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Date August 16; 1993

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STOCEASTIC TRENDS AND ECONOMIC FLUCTUATIONS IN A LARGE
OPEN ECONOMY: EVIDENCE FROM THE UNITED STATES

by
Stephen B. DeLoach

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

DOCTOR OF PHILOSOPHY

Department of Economics

1993

ABSTRACT

STOCHASTIC TRENDS AND ECONOMIC FLUCTUATIONS IN A LARGE
OPEN ECONOMY: EVIDENCE FROM THE UNITED STATES

BY
Stephen B. DeLoach

This dissertation examines the importance of stochastic
trends in explaining business cycles in the United States. In
particular, it investigates the role of open-economy variables
in accounting for economic fluctuations.

The focus of Chapter II is on the closed-economy common
trends models examined by King, Plosser, Stock, and watson
(KPSW 1991). First, their common trends model is examined in
light of the fact that it is implicitly an open-economy model.
Then, the issue of identification of the common trends is
explored” The evidence shows that their common trends are not
uniquely identified. This casts doubt on their interpretation
that permanent innovations in real interest rates appear to
account for the majority of the short-run forecast-error
variance of 0.8. output.

In Chapter III, the KPSW model in Chapter II is extended
to explicitly incorporate imports, exports, and exchange rates
into the model. There is evidence of a long-run import-demand
equation for the 0.8. which contains a significant
deterministic trend. However, the long-run import-demand
restriction does not appear to depend significantly upon the
real exchange rate. Innovations in the real exchange rate,

independent of output and inflation, account for a relatively

large jpercentage of ‘the forecast-error variance of U.S.
output.

In Chapter IV permanent innovations in foreign output are
introduced. There is evidence of a stable long-run U.S.
export-demand equation which contains foreign output, the real
exchange rate, and a significant deterministic trend. The
stochastic trend in the real exchange rate explains the
majority of both the short-run and long-run forecast-error
variance of exports. Though innovations in the real exchange
rate have no effect on imports in the long run, it has
significant effects in the short run. The majority of the
short-run variance in'U.S. output seems to be accounted for by

the combination of domestic and foreign productivity shocks.

This dissertation is dedicated to my mother, Bobbie,
and my father, Bill.

iv

ACKNOWLEDGEMENTS

The completion of this dissertation would have been
impossible without the contribution of a number of individuals
along the way. This expression of my appreciation to all of
the individuals who, in one way or another, have impacted my
life and my work, does not account for the true debt of
gratitude which I will forever owe.

My advisor Robert Rasche has exhibited seemingly endless
patience throughout the entire process. His keen perception
and understanding of economic issues, even those lying beyond
the normal realm of his concentration, has greatly sharpened
my focus. All of my future development as an economist will
be built upon what he has taught, or attempted to teach, me.

There have been a number of other faculty members who at
various stages of the process provided invaluable support and
guidance. I am grateful for their help and friendship. Also,
I am thankful for the monetary support of those participating
in the "fantasy baseball" league. Owen Irvine also provided
numerous insightful suggestions and comments at my defense,
and I am the wiser for it. I am especially indebted to Rowena
Pecchenino for reading many versions of my work from its
infantile stages through the oral defense. Throughout all of

my many, many years here, she always made her time available

to me -- not an insignificant contribution by any means.

The graduate student community within the department of
economics has offered immense support, both intellectually and
emotionally; Far too often one’s peers are overlooked in this
kind of endeavor. I simply would not have accomplished this
goal without the support of my peers. In particular, I thank
my very closest friends throughout.my years here -- Mary, Kel,
and Laura.

Finally, thanks goes to my family. Mom and Dad have
sacrificed many times over, and in many different ways.
Besides love (and money), the most important thing they have
given me is the philosophy that "education is a lifelong

process."

vi

TABLE OF CONTENTS
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . ix
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . xiv

CHAPTER I: INTRODUCTION . . . . . . . . . . . . . . . . 1

REFERENCES O O O O O O O O O O O O O O O O O O O O O 8

CHAPTER II: STOCHASTIC TRENDS AND ECONOMIC FLUCTUATIONS:
SOME FURTHER ANALYSIS

1. INTRODUCTION . . . . . . . . . . . . . . . . . . 6
2. KPSW (1991) REVISITED . . . . . . . . . . 7
2.1 THEORETICAL REVIEW OF KPSW (1991) . . . 7
2 2 THE COMMON TRENDS MODEL . . . . . . . . . 9
2.3 IDENTIFICATION OF THE COMMON TRENDS . . 11
2.4 IMPLICATIONS FOR THE CURRENT ACCOUNT . . 13
3. THE KPSW MODEL REVISED . . . . . . . . . . . . 14

3.1 IDENTIFICATION OF THE COMMON TRENDS . . 14
3.2 FURTHER MODEL SPECIFICATIONS . . . . . . 16
4 O CONCLUS I ON O O O O O O O O O O O O O O O O O O 2 0

REFERENCES O O O O O O O O O O O O O O O O O O O O 4 4

CHAPTER III: STOCHASTIC TRENDS IN A LARGE OPEN ECONOMY

1. INTRODUCTION . . . . . . . . . . . . . . . . 46
2. THEORETICAL BACKGROUND . . . . . . . . . . 47

3. LONG-RUN TIME SERIES PROPERTIES . . . . . . . 49
3.1 THE DATA . . . . . . . . . . . . . . . 49
3. 2 UNIVARIATE CHARACTERISTICS . . . . . . . 50
3. 3 MULTIVARIATE CHARACTERISTICS . . . . . . 50
4. EMPIRICAL RESULTS . . . . . . . . . . . . 54
4.1 AN OPEN- -ECONOMIY COMMON TRENDS MODEL . . 54
4.2 IMPULSE RESPONSE FUNCTIONS . . . . . . . 54
4. 3 VARIANCE DECOMPOSITIONS . . . . . . . 56

4. 4 AN OPEN-ECONOMY MODEL WITH EXPORTS . . . 58
5 O CONCLUS I ON O O O O O O O O O O O O O O O O O O 6 0

vii

APPENDIX O O O O O O O O O O O O O O O O O

REFERENCES O O O O O O O O O O O O O O O O

CHAPTER IV: THE EFFECT OF STOCHASTIC TRENDS IN
OUTPUT ON ECONOMIC FLUCTUATIONS IN
UNITED STATES

1. INTRODUCTION . . . . . . . . . . . . .
2. THEORETICAL BACKGROUND . . . . . . .
3. LONG-RUN TIME SERIES PROPERTIES . . .
3.1 THE DATA . . . . . . . . . .
3. 2 MULTIVARIATE CHARACTERISTICS . .
4. EMPIRICAL RESULTS . . . . . . . .

