moreover, if the whole southern Afiica region
or most of it faces a drought, Malawi and probably Zambia may be the preferred
destination for traders fi'om northern Mozambique due to the comparatively lower
transportation costs. As a consequence, the reduced quantities that can be transported to
the south in drought years are likely to be more expensive than they would be in a normal

season due to the scarcity of the product.

High transportation costs from northern to southern Mozambique result fi'om the
geographical characteristics of the country and the poor development of the transportation
system. First, although the country is bordered by the Indian Ocean from the north to the
south with good natural conditions for eflicient and active ports in most of the coast, a

poor development of the maritime transportation sector and the resulting high

25

transportation costs, added to the low operating scale and small operational capital for

nearly all the participants in the sector lead to the exclusive use of roads for most traders.

Second, the railway system in the country has been conceived to serve inland neighboring
countries. While the country is long from north to south, the most important and
systematically maintained highways and railways link the country’s three most important
ports to inland neighboring countries. In fact, Mozambique’s most important highways
and railways have been conceived in the colonial period, in the context of Mozambique as
an “economy of transportation services” to the-neighboring countries. And this policy
seems to be currently continued. Currently, the most important focus in road and railway
development is on the three most important lines linking Mozambique to the inland
neighboring countries. All three have been announced to be transformed into

“development corridors” in the last five years.

Finally, road linkages between north and south of Mozambique are difficult due to road
access problems. Both in a within province or in a inter-province context, nearly all the
maize trade from the producer to the deficit areas is done via roadways, but the poor
maintenance of the rural roads and the only road linking north to South leads to
considerable transportation problems. According to Tschirley and Santos (1998), in 1997
the margin of transport and handling cost as percent of the selling price was between 31%
and 34% from producer areas within Nampula province into Nampula city, and 38% fi'om

northern Zambezia to Nampula city. In turn, transporting product from the area of

26

Chirnoio in Manica province to Maputo represented a margin of 37% of the retail price in
Maputo. If maize trades occur between northern and southern Mozambique, these margin

can probably double due to the difficult road linkages between these two regions.

2.5.2 Instability of Returns and High Costs of Storage

Participants in the maize marketing channel in Mozambique face the problem of unstable
returns to storage. This directly affects primarily large traders and farmers. Because
returns to storage are uncertain, there is difliculty in the organization and consolidation of
a storage sector in the maize marketing channel. Three immediate consequences result
from this. First, large-scale wholesalers, who buy large quantities of maize grain usually
for exporting purposes, have their own storage infrastructures and assume individually the
risk of storing the product for an undetermined period if the market is uncertain. Second,
producers sufi‘er the consequences of this situation in that the lack of export or domestic
market implies uncertainty about sales in the subsequent seasons. Likewise, most
producers store their product in household-owned rudimentary storage infi'astructures,
hence they individually assume the risk associated with the volume stored, and experience
lack of market. Finally, small-scale assembler/wholesalers face extremely high storage
costs, and therefore do not engage in this function. Grain prices in retail markets therefore

show pronounced seasonal price swings.2

 

2

There is no available data series on storage cost for maize in Mozambique. However, the available
data on storage cost indicate that informal wholesalers both in Nampula and Maputo face extremely
high storage costs. For instance, in December 2000 the monthly storage cost of 428 Metical per
_ kilogram both in Nampula and Maputo represented a margin of 27% of the retail price for Nampula

27

2.5.3 Uncertainty About Market Opportunities

Uncertainty about market opportunities directly affects primarily farmers and large-scale
grain wholesalers. This problem is directly linked to that of instability of returns to
storage, and has two main consequences. First, there are no incentives to buy
considerable quantities from farmers unless a known market exists. Second, there exists a
disincentive to producers. The supply channel does not work properly. Most large-scale
traders are not willing to specialize in trading this product, and producers are uncertain

about the market, which leads to disincentives in production.

2.5.4 Limited Access to Working Capital

Participants in the maize subsector in Mozambique face the problem of limited access to
working capital. This afl’ects primarily small-scale wholesalers and retailers linking surplus
to deficit areas in the country. Limited access to working capital leads to high unit costs,
in that if traders do not have enough operating capital they cannot buy considerable

quantities of maize grain, and as a result, unit costs are very high.

2.5.5 Low Farm Yields
Farm yields in Mozambique’s maize subsector are very low even when compared to
southern Afiican average levels. This primarily afl‘ects both farmers and consumers. For

farmers, low yields lead to low returns to inputs, time and capital, and consequently low

 

and 17% for Maputo traders. lathe sameperiod, thepurchasingprice represented 71%ofthe selling
price for Nampula traders and 44% for Maputo traders.

28

household income. To consumers, low yields at the farm level imply high prices. This
happens for two reasons. First, the lower the quantity produced, the higher the price they
will face given inelastic demand. Second, low yields at the farm level imply higher unit

costs for traders.3

2.5.6 InelTiciency in the Small-Scale Milling Industry

lnefficiency in the small-scale milling industry has an impact on the price difl‘erential
between maize grain and maize flour especially in niral areas. Areas with lower density of
small-scale custom millers experience higher difl'erence between price of maize grain and

price of maize flour. More discussion on this problem is addressed in section 2.6.2.

2.6 Indicators of Performance in the Maize Subsector in Mozambique
Agricultural economists argue that the performance of a given industry or strbsector is
measured in several ways. According to Jesse (1978), many industrial organization
economists state that measures of performance require the use of standards to which
observed values should be compared. However, as Jesse underlines, it has often been

dificult to find consensus regarding such standards.

 

3

Highunitcostsfacedbytraders (andconsequentlybyconsumers)whenfannyieldsareloweanbe
explainedatleastintwoways. First, tradersneedmoretimetoaccumulateminimumquantitiesof
product necessary to ensure profitability. Second, when yields at farm level are low, full capacity of
transport may not be used, leading to high unit transport costs, and consequently, higher price to
consumers, afl‘ecting the subsector as a whole.

29

In evaluating performance in the maize subsector in Mozambique, the present section
examines the index of availability of maize grain and maize flour in markets, marketing
margins between prices of maize grain and maize meal, coordination of maize prices
between related producer and consumer markets, and price stability over time. These

measures of performance are not compared to any standard levels.

2.6.1 Index of Availability of Maize Grain and Maize Flour
Table 2.1 shows that product availability follows the same pattern throughout the country.
First, it shows that a high index of availability of a given product in the cities of Maputo

and Nampula corresponds to a high index of availability in the corresponding regions.‘

Second, (i) in all regions, domestic maize grain, hand processed maize flour, and whole
maize flour processed in small-scale custom mills are the products with the highest
availability index; (ii) industrially processed (refined) domestic maize flour and industrially
processed imported maize flour have a relatively higher availability index in southern
Mozambique, but a lower availability index in northern Mozambique; and (iii) imported
maize grain has a very small availability index in the whole country. The greater

availability of imported meal in the south is clear in the numbers.

 

4

Inthisresearch,theindexofavai1abilityofacomrnodityinmarkets isdefinedasthepereentageof
weeks in which the product was available in the market. Maize prices in Mozambique are collected
weekly. Table 1 shows, for instance, that maize grain was available in Maputo 99.8 percent of the
weeks between November 1992 and May 1999. Hence, the index of availability of maize grain in
Maputo was 99.8 percent in the period.

30

The index of availability of products is important in the sense that the higher the index of
availability of a given product, the better the access of consumers to the product, which
indicates that there are good levels of production. Also, when the index is similar
throughout the country, the whole system is functioning well. The product availability
index can be improved by reducing problems in transport and by ensuring better
infrastructure investment throughout the system. A recent major investment in a large-
scale maize milling unit in Nampula should improve the availability of refined meal in the

north while simultaneously providing a more stable source demand for northern farmers.

Table 2.1 Index of Availability of Product in Consumer Markets in Mozambique, 1992 -
1999

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

City/Region Percentage of Weeks Products Were Available
Grain Grain Refined Refined Hand Whole
(domestic) (imported) meal meal Processed meal
(domestiC) (imputed) meal
Northern Mozambique
Nampula 99.4 I 5.6 I 1.2 I 1.2 I 100.0 I998
All northern markets 90.3 I 0.9 I 0.9 I 4.2 I 62.7 I 99.0
Southern Mozambique ’
Maputo 99.8 I 8.1 56.5 I 89.6 I85.6 I 87.6
All southern markets 98.0 I 3.4 34.0 I 38.8 J 53.0 I 82.0

 

 

 

2.6.2 Marketing Margin Between Price of Maize Grain and Maize Flour
Table 2.2 shows that the marketing margins between real prices of maize grain and maize

flour at the retail markets in Mozambique followed different patterns over the period of

31

study. While in the north they increased slightly between 1993 and 1996 and decreased in
1999, in the south they tended to decrease fiom 1993 to 1996 and become stationary from
1996 onward. The path of the prices of maize grain and maize flour in the two regions
was not the same. In the south (Maputo), while real prices of maize grain decreased
between 1993 and 1999, maize meal prices did not decrease. In the north (Nampula), on

the other hand, both prices (maize grain and maize meal) tended to maintain over time.

Table 2.2. Average Annual Real Prices of Maize Grain and Whole Maize Flour in
Selected Retail Markets in Mozambique, 1993, 1996 and 1999 May1999 = 100)

 

 

 

 

 

 

 

 

 

 

 

 

 

Local Year Price of Price of Marketing Percentage
Maize Grain Maize Flour ‘ Margin 2 Margin
Maputo 1993 4028 4515 487 12.09
1996 3237 4440 1203 37.16
1999 3185 4531 1346 42.26
Nampula 1993 225 1 473 1 2480 1 10. 17
1996 1756 4204 2448 139.41
1999 2834 4892 2058 72.62

 

 

1 The data refers to whole maize meal processed in small-scale mills. Table 1 showed that this is
the quality of maize flour more widely available in Mozambique in both time and space
dimensions.

2 Refers to the marketing margin defined as the absolute difference between the price of whole
maizemealandthepriceofmaizegrain.

Table 2.2 also shows that the marketing margin is higher in Nampula than in Maputo.
This evolution of the maize marketing margins suggests the existence of problems in the

small-scale milling industry in the country. A very high level of marketing margin may

suggest a lack of competitiveness in the small-scale industry. This problem may be worse

32

in the center/north than in the south, and in the rural areas compared to the urban areas.
Finally, the high marketing margins in the south may suggest that prices paid for milling
maize grain is increasing in this region, which may indicate the need for new investments

in the small-scale milling industry.

2.6.3 Price coordination and stability

The evolution of retail maize prices in Nampula and Mocuba, and in Maputo and Manica
is graphically shown in Figures 4.1 and 4.2 respectively. These graphs indicate that real
retail prices in the two pairs of markets are highly correlated over time. Over the period,
prices in the producer districts of Manica and Mocuba are lower than those observed in
the consumer markets of Maputo and Nampula, a pattern that did not substantially change
over time, and reflects that Maputo and Nampula are supplied with maize grain fi'om
Manica and Mocuba. Also, Figures 4.1. and 4.2. suggest that prices follow a consistent
pattern of seasonal variations over time. For instance, nominal prices in Maputo increased
about 70% from March to November 1998, and decreased about 50% from November

1998 to March 1999. Similar levels of variations were observed in Manica.

However, although seasonal variations of prices Should be expected and are a sign of the
abundance or scarcity of the product in the different areas of the country, it should not be
very high. High price instability discourages producers for new investments in the sector
as a result of price uncertainty, and it does not benefit consumers not only when prices are

high but also because of budget planning problems.

33

2.7 Conclusions

The main conclusion of this chapter is that Mozambique’s maize marketing channel faces
coordination problems, which are reflected in the performance of the sector. However,
regardless of these coordination problems, most retail markets have a high level of product
availability and there is some level of product diversity, even though this varies across
regions. Moreover, marketing maize in Mozambique fi'om the producer to the consumer
areas depends upon the season, geographic location, the availability and cost of transport
and storing infrastructures, and the size of the harvest, both within the country and in the

neighboring countries.

Better decisions by farmers and other participants about the maize subsector in
Mozambique on when and where to sell maize, when and how to store, and whom to sell
to and at what price, depend on better investments in agricultural sector in particular and
in the rural economy in general. Roads and other infi'astructures are particularly important

to overcome the basic problems currently faced by the subsector.

34

Chapter 3

THEORETICAL FRAMEWORK AND METHODOLOGY

3.1 Introduction

A fOrecast is defined as a qualitative or quantitative estimate about the likelihood of future
events based on current and past information (Pindyck and Rubenfeld 1991, Aldridge
1999). The importance of price forecasting lies in the fact that prices play an important
role in guiding both production and consumption. The future is always uncertain, and
uncertainty in filture outcomes that results from present decisions can be reduced if
accurate forecasts are available. The more accurate the predictions, the greater the ability

that decision makers have in making appropriate and timely decisions (Holden 1990).

This chapter is organized as follows. Section 3 .2 reviews forecasting techniques, with an
emphasis on the quantitative techniques. Section 3 .3 addresses the theory behind
univariate time-series models, and section 3.4 discusses multivariate models. Section 3.5
presents a discussion on the methodology of time series analysis. Section 3.6 addresses
the issue of statistical and economic evaluation of forecasting accuracy, and section 3.7

presents the univariate and multivariate models to be estimated.

3.2 Forecasting Techniques
A conservative definition would conceptualize forecasting as a set of tools which allow ex

ante predictions of values of certain variables, outside the available sample of data,

35

typically for firture dates. However, in addition to ex ante predictions, there is also ex post
forecasting. ln ex post or in-sample forecasting, observations on both the endogenous and
exogenous variables are known with certainty during the forecast period. Ex post
forecasting is useful for the purpose of selecting, among different forecasting models, the
best fit of historical data, by comparing the observed with the predicted values over the
data period. On the other hand, ex ante or out-of-sample forecasting is a prediction of
values beyond the period covered by the observed data, and it is the most important

evaluation of the forecast accuracy of a model.

Forecasting can be qualitative, also known as subjective or implicit, or quantitative, also
called model-based or explicit. Qualitative forecasting is not based on quantitative
methods. Instead, predictions are made by difl‘erent expert individuals and/or institutions
based on their wisdom and experience regarding the structure of the industry, seasonal
production, consumption patterns, and international events that are likely to afi‘ect the
commodity. On the other hand, quantitative or model-based forecasts are based on

quantitative data analysis methods.

Qualitative models are often better for long-term forecasts than quantitative technique are,
because in the long term the structure of the economy tends to change, the data
generating mechanism might also be different, and historical data might not sumce or may
induce errors when performing a long-term forecasting (Aldridge, 1999). On the other

hand, although both the qualitative and the quantitative methods are used for forecasting,

36

quantitative forecasting is preferred when consistent data is available, and is commonly
used for short-term predictions. The results from a quantitative model, however, may be
subject to qualitative evaluations. Both forecasting methods incorporate information from

similar data sources.

In modeling maize prices in Mozambique, this research uses quantitative methods and
focuses on Short term forecasting. There are two quantitative forecasting methods: causal
or structural and non-causal. The casual method measures the structural relationships
between variables using econometric techniques, and the non-casual technique is based on
the evolution of the variable or variables to be analyzed with no concern about causal

relationships.

Causal or structural models are based on the study of the structural relationship between
variables, and appropriate economic theory has to be employed in the model building
process. The aim is to explain the behavior of the endogenous variable based on the level
and statistical significance of the parameters of the regression model. A linear single-
equation structural model with It explanatory variables explaining the variations in the

endogenous variable takes the form:

pi=B0+le1t+BZXZI+ +kah+et (1)

37

Ifthe results of the regression model are in accordance with economic theory, and are
statistically significant, then the estimated parameters are used to predict the future
behavior of the endogenous variable, based on a set of assumptions about the future
behavior of the explanatory variables, and assuming that the relationship between the

variables will continue.

As in all econometric models, building structural models for forecasting purposes implies a
careful selection of the explanatory variables according to economic theory, requires using
economic theory to formulate hypotheses on the signs of the parameters of the different
variables, finding data on the variables in the model, estimating the parameters in
accordance with appropriate econometric techniques, examining the model residuals
especially for serial correlations and heteroscedasticity, examining the validity of the
parameters based on the hypothesis previously formulated, and testing their statistical

significance for purposes of extrapolation into the future.

One important advantage of structural models is that, because they are based on economic
theory and identify the relationship between variables interacting in the price generating
process, they may allow decision makers to evaluate the impact of different alternative
policies. However, often there is lack of strong knowledge of the underlying economic
structure or the required data for a structural model is not available. Furthermore,
structural models are often complex, and require more data and time to build than non-

causal models, therefore they are more costly (Donovan 1996; Aldridge, 1999). For their

38

relative simplicity both in data requirements and modeling, non-causal models may be

preferred.

Non-causal models are grouped into two categories: univariate and multivariate models.
Univariate models have only One variable - the variable object of the analysis - and

multivariate models have more than one time-series variable in the model.

3.3 Univariate Models

The most common univariate forecasting techniques that are used to predict time series
data are the naive, the random walk models, trend extrapolation models, smoothing
models, and autoregressive integrated moving average (ARIMA) models, also known as

Box-Jenkins models. Each will be addressed in turns.

3.3.1 Naive and Random Walk Models

Naive models are the simplest form of time series econometric models. Building time
series econometric models is based on the theory of linear stochastic difl‘erence equations,
in which the difi‘erence equation describes the value of a variable as a function of its own
lagged observations, exogenous variables and a disturbance term (Enders 1995, Aldridge

1999). The naive model then is:

fit = pH (2)

where p, is a forecast of p, conditional on information available at time t-I. This would

imply a model for p, of the form:

39

i3. = pm + e. (3)
where the stochastic term e| is white noise.

The most important advantage of the random walk model is that it requires only a small
amount of data and no parameter estimation. The only information needed is the current
value of the variable. Moreover, because random walk models are stochastic, a standard
error of forecast can be computed, which allows forecast confidence intervals to be

constructed, if more .

3.3.2 Trend Extrapolation Models

Econometric trend models express the variable p, as a function of time, and are particularly
useful when the parameters describing the time series do not change over time, and when
the time series data tends to consistently follow a movement in a particular direction,
upwards or downwards. In the trend extrapolation methodology we can have linear or
nonlinear models. The type of trend observed in past values is projected into the future,
and one among several polynomial functions of time is estimated using regression methods

or by forming moving averages of the time series (Aldridge 1999).

The most widely employed trend extrapolation models are the linear trend, exponential
growth curve, and the quadratic, the autoregressive and the logarithmic curves. The model

to be employed depends upon the forecaster’s beliefs about the future evolution of the

40

variable which is object of the study. One noteworthy disadvantage of the trend
extrapolation models is that they often have large standard errors compared to some other
non-causal forecasting models, and thus they only tend to be used as a quick and

inexpensive way of formulating initial forecasts. .

3.3.3 Exponential Smoothing Models

The exponential smoothing technique is a method that gives more weight to the more
recent observations based on the use of a single or multiple smoothing parameters that are
determined by smoothing equations. Like all time series forecasting techniques, there is
no economic theory or statistical model supporting the exponential smoothing method. On
the contrary, it is a simple technique of adaptive forecasting where the forecasts adjust

based on past forecast errors of the type:
pH] = pt + Get (4)

where p,,, is the forecast price for period H I, based on p, forecast price for period t and

a, the smoothing or adjustment parameter. e, is the forecast error in period t.
In practice, using the smoothing technique, past forecast errors are used to correct the

next forecasts by adjusting them in a direction opposite to that of the past error

(Makridakis 1978, Aldridge 1999).

41

An advantage of smoothing techniques is that they do not require a large amount of time
series data, and are especially effective when the parameters describing the data change
slowly over time (Bowerman 1993, Aldridge 1999). However, smoothing models are
only suitable for one-step ahead forecasts, being less accurate when longer periods have to

be included.

3.3.4 ARIMA Models

ARIMA models have been found to give good forecasts in a wide variety of situations
and hence are one of the most popular forms of linear models which describe the data
generating mechanism with no resource to structural models. They were popularized by
Box and Jenkins, and as result they are also known as Box-Jenkins models. ARIMA
models explain the movement of a time series by relating its present values to its own past
observed values and/or to a weighed sum of the current and lagged random disturbances

(Aldridge, 1999).

ARIMA models are estimated under the assumption that many time series are generated
follOwing either an autoregressive (AR) process, a moving average (MA) process, or

some combinations of the two (ARMA) processes.