4.1 AN OPEN-ECONOMY COMMON TRENDS MODEL

4. 2 IMPULSE RESPONSE FUNCTIONS . . .
4.3 VARIANCE DECOMPOSITIONS . . . .
4.4 SENSITIVITY ANALYSIS . . . . . .
5. CONCLUSION . . . . . . . . . . . . . .
APPENDIX O O O O O O O O O O O O O O O O O

REFERENCES O O O O O O O O O O O O O O O O

viii

80

84

86
87
88
88
89
91
91
92
95
97
98

122

126

CHAPTER II

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

'PABLE

TABLE

1:

LIST OF TABLES

Percentage of Forecast-Error Variance
Attributed to the Balanced-Growth Shock

1 n KPSW made 1 O O O O O O O O O O O O O O O
Percentage of Forecast-Error Variance
Attributed to the Inflation Shock in

KP SW made 1 O O O O O O O O O O O O O O O O O
Percentage of Forecast-Error Variance
Attributed to the Real-Interest Shock

in KP SW "Ode 1 O O O O O O O O O O O O O O O
Long-Run Multipliers in KPSW Model . . . . .
Long-Run Multipliers in Alternative Ordering
Variance-Covariance Matrix in KPSW Model . .

Correlations between Shocks in KPSW Model .

ID Matrix in KPSW Model . . . . . . . . . .
Variance-Covariance Matrix in Alternative
ordering O O O O O O O O O O O O O O O O O O
Correlations between Shocks in Alternative
ordering O O O O O O O O O O O O O O O O O O
ID Matrix in Alternative Ordering . . . . .

Variance-Covariance Matrix with Stationary
M2 -VeIOCity O O O O O O O O O O O O O O O O

Correlations Between Shocks with Stationary
M2-Velocity . . . . . . . . . . . . . . . .

Ifl Matrix with Stationary M2-Velocity . . .

Variance-Covariance Matrix in Two Trend
”Ode 1 O O O O O O O O O O O O O O O O O O O

ix

22

22

23

23

24

24

24

25

25

25

25

26

26

26

26

TABLE 16: Correlations Between Shocks in Two-Trend
made 1 O O O O O O O O O O O O O O O O O O O

TABLE 17: In Matrix in Two-Trend Model . . . . . . . .

TABLE 18: Percentage of Forecast-Error Variance
Attributed to the Balanced-Growth Shock in
Alternative Model . . . . . . . . . . . . .

TABLE 19: Percentage of Forecast-Error Variance
Attributed to the Inflation Shock in
Alternative Model . . . . . . . . . . . . .

TABLE 20: Percentage of Forecast-Error Variance
Attributed to the Real-Interest Shock in
Alternative Model . . . . . . . . . . . . .

TABLE 21: Percentage of Forecast-Error Variance
Attributed to the Balanced-Growth Shock with
Stationary M2-Velocity Assumption . . . . .

TABLE 22: Percentage of Forecast-Error Variance
Attributed to the Inflation Shock with
Stationary M2-Velocity Assumption . . . . .

TABLE 23: Percentage of Forecast-Error Variance
Attributed to the Real-Interest Shock with
Stationary M2-Velocity Assumption . . . . .

TABLE 24: Percentage of Forecast-Error Variance
Attributed to the Balanced-Growth Shock in
Two-Trend Model . . . . . . . . . . . . . .

TABLE 25: Percentage of Forecast-Error Variance
Attributed to the Inflation Shock in
Two-Trend Model . . . . . . . . . . . . . .

TABLE 26: Percentage of the Forecast-Error Variance
Attributed to Transitory Shocks
in Each Model . . . . . . . . . . . . . . .

CHAPTER III

TABLE 1: Phillips-Perron Test for Non-Stationarity of
Univariate Time Series: 1951:4 - 1988:4 . .

TABLE 2: Kwiatkowski-Phillips-Schmidt-Shin Test for
Stationarity of Univariate Time Series:
1951:4 - 1988:4 O O O O O O O O O O O O O O

TABLE 3: Shin (1992) Residual-Based Cointegration Tests
of Vectors: 1954:1-1987:3 . . . . . . . . .

27

27

27

28

28

29

29

30

3O

31

31

63

64

65

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

'TABLE

11:

12:

13:

14:

17:

18:

Variance-Covariance Matrix of Permanent
Shocks in Baseline Model . . . . . . . . .

Correlations between the Permanent Shocks
in the Baseline Model . . . . . . . . . . .

'H in Baseline Model . . . . . . . . . .

Variance-Covariance Matrix of Permanent
Shocks in the 9-Variab1e Model . . . . . . .

Correlations Between the Permanent Shocks
in the 9-Variable Model . . . . . . . . . .

ID Matrix in the 9-Variable Model . . . . .

Long-Run Multipliers in Response to Changes
in the Three Common Trends
(order: Ap, g, y, with AR(6)) . . . . . .

Long-Run Multipliers in Response to Changes
in the Four Common Trends
(order: Ap, q, ex, y, with AR(6)) . . .