In an AR process current observations are assumed to have been generated by a weighed
average of past observations. An autoregressive process lagged up to length p is

represented as:

42

p. = 11 + «that + $29.2 + + ¢.p..+ 6. (5)

Likewise, in a MA process present observations of the variable are assumed to be
generated following a random disturbance pattern. A moving average process of a
weighed average of random disturbances going back q periods MA(q) is simply a linear

combination of white noise error terms, and is presented as:

Pt = l1 + 5t " Gigi-1 ' 925:4 ' ' eqei-q (6)

When the two components are present simultaneously in the time series data generating

process, as often happens, the ARMA (p, q) process is represented as:

p. = u + that + ¢2Pt-2 + + dim... + e. - 916... - 628.2 - - 9.6... (7)

where the auto-regressive component is the difference equation, and the moving average

component is the white noise process.

In building AR, MA or ARMA models we assume that the underlying random process that
generated the time series is stationary. However, in many time-series the processes are
non-stationary, thus difi‘erences have to be taken in order to eliminate unit roots and

transform them into stationary processes. The differences can be presented as:

43

wt = Apr: pt ' pt-l (8)

After the difi‘erences have been taken, the processes become ARlMA(p,d q), i.e.,
autoregressive integrated moving average processes, where I(d) denotes the number of
difi‘erences that were taken fi'om the original data until the time series became stationary.

The following equation represents an ARIMA (p, 1, q) model:
w'= O+¢1WH + ... +¢wa+£"ele‘,l ' ... -Oq€‘_q (9)

3.3.4.1 Identifying ARIMA Models

The identification procedures employed in the specification of the data generating
mechanism of ARIMA models involve examining the properties of the autocorrelation
functions (ACF) and partial autocorrelation coefficients (PAC) of the time series. The
autocorrelation functions are a sequence of correlation coefficients, where at each period
we have the correlation coeficient of the current value of the series with the series lagged
that number of periods. The partial autocorrelations at each point in time measure the
additional (or partial) predictive power of the series at that period after taking into

account the cumulative predictive power of all the values of the series with smaller lags.

In examining the ACF and the PAC, we have to to decide the number of AR, MA and
integration terms to include in the ARIMA model. Plotting the ACF and the PAC is a

simple way to examine the kind of data generating process that the time series follows.

44

The shape of both the ACF and the PAC suggests the for of the model. Ifthe ACF
declines geometrically and the PAC is zero after I: lags, then we have an AR(k) process.
Likewise, if the ACF were zero after low It lags and the PAC declined smoothly at a
geometric rate, a MA(k) model would appear appropriate. lfneither ACF nor PAC
converge to zero, we have to try a lower order ARMA model following the parsimonious
principle, i.e., starting from ARMA (1,1). If both the ACF and the PAC cut ofl‘
immediately, it is a white noise or purely random process, also known as an identically
independently distributed (iid) process with mean zero and constant variance. Finally, if
the ACF appears to have a seasonal fi'equency of spikes or cyclical “waves”, this could

suggest the existence of seasonality in the ARIMA model.

Plotting the ACF and PAC also suggests other characteristics of the time series data. For
instance, if the ACF and the PAC are very close to 1 at the first lag, and the ACF tends to
be a straight line instead of decaying geometrically, it might suggest that the time series is
stationary.

Finally, it should be noted that, in identifying the most suitable ARIMA model, the goal is
to have a final model that is a parsimonious representation of the data generating
mechanism. Hence, only the strictly necessary AR and MA terms should be included in
the model. Furthermore, the innovations of the tentative ARIMA model should be
checked for the existence of any serial correlations at every stage of the identification
procedure. A common way of testing for serial correlations in the innovations is

implementing Ljung-Box Q-Statistics tests.

45

3.4 Multivariate Models

In addition to the univariate forecasting models, multivariate models are also employed in
forecasting Among different multivariate, non-causal forecasting models, the vector
autoregression (VAR) and the vector error correction (VEC) models are the most
commonly used. VAR models result fi'om an extension of the univariate time series Box-

Jenkins methodology.

VAR models are built when the time series involved are not cointegrated. Ifthe two or
more nonstationary time series involved in the model are cointegrated, then the VAR
should be specified with error correction terms, and estimated as VEC models (see section
3.4.2). If the series are not cointegrated, then the system of nonstationary variables is run

in first differences (Aldridge 1999).’

3.4.1 VAR Models

The VAR is a multivariate time series technique is focused on the study of the degree of
association of two or more interrelated time series variables. VAR models can be viewed
as reduced-form equations for structural systems, particularly useful when time series data

is available for a multivariate model, but knowledge of the underlying economic structure

 

5

Cointegration is a concept often referred to in time series analysis involving more than one variable.
EngleandGranger(1987) indicatedthattwoormorenonstationarytime series mighthaveastationary
linearcombination, andthetwoormore nonstationarytimeseries are saidto becointegrated ifthis
stationary linear combination exists. A detailed discussion of cointegration can be seen in section
3.4.4.

46

is uncertain and therefore it might be difficult to conceptualize a structural relationship
between the variables (Sims 1980; Fackler 1988; Myers, Piggott and Tomek 1990,

Donovan 1996).

Although the variables in a VAR model are interrelated, there is no concern about any
causality relationship between the variables nor about an economic theory supporting the
structural relationship between the variables. VAR models are, therefore, non-structural
models which explain the dynamic structure of the data generating mechanism assuming
that the variables in the system follow an underlying relationship that does not change
through time. The VARS are, therefore, processes for which there is no concern about the
distinction between dependent and explanatory variables, and thus economic theory and
identifying restrictions are not necessary. In the model building process, it is necessary

only to identify and specify the variables that are assumed to interact.

Regardless of the non-structural relationship between the variables included in VAR
models, these models have been criticized for interpreting statistical parameters as
representing economic relationships, without knowledge of the price formation process
(Harris 1979, Donovan 1996). AS Faminow and Benson (1990) suggest, it is important to
know the underlying market structure when determining which prices - across markets or
across products - to select on the basis of what the statistical parameters can reveal. It is

important to evaluate whether or not the markets are competitive in price setting process,

47

and on the basis of this knowledge determine the appropriate models for price analysis

(Donovan 1996).

VAR models express variables as linear functions of the lagged values of each variable and
all other variables in the system. The standard VAR reduced-form equation is described

as:

Pt = 5 T ‘PrPt-l +‘l’zpt-z + + ‘Pth-p + ext + 3h (10)

where p, is a vector ofk variables and p-lagged values of p,, x, is a vector of variables such
as deterministic trends and seasonal dummies, 6 are the intercepts, (p and 0 are
unrestricted matrices of coeflicients to be estimated, and e, is a vector of individually

serially uncorrelated innovations with zero means and constant variances.

The statistical importance of the VAR models is that, being descriptions of the dynamic
interrelations between different time series variables in a vector, these descriptions can be

extrapolated into the future and used for forecasting purposes (Aldridge 1999).

A taro-variable VAR model with one lag, VAR(1), can be represented as follows:

Pit = 6l + (PllPr.t-r + ‘Plszt-l + 3n (11)

P2: = 62 + (lePl.t-l + ‘Pzszt-l + 5n (12)

48

While structural models have been found important for purposes of policy analysis and
evaluation of relationships in commodity prices, VAR models have traditionally been used
for forecasting systems of interrelated variables. In many cases, forecasts obtained from
VAR models are better than those extrapolated from more complex structural models
(Sims 1986, Donovan 1996, Aldridge 1999). In addition to avoiding the restriction
problem that characterizes identifying structural models, VAR models are simpler and less
costly than structural models. Usually, prior to the estimation of VAR models all
deterministic trends and seasonal components are removed from the series or trend and

seasonal variables are included directly in the VAR model (Donovan 1996).

Identification of VARS has been a source of considerable controversy. Early analysis
focused on using assumptions regarding the contemporaneous relationship between
variables to identify the system. More recent efforts by Blanchard and Quah (1989),
Lastrapes (1992), and others use information on the long-run effects and the infinite
moving average representation of the VAR to impose identifying restrictions on the
system. When there are nonstationary series and the possibility of cointegrating

relationships, the use of long-run identifying restrictions is key.

3.4.2 VEC Models
Ifin testing for cointegration among the variables involved in a multivariate model the
results indicate that the variables are nonstationary and cointegrated, then there exists an

error correction representation such that the differences respond to the previous period’s

49

deviation from long-run equilibrium (Aldridge 1999). As a result, estimating the
nonstationary prices as a VAR in first difi‘erences is inappropriate and results in a
misspecification error. Ifthe prices are cointegrated, then we should use VEC instead of

VAR.

VEC models are restricted VAR models that have cointegration 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, Aldridge 1999).

3.5 Methodology in Time Series Analysis

The basic steps in analyzing time series data involve investigating stationarity, testing for
the existence of a trend component in the time series, testing for cointegration when more
than one time series data is involved in the model, testing for autocorrelation and

heteroscedasticity in the error terms, and investigating seasonality.

3.5.1 Unit Root Tests

Testing for a unit root or nonstationarity is one of the most important steps in time series
data analysis. The data may be stationary around a constant mean, or it can be trend
stationary. The data is said to be stationary around a mean when there is no statistical
evidence that it grows with a trend component and it is stationary, and it is said to be trend

stationary when there is statistical evidence of the presence of a trend component and the

50

data is stationary after we account for the trend component. If the trend component is not
significant in the series, we test for a unit root assuming the null of a unit root without
drift against the alternative of stationarity around a constant mean. On the other hand, if
the trend is statistically Significant, we include the trend component and we test the null of

a unit root with drift against the alternative of trend stationarity.

Price data is said to be stationary if it has a constant mean over time, the variance is time
invariant, and the covariance between prices at different lags, say p, and pH, is always the
same, depending solely on the lag length j. Ifthe time series is stationary, then the sample
mean, variance and autocorrelations can be used to estimate the parameters of the
underlying data generating mechanism, and the model can be used to forecast the time
path of prices and future values of the variable. The starting point in building ARIMA
models is to test for stationarity to determine whether first differences Should be taken to
eliminate unit roots in the time series or if the model should be built using levels in the data

(Aldridge 1999).

A first-order autoregressive model is stationary if the absolute value of the parameter of

the lagged observation is smaller than 1, i.e., if |p| < 1 in:

pt=5+ppct+€o (13)

51

If the original data has a unit root, it is said to be nonstationary, and first difl‘erences have
to be taken to induce stationarity. I
There are three primary reasons for wanting to know whether the series contains a unit
roots. First, because in the presence of unit roots, the usual central limit theorem that
underlines the asymptotic standard normal distribution for the t-statistic does not apply,
the t-statistic does not have an approximate standard normal distribution even in large
sample sizes, and therefore we cannot make statistical inferences about regression model

parameters using the t and F statistics in the usual way‘ (Wooldridge, 2000).

Second, many time series may have time trends or seasonality and therefore regressing one
series on other might show high R2 and significant t-statistics even if they follow
independent data generating mechanisms. Testing the variables for a unit root might help
examine whether different variables are driven by the same data generating process, and

avoid spurious regressions.

Finally, in many works involving time series data, people often want to perform
sophisticated analysis such as testing whether two or more series are cointegrated or not.
Such analysis cannot be performed if we do not know the order of integration of the

variables.

 

6

The most well-known central limit theorem for time series data requires stationarity. The central limit

theorem states that the average fiom a random sample for any population (with finite variance), when
standardized, has an asymptotic standard normal distribution, i.e., the distribution of the estimator is
collapsing around the parameter as the sample size gets large (Wooldridge, 2000).

52

Testing for stationarity is carried out using the Dickey-Fuller and/or the Phillips-Perron
tests. Even though both are aimed at dealing with the potential existence of serially
correlated residuals, they are found to have different features. While the Dickey-Fuller
method is focused on allowing for the explicit presence of serial correlation in the models,
the Phillips-Perron method adjusts the test statistics but allows the disturbances of the
regression models in the procedure to be weakly dependent and heterogeneously
distributed (Lai 1999), and uses nonparametric methods of controlling for higher-order
correlations in a, to make corrections to the t-statistic of the coefficient from the AR(1)

regression (EVIEWS 3, 1998).

The Phillips-Perron method has been found to be simple and broadly applicable, and
therefore widely used. Nonetheless, it has also been demonstrated that this method sufl‘ers
from severe size distortions when there are negative moving average errors (Phillips and
Perron 1987; DeJong et al. 1992). On the other hand, in addition to easy implementation
and interpretation, the Dickey-Fuller tests are thought to be more usefirl for practical

purposes (DeJong et al. 1992; Perron and Ng 1996).

This research uses the Dickey-Fuller approach in testing for unit root. Formally, the
Dickey-Fuller test for unit root is performed under the null of Ho: p = 1 in (13), that is, the
time series has unit root, against the alternative of H,: p < 1, i.e., the time series is

stationary. In practice, however, the Dickey-Fuller test for unit root is carried out by

53

estimating an equation in which p,,l is subtracted from both sides of the equation (13), and

this results in:
p. - pm = 5 + 0 pm - pm + at, (14)
which is equal to
p. - pm = 5 + (p—1)p..t + 6.. (15)
which is equal to
Ap, = 6 + <1)p,_l + e, (16)

where 11> = p-l, and thus we test the null that H,: <I>=0, i.e., the time series contains unit

root, against the alternative that H,: d><0, i.e., the time series is stationary’.

The Dickey-Fuller test is applied solely in AR(1) models. Ifthe innovations from the
Dickey-Fuller test are found to be serially correlated, we implement the Augumented
Dickey-Fuller (ADF) test to control for higher-order serial correlations in the innovations.
The ADF test consists of adding lagged difi'erence terms of the dependent variable to the
right-hand side of the AR(1) regression model. The number of lagged first difi’erences
depends on the correction of the serial correlations in the innovations, and it does not
afi‘ect the asymptotic distribution of the t-statistic test on the coeficient 6 (EViews 3,

1998).

 

1

lfp >1, Pt is said to be an explosive series. All explosive time series makes little economic sense,
andtherefore is not allowed under H..

54

3.5.2 Testing for Trend Component

Many time series grow over time, i.e., they contain a time trend. When drawing inferences
on time series data based on the classical tests, we need to determine whether the data
series contains a trend component or not. Often, various time series variables seem to be
correlated solely because they all grow over time, following other, unobserved
phenomena. By including a time trend variable, we can avoid concluding that two or more
variables are related when they in fact are not, and we can avoid trusting in spurious
regressions involving time variables that have a positive or negative trend. A widely used
approach to address the problem of time trend when the data is stationary is to write the

series, say p, as:

Pr = Bo + B1t+ ”to (17)

where u. is independently and identically distributed (lid), with E(u,) = 0 and Var(u,) =
of . In equation (18) B, can be interpreted as the change in P, from one period to the next
due to the time factor, ceteris paribus, and is statistically tested with the null of Ho: B, = 0,
against the two-sided alternative of H, it 0, i.e., there is (either positive or negative) trend.
Ifthere is statistical significance of the existence of a trend component in the time series
variable, we control for it by including a time trend variable in the regression model.

When the data is nonstationary, first difi‘erences must be taken, and the evidence of a time

trend component is tested through the drift term. Ifthe drift term is positive, the expected

55

value of the time series is positively growing over time. A significant positive drift (i.e., a

significant constant in an equation in first differences) means series drift upward over time.

3.5.3 Checking for Seasonality

Seasonality can be defined as any consistent, periodic and natural movements in a time
series that are repeated cyclically at the same phase of the period (Goetz and Weber
1986), and is independent of Other factors affecting the fluctuations of the data over time.
For instance, even though prices of a commodity are constantly affected by several
demand and supply conditions, common sense suggests that, if the commodity is planted
in October/November and harvested in April/May, we should expect that prices would
usually be higher in January than in June or July, ceteris paribus. Commodity market data
often exhibit seasonality. Usually, the higher the fi'equency of the data collection the
higher the probability that the data contains seasonal effects. For instance, time series data
that is observed with high fi'equencies, such as daily, weekly, monthly or quarterly, is very

likely to exhibit seasonality.

Checking for seasonality can be conducted by plotting graphs on the original data and
examining the fiequency of persistent fluctuations. Another way is to use a correlograrn
of the autocorrelations and partial autocorrelations of the time series. Ifthe commodity
has a single marketing season per year - as is the case ofmaize in Mozambique - and the
ACFs show spikes consistently near every 12 observations in monthly data, that may

suggest the existence of a seasonal pattern in the data.

56

In ARIMA models, seasonality can be dealt with in two ways. The first is adjusting the
time series for seasonality, i.e., removing the seasonal factors from it before they are
modeled, and the second is modeling the seasonality. Even though some researchers
prefer to deseasonalyze the data before it is modeled, Enders (1995), Davidson &
Mckinnon (1993), and Aldridge (1999) argue against this approach, and point out that
seasonality and ARIMA coefficients are better identified and estimated when included

jointly in the model.

ARIMA models can be modeled with seasonality by including seasonal dummy variables
or estimating trigonometric-seasonality models. Because of their ability at capturing
periodic fluctuations, trigonometric functions have been used to describe seasonality in
time series. Seasonal dummy variables have also been found to be an effective tool to

capture seasonal patterns

The seasonal pattern of maize grain production in Mozambique suggests that the price
series should be investigated for seasonal patterns. The paper investigates seasonality by
including monthly seasonal dummy variables, due to their simplicity in calculation,
statistical interpretation and economic meaning. In practice, we test for seasonality after
checking for the order of integration. If the series is 1(0), and the data suggests the
presence of a time trend component and seasonality, a time trend is included in equation

(18) and both seasonality and time trend components are checked for at once.

57

plt=B0+Blt+B2dl+B3d2+W+B12dll+ut (18)

where t is the time trend and d1 through d1] are monthly seasonal dummies.

3.5.4 Cointegration and Vector Error Correction (VEC) Models

In a multivariate model, the time series are said to be cointegrated if each series is
stationary after difi‘erences at any order have been taken, say order d, I(d), and some linear
combination of them is stationary with order d-l, I(d-l). Specifically, if two time series,
say p,, and p2, are individually integrated of order 1, 1(1), then in general p,, - B pm is also
an [(1) process regardless of the value of B. However, if the two time series are driven by
the same stochastic trend, then there is a B a 0, such that the linear combination p,, - Bp,
is stationary 1(0). Ifsuch a B exists, we say that p ,, and p,, are cointegrated, and we call B

the cointegration parameter (Wooldridge, 2000).

3.5.4.1 VEC Models
Ifthe variables p ,, and p,, are both [(1) and are not cointegrated, we can estimate the VAR

model:

Aplt = 6i0 + ellApm-l + + elpAPIJ-p + leApzt-i + + YlpépZt-p + Pita (19)

Apr = 620 + 021AM.“ + + eszPht-p + 'YzzApzt-i T + 'szAPzt-p + 112a (20)

and perform the multivariate time series forecasting process using this model.

'58

If, instead, p 1.: and p2,, are both 1(1) and are cointegrated, where the cointegration equation

can be represented as:

pn-u-Bpfst. (21)

then we include the contegration equation (22) in the VAR model, and we form a vector
error correction (VEC) model. For instance, allowing the VAR model represented in
equations (19) and (20) for a single autoregressive lag, and including the cointegration

equation (21), yields the VEC model:

APit = 010 + eilApm-i + TriAchi + Susi-1+ Ht (22)

Apr: ‘3 920 + eziAPr,t-i + YzlAPztr + 52180-1+ lit (23)

which can be rewritten as:

APM = 910 + OIIAPIJJ + YizApzt-l + 811(p1.t-1 " ItI ' BPzt-i) + ”Lt (24)

Ap2,1= 620 + ezlAPi.t-i +122Ap2J-1 + 521031,” ' l1 ' szt-i) T Pat (25) i

In this VEC model, 5,(p,,,,, - Bpm) and 82(p,,,,, - szH) are error correction terms, and the
parameters 5, and 6, measure the speed and the direction of adjustment. This model
allows examining the short-run dynamics, while restricting the long-run behavior of the

endogenous variables to converge to their cointegration relationships.

59

Finally, if the two series are nonstationary and not cointegrated, we forecast using either
univariate ARIMA models or a multivariate VAR model, again on the first differences. To
increase the forecasting robustness, we might use both ARIMA and VAR models, but if
we have to choose one of the models we might prefer a VAR model because of its
advantages. Regardless of their lesser parsimony compared to ARIMA models, VAR
models have been found to do a good job of modeling many related commodity market
series, and are easy to estimate in that although they are multivariate, there is no need to

determine which variables are endogenous and which are exogenous.

3.5.5 Testing for Autocorrelation in the Error Term

Another important step in every analysis involving time series data is testing for
autocorrelation in the error terms of the time series. It is usual in regressions involving
time series that the residuals of a variable are serially correlated overtime. The existence
of serial correlations in the residuals violates the standard assumption of the OLS
regression theory that disturbances are not autocorrelated. Ifthe residuals of a regression
model are autocorrelated, OLS is no longer efficient among linear estimators, standard
errors fi'om OLS models are not correct, and are generally understated, and in presence of
lagged dependent variables on the right-hand side, OLS estimates are biased and

inconsistent.

A common approach in testing for serial correlation in the residuals of models involving

time series data is the examination of the shape of the autocorrelations and partial

60

autocorrelation functions of the residuals, together with the Ljung-Box Q-Statistics. Ifa
model does not have serial correlation in the residuals, a correlogram should indicate that
the autocorrelations and partial autocorrelations are nearly zero at all lags, and all Q-
statistics should be insignificant with large p-values. The null hypothesis in these tests is
that the residuals of the model are not serially correlated, against the alternative that there

is autocorrelation.

3.6 Evaluation of Forecasting Accuracy

By definition, forecasting is a process of predicting future values of a variable. The
confidence given to the predicted values lies on the assumption that the pattern identified
in the time series and described by the model parameters will not change in the fiiture
(Aldridge, 1999). However, because of the stochastic characteristic of the price data
generating process, there is a certain presence of error in every forecasting process
regardless of the technique employed. Therefore, there is a need to evaluate the accuracy

of every forecasting model.

3.6.1 Statistical Criteria

Statistical evaluation of forecasts is possible whenever we have actual values for the
forecast period, either in an in-sample or in an out-of-sample forecasting. However, we
should be especially concerned with the results of statistical evaluation criteria from out-

of-sample forecasts, as forecasting is basically an out-of-sample problem.

61

Uncertainty in the residuals is the major source of the out-of-sample forecasting prediction
eri’ors in time series models. Therefore, even if a model provides a good fit in an in-
sarnple forecasting context, it needs to show a good out-of-sample forecasting
performance, in order to give an idea of what we would have to expect in practice if we

did not yet know the fiiture values of the variable (Wooldridge, 2000).

Several statistical forecast evaluation methods evaluate the sum of the squared residuals.
Residual uncertainty exists because the unknown disturbances in the forecast period,
present in the equation, are replaced by their expected value of zero, while the actual
values are different from zero. The wider the deviation in the individual errors, the larger
the overall error in the forecasts. In time series forecasts, residual uncertainty is explained

by the fact that lagged dependent variables depend upon lagged disturbances.

The statistical criteria most widely used to evaluate and compare competitor forecasting
techniques are the mean square prediction error (MSE), the root mean squared error
(RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE),

Theil’s inequality coefficient (TIC), and the turning point error (TPE).
Ifwe assume that forecast users are risk averse, a loss function such as the mean square

prediction error (MSE) is a convenient method because it penalizes large errors more

heavily. Therefore, it is widely used.

62

By definition, the MSE is the sum of the squared differences between the observed and the
predicted value of the variable at time t, divided by the number of observations in the

sample:

MSE = infer, - p,)2 (26)
t-l

where p, is the actual price at time t, p“, is the predicted price for time t, and n is the number

of observation in sample.

The RMSE and MAE depend upon the scale of the dependent variable and are used as
relative measures to compare alternative models in forecasting the same series. The
decision rule is that the smaller the RMSE, MAE or MAPE, the better the accuracy of the
model in its forecasting ability. The Theil criterion is based on the U-statistic, which
varies fi'om 0 to 1, being equal to 0 when the forecast is exact, and equal to 1 when the

forecasting technique is no better than a naive method.
The TPE is another common evaluation tool, and indicates the ability of a model to predict ‘

changes in direction. This technique is especially used if the forecast user is particularly

concerned with predicting changes in the direction of the time series.

63

3.6.2 Economic Criteria

Agricultural commodity forecasts are made with the aim of helping participants in the"
sector to make better decisions in the production process, for better investment planning
and policy decisions. Yet forecasting models are typically subject only to statistical
evaluation. An implicit assumption in the statistical evaluation of forecasting models is
that the statistical criteria are consistent with, and optimal for, the subsequent use of the
forecast in the decision making process (Aldridge 1999). However, model selection
decisions based solely on the statistical evaluation criteria sometimes are not optimal from
the standpoint of economic decision making, hence there is a need for further evaluation
aimed at examining the extent to which forecast users are able to use the model to make
more profitable decisions (Brandt and Bessler 1983; Parks 1989; Wright et al.1986;
Gerlow 1993; Aldridge 1999). For this purpose, some literature argues that forecasting
models should be chosen in accordance with the preferences of the final users of the
forecast, rather than for their statistical fit. That is, economic evaluation should prevail
over statistical criteria (Brandt and Blessler 1983; Wright et al. 1986; Leitch and Tanner
1991; Gerlow 1993). This literature argues that sometimes forecasting models with poor
statistical performance may be better than those with better statistical accuracy when
evaluated using economic criteria. For example, Gerlow’s (1993) study indicated ARIMA
models have better economic results although their statistical accuracy is poor compared

to structural econometric models.

Results in economic evaluation have suggested that more complex models do a better job
than naive models in allowing profitable decisions in the production process. Aldridge, for
instance, forecasted that the random walk model is dominated by all other strategies in

terms of mean price received and average percent returns.

Usually, economic evaluation criteria are based upon the storage problem, where the
decisions to sell or store under each model are compared to “no model” scenarios. The
profitability of the decisions to sell or store under the difi'erent models’ strategies is
compared along with the “no model” or default strategies by the use of criteria such as the

mean price received, net to storage cost or not, and the percentage of correct decisions.

In evaluating the economic performance of the different forecasting models, this research
uses present value of the gross marginal revenue in addition to the mean price received
criterion and the percentage of correct decisions. The default strategies and three

economic criteria are presented and broadly discussed in chapter 6.

3.7 The Models

In the practice of price forecast modeling, it is usual to use prices at the producer level. In
this study, however, retail prices are used instead of producer prices, because the latter are
not available in a long time series in Mozambique. Also, checking for the correlation
between first difi‘erenced producer and retail prices in Mocuba and Manica for the period

in which both prices are available shows that in Mocuba the coefiicient of correlation is

65

0.867, significant at any conventional significance level. In Manica, the coefficient of
correlation between first difi‘erenced producer and retail prices is 0.918, also significant at
any reasonable significance level. These results suggest that there is a high co-movement
of producer and retail prices in both places, and therefore we could expect that the
forecasted values from our models could be used to infer expected prices at the producer
level. A graphical analysis involving producer and retail prices in Manica and Mocuba

support this idea.

3.7.l~ The ARIMA models for Nampula and Maputo

After taking differences in the price data if necessary, the tentative ARIMA models for
Nampula and Maputo will be specified using the following identification procedures:
First sample autocorrelation coefficients and partial autocorrelation coeficients will be

plotted. Then, using the parsimonious principle, an ARIMA(1,d,1) model of the form:
wt = 5 + q’rwr " 918:4 + at (27)
will be the first tentative model for each time series. The final ARIMA (mdn) models

will be determined according to the values of m, d and n afier the models have been

corrected for autocorrelation in the error term if necessary.

66

3.7.2 VAR Model for Nampula

In addition to the univariate ARIMA model, a VAR or VEC model will be estimated for
maize prices in Nampula city, depending on whether the data follows an 1(0) or an [(1)
process. The estimation of the VAR or VEC model is intended to reflect the fact that the
process generating maize prices in this city in northern Mozambique is strongly affected by
maize exports, especially to Malawi. As stated in chapter 1, about 70 percent of the maize
consumed in Nampula is brought from northern Zambezia, and considerable maize
produced in Nampula and Zambezia province is exported to Malawi. Therefore, there is
reason to expect that both demand for maize in the north of Mozambique and Nampula’s
maize price generating process involves both northern Zambezia prices and Malawian
production estimates, and therefore these variables influence the process of maize price
generation in Nampula city in particular and northern Mozambican in general. A VAR

model with a single autoregressive component for Nampula prices, VAR (1), can be

presented as:
Pit = 51 + ‘Prrppr,t-r + ‘Przpzt-r + Wily-1+ (P14q4.t-l+ 3n (28)
Pa: = 52 + ‘Perm-r + $229244 + (Pucks-1 +¢24Q4.r-l + 52: (29)

where p,, represents maize price in Nampula at time t, pz, represents prices of maize in
Mocuba, northern Zambezia, at time t, q ,, represents actual quantity of maize production
in Mozambique at time t, q” represents actual quantity of maize production in Malawi at

time t, 5, A, and (p are parameters to be estimated, and a, are the impulses.

67

3.7.3 VAR Model for Maputo

Like northern Mozambique, the price generating mechanism in the south of Mozambique
involves some exogenous variables. Most maize consumed in southern Mozambique is
either produced in central Mozambique or imported from South Africa. Therefore, both
prices in central Mozambique and estimates of production in South Africa are important
for the price generation mechanism in southern Mozambique. Maputo’s model will
therefore include both central Mozambique actual prices and predicted maize production

in South Afiica.

Because of its importance as one of the major sources of maize production and trade in
central Mozambique, prices of Manica district are taken as representative of the region. A

VAR (1,0) for Maputo prices is:

p11: 5 + ‘Prer-r + (PIZPZJ-l + 4,13%.“ +‘P14q4.r-t + 3n (30)

Pa = A + ‘Perm-r + ‘Pzzpzt-r +‘P23Q3.t-r +‘P24‘lstt-r + 52: (31)

where p,, represents prices of maize in Maputo at time t, pz, represents prices of maize in
Manica at time t, q,, represents actual maize production in Mozambique at time t, q“
represents predicted maize production in South Afiica at time t; 6, 2., y, and rp are

parameters to be estimated, and a. are the impulses.

68

In both the univariate and the multivariate models, maize prices in each region will be

forecasted out-of-sample. The research used ARMA, ARIMA, VAR and VEC models.

Production variables are used for the following reasons: (i) shocks in prices are expected
to be explained by production fluctuations. A decrease in production in a given
production year is expected to lead to an increase in the prices in the following marketing
year. Hence, production variables are expected to improve the level of predictability of
prices, and explain variations in prices. In addition to data on maize production in
Mozambique, the research uses production data in Malawi and South Africa. Northern
Mozambique is closely related to Malawi, if production in Malawi decreases prices in
northern Mozambique are expected to increase as exports to Malawi are likely to occur.
On the other side, if production in South Afiica decreases, prices in southern Mozambique
are expected to increase as this region considerably depends on imports from South

Africa.

69

Chapter 4

PRELIMINARY DATA ANALYSIS

4.1 Introduction

This research uses data on retail maize prices and volume of maize production to estimate
alternative time series models for forecasting maize prices in Mozambique. This chapter
reviews the characteristics of the price data, and the implications of such characteristics
for the results of the models. The chapter is organized as follows. Section 4.2 describes
the data and data sources. Section 4.3 explains the methods used in dealing with missing
data. Section 4.4 discusses the basic characteristics of the data. Section 4.5 addresses the
deterministic time trend and seasonality issues. Section 4.6 discusses structural shocks in
the data. Section 4.7 discusses on marketing margins between the pairs of markets
involved in the bivariate VAR models, and section 4.8 discusses the implications of the

data characteristics for the model results.

4.2 The Data

The data used in this research includes retail maize price in four Mozambican markets, and
maize production figures in Mozambique, Malawi and South Afiica. The data is monthly,
covering the period fi'om November 1992 to August 2000, and it was obtained fi'om
different sources. The data on maize prices is from the Agricultural Market Information
System (SIMA) in the Ministry of Agriculture and Rural Development of Mozambique.

These price series refer to the markets of Nampula and Mocuba in northern Mozambique,

7O

Manica in central Mozambique and Maputo in the south. In all cases, the prices are
nominal and refer to the most important retail market in the area, in terms of volume of

transactions.

The data on maize production in Mozambique and Malawi is the annual actual production
for 1992 through 1999 and production estimates for 2000, and is from the Southern
Afiican Development Community database. For each country, every annual figure is
repeated for the 12 months of the marketing year, from May to April, to match with the

monthly price data.’

The data on South Africa’s maize production estimates are forecasts from the South
Afiican Estimates National Committee (SAEC), under the Foreign Agriculture Services
(F AS) of the United States Department of Agriculture (USDA). The SAEC does monthly
updates of the agricultural production estimates. Every year, the first forecast estimates
are made either in February or March, and the last estimates are made in August. From
September through January or February, the August estimates are verified and used in the

estimation of the final figure for actual annual production.

 

In the southern African region, the average planting season occurs fi'om September to November, and
theharvestseasonstartsaroundApril. Thus iteanbeconsideredthattbemrketingyearin
Mozambique is fi'om May of one year to April of the following year.

71

All prices are given in Metical per kilogram (sometimes presented as Mt/kg in this
research). Metical is Mozambique’s currency. Figures on maize production are given in

thousands of metric tons. Table 4. 1. presents the summary statistics of the prices.

Table 4.1 Summary Statistics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variablel Mean I Std Dev I Minimum I Maximum

Northern Mozambique 7

Nampula Maize Price 1298 I 741.56 457 3896

Mocuba Maize Price 1111 . I 727.64 243 3215
Southern Mozambique

Maputo Maize Price 2276 I 889.78 695 3866

Manica Maize Price 1288 I 854.06 229 4643
Production Data

Mozambique Maize 836 310.14 133 1196
Production

Malawi Maize Production - 1713 527.47 , 657 2478

South Africa Maize 8405 2,511.63 3683 13906
Production
Number of Observations = 94

 

 

' Price data are nominal prices in Metical per kilogram, and production data is in metric tons.

Table 4.1 shows that the average price in the producer areas of Mocuba and Manica is

lower than that in the consumer areas of Nampula and Maputo respectively. Although

these price difl‘erentials are an important condition for arbitrage activities to take place,

too high a margin between prices in Manica and Maputo could be an indication that

traders face problems in trading the commodity from the exporting market to the

72

 

importing market. One of the weaknesses of Mozambique’s database is the lack of
systematic data on transportation cost, therefore no conclusive ideas can be drawn about

this issue on the basis of the price differentials.

Second, Figures 4.1 and 4.2 suggest that all the time series have a clear seasonal pattern,
where prices are in general higher between October and March and lower fiom April to
September. Also, the presence of some spikes in the series suggests that structural chocks
have affected the normal seasonal pattern in 1995, 1997 and 1998. Indeed, there was
huge drop in production in 1994/95, and large amounts of maize were exported fi'om

northern Mozambique to Malawi in 1997 and 1998.

Third, these Figures suggest that Mozambique’s maize price data should be investigated
for trend, as should be expected with nominal price series. Figures 4.1 and 4.2 suggest
that the rural markets are subject to greater seasonal price swings than are the urban
markets. The lower prices are observed during the harvest season and the higher, in the

planting and growing seasons.

Finally, Table 4.1 indicates that prices in both the rural and the urban areas are higher in
the center/south than in the north. Comparing Graphs 4.1 and 4.2 indicates that prices in
the north are systematically lower than in Manica and Maputo. This pattern reflects the
perpetual surplus conditions in the north, perpetual deficit in the south, and the proximity

of the center to the south, making trade possible and strengthening prices in the center.

73

 

 

 

 

 

 

Figure 4.1 Retail Maize Prices in Nampula and Mocuba, November 1992 - Auggst 2000
4000
3 _ .......................................................................................... ‘0 .....................
' 'i I s
.r ‘ i i
2000 - --------------------------------------------- i-. : --------------------------- I ----------- I --------------------
' . i I pans. I!" I. I o"\
" i " :' i z,
1000 ‘ """""""""""""""""" ;°_" """i‘ """ I """ 1 °°°°°°°°° t, """"""""" I'°°":r"° """"""
“| I ' x’ "J, L
r --‘ t\ I I 'v'
0 .l
93 94 95 96 97 98 99 00
I Nampula ----- Mocuba I

 

 

 

 

Figures 4.1 and 4.2 also show that prior to 1994, maize prices in Mozambique were
relatively stable, suggesting either production stability or poor performance of the
markets. Indeed, prior to October 1992, Mozambique was under a civil war and markets
were nearly isolated from each other. Between 1992 and 1994, the country experienced a
period of transition fiom war to peace and economic stability. For the first time in more
than 10 years, traders started trading agricultural commodities between the producer areas
and the consumer markets. This activity, however, did not become intense and solid until
late 1994 and early 1995, when the first democratic elections were held in the country,

peace and stability took place, and markets started operating more normally.

74

Figure 4.2 Maize Retail Prices in Maputo and Manica, November 1992 - August 2000

 

 

 

 

 

5000
.1
4000 - ----------------------------------------------- fl --------------------------------------------------------------------
l
3000 Jr ----------------------------------------------- I -------------------- fl ---------------------
2000 ................................ {i "I ................. I “I ..... .- ............
{o I: I! \ 'f"\‘] ”if c K
° '-/\\ I ‘s _t‘_o"\\‘ O. \ I, I l'. I
1” "°"° "”"u" u '-’-;j ------- ’ -------------- ‘- Vet ---------- “I! ----------- T ------------ k;)J-----°'-°----‘\;<
I
.".“~ ----------- J
0 .........................................................................................
93 94 95 96 97 98 99 00
I — Maputo ----- Monica I

 

 

 

 

4.3 Missing Data

There were a few missing values in maize prices in some of the markets of study. For
Manica and Nampula, for instance, price data were missing for the first two observations,
which suggests that the data collection in these two markets started Mo months later
compared to Maputo and Mocuba. The missing values were completed using regression
models. For Nampula, a regression of Nampula prices on Mocuba was run and the
estimates used to predict the missing values in the Nampula series. Likewise, Manica
price series was regressed on Beira, the closest major market, and the estimates fi'om this
model were used to fill in the missing values in Manica. This approach was chosen for
two reasons. First, it was not possible to regress retail prices on prices at other

transaction levels either in Nampula or in Manica because the collection of data on other

75

transaction levels started later compared to the retail level. Second, other statistical
approaches such as average prices of the surrounding months were not appropriate

because the missing values were the first observations in the series.

Before the regression models were estimated in order to find the estimates for the missing
values, each one of the time series involved in the regression models was tested for

stationarity and the innovations were checked for serial correlations.

Mocuba had missing values in February and December 1993 and in August 1994. An
examination of the prices immediately before and afier the missing values suggested that
alternative statistical approaches to regressing this price series on another price series
could be followed. In this case, for each month with missing data, a simple average of the
prices of the immediately preceding month and the immediately following month was used
to fill in each missing data point. This procedure was used for two reasons: there was not
a complete series related to Mocuba which could be used to estimate the missing data in
this series, and, a visual inspection indicated a consistent increase or decrease of the prices

surrounding each missing value.

4.4 Characteristic Time Series Properties of Commodity Prices
This section reviews the most important characteristics of maize prices in the country.

Specifically, this analysis involves the stochastic trend or unit root property, and the

property of time—varying volatility.

76

4.4.1 Unit Root or Stochastic Trends

Many commodity price series appear to share several stochastic properties, such as
stochastic trends, price comovement and volatility (Myers 1994). For proper modeling of
the underlying data generating process and a better understanding of the results of the time
series models, it is of critical importance to examine these stochastic properties of time
series data prior to building forecasting models with time series methods. The challenge
then is to estimate time series models that can make efiicient use of the essence of the data

generating process by examining the stochastic properties of the data.

As it has been noted in chapter 3, out-of-sample forecasts obtained from time series
models can be highly divergent over time. These forecast errors can become larger over
time if they contain a stochastic trend - or a unit root - which is not accounted for. As
Myers (1994), and Asche, Bremes and Wessells (1999) noted, several empirical studies of

commodity prices have found evidence of unit roots.

As noted in chapter 3, the Dickey-Fuller, the Augmented Dickey-Fuller and the Phillips-

Perron tests are the most common tests used to test the hypothesis of a stochastic trend.

In this research, Dickey-Fuller tests are used to test for unit roots. When the results reveal
that the innovations are serially correlated, the ADF was performed. The null hypothesis in
these tests, as indicated in chapter 3, is that the data contains a stochastic trend. The

results of the tests for stochastic trend are presented next.

77

4.4.1.1 Unit Root Tests

The Dickey-Fuller and Augmented Dickey-Fuller tests can be carried out with the

inclusion or not of seasonal dummies and a time trend variable. Visual inspections of the

data series used in this research suggests that they could contain seasonality and upward

time trends. The BF tests are then conducted with the inclusion of time trends and

monthly seasonal dummy variables. The number of lags in the DF tests was chosen so that

the highest lag significantly different from zero is included in the test for the levels of the

prices, thus white noise residuals are generated. Table 4.2 presents the results of the DF

tests for unit root for the four maize price series.