Percentage of Forecast-Error Variance
Attributed to the Balanced-Growth Shock
in the Baseline Model . . . . . . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Real-Exchange-Rate
Shock in the Baseline Model . . . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Inflation Shock in
the Baseline Model . . . . . . . . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Balanced-Growth Shock
in the 9-Variab1e Model . . . . . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Real-Exchange-Rate
Shock in the 9-Variable Model . . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Inflation Shock in the
g-variable MOdEI O O O O O O O O O O O O O O

Percentage of Forecast-Error Variance

Attributed to the Export Shock in the
9-Variable Model . . . . . . . . . . . . . .

xi

65

66

66

66

67

67

67

68

68

69

69

69

7O

7O

71

TABLE

CHAPTER IV

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

19:

1:

2:

10:

12:

Percentage of the Forecast-Error Variance
Attributed to Transitory Shocks
in EaCh MOdel O O O O O O O O O O O O O O O

Phillips-Perron Test for Non-Stationarity of
Univariate Time Series: 1957:2 - 1988:4 . .

Kwiatkowski-Phillips-Schmidt-Shin Test for
Stationarity of Univariate Time Series:
1957:2 - 1988:4 O O O O O O O O O O O O O O

Residual-Based Cointegration Tests of
Vectors Without a Time Trend:
1959:2-1987:3 O O O O O O O O O O O O O O O

Residual-Based Cointegration Tests of
Vectors With a Time Trend:
1959:2-1987:3 O O O O O O O O O O O O O O O

Variance-Covariance Matrix of Permanent
Shocks in the Baseline Model . . . . . . . .

Correlations between the Four Permanent
Shocks in the Baseline Model . . . . . . . .

ID Matrix in the Baseline Model . . . . . .

Variance-Covariance Matrix of Permanent
Shocks in the Alternative Model . . . . . .

Correlations between the Four Permanent
Shocks in the Alternative Model . . . . . .

IH Matrix in the Alternative Model . . . . .

Long-Run Multipliers in the Baseline Model
in Response to Changes in the Four Common
Trends O O O O O O O O O O O O O O O O O O O

Long-Run Multipliers in the Alternative
Model in Response to Changes in the Four
Common Trends . . . . . . . . . . . . . . .

Percentage of Forecast-Error Variance

Attributed to the Domestic Balanced-Growth
Shock in the Baseline Model . . . . . . . .

xii

71

100

101

102

102

103

103

103

104

104

104

105

105

106

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

TABLE

14:

15:

16:

18:

19:

20:

Percentage of Forecast-Error Variance
Attributed to the Foreign Productivity
Shock in the Baseline Model . . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Real-Exchange-Rate
Shock in the Baseline Model . . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Inflation Shock in
the Baseline Model . . . . . . . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Domestic Balanced-Growth
Shock in the Alternative Model . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Foreign Productivity
Shock in the Alternative Model . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Real-Exchange-Rate
Shock in the Alternative Model . . . . . .

Percentage of Forecast-Error Variance
Attributed to the Inflation Shock in
the Alternative Model . . . . . . . . . .

Percentage of Forecast-Error Variance

Attributed to the Transitory Shocks
in EaCh MOdel O O O O O O O O O O O O O O

xiii

106

107

107

108

108

109

109

109

CHAPTER II

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

1:

LIST OF FIGURES

Consumption in Response to a One-Standard
Deviation Balanced-Growth Shock in KPSW .

Investment in Response to a One-Standard
Deviation Balanced-Growth Shock in KPSW .

Output in Response to a One-Standard
Deviation Balanced-Growth Shock in KPSW .

Net Exports in Response to a One-Standard
Deviation Balanced-Growth Shock in KPSW .

Consumption in Response to a One-Standard
Deviation Real-Interest-Rate Shock in KPSW

Investment in Response to a One-Standard
Deviation Real-Interest-Rate Shock in KPSW

Output in Response to a One-Standard
Deviation Real-Interest-Rate Shock in KPSW

Net Exports in Response to a One-Standard
Deviation Real-Interest-Rate Shock in KPSW

Consumption in Response to a One-Standard
Deviation Inflation Shock in KPSW . . . .

Investment in Response to a One-Standard
Deviation Inflation Shock in KPSW . . . .

Output in Response to a One-Standard
Deviation Inflation Shock in KPSW . . . .

Net Exports in Response to a One-Standard
Deviation Inflation Shock in KPSW . . . .

Consumption in Response to a One-Standard

Deviation Balanced-Growth Shock in
Alternative Ordering . . . . . . . . . . .

xiv

32

33

34

34

35

35

36

36

37

37

38

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

CHAPTER III

FIGURE

FIGURE

14:

17:

18:

19:

20:

21:

22:

23:

24:

1:

2:

Investment in Response to a One-Standard
Deviation Balanced-Growth Shock in
Alternative Ordering . . . . . . . . . . .

Output in Response to a One-Standard
Deviation Balanced-Growth Shock in
Alternative Ordering . . . . . . . . . . .

Net Exports in Response to a One-Standard
Deviation Balanced-Growth Shock in
Alternative Ordering . . . . . . . . . . .

Consumption in Response to a One—Standard
Deviation Real-Interest-Rate Shock within
Alternative Ordering . . . . . . . . . . .

Investment in Response to a One-Standard
Deviation Real-Interest-Rate Shock with
Alternative Ordering . . . . . . . . . . .

Output in Response to a One-Standard
Deviation Real-Interest-Rate Shock with
Alternative Ordering . . . . . . . . . . .

Net Exports in Response to a One-Standard
Deviation Real-Interest-Rate Shock with
Alternative Ordering . . . . . . . . . . .

Consumption in Response to a One-Standard
Deviation Inflation Shock with Alternative
ordering O O O O O O O O O O O O O O O O O

Investment in Response to a One-Standard
Deviation Inflation Shock with Alternative
Ordering . . . . . . . . . . . . . . . . .

Output in Response to a One-Standard
Deviation Inflation Shock with Alternative
"Ode 1 O O O O O O O O O O O O O O O O O O

Net Exports in Response to a One-Standard
Deviation Inflation Shock with Alternative
ordering O O O O O O O O O O O O O O O O O

Consumption in Response to a One-Standard
Deviation Balanced-Growth Shock . . . . .

Investment in Response to a One-Standard
Deviation Balanced-Growth Shock . . . . .

38

39

39

40

40

41

41

42

42

43

43

72

72

FIGURE 3: Imports in Response to a One-Standard

Deviation Balanced-Growth Shock . . . . . 73
FIGURE 4: Output in Response to a One-Standard

Deviation Balanced-Growth Shock . . . . . 73
FIGURE 5: Net Exports in Response to a One-Standard

Deviation Balanced-Growth Shock . . . . . 74
FIGURE 6: Consumption in Response to a One-Standard

Deviation Real-Exchange-Rate Shock . . . . 74
FIGURE 7: Investment in Response to a One-Standard

Deviation Real-Exchange-Rate Shock . . . . 75
FIGURE 8: Imports in Response to a One-Standard

Deviation Real-Exchange-Rate Shock . . . . 75
FIGURE 9: Output in Response to a One-Standard

Deviation Real-Exchange-Rate Shock . . . . 76

FIGURE 10: Net Exports in Response to a One-Standard
Deviation Real-Exchange—Rate Shock . . . . 76

FIGURE 11: Consumption in Response to a One-Standard
Deviation Inflation Shock . . . . . . . . 77
FIGURE 12: Investment in Response to a One-Standard
Deviation Inflation Shock . . . . . . . . 78
FIGURE 13: Imports in Response to a One-Standard
Deviation Inflation Shock . . . . . . . . 78

FIGURE 14: Output in Response to a One-Standard
Deviation Inflation Shock . . . . . . . . 79

FIGURE 15: Net Exports in Response to a One-Standard

Deviation Inflation Shock . . . . . . . . 79
CHAPTER IV
FIGURE 1: Consumption in Response to a One-Standard

Deviation Domestic Productivity Shock . . 110
FIGURE 2: Investment in Response to a One-Standard

Deviation Domestic Productivity Shock . . 110
FIGURE 3: Imports in Response to a One-Standard

Deviation Domestic Productivity Shock . . 111
FIGURE 4: Exports in Response to a One-Standard

Deviation Domestic Productivity Shock . . 111

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

FIGURE

14:

15:

16:

17:

18:

20:

21:

Output in Response to a One-Standard
Deviation Domestic Productivity Shock . .

Net Exports in Response to a One-Standard
Deviation Domestic Productivity Shock . .

Consumption in Response to a One-Standard
Deviation Foreign Productivity Shock . . .

Investment in Response to a One-Standard
Deviation Foreign Productivity Shock . . .

Imports in Response to a One-Standard
Deviation Foreign Productivity Shock . . .

Exports in Response to a One-Standard
Deviation Foreign Productivity Shock . . .

Output in Response to a One-Standard
Deviation Foreign Productivity Shock . . .

Net Exports in Response to a One-Standard
Deviation Foreign Productivity Shock . . .

Consumption in Response to a One-Standard
Deviation Real-Exchange-Rate Shock . . . .

Investment in Response to a One-Standard
Deviation Real-Exchange-Rate Shock . . . .

Imports in Response to a One-Standard
Deviation Real-Exchange-Rate Shock . . . .

Exports in Response to a One-Standard
Deviation Real-Exchange-Rate Shock . . . .

Output in Response to a One-Standard
Deviation Real-Exchange-Rate Shock . . . .

Net Exports in Response to a One-Standard
Deviation Real-Exchange-Rate Shock . . . .

Consumption in Response to a One-Standard
Deviation Inflation Shock . . . . . . . .

Investment in Response to a One-Standard
Deviation Inflation Shock . . . . . . . .

Imports in Response to a One-Standard
Deviation Inflation Shock . . . . . . . .

Exports in Response to a One-Standard
Deviation Inflation Shock . . . . . . . .

xvii

112

112

113

113

114

114

115

115

116

116

117

117

118

118

119

119

120

120

FIGURE 23: Output in Response to a One-Standard
Deviation Inflation Shock . . . . . . . . 121

FIGURE 24: Net Exports in Response to a One-Standard
Deviation Inflation Shock . . . . . . . . 121

xviii

I : INTRODUCTION

CHAPTER I
INTRODUCTION

Traditionally, business cycles have been thought to be
the result of temporary stochastic shocks to the economy,
while the long-run paths of real flow variables, such as
consumption, investment, and output, are restricted to a
steady-state growth rate. This steady-state growth rate is
presumably determined by the rate of technological progress in
the economy, Solow (1970) . Economic fluctuations in this case
should be studied as deviations around a mean, or around a
mean plus trend growth rate.

This interpretation has strict implications for the time
series of the relevant economic variables. For example,

assume there exists a time series of the form

yt'p'c+et (1’

where at is white noise, and

”c'pc—1+B+nc (2’

Harvey (1990) defines B as the deterministic trend of yc, and
up. as the stochastic trend of yt. In equation (2) the
stochastic trend, pc, is characterized as a random walk plus
drift. Therefore, the permanent disturbance in the stochastic
trend is n c. If the variance of n t is zero, then the series

reduces to

y't-u.o+[it:+ec (3)

If fluctuations are due to transitory shocks, as is the
traditional view, then the series should be written as
containing a deterministic trend plus white noise, equation
(3). Since s: has a mean of zero, and a constant variance,
then shocks to CC will have only temporary effects on y}. ec
would be the source of the observed business cycle behavior,
since it is the only source of deviations from the long-run
trend.