Table 4.2 Unit Root Tests for Maize Prices in Mozambique, with trend and seasonal

 

 

 

 

 

 

 

 

dummies
Coeflicient of The Unit Root Test
Levels First Difl‘erences
Northern Mozambique
Nampula -2. 18 -6.3 1
Mocuba -l .74 -6.96
Southren Mozambique
Maputo ‘ -0.77 -4.86
Manica -2.24 -5.48

 

 

 

 

With a critical value at a 5% level of -3.41 (due to the inclusion of a trend variable), Table
4.2 shows that the null hypothesis of nonstationarity cannot be rejected for the price series

in levels, but it is rejected for all the series in first difi‘erences. Hence we conclude that all

78

 

the price series are nonstationary in levels and are integrated of order one, 1(1). In order
to have white noise innovations, lags were added to the DF tests for all the prices series
when testing for unit root in levels. There was no need to add lags in the Nampula and

Mocuba price series when testing for unit root in first differences.9

Recall that structural changes can affect the Dickey-Fuller tests. As Asche, Bremes and
Wessells (1999) noted, a data series with structural change may seem nonstationary if the
structural change is not taken into account, but stationary if it is accounted for. Tests for
structural shocks in the data used in this research, whose results are presented and
discussed in section 4.7, indicate that this data does not contain significant structural

changes.

4.4.2 Time-Varying Volatility

In addition to not having a constant mean, many commodity prices are highly volatile, with
implications to producers and consumers, and to the economy as a whole, especially in
countries where the gross domestic product and exports depend mainly on primary
commodities (Myers 1994). This high volatility may indicate an overall market
inemciency and risk management problems particularly when all the necessary institutions

for a well-firnctioning market are not in place. In addition, volatility of commodity prices

 

Time series literature indicate that Dickey-Fuller tests should be compared to the critical values of -
2.86 (when there is no a time trend variable), or -3.41 (when a time trend component is included inthe
test), at 5% level. Comprehensive Tables with the DF critical values also include 1%, 2.5% and 10%
levels.

79

tends not to be uniform over time. As Myers (1994) noted, several studies have found that
usually, periods of relative tranquility, where small changes in prices are followed by other
small changes, are often followed by periods of high volatility, in which large changes in

prices are followed by other large changes. .

High volatility alone does not imply specific statistical problems. The concern with high
volatility is to understand the reasons behind this problem and how to minimize the
consequences. Advanced methods have been found to deal with the time-varying volatility
problem. Such methods involve the use of the autoregressive conditional
heteroscedasticity (ARCH) models and generalized autoregressive conditional
heteroscedasticity (GARCH) models. Although Mozambique maize price data suggests
the existence of high volatility, visual inspection does not suggest that this volatility is
time-varying. This research does not estimate models with either ARCH or_ GARCH

efi‘ects.

4.5 Deterministic Time Trend and Seasonality

Section 4.4.1 discussed the stochastic trend or unit root problem, and indicated that many
time series of commodity prices contain stochastic trends. However, it did not discuss the
issue of deterministic time trend. Indeed, a special case of a potential violation of the
stationarity assumption is when the data grows with a trend, common in many time series.
Because deterministic trends have a permanent and constant effect in the long term and

lead to trend-stationary time series, while stochastic trends or unit roots lead to

80

continuous changes in the conditional mean or intercept of the forecasts, it is important to

determine whether the trend is deterministic or stochastic.

The nature of trend is examined when the data is tested for unit root. Ifit is found that the
time series is trend stationary, then we are in presence of a deterministic trend, and this
kind of trend can be controlled for by estimating equations with a polynomial trend such as
described in equation (18). If, on the other hand, differences have to be taken in order to
control for the trend component, then we are in presence of a stochastic trend, and the

process is called difi‘erence-stationary.

The tests on the unit root presented in section 4.4 indicated that all the series of price data
used in this research have unit root in levels and are all [(1). When differences of the data

are taken, any linear trend is automatically removed from the series.
Because the tests on the unit root indicated that all the price series used in this research

are I(l), this research tests jointly for drifi and seasonality in each price series, in first

difi‘erences. Table 4.3 has the results of these tests.

81

Table 4.3 Drift and Seasonality in First Difi‘erences in Maize Prices in Mozambique

 

 

 

 

 

 

 

 

Coefficient
Northern Mozamb' e
rqu Driftl F Statistic for Seasonal Dummies
Model F Statistic Critical Value
Nampula 423.17 5.35 Fm ,0, = 2.04
(109.69)
Mocuba 150.92 8.90 Pro. .1) = 2.20
(98.78)
Central/Southren Mozambique
Maputo 172.35 5.26 For. 7., =
(112.18) 1.94
Manica 177.25 3.34 Foam =
(160.05) 1.94

 

 

 

 

 

 

‘Numbers in parenthesis are standard errors

The results in Table 4.3 suggest that Mozambique’s maize prices have a positive but
generally insignificant drift term, and a significant seasonality in the drifi. In fact, at a 5%
level critical value of 1.96, the 1 statistic tests for the drifi terms, fail to reject the null
hypothesis of no drift for Mocuba, Manica and Maputo. Nampula’s price series is the only
one with a significant positive drift at 5% level of significance. Similarly, the tests for the
joint significance of the seasonal dummies indicate that, at the 5% level, there is a '
significant evidence of seasonal growth rates in all the time series. The model F statistics

are higher than the critical values for all the time series.

82

4.6 Structural Shocks

In time series data, it is important to check for data stability if there are reasons to believe
that structural shocks could have afl‘ected the data. Controlling for such structural shocks
is a way to obtain better understanding of the results fi'om the models. A common

approach to control for structural shocks is by applying Chow’s Breakpoint Tests.

In the application of Chow Breakpoint tests, the sample is divided into the number of sub-
samples suggested by the data path. The number of observations in each sub-sample
should be higher than the number of coefficients in the equation being estimated. Dividing
the sample into sub-samples and running Chow Breakpoint tests gives coefficients that are
used to investigate for stability in the data. In practice, the Chow Statistic test for a time .
series with a single breakpoint is run by estimating the sample equation for the two sub-
samples. The coefiicients from the two sub-samples are compared under the null

hypothesis that they are not different. A rejection of the null means that there is structural

shock with a strong impact on the data.

The practical procedure to perform a Chow test for a structural change is based upon the
restricted and the unrestricted models. Summing the squared residuals from the two sub-
samples gives the unrestricted residual sum of squares. The equation is then fitted to the
complete set of sample observations, which yields the restricted residual sum of squares.
An F statistic is calculated as follows: F=[(SSRT-(SSR,+SSR2)]/(SSR,+SSR2)*[n-

2(k+1)]/(k+1), where SSRT is the sum of squared residuals from the whole sample’s

83

equation, SSRl and SSR2 are the sum of squared residuals from sub-samples one and two
respectively, n is the number of observations, and k is the number of explanatory variables.

The null hypothesis is tested by comparing the estimated F statistic to critical F values.

The data is said to be stable if the coefiicient is constant over the sub-samples. Ifthe data
is stable, it can be concluded that the data generating mechanism was the same before and

afier the structural shock.

These sudden changes in the prices may cause difficulties in estimating price prediction
models, especially when using time-series models which do not take into account these
structural changes. Problems in modeling data with these kinds of shocks could be
minimized if more information were available and structural models could be estimated.
However, there is limited availability of consistent historical data on maize in Mozambique
and Malawi. In this research, the existing price data was then used to test for stability by
the use of Chow Breakpoint tests. November 1995 was considered the breakpoint. The
results of the test indicate an F(66, 14) statistic of 1.64, leading to a failure to reject the

null hypothesis of stability at any reasonable critical value.

In southern Mozambique, in turn, prices only had an extraordinarily high increase in 1995
afier the period of stability prior to this date. As pointed out in chapter 1, southern and
central Mozambique are highly linked by comparatively less precarious roads. Because

maize production in central Mozambique has been considerably stable except for 1995,

84

maize supply to southern Mozambique and to the net consumer areas in central

Mozambique has also been stable most of the period of study.

Moreover, because southern Mozambique, especially Maputo, is a considerable
consumption market, if there is a sudden drop in maize supply from central Mozambique,
maize grain or maize flour can be imported from South Afiica and other neighboring
countries. As a result, prices in Maputo are expected to be more stable than those in
northern Mozambique, unless unexpected, strong events occur, like the February/March
2000 floods. Indeed, prices in southern Mozambique increased unexpectedly high in
March and April 2000, against the usual pattern of low prices fiom March through
September every year. With the floods, the southern region of Mozambique was isolated
from the rest of the country for the next two to three months and, because considerable
maize consumed in Maputo is supplied from central Mozambique, this isolation of the
southern portion of Mozambique led to this unusual price spike in March and April in

2000.

This research had intended to run a Chow Breakpoint test to capture this event, but
because the data used in this research goes only through August 2000 - there are only 6
observations between March and August 2000 - this test could not be run. Future
research, however, could be able to capture this event with the Chow Breakpoint test

approach. A Chow Breakpoint for 1995 indicated no evidence of structural shock. Using

85

October 1995 as the breakpoint, an F(62, 16) of .1 .60 was found, with leads to a failure to

reject of the null hypothesis of stability.

4.7 Marketing Margins

When prices of a commodity involve two or more different levels of transaction or two or
more geographically separated markets, one common concern is that of marketing margins
between the levels of prices. This research uses related price time series to estimate

multivariate time series models. As such, the issue of marketing margin is of interest.

Marketing margins can be defined, simply, as the difference in the price of a commodity
between two stages of transaction of the commodity. As Tomek and Robinson (1987)
noted, marketing margin can be viewed either fi'om the perspective of price difl‘erence
between the two stages of production, usually between the producer and final consumer
levels, or from the standpoint of the prices of the marketing services, the most important
of which, from the agricultural commodities point of view, are the costs involved in

packing, transporting, handling and storing the commodities.

Figure 4.3 shows the margins between maize retail prices in Nampula and Mocuba. This
Figure indicates that the margin of maize prices between Nampula and Mocuba is positive
in most of the period (i.e., Nampula prices are generally higher than Mocuba prices).
Prices in Mocuba tended to be less variable before 1995 than from 1995/96 onward. Both

the lowest price ratio of 0.79 and the highest value of 3.2 were observed between 1998

86

and 1999. Also, negative marketing margins between Nampula and Mocuba tend to
occur during the growing months of November, December and January. This pattern is in
accordance with the finding that the seasonal pattern is more accentuated in the rural areas
(Mocuba) compared to the urban areas (Nampula), given that the urban areas have better
storage infiastructure than the rural areas. Furthermore, urban markets are supplied with

product from different origins, and the markets are bigger and more stable.

Figure 4.3 Marketing Margin for Maize Prices, Nampula - Mocuba, Nov 1992 - Aug
2000

 

 

 

~500

 

 

-1000

 

 

 

 

Marketing Margo I

 

 

 

Figure 4.3 also suggests that these marketing margins may have increased over time. A

simple linear regression of the marketing margins on time trend indicates, however, that

87

this positive tendency of the marketing margin is not significant at any reasonable
significance level. The coefficient on the time trend of 0.92, with a 1 statistic of 0.77 after
ensuring that the innovations are white noise suggests that there is no evidence to reject

the null hypothesis of no trend in this marketing margin.

The marketing margin of nominal maize prices between Maputo and Manica is positive
except in January and February of 1996. As explained in section 5.4., a considerable drop
in production took place in Mozambique in 1995, and prices in the producer areas in
northern and central Mozambique increased strongly in late 1995 and early 1996. This
structural shock did not affect southern Mozambique, especially Maputo, where imported
yellow and white maize, either through commercial imports or through food aid programs,

was available.

In the remaining of the period, prices in Manica were higher than those in Maputo
although prices in Manica also tended to have some clearly accentuated seasonal
fluctuations. The long distance between Manica and Maputo that partly explains the high
price difl‘erential between these two markets, is responsible for the systematic positive
marketing margin between the two markets, in addition to Maputo’s better access to

alternative sources of maize supply than other Mozambican markets.

88

Figure 4.4 Marketing Margins for Maize Prices, Maputo - Manica, Nov 1992 - Aug 2000

2500

 

1500

1000

500

 

 

 

 

 

 

 

Marketing Margin J

 

 

 

Furthermore, the marketing margin of maize prices between Maputo and Manica is more
accentuated than that between Nampula and Mocuba, and seems to be increasing. A

linear regression of the marketing margin on time indicates that the coeflicient of 2.93. on
the time variable, with a 1 statistic of 2.01, white noise innovations ensured, is statistically

significant at 5% level.

4.8 Implications of the Characteristics of the Data
When analyzing the results of any modeling based upon time series data, the
characteristics of the data generating process have to be taken into consideration. A first

step is to determine whether the price data is stationary or has unit root. Stationary data is

89

different fi'om nonstationary data in important dimensions. As Gujarati (1995) indicated,
if there is a unit root in the data at any period t, the time series fluctuates not only as a
result of shocks to the transitory component but also to the trend component, altering
permanently their level, and resulting in weak inferences. This chapter has examined the

stochastic trend problem, and it has been found that all the price series have a unit root.

The second concern when using Mozambique’s maize data is related to the presence or
not of a deterministic time trend and seasonality. Because the data series are
nonstationary, this chapter has also investigated for drift and seasonality in first
differences, and has found that there is no evidence of a drift in Mocuba, Maputo and
Manica, but,there is evidence of seasonal drifts in all the time series. Note that a
significant drift in differenced data is equivalent to a positive deterministic trend in levels.
These results suggest that there is a need to include seasonality when modeling maize

prices in Mozambique.

Finally, the three series on production data that are used in addition to the price data have
also been tested for unit root and they all were found to be 1(1). Recall that the initial
interest in this research was to use data on production estimates for the three countries,
but lack of this kind of data for Mozambique and Malawi leads to the use of data on actual

production instead.

90

Chapter 5

ESTIMATION OF THE ALTERNATIVE FORECASTING MODELS

5.1 Introduction

The main objective of this research is to forecast maize prices in Mozambique. In this
chapter, several forecasting models are developed and results presented. In chapter 6,
forecasting performance is compared by the use of statistical and economic criteria. The
unit root tests presented in the previous chapter indicated that maize prices in
Mozambique are 1(1) thus models in first differences should be estimated. In this research,
however, in addition to estimating models in first differences, other models are estimated
in levels, i.e., with no regard to whether the data is stationary or nonstationary, and the
forecasting accuracy of all models is compared. This is a common practice when the final
goal of estimating univariate and multivariate time series models is to perform forecasts.
Even though the distinction between stationary and nonstationary data is crucial for time
series data analysis and inferences, it is not of major importance when the final objective is
short-term forecasting. Because the objective is' forecasting and not hypothesis testing,
the main criterion for model selection should be out of sample forecasting performance,
not the results of unit root tests. For this reason, we examine models both with and
without unit root and cointegration restrictions and compare their out of sample

forecasting performance.

91

This chapter is organized as follows. Section 5.2 presents the specification of the
univariate models, and the forecasts from these models. This discussion is presented by
region, first for northern Mozambique, and then for southern Mozambique. Section 5.3
presents the model estimation and forecasting for multivariate models. Like in section 5.2,
the discussion in this section is organized by region. The estimation of the multivariate
models in section 5.3 is preceded by Cointegration tests. Finally, section 5.4 presents the

conclusions of the chapter.

5.2 ARIMA Model Specifications

For the Nampula and Maputo price series, ARIMA models are estimated and used for a
total of twelve one-step-ahead forecasts. These twelve monthly forecasts are obtained as
follows. First, for each price series, an ARIMA model is estimated for the model
estimation sample of November 1992 through August 1999, and a price for September
1999 is forecasted. Next, the model estimation sample is increased to September 1999,
the ARIMA model is re-estimated, and a price for October is forecasted. This procedure
is repeated until an ARIMA model with the model estimation sample of November 1992

through July 2000 is estimated and a price for August 2000 is predicted.

Two specifications of ARIMA models are used for each series. First, as the results of the
test for trend and seasonality suggested the evidence of seasonality in each of the price
time series, an ARIMA with monthly seasonal dummy variables is estimated for each

series. Second, even though there is evidence of seasonality, ARIMA models without

92

seasonality are estimated. These models are estimated for two reasons. First, because not
all the months seemed to have significant coefficients when the models are checked for
seasonality. Second, when estimating the ARIMA with monthly seasonal dummy
variables, there is an indication that the forecast values tended to overestimate. The
results fi'om these ARIMA models with seasonal dummies are then compared to those
from ARIMA models without monthly seasonal dummies. Random walk models are used

as a point of comparison for more sophisticated models are estimated.

5.2.1 ARIMA Specification for Northern Mozambique

The procedures just described are applied first for Nampula maize prices. To have a good
specification of the ARIMA model, a correlogram with the autocorrelation coeflicients
and partial autocorrelation coefiicients for the Nampula price series is checked. As
indicated in chapter 3, investigating the shape and behavior of both the ACF and PAC
gives a plausible indication of the tentative ARIMA model. Figure 5.1 is the correlogram
with the autocorrelation coefiicients and partial autocorrelation coefficients for Nampula

maize prices.

The correlogram on Nampula nominal prices indicates that the ACF tends to decay
geometrically and the PAC goes to zero after 3 lags. Together, the path of the ACF and
PAC suggest that the Nampula price time series data could be an AR(3) process,

integrated of order 1, 1(1), with a presence of some orders of an MA component -

93

Figure 5.1 Autocorrelation and Partial Autocorrelation Coeficients for Nampula Prices

Autocorrelation Coefficients

 

    

 

 

 

 

 

 

 

 

1.0
5.
a... IIIIIIIIIIIII
.5. —
Willis
40 ‘_"ffi_vfi__f‘___-W
12 3 4 5 6 7 8 910111213141510
LagNumbcr
Partial Autocorrelation Coeff.
1.0
.sr
0.01
-.5I _ .
cum-mum
.10 -cootnctcnr

 

 

 

 

 

 

94

ARIMA(2, 1,n). Additionally, the fact that the ACF has a seasonal fi'equency of cyclical

“waves” strengthens the idea that this time series follows a monthly seasonal pattern.

When these identification procedures are applied to estimate the ARIMA model for
Nampula retail maize prices, an ARIMA (1,1,0) model is identified with the inclusion of
monthly seasonal dummies. This ARIMA model is then estimated and the results are
presented in Table 5.1a. An exercise of adding and/or reducing orders of the AR and the

MA components suggests the (1,1,0) model is a good, parsimonious model.

When the same estimation procedures are applied in searching for a parsimonious model
with white noise innovations, an ARIMA (5,1,0) is found to be a good representation of
the data generating mechanism when seasonal dummies are not controlled for. The results

of this model are also in Table 5.1a.

In addition to the joint significance of the seasonal dummies described in chapter 4, the
ARIMA specifications presented in Table 5.1a suggest that price changes in Nampula are
significant at 5% level for all months except October. In the model without seasonal
dummies, the second, third and fourth AR components are not significant. The fifth AR
component, however, is significant and ensures white noise innovations. Table 5.1b
presents the results of the Ljung-Box Q statistics test for serial correlation in the

innovations of both models.