Nelson and Plosser (1982) found that the trend component
of most economic time series can be characterized as a random

walk plus drift, equation (2). More specifically,

Apt-3+“; (‘)

That is, most.economic time series containla stochastic trend.
This stochastic trend should be interpreted as the permanent
component of the series. This presents an entirely different
explanation of business cycles. If economic time series
contain both a permanent and a transitory component, then the
traditional way of thinking about business cycles may not be
correct. Business cycles may be the result of permanent
shocks, such as productivity or permanent inflation shocks.
Recently, several studies have attempted to address the
question of whether business cycles are primarily the result
of temporary or permanent shocks, (Blanchard.and.Quah (1989),

King, Plosser, Stock, and Watson (1991), Gali (1992)). In

3
addition, ‘Mellander, Vredin, and Warne (1992) examined
stochastic trends in a small open economy. To date, however,
no study has examined the issue in a large open economy. The
focus of this dissertation is to fill this void.

Chapter II examines King, Plosser, Stock, and Watson's
(KPSW) (1991) closed-economy common trends model of the U.S.,
and its implications with regards to net exports. The
assumptions and long-run restrictions they'use to identify the
reduced-form are critically examined. In addition, the issue
of proper identification of the permanent shocks is explored.
An alternative specification of the model is then proposed and
estimated.

Since the models tested in Chapter II do not appear to
capture all of the open-economy effects that theoretically
exist, they should be extended. The models in Chapter III
extend the revised KPSW model of Chapter II to incorporate
U.S. demand.for imports. lkiaddition, another common trend is
introduced to the economy, a permanent shock to real exchange
rates. Though the U.S. demand for imports is not dependent
upon.the real exchange rate in the long run, the real exchange
rate does have an effect on the domestic variables through its
effect on U.S. exports.

Finally, Chapter IV completes the open-economy model
specified in Chapter III by adding another long-run
restriction. This restriction is the long-run demand for U.S.
exports. ‘This demand is dependent upon the real exchange rate

and foreign income (output). The complete model contains four

4
common trends: (1) domestic productivity; (2) foreign
productivity; (3) domestic inflation; (4) the real exchange
rate. The results suggest that the two productivity shocks
account for the majority of U.S. economic fluctuations.
Furthermore, the two external shocks, real exchange rate and
foreign productivity, play a significant role in explaining
domestic business cycles. This is a surprising result for

such a large open economy as the U.S..

5

REFERENCES

Backus, D., Kehoe, P. and Kydland, F. (1992), "International
Real Business Cycles," Jon 0 o 't'c c o ,
100:4, 745-775.

Blanchard, O. and Quah, D. (1989), "The Dynamic Effects of
Aggregate Supply' and Demand. Disturbances," Anerignn

Ecgnomic Revlew, 79, 655-673.

Gali, J. (1992), "How Well Does the IS-LM Model Fit Postwar
U.S. Data?" Quarterly Journal or Econgnicg, May, 709-738.

Harvey, A. (1990), e c o 'c 's ' ,
Cambridge: MIT Press, 1990.

King, R. G., Plosser, C. 1., Stock, J. H. and Watson, M. W.
(1991), "Stochastic Trends and Economic Fluctuations,"

American Economic Revlew, 81, 819-840.

Mellander, E., Vredin, E. and Warne, A. (1992), "Stochastic
Trends and Economic Fluctuations in a Small Open

Economy," Journal or Applled Egononins, 7, 369-394.

Nelson, C. and Plosser, C. (1982), "Trends and.Random Walks in
Economic Time Series: Some Evidence and Implications,"

Journal of Monetary Econonlcs, 10, 139-162.
Solow, R. M. (1970), Growth Theory: An Erngsltlgn, Oxford:

Clarendon Press, 1970.

II: STOCHASTIC TRENDS AND ECONOMIC FLUCTUATIONS:

SOME FURTHER ANALYSIS

CHAPTER II

STOCHASTIC TRENDS AND ECONOMIC FLUCTUATIONS:
SOME FURTHER ANALYSIS

1. INTRODUCTION

King, Plosser, Stock and Watson (1991) have investigated
the implication of a single permanent stochastic shock found
in one-sector Real Business Cycle models. To test this
implication empirically, they construct a closed economy
common trends model for the U.S. in the postwar period.
However, in doing so, they fail to account for net exports1

in their market clearing condition

l'-(?+ I (1)

where, output is defined as private GNP (Y-G) . Clearly,
equation (1) is not a market-clearing condition since net
exports are not accounted for (either by inclusion on the
right-hand side, or subtraction from the left-hand side).
The purpose of this chapter is two-fold. Primarily, it
examines the King, Plosser, Stock and Watson (KPSW) common
trends model in light of the "adding-up" problem.
Specifically, this involves investigating the implications

that the model has for the current account. Secondly, in the

 

1Actually, the omitted variable from the closed-economy
market-clearing condition is net exports plus changes in
inventories (see footnote 2). However, in this study I will
simply make reference to "net exports" when impulse response
functions are constructed. ‘There is no reason to believe that
the interpretation of the results are sensitive to the
omission of the changes in inventories in "investment."

6

7
process of replicating their model the issue of identification
of the permanent components is encountered.

The organization of this chapter is as follows: (1) the
theoretical justifications for the restrictions used by KPSW
(1991) are reviewed; (2) the econometric methodology of KPSW
(1991) is reviewed; (3) their model is replicated and the
issue of identification is explored; (4) impulse-response
functions for net exports are calculated as a residual of
private GNP less consumption and investment, and the
implications are examined; (5) an alternative ordering of the
permanent shocks in the KPSW model is produced and the results
are contrasted with their specification; (6) specification of
the permanent shocks is further examined in light of evidence
that a common trend associated with the real interest rate is
not identified in this model, and an alternative model is

estimated.
2. RPS. (1991) REVISITED

2.1 THEORETICAL REVIEW OF RPS. (1991)

This section reviews the theoretical justifications
underlying the long-run restrictions imposed by KPSW (1991).
The long-run restrictions they impose will be maintained to
begin with in this study.