95

Table 5.1a ARIMA Models for Nampula Maize Prices

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARIMA(l,l,0) with Seasonal ARIMA(5,1,0)withnoseasonal
Dummies dummies

Coefficient t statistic Coefficient t statistic

Constant 463.55 (4.13) 18.98 (0.67)
Jan -37020 (-2.85)
Feb -321.63 (-2.l9)
Mar -558.33 (-3.68)
Apr -8l4.48 (533)
May -845.72 (5.53)
Jun -514.87 (-3.36)
Jul -484.37 (-3.17)
Aug 437.19 (-2.86)
Sep -429.l8 (-2.73)
Oct -263.46 (-172)
Nov -312.07 (-2.29)

AR(l) 0.27 (2.29) 0.36 (3.23)

AR(Z) 005 (-0.45)

AR(3) .008 (-0.69)

AR(4) 0.02 (0.17)

AR(S) .043 (-3.60)

 

 

 

96

 

Table 5. lb Correlogram for the Nampula ARIMA Models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARIMA(1,1,0) with Seasonal Dummies ARIMA(5,1,0) withnoSsasonal Dummies
Lag AC PAC Q Statistic p-value AC PAC Q Statistic p-value
T 0.02 0.02 0.02 -0.02 -0.02 0.03
2 -0.11 -0.11 0.95 (0.33) —0. 12 ~0. 12 1.11
3 -0.06 -0.05 1.22 (0.54) -0.06 -0.06 1.37
4 0.05 0.04 1.39 (0.71) -0.06 -0.08 1.70
5 -0.28 -0.30 8.22 (0.08) 0.00 -0.02 1.71
6 0.00 0.02 8.22 (0.15) 0.08 0.06 2.21 (0.14)
7 -0.09 -0.17 8.98 (0.18) -0.13 -0.14 3.69 (0.16)
8 ' 0.02 -0.01 9.03 (0.25) -0.06 -0.06 4.03 (0.26)
9 -0.05 -0.07 9.27 (0.32) -0.03 -0.07 4.12 (0.39)
10 0.17 0.08 12.00 (0.21) -0.02 -0.05 4.15 (0.53) ‘
11 0.06 0.06 12.36 (0.26) 0.01 -0.03 4.17 (0.65)
12 -0. 14 -0.22 14.24 (0.22) 0.14 0.11 5.89 (0.55)
13 -0.08 -0.03 14.92 (0.25) -0.04 -0.04 6.08 (0.64)
14 0.12 0.03 16.42 (0.23) 0.08 0.10 6.67 (0.67)
15 -0.13 -0.13 18.18 (0.20) -0.12 -0.13 8.10 (0.62)

 

 

 

97

 

The results in Table 5.1b indicate that both ARIMA models for Nampula prices do not
have serial correlations in the innovations. EViews adjusts for the AR and MA terms
included in the ARIMA estimation, thus it does not report the p-values associated to the Q
statistics for a number of lags equal to the number of AR and MA terms. For instance, in
Table 5.1b, p-values associated to the first lag in the ARIMA model with seasonal
dummies and the first 5 lags in the ARIMA model without seasonal dummies are not
reported. For the lags where the probability values are reported, the statistic tests indicate
that, at 10% level, we reject the null of no serially correlated innovations for all lags in the
two models. Econometric packages such as GAUSSX enable calculating the p-values
associated to X’ and z-statistic for all lags. An inspection of those results confirms the

conclusions drawn fi'om the Q tests outlined in this research.

5.2.2 ARIMA Forecasting for Northern Mozambique
The two ARIMA models are used to perform short-term out of sample forecasts. Figure

5.2 shows the graphs with the ARIMA forecasts fi'om the two Nampula price models.

Except for the first and second observations, the out-of-sample forecasts fiom the two
comparative ARIMA models suggest that the model without seasonal dummies tends to
predict better than the model with seasonal dummies. Comparing the two models
suggests that the seasonal dummies appear to overestimate the actual price changes. This

finding, however, seems not to be in accordance with what could be expected from the

98

Figure 5.2 Out-of-Sample Forecasts for Nampula Prices, ARIMA Models, Sep 1999 -

Aug 2000

 

raoo

ARIMA(t.1.0)wthaaacnalDummlas

 

1m

1400

1200

1G»

 

 

 

 

18m

 

 

ARIMA (5,0,0) wlth no Seasonal Dummies

 

1000

1400

1200

1”

 

 

 

 

 

 

 

99

 

two models. Indeed, when the data was checked for seasonality, there was found
evidence of seasonality thus the ARIMA model with seasonal dummies should do a better
job in predicting filture values of the variable than the model without seasonal dummies.
The fact that this is not observed indicates that, either there is a problem in the
specification of the ARIMA model with seasonal dummies, or that the pattern of
seasonality had changed considerably between the model estimation sample and the
forecasting sample. Because including higher AR components worsens the forecasting
ability of the model, the mis-specification hypothesis is rejected, and the possibility that the
pattern of the seasonal dummies is different between the model estimation period and the
forecasting period is considered. Figure 4.1 suggested this difference in the seasonal

plice movements.

5.2.3 ARMA Models for Northern Mozambique

As stated earlier, when the primary objective of the research is forecasting, we can
estimate forecasts without regard to whether the original data contains a unit root or not.
In this work, even though there was evidence that the Nampula price series is
nonstationary when testing for a unit root in the original data prices, ARMA models are
estimated in addition to the ARIMA models, and the forecasting performance of all

models is compared.

100

Table 5.2a ARMA Models for Nampula Maize Prices

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARMA (2,0) with Seasonal Dummies ARMA (2,0) with no Seasonal
Dummies

Coefficient t statistic Coefficient t statistic
Constant 1844.05 (5.06) 1334.17 (5.27)
Jan 73.17 (0.72)
Feb 191.08 (1.21)
Mar 72.41 (0.37)
Apr -30047 (-1.36)
May -702.08 (-299)
Jun -77034 (-320)
Jul. -805.83 (-3.38)
Aug -79212 (-3.48)
Sep -773.88 (-379)
Oct -589.24 (-354)
Nov 451.54 (4.19)
AR(l) 1.22 (10.62) 1.33 (13.20)
AR(2) -031 (-270) -0.46 (-4.60)

 

101

 

Table 5.2b Correlogram for the Nampula ARMA Models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARMA (2,0) with Seasonal Dummies ARMA (2,0) with no Seasonal Dummies

Lag AC PAC Q Statistic p-value AC PAC Q Statistic p-value
1 .0.01 -0.01 0.00 -0.02 -0.02 0.04

2 -0.07 -0.07 0.45 V 0.05 0.05 0.25

3 -0.01 -0.01 0.46 (0.50) -0.01 -o.01 0.26 (0.61)
4 0.11 0.11 1.50 (0.47) 0.10 0.10 1.20 (0.55)
5 -0.23 .0.23 5.93 (0.12) -0.25 .025 6.77 (0.08)
6 0.07 0.09 6.35 ' (0.17) 0.08 0.07 7.32 (0.12)
7 .005 .009 6.58 (0.25) .009 -0.08 8.11 (0.15)
8 0.06 0.06 6.90 (0.33) 0.02 0.01 8.15 (0.23)
9 -0.04 0.00 7.02 (0.43) -0.06 -0.01 8.49 (0.29)
10 0.19 0.14 10.36 (0.24) 0.17 0.11 11.30 (0.19)
11 0.07 0.12 10.85 (0.29) 0.08 0.14 11.91 (0.22)
12 -0.14 -0.18 12.59 (0.25) 0.18 0.13 14.88 ' (0.14)
13 -0.08 0.00 13.20 (0.28) 0.00 0.02 14.88 (0.19)
14 0.13 0.06 14.89 (0.25) 0.16 0.11 17.30 (0.14)
15 -0.14 -0.11 16.77 (0.21) -0. 10 -0.06 18.25 (0.15)

 

 

 

 

 

 

 

 

102

Similar to the ARIMA models, two ARMA models are estimated, one with monthly
seasonal dummy variables, and the second without seasonal dummies. An ARMA(2,0)
with seasonal dummies and an ARMA(2,0) without seasonal dummies are estimated.
Table 5.3a has the results of the models, Table 5.2b has the correlogram with the ACF and

PAC, and Figure 5.3 presents the out-of-sample forecasts of the two ARMA models.

Like in the ARIMA models case, the significance of the seasonal dummies described in ‘
chapter 4 is confirmed by the individual coefficients of the monthly seasonal dummies in
the ARMA (2,0) model. However, compared to the ARIMA model, the ARMA model
indicates that from January to April the seasonal dummies are not significant at any
conventional significance level. In both ARMA structures, with and without monthly
seasonal dummies, the AR components are significant at 5% level, and the innovations are

white noise as indicated in Table 5.2b.

The probability values associated to the Q tests in Table 5.2b indicate that, except for lag
5 of the ARMA model with no seasonal dummies which is statistically significant at 10%
level but is not significant at 5% level, all the other lags for the two models are not
significant at any reasonable significant level, which is an indication of no serial correlation
in the innovations of the two models. With these results, the two ARMA models are used
for forecasting purposes. A graphic view of the forecasts fiom the two models is

presented in Figure 5.3.

103

Figure 5.3 Out-of-Sample Forecasts for Nampula Prices, ARMA Models, Sep 1999 -
Aug 2000

ARMA (2.0)wi1h Seasonal Dummies
1800

 

1600

1400

1200

1000

 

 

 

 

 

1500

 

1400

1300

1200

1100

1000

 

 

 

 

 

 

 

 

 

104

As in the case of the ARIMA models, Figure 5.3 suggests that the seasonal dummies
overestimate the monthly changes in the prices in the forecast period, and hence the
ARMA model with seasonal dummies seems to predict higher changes in prices than the
actually observed variations. As a result, the ARMA model with no seasonal dummies
appears to generate better forecasts. Similar explanation to that of the ARIMA models

seems to be valid for the ARM‘A models.

5.2.4 ARIMA Specification for Central/Southern Mozambique
This section estimates ARIMA and ARMA models for maize prices in Maputo. Like in
the Nampula case, a correlogram with the ACF and PAC of Maputo maize prices is used

as an initial indication of the tentative ARIMA model for this price series.

The geometrical decaying of the ACF of Maputo prices and the tendency of the PAC to be
within the confidence limits after 2 lags shown in Figure 5.4 suggest that Maputo maize
price could be an ARIMA model with at least 3 AR components. Furthermore, the slow
geometrical decay of the ACF suggests the presence of some MA components. The less
pronounced “waving” of the ACF compared to that in Nampula suggests a weaker
seasonality in Maputo. However, there still is evidence of seasonality. Thus ARIMA
models with seasonal dummies are investigated. Additionally, the fact that the ACF and
PAC are very close to 1 at the first lag is in accordance with the conclusion fi'om the unit

root tests that this process is nonstationary. Following these indications, tentative

105

Fifi!” 5.4 Autocorrelation and Partial Autocorrelation Coefficients for Maputo Prices

 

 

  

 

 

 

 

 

 

 

 

 

 

 

Autocorrelation Coefficients
1.0
M
,,. Illllllllllllll
.5. _
mums
o1.0fi'______“_'j_‘_-Oosfllelenl
2 3 4 5 0 7 0 910111213141510
LagNunber
Partial Autocorrelation Coeff.
1.0
.5:
0.04
-.54 —
mum
4.0 .W
1' 2 5 71 5 6 7 5 éfilliriréliréfii
LagNumber

 

106

 

Table 5.3a ARIMA Models for Maputo Maize Prices

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARIMA(2,1,1) with Seasonal ARIMA(3,1,1) withno
Dununies seasonal dummies
Coefficients t . Coefficients t .
81311an statlstrc
s s
Constant 1 12.84 (1.00) 19.12 (0.82)
Jan 23.14 (0.16)
Feb -95.38 {-0.75)
Mar -564.70 (-3.47)
Apr 438.29 (-3. 14)
May -90.25 (-0.55)
Jun -154.86 (-1.09)
Jul -121.66 («0.75)
Aug 138.37 (0.99)
Sep 11.48 (0.07)
Oct 40.11 (0.31)
Nov -18.14 (-0.12)
AR(l) -0.39 (-1.48) 0.90 (4.74)
AR(2) 0.35 (3.00) -0.04 (-0.22)
AR(3) -0.28 (-2.43)
MA(1) 0.56 2.11 -0.72 (-3.90)

 

107

 

Table 5.3b Correlgram for the Maputo ARIMA Models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARIMA(2,1,1) with Seasonal Dummies ARIMA(3,1,1) withnoseasonal
dummies
Lag AC PAC Q Statistic p-value AC PAC Q p-value
Statistic

l 0.04 0.04 0.14 0.00 0.00 0.00

2 0.03 0.03 0.21 -0.01 -0.01 0.01

3 -0.14 -0.15 1.96 0.00 0.00 0.01

4 -0.14 -0. 13 3.69 (0.23) 0.13 0.13 1.33

5 -0.17 -0. 16 6.10 (0.11) -0. 13 -0.13 2.78 (0.12)
6 -0.10 -0. 12 7.05 (0.20) 0.01 0.02 2.79 (0.27)
7 0.02 -0.02 7.08 (0.32) -0.08 -0.08 3.30 (0.40)
8 0.18 0.12 9.83 (0.12) 0.09 0.08 4.05 (0.50)
9 0.08 0.01 10.46 (0.19) 0.06 0.09 4.39 (0.39)
10 -0.01 -0.07 10.47 (0.27) ' -0.15 -0. 18 6.50 (0.45)
11 0.21 0.24 14.77 (0.09) 0.1 1 0.16 7.69 (0.22)
12 -0. 16 -0.13 17.07 (0.08) 0.21 0.17 11.94 (0.06)
13 -0.12 -0.10 18.55 (0.07) -0.04 -0.05 12.12 (0.09)
14 -0.02 0.11 18.58 (0.09) -0. 14 -0. 10 14.14 (0.09)
15 -0.01 -0.01 18.60 (0.12) 0.08 0.02 14.73 (0.12)

 

108

 

ARIMA models are estimated, and a final ARIMA (2,1,1) with seasonal dummy variables

is identified. The results are presented in Table 5.3a.

Similar to Nampula, as the unit root tests indicated that Maputo is an 1(1) series, an
ARIMA model without monthly seasonal dummy variables is estimated and the
forecasting performance of both ARIMA models is compared to that of the other
forecasting models to be estimated later on in the chapter. When the traditional
identification procedures are applied, an ARIMA (3,1,1) model without monthly seasonal

dummies is identified for the Maputo prices.

The results of this ARIMA model are also presented in Table 5.3a, and the Q statistics for
the ACF and PAC of both ARIMA models are presented in Table 5.3b. Table 5.3b shows
that, in addition to the individual significance of the AR and MA components in both
ARIMA models, these ARIMA models have no serial correlation. Indeed, the probability
values associated to the Q statistics suggest a non-rejection of the null hypothesis of no
autocorrelated innovations at the 5% level. Recall that the absence of probability values
for the first 3(4) lags for the ARIMA model with(without) seasonal dummies indicates the
inclusion of 2(3) AR and 1 MA component in the models. With these results, these

ARIMA models can then be used to predict filture prices for Maputo.

109

5.2.5 ARIMA Forecasting for Central/Southern Mozambique

The forecasting ability of the two ARIMA models for maize prices in Maputo, presented
in Figure 5.5, suggest that, even though the two models exhibit similar pattern in
predicting the future prices, the model with seasonal dummies appears to overweight the
path of seasonality. For instance, in February 2000, the two models predict that the price
in March will be lower, but while the ARIMA model without seasonal dummies forecasts
a decrease fi'om the actual price of 2,892 Mt/kg February to 2,711 Mt/kg in March, the
ARIMA model with seasonal dummies predicts that the price in March will be 2,263
Mt/kg. Like in the Nampula case, a comparative examination of the price path between
the model estimation and the forecasting sample indicate that the smooth seasonality
observed over the model estimation sample is not repeated in the forecasting sample, thus
the seasonal dummies appear to predict a seasonal pattern that is not observed in the out-

of-sample forecasting sample.

110

Figure 5.5 out-of-Sample Forecasts for Maputo Prices, ARIMA Models, Sep 1999 - Aug
2000

 

ARIMA (2.1.1) with Seasonal Dummies

 

3200

2800

2400

 

 

 

 

99:09 ' 99:11 00:01 ' 00:0'3 ' 00:05 ' 00:07

 

I — Actual ----- Forecast I

 

 

 

 

 

99:09 99:11 ' 00:0'1 ' 00:63 ' 00:0'5 ' 00:07

 

L— Actual ----- Forecast I

 

 

 

 

111

5.2.6 ARMA Models for Central/Southern Mozambique

Similar to the case of Nampula, two ARMA models are estimated for the Maputo price, in
addition to the ARIMA models. Using the identification procedures and ensuring that the
most parsimonious models should be chosen among the tentative ARMA models, a final
ARMA (3,1) model with seasonal dummies and an ARMA (1,3) without seasonal
dummies are identified and estimated. The results of both models are presented in Table

5.4a.

As indicated by the values of the t statistics, all the AR and MA components are
significant at 5% or higher level of significance. Additionally, Table 5.4b indicates that
there is no evidence of serial correlation in the innovations at 5% level of significance in
both models. Hence these two ARMA models seem to be good models to predict the out-
of-sample path of maize prices in Maputo. Similar to Nampula, there is no consistency in

the ARMA and ARIMA models specifications in central/southern Mozambique.

With the above conclusions, the two ARMA models are used to perform out-of-sample
forecasts for maize prices in Maputo. Figure 5.6 presents the forecasts obtained from the

two ARMA models.

The out-of-sample forecasts from the two comparative ARMA models suggest that the
model without seasonal dummies tends to predict better than the model with seasonal

dummies. Examining the two models suggests that the seasonal dummies appear again to

112

overestimate the forecast values. The procedures used to identify the ARMA models

have been observed, and the

Table 5.4a ARMA Models for Maputo Maize Prices

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARMA(1,2) with Seasonal ARMA(3,1)withno Seasonal
Dummies Dummies
Coefficient t statistic Coeficient t statistic
Constant 2612.90 (5.18) 2211.83 (5.53)
Jan 141.73 (1.47)
Feb 145.89 (1.00)
Mar -309.33 (-1.64)
Apr 649.10 (-3.02)
May -632.06 (-2.75)
Jun -685.99 (-2.91)
Jul -700.32 (-3.01)
Aug -458.60 (-2.08)
Sep -345.12 (-1.78)
Oct -207.23 (-1 .39)
Nov -102.69 (-l.05)
AR(l) 0.91 (17.20) 0.52 (2.04)
AR(2) 0.72 (2.81)
AR(3) -0.38 (-3.44)
MA( 1) 0.27 (2.22) 0.71 (2.79)
MA(2) 0.36 (3.02)

 

 

 

113

 

Table 5.4b Correlogram for the Maputo ARMA Models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ARMA(l,2)withSeasonal Dummies ARMA(3,1) withnoSeasonalDummies

Lag AC PAC Q Statistic p-value AC PAC Q Statistic p-valuc
1 -0.03 -0.03 0.09 0.03 0.03 0.09

2 0.02 0.02 0.12 0.02 0.02 0.13

3 -0.10 -0.10 1.06 -0.01 -0.02 0.15

4 0.07 0.06 1.46 (0.23) 002 -0.02 0.18

5 -0.18 -0. 18 4.47 (0.11) -0. l6 -0. 16 2.45 (0.12)
6 -0.04 -0.07 4.64 (0.20) -0.04 -0.03 2.62 (0.27)
7 0.03 0.04 4.71 (0.32) -0.06 -0.05 2.96 (0.40)
8 0.21 0.18 8.77 (0.12) 0.07 0.07 3.37 (0.50)
9 0.01 0.03 8.77 (0.19) 0.14 0.14 5.21 (0.39)
10 -0.01 -0.04 8.79 (0.27) -0.08 -0. 12 5.79 (0.45)
11 0.23 0.26 13.86 (0.09) 0.20 0.20 9.43 (0.22)
12 -0.13 -0.15 15.57 (0.08) 0.24 0.24 15.03 (0.06)
13 -0. 14 -0. 10 17.47 (0.07) 0.03 0.03 15.11 (0.09)
14 0.01 0.1 1 17.49 (0.09) -0.1 1 -0.08 16.36 (0.09)
15 0.05 -0.03 17.73 (0.12) 0.06 0.07 16.77 (0.12)

 

114

 

Figure 5.6 Out-of-Sample Forecasts for Maputo Prices, ARMA Models, Sep 1999 - Aug
2000

 

 

 

 

 

 

 

 

 

   

 

ARMA (1.2) with Seasonal Dunmiss
3900
3200
2900
2400
21130
161!) r r , q
9909 99 11 0001 00:03 00 05 00:07
[— Actual ----- Forecast J
ARMA (3,1) with no Seasonal Dummies
3600
A,
I ~,
32m “ °"-;"' ''''' 35‘; ----------------------- ;I\; -----------------------------

 

12800 -

2400 - - -------------------------------------------------------------------------------------------------------------

 

 

 

I"
,1
2000 41'! ....................................................................................................................
1600 . , . , . , . j , ,
99:09 99:1 1 00:01 00:03 00:05 00:07

 

 

 

 

 

115

preliminary data analysis suggested the evidence of seasonality in this price series. Thus,
the poor forecasting performance of the ARMA model with seasonal dummies compared
to the ARMA model without seasonal dummies is an indication that the pattern of
seasonality had changed considerably between the model estimation period and the

forecasting period.

5.3 Multivariate Models

The forecasting ability of the univariate models thus far estimated for the two regions is
compared to that of multivariate models. Because the multivariate models include related
price and production series to the Nampula and Maputo maize prices, it is hypothesized

that these models will improve the forecasting performance of the univariate models.

Recall that this research has found that the Mocuba and Manica price series used to model
price forecasting in, respectively, Nampula and Maputo, follow 1(1) processes. Therefore
estimation of the multivariate models is preceded by cointegration tests. Specifically,
cointegration tests are applied to Nampula and Mocuba price series in northern
Mozambique, and similar test is performed for the Maputo and Manica prices for the
central/southern Mozambique models. Ifthe two series in each region are found to be

cointegrated, VEC models are estimated.

116

5.3.1 Cointegration Models

Testing for cointegration is preceded by checking whether deterministic trends and
intercepts should be included in the cointegration tests. EVIEWS, the econometric
package used in the estimation of the models in this research, allows for five specifications
of the deterministic trend. Table 5.5 has the five specifications and the results of checking
for these two components. The Akaike Information criterion and the Schwarz Criterion
are used in these tests. The bold numbers in the Table are the smallest values under each

criterion. ‘°

Table 5.5 Cointegrating Equations and Deterministic Trend Assumptions

 

 

 

 

 

 

 

 

 

 

 

IData Trend: None None Linear Linear Quadrati
c
No Intercept Intercept Intercept Intercept
ointegrating Equation Intercept No Trend No Trend Trend Trend
No Trend

INorthem Mozambique . -
Akaikelnforrnation Criterion I 21.727 I 21.667 I 21.648 I 21.665 I21.687
Schwarz Criterion I 22.057 I22.025 I 22.034 I 22.078 I22.128

entral/Southern Mozambique

 

I AkaikeInformation Criterion I 22.227 I 22.194 I 22.172 I 22.194 I22.212
I 22.559 I 22.646 I 22.646 I 22.739 I22.739

 

 

 

I Schwarz Criterion

 

10

'I‘heAkaikeInromation Criterion isbasedonthesumofsquaredresiduals,and guidesinselecting
the number of coeflicients or the length of a lag distribution in an equation. Smaller values of the AIC
are preferable. The Schwarz criterion is an alternative to the AIC, with basically the same
interpretation, but a larger penalty for extra coefficients (EVIEWS 3, 1998).

117

Two lags are incorporated in these tests. These results suggest that test for cointegration
in maize prices between Nampula and Mocuba could be performed considering either that
the data has a deterrninist trend or it has not. The Akaike Information Criterion suggests
that the data has a deterministic trend component, which the Schwarz Criterion
contradicts. Preliminary analysis of this data has indicated that both the Nampula and
Mocuba prices have a slight positive linear trend but it is not significant in Mocuba, and in
Nampula it is not significant at 5% but significant at 10% significant level. Thus,
cointegration tests are run considering that the data has no significant deterministic trend.
This assumption is also held in the estimation of the VEC model for northern

Mozambique.

A similar conclusion is drawn for Maputo and Manica prices. While the Akaike
Information Criterion suggests that the data has a deterministic trend component, the
Schwarz Criterion suggests that it has neither a deterministic trend nor an intercept. Note
that the values under the assumption of intercept and no linear trend and intercept and
linear trend are very similar for each criterion, and the Schwarz Criterion imposes larger
penalty for additional coefficients compared to the Akaike Information Criterion. Thus
while the Akaike Information Criterion does not penalize the linear trend, the Schwarz
Criterion does, which does not mean any contradiction between the two criteria, and both

cases could be considered as having an intercept but with little evidence of a linear trend.

118

Wlth these conclusions, cointegration tests are performed for the two pairs of prices. In
these tests, the null that the two price series are not cointegrated is tested against the

alternative that they are cointegrated. Table 5.6 has the results of these tests.

Table 5.6 Cointegration Tests for Mozambique Maize Prices

 

 

 

 

 

 

ointegration Equation Likelihood 5%Critical Value 1% Critical Value
Ratio
INampula - Mocuba 38.3598 15.41" 20.04"
IMaputo - Manica 33.56111 1541" 20.04“

 

 

*(**) denotes rejection of the hypothesis at 5%(1%) significance level

The Johansen’s cointegration test indicates that the Likelihood Ratio for the cointegration
equation under the assumption of no linear trend assumptions is 38.36 for northern
Mozambique and 33.56 for central/southern Mozambique. These Likelihood values are
higher than the adjusted critical values of 15.41 at 5% level or 20.04 at 1% significance
level. Therefore it can be concluded that there is evidence of cointegration between

Nampula and Mocuba maize prices, and between Maputo and Manica maize prices.

The Engle and Granger’s two-Step cointegration test are run for the two pairs of prices,
without a linear trend but with the inclusion of monthly seasonal dummy variables. The
conclusion drawn from the Johansen tests is confirmed. The results indicate that, at a
critical value of -3.34 at 5% level, we reject the null of no cointegration in favor of the
alternative that the prices are cointegrated in both cases. The cointegration coeficient for

Nampula—Mocuba is -4.62, and the coemcient for Maputo-Monica is -3.84.

119

 

5.3.2 VEC Specifications and Forecasting

The Granger causality tests just carried out indicated that there is evidence that Mocuba
and Manica Granger cause Nampula and Maputo prices respectively. Additionally, the
cointegration tests indicated that there is evidence of a long term linear relationship
between the exporting and the importing market in each region. This section uses these

results to specify and estimate multivariate models for the two regions of Mozambique.

5.3.2.1 Northern Mozambique

The Granger causality and cointegration tests for northern Mozambique indicated that
Mocuba prices are expected to help explain variations in the Nampula prices, and that the
price series have a significant linear relationship in the long run. Mocuba prices are
modeled as the second endogenous variable in the VEC model for maize prices in northern
Mozambique in addition to the Nampula maize prices. Actual production in Mozambique
and Malawi are two exogenous variables in this model, in addition to monthly dummy
variables aimed to control for the already identified significant seasonality in the two price
series. Two lags were included in the cointegrating equations based on EVIEWS’
suggestion, and are also included in the VEC model for northern Mozambique. This VEC

model is calculated as follows:

APlt = 911131.91 '1 44921.1 +291 12) +110 + 711AP1.t-l *‘leAPu-z +713AP291 *‘YlsAPzrez +5131 +311 (32)

AP: = 94191.14 '1 44112.14 +291 12) +720 +721AP134 +'YzzAPlna *‘YzaApzt-l *‘YuApzsz +599 '1’ 521 (33)

120

where p, is maize price in Nampula, p, is maize price in Mocuba, a. and a, are coeficients
on the error correction terms, 1. ., through 12. are coefiicients to be estimated on the
autoregressive terms, 1: is a set of deterministic or exogenous variables, which include
Mozambique and Malawi production data and 11 monthly seasonal dummies, B. and B; are
coeficients on the exogenous variables, and a" and e, are the innovations, assumed to be

serially uncorrelated within an equation, but correlated across equations."

Lower or higher orders of autoregressive lags were tried, and they did not improve the
significance of the individual coefiicient nor the forecasting ability of the VEC (2,0)
model. Thus, a model with two autoregressive lags was identified as the final VEC model.

Table 5.7 presents the results of the VEC model for maize prices in northern Mozambique.

Alternative to the VEC (2,0) with seasonal dummies just described, another VEC, also
with two autoregressive lags but without seasonal dummies is estimated and the
forecasting ability of the two models is compared to all the models for the Nampula prices.
Table 5.8 indicates that all the parameters in the cointegration equation are significant at
5% level in both VEC models. However, three of the four lags of both APl and AP2 do
not improve much the significance of the two models. Among the maize production

variables, Q , improves only in the model without seasonal dummies. Recall that the

 

11

The selection ofthe lagorder for VAR/VEC models is somehow arbitrary. Too small lag lengths may
not ensure white noise residuals, and too large lag lengths might result in imprecise estimates.

121

 

production variables are annual figures, and they are repeated for the 12 months of each

marketing year, thus they have little monthly variability.

The two VEC (2,0) models are next used to forecast Nampula prices outside the model

estimation sample. Figure 5.7 has the graphics of the forecasts of the two models.

Figure 5.7 suggests that, like in the case of the univariate models, the two models do not
difi'er much in their power of predicting the path of the prices outside the estimation
sample, but it seems that the model without seasonal dummies predicts with better
accuracy the changes in prices when high increases or decreases are'expected to happen,
due to the difi‘erent seasonal path in the prices between the model estimation period and

the forecasting period.

122

Table 5.7 VEC (2,0) Model for Maize prices in Northern Mozambique

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With Seasonal Dummies With no Seasonal
Dummies
Variable 4 AP. AP, AP, AP,
Coeff t stat Coeff tstat Coeff tstat Coeff t stat
lcoimogmioo Equation -0.23 (-2.21) 0.27 (2.16) -0.02 (.042) 0.32 (4.73)
AP,“ 0.14 (1.08) 0.03 (0.18) 0.04 (0.28) 0.12 (0.75)
AP”,2 -0.20 (-1.614) 0.01 (0.09) -0.14 (-1.18) 0.21 (1.43)
AP,“ 0.08 (0.54) 0.34 (1.94) 0.43 (4.21) 0.66 (5.27)
AP”2 0.05 (0.36) 0.09 (0.54) 0.14 (1.18) 0.07 (0.49)
(instant 559.41 (3.38) 145.03 (0.72) 99.36 (0.69) 426.59 (-243),
IQl (Mozambique production) -0.12 (.097) 0.09 (0.58) 0.01 (0.08) 0.47 (2.60)
IQ2 (lvtalawi production) -0.08 (.100) -0.01 I(-0.08) -0.06 (-0.745) 0.03 (0.25)
IJan -338.82 (-2.28) -6.99 I(-0.04)
IFeb -283.27 (.202) -52.80 I(-0.31)
or -594.46 (4.27) -662.08I(-3.93)
Apr -595.33 (-3.76) 424.12 I(-3.78)
y 428.92 (-2.42) -240.59I(-1.12)
Jun -228.84 (-1.33) -187.12 I(-0.90)
Jul 422.44 (-1.96) -176.80F-0.89)
Aug -281.25 (-1.87) -251.75I(-1.38)
Sep -297.74 (-1.98) -64.11I(-0.35)
Ioct -190.86 (4.31) -1.98 [(0.01)
INov -304.87 (.211) 9.00 (0.05)
[Log likelihood -535.90 -550.93 .55097 -566.71
IAkaike AIC 11.21 11.59 11.31 11.72
ISchwarz SC 11.78 12.16 11.55 11.95
odel Statistics
Log Likelihood 4073.52 -1100.81
Akaike Information Criteria 22.51 22.65
Schwarz Criteria 23.71 23.19

 

 

123

Figure 5.7 Out-of-Sample Forecasts for Nampula, VEC Model, Sep 1999 - Aug 2000 .

VEC (2.0)mh8eaaonalDunmiss

1m

 

 

 

 

 

 

 

 

1500

 

1400

1300

1200

1100

1000

 

 

 

 

 

 

 

 

 

124

5.3.2.2 Central/Southern Mozambique

Like in the case of northern Mozambique, two autoregressive lags are used to estimate the
tentative VEC model for central/southern Mozambique. Maputo and Manica price series,
which have already been used in the Granger causality tests and in the cointegrating
equations, are the two endogenousvariables in the VEC model for central/southern
Mozambique. In addition to the two variables, data on volume of maize production in
Mozambique and South Afiica are used as exogenous variables. Monthly dummy
variables are also included as exogenous variables in the VEC (2,0) model, which has the

following representation:

APlt =111031.14 '1-09p2.t-1 “862-99 ) +710 +711AP1.1.1 *‘leAPls-z ”lsAstl *‘714Apzc2 1131131 +811 (34)

AP: =02(P1.t-1 '1 09132.14 '862-99) +720 +721APl.t.l +722APl.t-2 +723AP2M WuAPzt-z +521“: ‘1' 5a (35)

where p, is maize price in Maputo, p, is maize price in Manica, a. and 112 are coeficients
on the error correction terms, 1", through 12.. are coefficients to be estimated on the
autoregressive terms, x is a set of deterministic or exogenous variables, which include
Mozambique and South Afiica production data and 11 monthly seasonal dummies, B are
coeficients on the exogenous variables, and 9., and 9,. are the innovations, assumed to be
serially uncorrelated within equation, but correlated across equations. Table 5.8 presents

the results of the VEC (2,0) model for maize prices in northern Mozambique.

125

Table 5.8 shows that all the parameters in the cointegrating equation of the two VEC (2,0)
models are significant at 5% significance level, and most times the lags of the difi‘erences
of the price series are not significant at 5% level. However, all of them are significant at
the 10% level of significance. The exogenous production variables are generally more

significant here than in northern Mozambique.

Inclusion of higher orders of autoregressive terms in both VEC models did not improve
the significance of the parameters of these models, neither did it increase the forecasting
power of the models. Hence, the two VEC (2,0) models are used to forecast prices

maize prices in Maputo outside the model estimation sample. Figure 5.8 has the graphs

with the forecasts fi'om the two models.

The main conclusion drawn from these graphs is that, similar to the univariate models, the
multivariate VEC models for Maputo prices indicate that the monthly seasonal dummies
appear to overweight the monthly changes of the prices over the out-pf-sample forecasting
period when considerable changes are expected to occur. Overall there is not much

difference in the forecasting performance of the two VEC models.

126

 

Table 5.8 VEC (2,0) Model for Maize prices in Central/Southern Mozambiw

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With Seasonal Dummies With no Seasonal Dummies
Variable AP' AP’ Ap' “’1
Coefl‘tstatCoefftstatCoefl‘tstatCoefi‘tstat

lCointegration Equatlon -0.14 (4.15) 0.22 (2.75) -0.16 (4.04) 0.25 (2.68)
AP,“ 0.14 (1.06) 0.29 (1.89) 0.21 (1.61) 0.31 (2.04)
APM 0.16 (1.31) -0.06 I(-0.39) 0.06 (0.50) -0.10 (-0.66)
AP,“ 0.20 (1.98) 0.43 I(3.60) 0.29 (2.81) 0.51 (4.14)
AP,“ 4.17 (4.61) -0.21 I(4.66) -0.25 (4.25) -0.20 (4.57)
[Constant 44.51 (4.34) 685.62 I(3.03) -224.69 (4.33) 433.83 (2.16)
IQl (Mozambique production) 0.06 (0.56) -0.26 I(4.92) 0.18 (1.38) -0.23 (4.46)
IQ2 (South Africa production) 0.01 (0.49) 4.04 I(-2.55) 0.01 (0.70) .003 (4.88)
Iron 18.15 (0.13) 19.51I(0.11)
IFeb -88.44 (-0.64) -229.29I(4.39)
IM" 401.55 (4.59) -674.85 I(4.05)
IApr 484.51 (4.12) -185.70I(-0.94)
IMay 84.73 (0.51) .224.47I(4.14)
Jun 40.51 (4.27) .249.30I(4.39)
Jul 41.35 (4.30) -103.06I(-0.62)
Aug 205.28 (1.48) «73.87 I(-0.44)
Sep 77.29 (0.53) 40.59 I(-0.29)
IO“ 34.37 (0.24) -155.16I(-0.91)
|Nov 45.03 (0.31) 26.25 I(0.15)
Log likelihood 436.00 450.00 453.12 466.64
Akaike AIC 11.21 11.57 11.37 11.71
Schwarz sc 11.78 12.14 11.61 11.95
[Model Statistics

Log Likelihood 4082.17 4108.56

Akaike Information Criteria 22.73 22.84

Schwarz Criteria 23.93 . 23.38

 

 

 

 

127

 

Figure 5.8 Out-of-Sample Forecasts for Maputo Prices, VEC Models, Sep 1999 - Aug
2000

 

VEC (2,0) with Seasonal Dummies

 

 

”£1338“

 

 

 

 

 

 

3200

2800

2400

 

 

 

 

 

 

 

 

 

128

5.3.3 VAR Specifications and Forecasting

Similar to the univariate models, even though the preliminary data searching indicated that
the VEC models are the most appropriate multivariate models for both northern and
central/southern Mozambique, VAR models are also specified and estimated for both
regions, and the forecasting power of both the VEC and the VAR models is compared to
that of the univariate ARIMA and ARMA models. The remainder of this chapter presents
the VAR specifications and estimations, and the forecasting. First, VAR models for
northern Mozambique are estimated, followed by VAR models for central/southern

Mozambique.

5.3.3.1 Northern Mozambique

With two autoregressive lags, two VAR models are estimated for maize prices in northern
Mozambique. Both models have maize prices in Nampula and Mocuba as endogenous
variables, and the data on maize production in Mozambique and Malawi as exogenous
variables. The difi‘erence between the two models is that one of them has monthly
seasonal dummy variables while the other does not. Table 5.9 presents the results of both
VAR models, and the forecasts from both are presented in Figure 5.9, and the two

models’ out-of-sample forecasts are shown in Figure 5.9.

129

 

Table 5.9 VAR (2,0) Model for Maize prices in Northern Mozambique

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With Seasonal Dummies With no Seasonal Dummies
Variable P1 P2 PI ’2
Coefi‘ tstat Coefl‘ tstat Coeff tstat Coeff t stat

[PW 0.82 (5.87) 0.22 (1.31) 0.76 (5.61) 0.29 (1.59)
IP14: -0.25 (4.12) -0.16 (4.14) -0.21 (4.99) -0.26 (4.82)
IP24 0.36 (3.10) 0.92 (6.58) 0.49 (5.42) 1.09 (8.73)
IP24 0.00 (-0.02) -0.25 (4.59) -0.15 (4.41) -0.45 (4.12)
IConstant 375.52 (2.57) 221.08 (1.25) 50.86 (0.47) 44.56 (-0.16)
IQl (Mozambique production) 0.25 (1.48) 0.42 (2.05) 0.34 (2.43) 0.55 (2.90)
IQ2 (Malawi production) -0.06 (4.94) .004 (-0.45) -0.06 (-0.89) -0.03 (-0.32)
IJan 402.23 (4.24) 44.91 (0.27)
Ifeb' 407.19 (4.54) 50.56 (0.31)
IM‘" 439.51 (4.23) 453.37 (4.35)
IApr 489.38 (4.22) -639.88 (4.47)
My 402.20 (4.51) 468.67 (4.38)
Jun 493.18 (4.26) 452.07 (4.35)
Jul 487.97 (4.98) 437.51 (4.34)
Aug -308.09 (4.20) 403.64 (4.78)
Sep 426.74 (4.32) 417.21 (-0.69)
loot 418.28 (4.59) 44.45 (4.33)
INov 405.00 (4.27) 40.62 (-0.13)
ILog likelihood 438.85 454.13 448.36 473.33
IAkaike AIC 11.08 11.47 11.05 11.67
ISchwatz SC 11.61 12.00 11.25 11.88
iModel Statistics

Log Likelihood -1083.44 -1109.82

Akaike Information Criteria 22.31 22.42

Schwarz Criteria 23.38 22.84

 

 

 

 

 

130

Figure 5.9 Out-of-Sample Forecasts for Nampula Prices, VAR Models, Sep 1999 - Aug

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2000
. VAR (2.0) with Seasonal Durnmies
18m
reoo
1400
1200
1d!)
aoo . , r - r
was as 1 1 oo 01 00:03 00 05 0007
[ — Actual ----- Forecast 1
VAR (2,0) with no Seasonal Dummies
1800
1600
1400
1200
1000
99:09 99:11 00:01 00:03 00:05 00:07
I —— Actual ----- Forecast I

 

 

 

131

 

 

The main finding is that the two VAR models appear to be good representations of the
path of the data prices for northern Mozambique. Even though the second lag is not
Significant at 5% level, it appears to increase slightly the forecasting properties of these

VAR models, Mozambique production is significant in three of the four equations.

5.3.3.2 Central/Southern Mozambique

Two VAR models are estimated for maize prices in central/southern Mozambique. Both
models have two autoregressive lags each, and the difi‘erence between the two models is
that one of them has monthly seasonal dummy variables while the other does not. Both
models have maize prices in Maputo and Manica as endogenous variables, and the data on
maize production in Mozambique and Malawi as exogenous variables. Monthly seasonal
dummies are additional exogenous variables in the model that controls for seasonality.
Table 5.10 has the results of both models, and the forecasts fi'om both are presented in

Figure 5.10.

The autoregressive components of Maputo and Manica prices in the two alternative VAR
models for central/southern Mozambique are significant at 5% level. Mozambique
production is significant in both Maputo equations, while South Afiica production is
significant in both Manica equations. Because Maputo is closer to South Afiica and is the
market which efl‘ectively imports maize from South Afiica compared to Manica, it should
be expected that South Afiican production is more significant in explaining Maputo prices

than Manica prices. However, this did not happen, and the reason seems to be in the

132

difi‘erent sizes of Maputo and Manica markets, reflected in the extent to which the two
markets are affected by regional droughts. While Maputo can import maize, Manica is so
small that does not attract importers. This happened in 1995, when Maputo prices did not
reflect the drought conditions while South Afiica production and Manica prices did.