Solow (1970) suggests 'that. there exists a long-run
relationship between consumption and output and investment and
output. In Solow growth models, per capita output,

consumption, and investment all grow at the same rate along a

8
balanced—growth path. This implies that the ratios of real
per capita consumption to real per capita output and real per
capita investment to real per capita output are stationary

stochastic processes. That is,

Cc’yt'el.c;€1.c"I(o) (2)

it‘yt'ez.c;€2.c"I(o) (3)

This implies that real.per capita consumption, real per capita
investment, and real per capita output each possess a common
stochastic trend. This common trend is assumed to represent
innovations in total factor productivity. The one-sector
Solow growth model has recently been extended by Kydland and
Prescott (1982) and King, Plosser, and Rebelo (1988). These
Real Business Cycle models predict that innovations in total
factor productivity are potentially capable of accounting for
short-run economic fluctuations as well as long-run growth.
KPSW (1991) augment the "great ratios" which are implied by
Solow' models by including' a real interest rate in the
theoretical long-run relationship. Theoretically, a
permanently higher real interest rate implies that a smaller
share of output goes to investment and a larger share goes to
consumption.

KPSW (1991) introduce nominal shocks into the model
through the money-demand function. Though the demand for
money is a demand for real balances, it is possible that

because:of frictions, or incomplete information, in the short-

9
run changes in inflation can have real effects. In addition,
they assume that the Fisher equation holds in the long run.

That is,

Rt - It 4» Apt (4)

where r, is the real interest rate. Therefore, the real
interest rate is equal to the difference between the nominal
interest rate and inflation. Furthermore, they explicitly
assume the real interest rate to be non-stationary.
Therefore, there is a permanent stochastic trend associated

with the real interest rate.

2.2 THE COMMON TRENDS MODEL
The methodology described in KPSW (1991) consists of:
(1) a reduced—form represented by a Wold representation of the

series in first differences

AXt-|J.+C(L)e:c (5)

where Xt - (c,i,m-p,y,Ap,R)’ and e, is the vector of one-step-
ahead forecast errors in Xt, given information on lagged

values of X}; (2) a structural model given by
Axc'F‘JYLM c (5)

where 11t is a 6x1 vector of serially uncorrelated structural

disturbances, consisting of permanent innovations, 111., and

transitory innovations,ni. Therefore, if €¢"IBH¢. where Po

10

is the structural impact multiplier, C(L) - I‘alI‘(L) .2

Their model consists of three permanent stochastic shocks
to the system: a real balanced-growth shock, an inflation
shock, and a real-interest-rate shock. The reduced-form,
equation (5) , is estimated as a Vector-Error Correction model
with 8 lags and three error correction terms. After
estimating equation (13) I‘o and 111. can be deduced since C(L)
and I‘(1) are known.

Identification of the model is accomplished by imposing
two restrictions. First, three cointegrating vectors are
specified in order to restrict the matrix of long-run
multipliers. Secondly, innovations in the permanent
components are assumed to be mutually uncorrelated, as well as
uncorrelated with innovations in the transitory components.

The matrix of long-run multipliers consists of the three
cointegrating vectors and three "common trends", or permanent
shocks. KPSW ( 1991) order the shocks as: ( 1) a balanced-
growth shock; (2) an inflation shock; and (3) a real-interest-

rate shock. Their cointegrating vectors are

m-pc - 1.197yt - 0-013R. (7)
ct-yt - 0.0033(Rt-Apt) (8)
it-yt - -0.0028(Rt-Apt) (9)

 

2see KPSW (1991) Appendix.

11
In matrix notation,
0 0 1.0 ~1.197 0 .013

B’- 1.0 0 0 -1.0 .0033 -.0033 (10)
o 1.0 0 -1.0 —.0028 .0028

Therefore, the first restriction, the matrix of long-run

multipliers is written as

I‘(1)-[A'OII:0] (11)

A}, is orthogonal to B’ and is a 6x3 matrix partitioned into
three cointegrating vectors and three common trends. II is a
3x3 lower triangular matrix where the first column represents
the impact of the first shock, and so forth. Specifically, II
is the Cholesky decomposition of the variance-covariance
matrix of the permanent components, where the values on the
diagonal are normalized to 1.00. 0 is a 6x3 matrix of 0’s,
which represent the long-run effects of the three transitory

shocks on the six variables in the system.

2.3 IDENTIFICATION OF THE COMMON TRENDS

In order to identify the permanent components of the
trends, innovations in the permanent components (11%) are
assumed to be mutually uncorrelated, as well as being

uncorrelated with innovations in the transitory components

(fit). II (3x3) is the lower triangular decomposition of the
variance-covariance matrix of the permanent components, where
the values on the diagonal are normalized to 1.00. 11 is

given in Table 6 for the original KPSW model. The estimated

12
long-run multipliers for the permanent innovations in their
model are reported in Table 4.

In order to construct the common trends it is necessary
to assume that the three permanent shocks are uncorrelated.
This assumption has an implication for the II matrix.
Specifically, if the permanent shocks are uncorrelated, the H
matrix should be the identity matrix. If II is the identity
matrix, the ordering of the shocks would be of no consequence.
However, since the H matrix resulting from the original KPSW
model, reported here in Table 6, is not close to identity,
this has implications for the effect of the balanced-growth
shock on subsequent shocks.

As Table 4 shows, the long-run response of inflation to
a one-percent balanced-growth shock is an increase of 6~31
percent. In addition, a one-percent balanced-growth shock
will lead to a decrease in the nominal interest rate of 35.32
percent. Since the one-percent balanced-growth shock leads to
both an increase in inflation and a decrease in the nominal
interest rate, it can be concluded that the same shock leads
to a decrease in the real interest rate. .As they are ordered,
the permanent shocks do not correspond to the shocks which
they claim that they represent. In addition, though the long-
run multiplier of the balanced-growth.shock.on income is 1.00,
the long-run multipliers of the balanced-growth shock on
consumption and investment are 0.86 and 1.12, respectively.
This is inconsistent. with. the notion of a steady-state

balanced-growth shock.