Also, even if Maputo imports fi'om South Africa, these imports are so small compared to

South Afiican production that they do not affect South African market conditions. E

 

I33

Table 5.10 VAR (2,0) Model for Maize prices in Central/Southern Mozambique

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With Seasonal Dummies With no Seasonal Dummies
Variable AP' AP’ AP‘ AP:
Coefl‘tstatCoefl‘tstat Cocfl‘tstatCoefl‘tstat
APw 0.88 (7.13) 0.39 (2.82) 1.00 (8.06) 0.45 (3.15)
AP,” 4.09 (4.79) 4.28 (4.08) 4.22 (4.77) 4.33 (4.38)
AP,“ 0.27 (2.79) 1.06 (9.78) 0.32 (3.31) 1.11 (10.06)
AP», 4.15 (4.46) 4.35 (4.12) 4.25 (4.52) 4.43 (4.86)
onstant 303.86 (1.71) 578.99 (2.91) 139.83 (0.93) 330.17 (1.93)
IQl 0.26 (1.81) 0.08 (0.51) 0.37 (2.45) 0.19 (1.06)
F), 0.00 (4.41) 4.04 (4.87) 4.01 (4.54) 4.04 (4.68)
Iron 41.37 (4.53) 45.95 (4.57)
IFeb 470.24 (4.26) 497.40 (4.31)
IMar 488.42 (4.57) -603.60 (4.94)
IApr 457.24 (4.35) 442.11 (4.42)
III/fay 48.08 (4.53) 483.73 (4.72)
Jun 423.91 (4.55) 479.90 (4.730)
Jul 404.43 (4.43) 496.43 (4.23)
Aug 20.52 (0.14) 476.79 (4.11)
Sep 41.98 (4.30) 436.85 (4.86)
ct 40.97 (4.58) 406.70 (4.33)
ov -88.79 (-0.64) -98.95 (4.64)
Log likelihood 410.51 420.52 459.01 469.80
Akaike AIC 11.29 11.51 11.31 11.58
Schwarz sc 11.79 12.01 11.52 11.79
odel Statistics
Log Likelihood 4227.98 4121.21
Akaike Information Criteria 22.73 22.70
Schwarz Criteria 23.73 23.12

 

 

 

 

134

 

Figure 5.10 Out-of-Sample Forecasts for Maputo Prices, VAR Models, Sep 1999 - Aug
2000.

 

VAR (2,0) with no Seasonal Dummies

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

135

Finally, similar to northern Mozambique, the two VAR models seem to be good
representations of the path of the data prices for southern Mozambique. These two VAR
(2,0) models are then used to perform twelve one-step-ahead forecast for Maputo prices,
re-estimated at every step, and their forecasting ability is used in the forecasting evaluation
along with the other multivariate and univariate models. The results of the two VAR _

models are presented in Figure 5.10.

5.4 Conclusions
The main conclusion of this chapter is that, in each class of models (ARMA, ARIMA,
VAR and VEC), the models with seasonal dummies overestimate the seasonal

movements. The reason for this is that seasonal price movements were much less

pronounced during the forecasting period than they typically were during the estimation

period.

Second, the multivariate models seem to perform slightly better than the univariate
models. The quality of the data, especially the production data for Mozambique and
Malawi, could be the reason that the multivariate approach did not deliver greater

improvements in performance.

136

Chapter 6

FORECAST EVALUATION

6.1 Introduction

This chapter evaluates the competitor forecasting models’ ability to perform out-of-sample
forecasts. Along with the univariate ARMA and ARIMA models and the multivariate
VAR and VEC models, random walk models’ forecasts evaluated. This chapter is
organized as follows. Section 6.2 advances a discussion of basic characteristics of the
prices that are expected to help explain the results of ihe forecasting models. Section 6.3
presents and discusses statistical evaluation criteria, section 6.4 addresses a discussion on
the economic evaluation criteria for the competitor forecasting models, and section 6.5

presents the conclusions.

6.2 Preliminary Data Search

Comparing the ability of alternative models in accurately forecasting prices requires
understanding the data itself. Performing statistical evaluation of different time series
models without understanding the behavior of the prices over time and the reasons of the
given behavior may lead to misleading conclusions. A description of several properties of
the price time series used in this research has been presented in chapter 4. This chapter,
however, revisits some of the issues discussed in chapter 4, to allow better understanding
of the findings on the statistical and economic evaluation criteria for the competitor

forecasting models.

137

Iiigure 6.1 Maize Retail Prices in Nampula, November 1992 - August 2000

 

 

 

 

 

40m 3:: : :f: if}. I ..I :1.- I i :1:
0 cl
93 94 95 96 97 98 99 00
I— Price I

 

 

 

 

Figure 6.1 shows nominal retail prices for maize in Nampula. The shadowed area shows
the forecasting period. This graph shows that prices in Nampula were stable until late
1994. Between 1995 and mid 1999 they were unstable, with periods of some stability and
others of strong spikes. This behavior is not observed during the forecasting period of

mid 1999 through August 2000.

Figure 6.2 shows the Maputo case. This figures indicates that in Maputo, similar to
Nampula, maize prices tended to remain somewhat stable at low levels until early 1995.

Prices in Maputo, however, were not as stable as those in Nampula in this period.

138

Figure 6.2 Maize Retail Prices in Maputo, November 1992 - August 2000

 

 

 

 

 

 

 

4000
3000 .. .............................................................................................
2000 .. -----------------------------------------------------------------------------------------------
1 000 - -----------------------------------------------------------------------------------------------
o vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv I vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv f vvvvvvvvvvvvvvvv
93 94 95 96 97 98 99

 

 

 

 

Like in Nampula, high spikes are observed in Maputo maize prices between 1995 and

1999, even though they were comparatively less accentuated.

Also, the behavior of these prices in Maputo over the sample estimation period of
November 1992 through August 1999 is different fi'om that of the out-of-forecast period
of September 1999 through August 2000. In fact, prices tended to follow the normal
seasonality between 1999 and 2000, but in 2000 (i) seasonal peak occurred in October,
was very early compared to January, when it usually happens, (ii) seasonal decline started
in June, instead of the normal decline in April, and (iii) there were monthly or bimonthly

variations in the prices between October 1999 and March 2000, not observed in the same

139

months over the model estimation period. This could be expected to be a source of “out-

of-normal” forecasting errors, especially for the univariate models.

6.3 Statistical Evaluation

Having in mind the price characteristics just outlined, this section presents and discusses
the comparative forecasting models’ performance based on the results from statistical
criteria As suggested by theory, the different forecasting models employed in this
research are expected to give difi‘erent forecasts. Three statistical criteria are used, namely
the root mean squared error(RMSE), the mean absolute percentage error (MAPE), and
the turning point error (TPE). While the RMSE depends on the scale of the variable being
forecast, the MAPE and the TPE do not. The performance of the different models is
compared under the rule that the lower the value of the RMSE, the MAPE or the TPE,

the better the model’s ability to forecast the time series.

6.3.1 Nampula Prices

The fact that seasonal price behavior changed over the out-of-sample forecast period
suggests we would expect a poor forecasting performance of the models used in this
research, especially the univariate models. The ability of the alternative models’ in

forecasting maize prices in Nampula is presented in Table 6.1.

140

Table 6.1 Statistical Evaluation of the Price ForecastingCompetitor Models for Nampula

 

 

 

 

Model Statistical Criterion
RMSE MAPE TPE
(%)
ARMA Models ARMA (2,0) with no seasonal dummies 94.83 0.06 83.00
ARMA (2,1) with monthly dummies 157.37 0.11 83.00

 

ARIMA Models ARIMA (1,1,0) with no seasonal dummies 195.10 0.04 83.00

 

ARIMA (1,1,0) with monthly dummies 170.30 0.06 50.00

 

 

 

 

 

 

 

 

 

 

VAR Models VAR with no seasonal dummies 120.35 0.04 83.00
VAR with seasonal dummies 152.33 0.10 33.00
VEC Models VEC with no seasonal dummies 78.339 0.06 50.00
VEC with monthly dummies 159.30 0.09 67.00
Iliandom Walk Model 99.40 0.05 100.00

 

 

The results in Table 6.1 suggest three things. First, the three criteria do not lead to a
similar conclusions regarding the “best” model. Overall, the multivariate models do a
somewhat better job than the univariate model do. This should be expected as the
univariate models are based solely on the variable to be forecast, thus they Should be
expected to have limitations in predicting their own future behavior especially when there
is much unpredictability in the fluctuations of the time series. The multivariate models, on
the other hand, involve the production variables in addition to the prices in Mocuba ,
which are thought to help explain the behavior of the Nampula price, and hence to control

for most of the fluctuations in the Nampula prices.

141

Second, among the univariate models, the ARMA models seem to do a better job than the
ARIMA models, while there is not a substantial difference between the VAR and the VEC
models. In fact, it is often true that the ARMA and VAR models, which are based on
price levels - used, in this case, with no regard on the nonstationarity of the price series in
levels - forecast better than the ARIMA and VEC models, estimated with the first

difference—stationary prices, when the time series are not long enough.

Finally, among the ARMA models, the VAR models and VEC models, the models with no
seasonal dummies appear to do a better job in forecasting compared to the models with
seasonal dummies. This is not surprising as Figure 6.1 showed that the extraordinarily
high peaks observed several times over the model estimation sample are not repeated in
the forecast sample, thus the seasonal variables, while controlling for these peaks in the

model, predict similar behavior over the forecast period.

6.3.2 Maputo Prices

As in Nampula, examining the behavior of the time series between the model estimation
period and the forecast period shows that the behavior in the two sub-samples is not the
same, thus the models could have problems predicting the path of future prices. Table 6.2
has the results of the statistical criteria used to compare the ability of the alternative

forecasting models.

142

Table 6.2 Statistical Evaluation of the Price Forecasting Com

itor Models for Maputo

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Model Statistical Criterion

RMSE MAPE TPE

(°/o)

ARMA Models WA (3,1) with no seasonal dummies 345.04 0.10 80.00
ARMA (1,2) with seasonal dummies 396.24 0.11 80.00

WA Models ARIMA (3,1,0) with no seasonal dummies 331.58 0.09 100.00
ARIMA (2,1,0) with seasonal dummies 410.15 0.11 100.00
VAR Models VAR with no seasonal dummies 290.10 0.01 ,100.00
VAR with seasonal dummies 336.25 0.04 100.00
VEC Models VEC with no seasonal dummies 343.45 0.10 100.00
Mac with seasonal dummies 378.80 0.03 80.00
[Random Walk Model 311.18 0.09 100.00

 

 

 

As in Nampula, the three statistical criteria lead to difi'erent conclusions concerning the

“best” model in performing out-of-sample forecasts for Maputo price series. In general,

however, the multivariate models appear to perform better than the univariate models.

Excluding the values of the RMSE for the VEC model with seasonal dummies, the RMSE

and the MAPE lead to the conclusion that the multivariate models forecast better than the

univariate models. This is in accordance with the economic theory as the multivariate

models have better explanatory power of the variations of the forecast variable. The

multivariate models include price of maize and maize production figures in Mozambique

a~t'ad South Afiica in addition to the Maputo maize prices.

143

 

Secondly, because seasonal peaks observed in the model estimation period are not
observed in the forecast period, and seasonality in Maputo maize prices is not strong in
every single month even though the joint significance of the seasonal dummies is
significant, the models that do not control for seasonality forecast better than those with

seasonal dummy variables.

Thirdly, out of the three statistical evaluation criteria, the MAPE and the TPE indicate that
the VAR with no seasonal dummies does the best job in forecasting this time series. It has
the lowest RMSE and MAPE. It should be noted, however, that there is no single model
that clearly outperforms the other models in forecasting the values for all observations in
the period. Both in Nampula and in Maputo, all the models do a good job in forecasting
some values, and they perform poorly in other occasions. Finally, all the models perform
poorly in capturing the turning point errors when performing out-of-sample forecasts for

Maputo maize prices.

6.4 Economic Evaluation
Under statistical evaluation criteria, models are examined from the standpoint of
minimizing forecasting errors. Such criteria are not necessarily the most relevant in a
decision-making fiamework, thus they do not tell how good the models are fi'om the point
of view of making profitable decisions based on the forecasts. Explicit economic

e\raluation criteria are needed to compare the models.

144

Often, economic performance of alternative forecasting models is evaluated based on the

extent to which they lead to profitable sell or store decisions based on the signals

generated by the forecast values.

To compare how well comparative models or lead to profitable decisions, sell or store

signals, shown in equation (42), are calculated for each model and compared across

models.
Sell when P,(1 +r) > A, ,; Store otherwise (36)

where P, is the actual price at month t and 19“, is the forecast price at month (+1.

Because each model gives different forecast values, sell/store signals could be different
across models depending on the number of months in which, for each model, equation

(37) suggests to sell or store. In this sense, each model generates a specific sell/store

strategy.

In this research, the difi‘erent strategies are compared to a default or “no mode ” strategy.
This strategy consists of buying product in the harvest months of May, June and July, and
selling equal amounts of 11.1% of product fi'om August to April with no regard to

sell/store signals. This is a reasonable strategy for three reasons. First, traders have

e3-qaectation of peak prices in the hungry season thus they want to take advantage of the

145

higher prices in later months instead of selling product according to the sell or store
monthly signals. Second, traders are risk averse; they know that storing product for later
months according to the sell/store signals involves risk. Since there is no certainty about
the future price, thus selling equal amounts of product every month is less risky. Finally,
traders need constant cash flows for operating capital, and selling product every month,
whether prices are attractive or no, ensures operating capital. Under each model-
generated strategy, the decision on whether the amount of product previously planned to
be sold in month t is actually sold in that month or is stored into month (+1 depends on
the sale/store signals given by the forecasts. When the forecast price for month 1+1 is
higher than the actual price in month 1 plus the opportunity cost of capital, the amount
planned to be sold in month t is stored into month 1+1. When, on the other hand, the
price forecasted for month 1+ 1 is lower than the actual price in month 1 plus the
opportunity cost of capital, then the amount of product previously planned to be sold in
month t is efl‘ectively sold in month 1. Any amount of product available in April, either

stored from previous months or simply the amount planned to be sold in that month is sold

regardless of the sell or store si .‘2

‘

a:
’Theproceduretocalculatethesell orstoresignals consistsinusingtheannual lendinginterestrate
Of 22.8%, and obtaining the monthly compounded prices. The monthly interest rate is multiplied by
thecurl'entpriceateachmonthr,andthecornpounded value ofP,formontht+1 isobtained. This
indicatesthevalue oftheactual price inmonthtcompoundcd intotllenextmonth. Nemtberorceast
price for month 1+1 is compared to the compounded value ofthe actual price in month t. This
cOrrlparison indicates whether selling the product at the actual price in month t is better or not than
st<31ingitintothcnextmonth, 1+1, facingthestoragecosts. Theopportunitycostofcapital isused
as aproxytothephysieal storagecostduetolackofhistoricaldataon storagecosts.1ftheactual
price in month 1 plus the monthly opportunity cost of capital - i.e., the actual price in month t
Wintothenextmonth- is higherthantheforecast price formonth 1+1, thenthedecision
‘8 to sell in month 1. Store otherwise.

146

In evaluating the profitability of the decisions derived from the comparative models , this
research uses three economic criteria . The first is the mean price received, the second is

the present value of the marginal revenue, and the third is the percentage of correct

decisions.

The mean price received is the average price received when the sell/store signals generated
by each strategy are observed, i.e., for the months in which product is sold under each
strategy. Ifthe strategy derived fi'om a model predicts, every month, a lower price for the
following month, then traders will never store additional product fi'om one period into the
next period, and the average price received will be the average monthly price for the
whole period. If, on the other hand, a strategy whose one-step-ahead forecasts suggest to
sell in March, June and September, and traders in fact only sell product in these three

months, the mean price received by traders will be the average of the actual price in these

three months.

The mean price received indicates how good or poor are the difi‘erent strategies in leading
to decisions which result in a high average price received. The higher the mean price
received, the better the strategy generated by the model. In this regard, it is of special
interest to compare the different Strategies to the default strategy, and a strategy with a

mean price lower than that obtained from the default strategy indicates incorrect sell/store

decisions compared to selling equal amounts every month.

147

However, regardless of its importance in measuring future earnings, the mean price
received does not take into account storage costs, thus it does not formally compare the
profitability of the different strategies to buying and selling everything in July without
incurring in storage costs. This is taken into account in the next criteria, the present value

of the marginal revenue.

The present value of the marginal revenue is the difference between the discounted price
at month 1+» and July’s price, weighted by the percentage of product sold in that month,
where the proportion might change across months depending on the sell/store signals. If
these signals indicate that the 11.1% planned to be sold in a given month should efl‘ectively
be sold, then the actual price of that month is multiplied by 11.1% when calculating the
gross marginal revenue. If, on the other hand, the sell-or-store signals suggest that the
11.1% of product previously planned to be sold in month I should be stored into month
t+1, and they are effectively sold in the month 1+] in addition to the 11.1% previously

planned to be sold in that month, then the actual price of month 1+] is weighted by 22.2%.
Summing the monthly present value of the marginal revenue under each strategy, gives

Present value of the marginal revenue for that strategy. Equation (3 8) represents this

Strategy.

8
gmmluqu (37)

148

where P1, is the actual price in month t, Pt+n is the forecast price for month (+71, 71 is the
number of the month in the marketing year, being July = 1, sis the number of months in
which product is sold under each strategy, I is July, (1+r) is a discount factor, and q is the

proportion of the total product that is sold in each month where sales take place. '3

The present value of the marginal gross revenue is a revenue above July’s price, obtained
fi'om storing the product beyond July and facing positive storage costs, and indicates
whether the strategy, overall, leads to profitable decisions or not compared to selling all
the product in July. Ifthe marginal revenue is positive, the marketing strategy leads to an
overall profitable decision process compared to selling everything in July. Under the
assumption that product can be sold in any of the 9 months of the marketing year, and that
each strategy leads to a particular number of months in which product should be sold or

stored, the values of the different economic criteria are expected to vary by strategy.

The percentage of correct decision criterion is a measure of accuracy of the strategies in
predicting the right price direction change. A decision to sell or to store product is
considered correct if the model predicts that the price in month t+1 will be higher than the

actual price in month 1 plus the opportunity cost of capital, and this indeed happens. Ifthe

‘

13

The procedure to calculate the present value of the nurginal revenue involves: (i) discounting the

actual price for each month (+1: in which product is sold to obtain the present value of PM, at the

harvestmonthl’g; (ii) calculafingflwdifl’emncebetweenthepresentvalueoftheaaualpnceforeach

t‘lonth t+n with the actual price in July, to obtain the present value of the marginal revenue for each
“loath. This is then weighted with the proportion of product sold in that month. In this research, prices
ahe discounted at the opportunity cost of capital of 22.8%.

149

opposite happens, i.e., the model predicts one direction in the evolution of the price and
the observed price in month 1+1 is the in the opposite direction, then the model has led to

an unprofitable sell or store decision.

6.4.1 Sell-or-Store Signals
Tables 6.3a and 6.3b have the results of how many months (and in which) sellers in
Nampula and Maputo respectively would sell product based upon the sell and store sigmls

given by each forecasting model or strategy.

Table 6.3a Post-Harvest Marketing Strategies Generated from Forecasting Models in
Nampula

 

 

 

 

 

 

 

 

 

 

 

Strategy/Forecasting Model Action-Sell in Nampula‘

ARMA (3,1) no seas. dummies Aug, Sep, Oct, Nov, Jan, Feb, Mar, Apr (1)
ARMA (1,2) with seas. dummies Aug, Dec, Feb, Mar, Apr (4)
ARMA(3,1,0) no seas. dummies Oct, Jan, Feb, Apr (5)
ARIMA (2,1,0) w/seas. dummies Dec, Feb, Mar, Apr (5)
VAR no seasonal dummies Apr (3)
VAR with seasonal dummies Aug, Sep, Oct, Nov, Jan, Feb, Mar, Apr (1)
VEC no seasonal dummies Sep, Dec, Jan, Feb, Mar, Apr (3)
VEC with seasonal dummies Sep, Oct, Dec, Jan, Feb, Mar, Apr (2)
Random Walk All 9 months (0)

 

 

 

1 Numbers in parenthesis are the number ofmonths with no sales; product is stored into the next
month.

Tables 6.3a and 6.3b indicate that the different strategies lead to different indications of

the number of months in which selling product would be reasonable and those in which it

150

would be preferable to store based on the buy and sell rule. For instance, the ARMA
model with no seasonal dummies and the VAR with seasonal dummies forecast that prices
will be lower in the following month for most of the months, while the VAR model with
no seasonal dummies forecasts sufiicient increases in prices to justify storage during 8 of
the 9 months over the marketing year of 1999/2000. Iftraders in Nampula follow the sell
or store signals given either by the ARMA model with no seasonal dummies or by the
VAR with seasonal dummies, they will sell their product every month except in December,
as these models suggest that the spot price in the following month will be lower than the
actual price in the current month plus the opportunity cost of capital. On the other hand,
if the least strategy is used (VAR with no seasonal dummies), sellers in Nampula will sell
product only in April of 2000 over the marketing year as, in each month through February,

this model, suggests that the price in month 1+ 1 will be lower than Pt(l+1').