13

2.4 IMPLICATIONS FOR THE CURRENT ACCOUNT

Having satisfactorily duplicated the KPSW model, I turn
to the question of implications for the current account. To
do this, impulse-response functions are estimated for the real
flow variables (y,c,i,x-m). Mean impulse responses with
respect to a one-standard-deviation shock in each of the
common trends, along with their respective 95% confidence
intervals are calculated and shown in Figures 1-12.3 Impulse
responses for' net exports are (calculated by subtracting
consumption and investment responses from that of output. It
is not appropriate to estimate confidence intervals in the
same way, since these are non-linear.

The implications for net exports can be seen in Figures
4, 8 and 12. The KPSW model as constructed implies that a
permanent balanced-growth shock leads to a short run
improvement in the current accounts In the long run, however,
it leads to a permanent worsening of the current account (a
decrease in net exports). In addition, the model implies that
permanent shocks to inflation and the real interest rate lead
to temporary' worsening of ‘the current account. It is
plausible that an increase in the real interest rate would
have this effect if it leads to an equal improvement in the
capital account (vis-a-vis a depreciation of the real exchange

rate). However, even if prices are "sticky" in the short run,

 

3Following Kloek and Van Kijk (1978), confidence
intervals were constructed by taking 1000 random draws from
the posterior distribution of the orthogonalized impulse
responses in the VECM and computing means and variances.

14
Dornbusch (1976) , an increase in domestic prices would lead to
a depreciation of the real exchange rate in the short run. In
that case, one would expect that the Current account would
improve in the short run. 0n the other hand, if net exports
in response to changes in real exchange rates follow a J-

curve, then this observed response would be plausible.
3. THE KPSW MODEL REVISED

3.1 IDENTIFICATION OF THE COMMON TRENDS

Since the II matrix in the KPSW model is not close to
identity, the permanent components of the three variables do
not correspond to the common trends as specified. To rectify
this problem alternative orderings were used in order to find
an ordering which produces aiH matrix which is as close to an
identity matrix as possible. This is reported in Table 9.
The ordering which yields the most desirable properties is one
in which the real-interest shock is first, the inflation shock
is second, and the balanced-growth shock is third.‘ The long-
run multipliers are provided in Table 5.

It is interesting to compare the long-run multipliers in
Table 5 with those from the KPSW model in Table 4. First,

with the alternative ordering, the balanced-growth shock has

 

l'It should be pointed out that this alternative ordering
is considered in KPSW (1991). However, they conclude that
this alternative does not "change the main qualitative feature
of the results." The argument here is that KPSW's preferred
ordering of the common trends simply does not correspond to
the permanent components of the variables. That is, the
actual common trends in the KPSW model simply are not the
common trends which they are attempting to identify.

15
no long-run effect on either inflation or the real interest
rate since it is ordered last. Neither the inflation nor the
real-interest shock have an effect on real output, since “31

and «52 are zero for all practical purposes. Further, the

inflation shock leads to proportional increases in both
inflation and the nominal interest rate. The inflation shock
has no effect on the real interest rate, since the real-
interest shock is ordered first.

There are several important things worth noting about the
variance decompositions reported in Tables 18-20, and the ones
ordered in KPSW (1991), Tables 1-3. First, the Real Business
Cycle theory's implication that the balanced-growth shock
should explain a majority of both the short-run and long-run
variability of real macroeconomic variables is not supported
in the KPSW model. The alternative ordering does not change
this result, the primary result of their paper. Though after
4 quarters, the balanced-growth shock.explains 30% (versus 3%)
of the variance in output, it has even less explanatory power
in the long run. Even up to 24 quarters the balanced-growth
shock explains less than half of the variance in output.
Further, KPSW (1991) were surprised that the inflation shock
had a negligible effect on the real variables in the short
run. However, with the alternative ordering, the inflation
shock’s effect is significantly increased. Though it still
has a negligible effect of consumption, it does have important
effects on output and investment. In fact, over the first 8

quarters, the inflation shock is the single most important

16
determinant of the variance in investment.

The impulse—response function of net exports in Figure 16
is consistent with that in Figure 4. The balanced-growth
shock leads to a permanent worsening of the current account.
The initial effect.of an increase in the balanced-growth.shock
is to improve the current account (surplus). Furthermore,
Figure 18 shows that the response of investment to an increase
in the real interest rate is now consistent with the theory
outlined in Section 2.1. The hypothesized immediate decrease

in investment cannot be rejected.

3.2 FURTHER MODEL SPECIFICATIONS

In this section two further specifications are
considered. First, the KPSW model, with alternative ordering,
is re-estimated to consider the possibility that the velocity
of M2 (money supply) is stationary. Second, the stationarity
of the real interest rate is explored.

Hallman, Porter, and Small ( 1991) model the long-run

money-demand equation as

117—L); - Y: - €3,130. 83'; ~ I(0) (12’

This differs from the standard money-demand function in
equation (9) in that it does not contain the nominal interest
rate as an explanatory variable. They reject the null of a
unit root for the residual in equation (12). That is, the
velocity of M2 is stationary. Since the long-run restriction

implied by equation (12) cannot be rejected, I estimate the

17

VECM with money demand specified as equation (12) instead of
(9) . Tables 21-23 summarize the forecast-error variance
decompositions for this model. The main difference between
these estimates and those of the alternative model is that
without the nominal interest rate in the money-demand
equation, the influence of the inflation shock is minimal,
even for investment. These are very similar quantitatively
with KPSW's (1991) original results.