151

Table 6.3b Post-Harvest Marketing Strategies Generated fi'om Forecasting Models in
Maputo

 

 

 

 

 

 

 

 

 

 

Strategy/Forecasting Model Action-Sell '

ARMA (3,1) no seas. dummies Nov, Jan, Feb, Apr (5)
ARMA (1,2) with seas. dummies Feb, Mar, Apr (5)
ARIMA(3,l,O) no seas. dummies Nov, Jan, Feb, Mar, Apr (4)
ARIMA (2,1,0) w/seas. dummies Nov, Feb, Mar, Apr (5)
VAR no seasonal dummies Jan, Feb, Mar, Apr (5)
VAR w/seasonal dummies Jan, Feb, Mar, Apr (5)
VEC no seasonal dummies Nov, Feb, Mar, Apr (5)
VEC w/seasonal dummies Nov, Feb, Mar, Apr (5)
Random Walk All 9 months (0)

 

 

 

 

' Numbers in parenthesis are the number of months in which product is stored under each strategy.

In Maputo, four models generate strategies that lead to storing product through
November, and three indicate that product should not be sold before 2000. Additionally,
both in Nampula and in Maputo, the random walk models generate strategies which are
similar to the default strategy as they suggest that product should be sold every month.
Every month, the random walk models predict lower prices for the following month,

discounting factor accounted for.

6.4.2 The Evaluation Criteria
The profitability of the decisions based on the strategies are evaluated using the three

economic criteria. The results for Nampula and Maputo are presented in Tables 6.4a and

6.4b respectively.

152

Table 6.4a Economic Results of Post-Harvest Marketing_Strategies for Nam ula

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mean Price PV of Total Percentage
Received Weighted of
Marginal Revenue Correct
Decisions

fault Strategy 1341 -86 78
ARMA (2,0) with no seasonal dummies 1330 -92 67
WA (2,1) with seasonal dummies 1375 -43 56
ARIMA (1,1,0) with no seasonal dummies 1345 -103 44
ARIMA (1,1,0) with seasonal dummies 1391 -55 44
VAR with no seasonal dummies 1399 -1 17 33
VAR with seasonal dummies 1330 -92 44
VEC with no seasonal dummies 1374 -62 67
VEC with monthly dummies 1360 -77 78

 

 

Table 6.4a indicates that, if the strategy generated by the ARMA model with no seasonal
dummies is followed, traders in Nampula are expected to receive the mean price of
1,330.10 Mt/kg over the marketing year. If, instead, the strategy to follow is that
generated by the ARMA model with seasonal dummies, the average price received over
the marketing year by Nampula traders would be 1,374.97 Mt/kg. As indicated in Table
6.4b, the same two strategies would yield a mean price received of 2,905. 16 Mt/kg and

2,982.82 Mt/kg, respectively, for traders in Maputo.

On the whole, this criteria indicates that the best strategy for traders in Nampula is that
generated by the VAR model with no monthly seasonal dummies, followed by the strategy

derived from the ARIMA model with seasonal dummies. The least profitable strategies

153

are those given by the ARMA with no seasonal dummies and the VAR model with

seasonal dummies.

Table 6.4b Economic Results of Post-Harvest Marketing Strategies for Maputo

 

 

 

 

 

 

 

 

 

 

 

Mean PV of PV of Total [Percentage ofl
Price Received Weighted Correct
Marginal Decisions
Revenue
ault Strategy 2728 588 44

ARMA (2,0) with no seasonal dummies 2905 632 44
ARMA (2,1) with seasonal dummies 2983 672 56 '
ARIMA ( 1,1,0) with no seasonal dummies 2905 632 44
WA (1,1,0) with seasonal dummies 2881 601 44 .
VAR with no seasonal dummies 2987 766 56
VAR with seasonal dummies 2987 766 56
VEC with no seasonal dummies 2881 601 33
VEC with monthly dummies 2881 454 44

 

 

 

 

 

These results suggest that, for maize traders in Nampula, the most profitable strategy
would be to buy product in the harvest months of May, June and July and store it through
April and sell in this month. In fact, Figure 5.1 showed that, between August 1999 and
March 2000, prices did not increase much. The average of monthly maize prices in
Nampula over this period was 1,334.01 Mt/kg, smaller than the observed price of
1,398.98 Mng in April 2000. Note that the mean price received does not take into
account storage costs, thus if prices of maize have a decreasing trend over the period and
then increase in the last month, as it happened in this marketing year, storing the product

154 ’

over the period with zero storage costs is better than any strategy which involves facing
the low prices prior to April. This could be true for farm producers and large scale
wholesalers in northern Mozambique, who have their own storage infiastructures and do

not pay for storage service.

For traders in Maputo, in turn, the mean price received criteria indicates that the best
strategies to follow are those generated by the two VAR models, and the second
profitable strategy is that derived from the ARMA model with seasonal dummies. The
least profitable strategies for Maputo are those given by the no-model and the random
walk model. These results suggest that for maize traders in Maputo, the best strategy for
the 1999/2000 marketing year was to buy product in the harvest months pf May, June and
July 1999, and sell it fi'om January to April 2000.

All the strategies, except the ARMA with no seasonal dummies and the VAR model with
seasonal dummies in Nampula, give better results when compared to the default or “no

mode ” strategy.

Similar to the mean price received, this measure takes into account buying the product in
May, June and July and making sell/store decisions according to equation (42)’s decision
rule. Because the present value of the marginal gross revenue compares the average of
the present value of the price received for each strategy to the price in the harvest month
of July, it is expected to be either positive, null, or negative. A positive PV marginal gross

revenue indicates that the strategy leads to a more profitable sale/storage strategy

155

compared to the marketing mark-up given by buying and selling the product in July, with
zero storage cost. A negative PV marginal gross revenue indicates that traders are better
ofi‘ buying and reselling everything in July (or May, June and July). Finally, a null PV
marginal gross revenue could indicate indifference between buying and reselling
everything in July and following the strategy. However, indifi‘erence could not happen as
risk averse traders would prefer to sell everything in July and invest the capital in less risky
activities such as to earn the opportunity cost of capital. Traders with a more speculative
behavior, on the other hand, would probably store product and expect to gain from better

prices in the future.

Table 6.4a indicates that all the strategies lead to unprofitable decisions in Nampula
compared to buying and selling the product in July. However, the ARMA and ARIMA
models with no seasonal dummies, and the two VEC models lead to better strategies than
the default strategy. In fact, the fact that the price behavior was highly different between
the model estimation period and the forecasting period led to unprofitable sell/store
decisions. For instance, the sell/store signals indicated that the best strategy would be to
store everything through April 2000, but when the opportunity cost of capital is included
in the analysis, this strategy generates the worse results. Also, the percentage of correct
decisions criterion indicates that, under this strategy, 67% of the decisions were not

correct, i.e., out of the nine months, the decisions were correct only in three months.

156

Table 6.4b indicates positive marginal gross revenue, which suggests that all strategies are
more profitable than buying and selling everything in July. Also, except the VEC model

with seasonal dummies, all the other models give better results than the default strategy.

Finally, the percentage of correct decisions criterion indicates that the strategies leading to
accurate decisions most of the times in Nampula are those originated from the VEC with
seasonal dummies and the default model. The least accurate strategies in Nampula is that
derived from the VAR model with no seasonal dummies. In Maputo, in turn, the ARIMA
model with seasonal dummies and the two VAR models are those leading to correct

decisions most times than the others.

Overall, the economic criteria suggest that the multivariate models lead to better sell/store
decisions compared to the univariate models. Also, the models tend to do a better job in
Maputo than they do in Nampula. This is not surprising as the difl‘erence in the behavior
of the prices between the model estimation period and the forecasting period is
substantially higher in Nampula than in Maputo, as suggested by Figures 5.1 and 5.2.

Under such circumstances, time series models hardly could predict the path of the price.

6.5 Conclusions
The statistical evaluation has shown that, for each model, there are periods of good
forecasts and others of major problems. The statistical evaluation criteria have shown that

the multivariate models tend to do better forecasts over the harvest season compared to

157

the univariate models both in Nampula and in Maputo. This conclusion is also met when
the economical criteria are applied. However, the multivariate models do not seem to lead
to much improvement in the forecasting ability of the univariate models. This could be
related to two things. First, the data on production, which could be expected to explain
the high fluctuations in the forecast prices do not seem to do this job. The data does not
meet the quality requirements needed for it to improve the quality of the models. Second,
these models could be better if more variables were added, variables thought of as helping

explain the shocks to the forecast time series.

Also, it seems that models with seasonal dummies tend to have considerable forecasting
errors over the months of high peaks, as the data tended to have considerable picks over
the model estimation period, which the models expect to happen in the forecast period,

but did not happen.

Finally, the negative mean gross marginal revenue under all strategies in Nampula suggest
that, in this market, traders are not using the storage facilities or other ways of payment
rather than cash payment are being used. The extreme case that no storage cost is faced
or no product is stored for a month or more is the only situation which can explain that

traders operate in this market.

158

Chapter 7

CONCLUSIONS AND IMPLICATIONS

7.1 Introduction and Research Questions

Price forecasting is an important tool to ensure that participants in the food system plan
the quantity and quality of product to produce, store, sell or consume. Predictions of the
path of agricultural commodities prices is critical in countries like Mozambique, whose
economy basically depends upon agricultural commodities. The importance of such
predictions in reducing uncertainty about returns to production and trade depend,
however, on consistent public policies aimed at ensuring broad improvement of the whole
set of conditions in the economy as a whole, and incentives to the private sector for solid
investments in the agricultural sector and the rural economy. Govemment’s role is very
important in this context. Better physical infi'astructure, consistent policies for better
production and trade, and solid marketing institutions are critical for the success

prediction models.

Maize production in Mozambique depends on natural conditions, and maize prices
fluctuate considerably between the harvest and the planting seasons, and between
producer and deficit areas. Nearly all maize is produced by smallholder households.
Expected profits are usually low compared to cash crops, and producers assume
individually the risk associated with the quality of product, and the decision of how much

to produce, store and sell. The level of uncertainty can, however, be reduced if accurate

159

and timely predictions of firture behavior take place along with consistent policies by the

public sector and incentives for solid investments by the private sector.

This research is a first step in building forecasting models for maize prices in Mozambique.
The research has been directed toward two main objectives. The first objective was to
estimate alternative univariate and multivariate models for short-term forecasts of maize
prices in Mozambique, and examine how well they can improve forecasts as compared to
random walk models. The second objective was to evaluate, using statistical and
economic criteria, how the alternative forecasting models, built upon limited price. and

production data, do in giving forecasts outside the model estimation period.

7.2 Research Methods
The present research used monthly retail price data for four Mozambican markets, data on
actual maize production in Mozambique and Malawi, and monthly maize production

estimates in South Afiica.

In modeling maize prices in Mozambique, two regions were identified, the northern region '
and the central/southern region. Retail maize prices for Nampula and Mocuba, and data
on actual production in Mozambique and Malawi were used for the northern region.
Retail maize prices for Maputo and Manica, and production data for Mozambique and

South Afiica were used for the central/southern region.

160

Time series techniques were employed to identify the data generating process for all the
data series. Specifically, Dickey-Fuller and augmented Dickey-Fuller tests were used to
perform unit root tests on the data. These tests indicated that the data generating
mechanism for all the data series had a unit root, thus first differences were taken before
other preliminary data search tools, such as checking for seasonality and linear trend, were
used. The final univariate models were estimated based on the investigations of the
autocorrelation functions and partial autocorrelation firnctions. Granger causality tests
and cointegration tests were used as a basis for identifying the degree of relationship of the

price series involved in the multivariate models.

Knowledge of the structure and organization of the subsector is key for well-formulated
price analysis. As a way to understand the characteristics, structure and organization of
Mozambique’s maize subsector, this research reviewed the basic conditions in this
subsector, including agro-ecological and technological conditions on the supply side, and
the basic characteristics of demand. Detailed subsector maps were developed for each
region, and the characteristics and functions of the participants in the supply chain were
examined. Coordination problems and indicators of performance of the subsector were

also reviewed.

Finally, several univariate and multivariate forecasting models were estimated and their
forecasting ability compared along with the random walk models. Both statistical and

economic evaluation criteria were used. The economic evaluation involved storage

161

problems. The basic rule of the storage problem was that product would be stored until
price is higher than today’s unit price plus per unit storage cost. Because historical
information on storage costs is not available, the opportunity cost of capital was used.
The decision rule became, then, that product would be stored fi'om period t into period
1+1 if price at period t plus the opportunity cost of capital were lower than the predicted
price for period H 1. The profitability of the different models were compared to that fiom
a default model of selling equal amounts every month, and with the scenario of selling

everything in July with zero storage cost.

7.3 General Findings

The difl‘erent stages of data investigation and model estimation led to several important
findings, systemized and grouped into 1) those related to the organization of the maize
subsector in the country, 2) those related to the characteristics of the maize data, and 3)

those regarding the comparative performance of the forecasting models.

7.3.1 Organization of the Maize Subsector

Agricultural technology is rudimentary in Mozambique. Nearly all maize is cultivated by
smallholder households, with the use of hand tools, and around 90 percent of the
produced grain is consumed on the farm. Due to normal lag in production and the use of

rudimentary tools, maize in Mozambique is supply inelastic in the short-run.

162

These characteristics of farm level production have a relationship with the organization in
the remaining stages of the subsector. For instance, maize assemblers in Mozambique
acquire small quantities from many small farmers, thus assembling product takes longer
that it would under other circumstances. The level of participation of formal and informal
traders is difl‘erent between the north and the center/south. While in the north, the
informal sector is still very weak and large-scale wholesalers trade maize, there is a solid
and specialized informal sector in the center/south, where formal traders import maize but

do not trade domestic maize.

In addition, most of the informal maize grain wholesalers in Mozambique operate at a
small scale, usually located in the most important consumer centers or geographically
strategic areas, and without access to formal credit. Large-scale wholesalers, with access
to working capital, entered into the maize marketing system in the north when

opportunities to export grain to neighboring countries, especially into Malawi, appeared.

Finally, because maize is a basic food crop in Mozambique, it is demand inelastic.
Furthermore, the maize subsector in Mozambique faces coordination problems, the most
important of which are: the high cost of marketing from north to south, instability of
returns to storage for large-scale traders and extremely high operating costs and low
returns to storage for small-scale traders, limited information about market opportunities,
difiicult and high-cost access to working capital, very low farm yields, and inefiiciency in

the small-scale custom milling industry.

163

7.3.2 Characteristics of the Data

In this research, the prices were subject to various specifications of the Dickey-Fuller
tests, and augmented Dickey-Fuller tests when the results revealed that the innovations
were serially correlated. The results of these tests indicated that Mozambique’s maize
retail prices are stationary in first differences, i.e., contain a stochastic trend, and after first
difi‘erences were taken, the results indicated that there is an upwards drift, but it is not
significant in three of the four series. All the price data were found to have a significant
seasonal component. Seasonal dummy variables were found to be jointly significant in all

the time series, thus models with monthly seasonal dummy variables were estimated.

The data series were also checked for structural shocks, as it appears that there could be
structural shocks afi‘ecting the normal fluctuation of maize prices in Mozambique.

Nonetheless, there was no statistical evidence of structural shocks.

7.3.3 Forecasting Models Results

Although the distinction between data with and without unit root is of crucial importance
in time series analysis, it is not of critical importance when the final objective is to perform
short-term forecasts. This research estimated ARMA, ARIMA, VAR and VEC models,
and found that, in each class of models, the models with seasonal dummies generally
overestimated seasonal movements, because price movement during the forecasting period

was much less than typical movement during the estimation period.

164

Second, the multivariate models slightly improved the forecasting ability of the univariate
models. The univariate models were outperformed by the multivariate models because,
while in the former models the time series itself explains variations in the price series and
predicts future values of the price, in the multivariate models other variables, hypothesized
to increase the power of explanation of the data generating mechanism of the series to be
forecast are included. This improvement was not major because the poor quality of the

' additional data, especially the data on maize production in Mozambique and Malawi.

The statistical evaluation indicated that, for each model, there are periods of good
forecasts and others with major problems. The statistical evaluation criteria also showed
that the multivariate models tended to do better forecasts compared to the univariate

models.

Finally, economic evaluation showed that, in Nampula, all the models led to unprofitable
sell/store decisions compared to selling everything in July, while in Maputo they led to
positive results. Prices in Nampula were very low during the forecasting period,
compared to those in Maputo. Compared to the opportunity cost of capital, net returns in

Nampula easily become negative while in Maputo can still profitable.

When compared to the default strategy, the difi‘erent economic criteria indicate that, for
Nampula, only the ARMA model without seasonal dummies and the VAR model with

seasonal dummies lead to less profitable sell/store signals, while the default strategy gives

165

better economic results than all the models except the VEC models under the present
value of the marginal revenue, and is more profitable than all the models except the VEC
model with monthly seasonal dummies under the percentage of correct decisions. In
Maputo, the mean price received indicates that default strategy is outperformed by all the
model-generated strategies, and this finding is not contradicted when the present value of
the marginal revenue and the percentage of correct decisions criteria are considered. Only
the VEC models (with seasonal dummies and without seasonal dummies, respectively)

give less profitability than the default strategy.

7.4 Lessons and Implications for Further Research

Given the importance of price predictions for the stability of production and prices to the
food system and to the economy as a whole, systematic and solid price analysis and
modeling is needed in Mozambique. When farmers have knowledge of the predictions of
the price path, they easily adjust volumes to produce, to store and sell, increasing their
earnings and family income. Likewise, if traders have knowledge of the prediction of the
prices, they plan better where to buy and sell their product, reducing the level of
uncertainty. In addition, previous knowledge of the path of the prices improves
consumers’ budget planning and policymakers’ national programs for the agricultural
sector, food security, and rural development. However, knowledge of the prediction of
price paths only can be usefirl to producers and consumers if the system as a whole has
improved conditions. Access to information, credit, improved storage infiastructure and

better roads are other variables needed for the aimed reduction of uncertainty.

166

In Mozambique, there is a consistent database on maize and other food crop staples prices
at various transaction levels covering most of the rural and urban areas of the country.
This database is, however, still weak. Weaker, yet, is the data on producer level price.
For this reason, this research modeled retail prices instead of producer prices, the latter
being more commonly used in this nature of research. Ifthe systematic price data
collection process, started by Mozambique’s SIMA in 1991, and improved and extended
over the decade, continues, models with producer prices can be estimated in the near

firture.

The quality of the data on maize production needs to be improved. Because monthly
updates of production in Mozambique and Malawi were not available, annual figures were
repeated monthly, which reduced the variability of these data series and hence their power
of improving the multivariate models. Second, the data on Mozambique production does
not show the drought of 1994/95, therefore it does not help explain the spike in the prices

observed in 1995/96.

This research is but a first step in the use of data on Mozambique’s maize price and
production to develop forecasting models for the country. In addition to the need to
continue the systematic and consistent work that Mozambique’s SIMA has been doing,
much more analysis can be done using SIMA data. The models developed in this research
can be improved and updated with the use of additional data on the variables, and with the

inclusion of other variables such as producer and wholesaler prices, monthly updates of

167

production estimates for Mozambique and neighboring countries, and information on
carry-out/carry-in stocks, especially at the farm level. Also, models with logarithmic

variables can be examined and compared to models with the variables in levels.

The limitations of this research have implications for further analyses, both under the
current and under other model specifications. In general, univariate econometric time-
series models are unlikely to give good predictions if the price path changes frequently and
substantial differences are observed between the model estimation period and the out-of-
sample forecasting period. The results of this research suggest that under the current
specifications, multivariate models are likely to overcome this limitation of the univariate
models if higher quality data is available. Moreover, other model specifications, especially
structural models, should also be examined in future work. In addition, the forecast
performance of the models should be subject to a comparative examination involving years
with different price evolution patterns, along with a permanent update of qualitative

information.

168

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