In both orderings of KPSW’s model considered, there was
a negative correlation between the real interest shock and.the
inflation shock, as seen in Tables 6 and 9. In the model with
the shocks most closely identified as a balanced-growth, an
inflation, and a real-interest shock, the real-interest shock
is ordered first. While it is possible that a change in the
real interest rate could lead to a change in inflation, the
negative correlation is inconsistent with this ordering. For
example, suppose the monetary authorities are targeting
nominal interest rates. Now, suppose there is a positive
shock to the real interest rate. The nominal interest rate
will increase proportionally, according to the assumption of
the long-run Fisher equation. If monetary authorities stick
to the rule, then they must increase the money supply in order
to keep nominal interest rates within the target range.
Therefore, in the long run inflation should increase. Thus,
under such a rule, a positive shock to the real interest rate
will lead to a positive increase in inflation. But, this is

opposite of what the model predicts when the real-interest

18
shock is ordered first.
In light of this inconsistency, the inflation shock

should be ordered first. The resulting H matrix is

1 0 0
n - -0.97 1 0 (13)
0.003 -0.007 1
When the inflation shock is ordered first, a real interest
rate shock is not uniquely identified. Rather, the real-
interest shock is a linear combination of the first and second
shock. Specifically, It - R - 0.97Apt. This leads me to
question whether or not the real interest rate is stationary.
If it is, then innovations in the real interest rate are only
transitory, and, therefore, cannot be identified as a common
trend. In addition, if the real interest rate is stationary,
then it does not belong on the right-hand side of equations
(7) and (a).

KPSW (1991) test the existence of a stable
(cointegrating) relationship between the nominal interest rate
and inflation. They find no evidence of a stable long-run
relationship. Therefore, assuming the long-run Fisher
equation (4), they argue that the real interest rate is non-
stationary. Recently, Mishkin (1992) and Crowder and Hoffman
(1993) have both found evidence of a single common trend
between inflation and nominal interest rates. While Mishkin
tested the standard Fisher equation (4), Crowder and Hoffman
tested the tax-adjusted Fisher equation. Darby (1975) argued

that the Fisher equation.should.take intolaccount tax effects.

19
Following this logic, the appropriate the long-run Fisher

equation should be

Rt - I; + 1.30mApc (14)

where r; is defined as the after-tax real interest rate.

Crowder and Hoffman (1992) find that when the Fisher equation
is generalized in this way, the hypothesis that the after-tax

real interest rate is stationary cannot be rejected, since

Rt - 1.30*Apt - e", ; e", ~ I(0) (15)

Tables 24 and 25 summarize variance decompositions in the
model with the common trends: inflation and balanced growth.
I have assumed the long-run relationship between inflation and
nominal interest rates given by the Fisher-Darby (after-tax
Fisher equation) equation (15). In addition, the
cointegrating vectors described in equations (8) and (9) are
no longer used. Instead, the cointegrating vectors implied by
the standard Solow growth model, equations (2) and (3), are
used. Compared with the alternative ordering of the original
KPSW model specification, the balanced-growth shock actually
accounts for more of the variance in output in both the short-
run and the long-run. Again, the inflation shock does not
account for much of the variance in either consumption,
investment, or output. While it does not account for the
majority of the short-run changes in the nominal interest
rate, it does explain the long-run nominal interest rate,

which is consistent with the cointegrating vector in equation

20

(15). The short-run changes in the nominal interest rate must
be dominated by transitory changes in the real interest rate.

Table 26 summarizes the variances due to the transitory
shocks in all four of the models examined here at both 12 and
120 quarters. Interestingly, the majority of variance in the
real flow variables is not due to either inflation or the
balanced-growth shocks. The majority of changes in these
variables is due to transitory shocks, likely transitory real
interest rate changes. This is in sharp contrast with the
results in the VECMs with the real interest rate included as
a permanent trend. This conclusion differs form KPSW's (1991)
claims that permanent stochastic shocks explain the majority

of short-run economic fluctuations.

4. CONCLUSION

This chapter questions the conclusions of KPSW (1991) on
two basic grounds. The common trends model as they develop
it, is implicitly an open-economy model. Their model implies
that the current account is a residual of output minus
absorption. Their model predicts that an increase in the
balanced-growth shock leads to a permanent worsening of the
current account" If imports are dependent on income, then one
would expect that a permanent increase in income would lead to
permanent worsening of the current account. However, it says
nothing about the role of the real exchange rate, and in fact
implies that there is no role for the real exchange rate in

the long run. This is only true if permanent changes in the

21
real exchange rate have only transitory effects on the real
variables. Most notably, imports and exports are not
dependent upon exchange rates in the long run.

Secondly, the KPSW model fails to identify the three
common trends which they propose to model: the balanced-
growth, inflation, and real-interest shocks. That is, since
the II matrix they estimate is not close to an identity
matrix, the three permanent shocks are not independent. Thus,
a true balanced-growth shock fails to be identified in their
model. When the shocks are reordered to take this issue into
account, the balanced-growth. shock fails to explain the
majority of the short-run or long-run variance of the real
variables, the main result of KPSW (1991). In addition, in
the alternative specification of their model in which there is
no common trend associated with the real interest rate, the
permanent shocks are not able to account for the majority of
short-run fluctuations. With these short-comings in mind,
subsequent chapters will focus on extending the revised KPSW
model in order to construct an open-economy common trends

model for the United States.

22

TABLE 1

Percentage of Forecast-Error Variance Attributed
to the Balanced-Growth Shock in KPSW Model

 

 

, 1 4 8 12 16 20 24 120 i
* c 2 15 31 48 59 63 65 87
t 1' 14 6 15 27 32 33 33 65 f
' m—p 79 77 70 72 74 75 77 79 l
-, y 1 3 21 43 53 58 61 90 ~
' Ap 31 23 21 17 16 15 14 6
- R 13 12 11 11 11 12 14 22
TABLE 2

Percentage of Forecast-Error Variance Attributed
to the Inflation Shock in KPSW Model

 

 

 

 

=_.__7 g: Period 41

1 4 8 12 16
C 1 1 0 l 1
.1 8 23 20 12 10
m—p 1 4 1 l l
y 0 3 3 2 2
Ap 45 39 45 50 54
R - 3 4 2 2 1 3

 

 

23

TABLE 3

Percentage of Forecast-Error Variance Attributed
to the Real-Interest Shock in KPSW Model

Period

 

 

 

TABLE 4

Long—Run Multipliers in KPSW Model

 

 

 

 

 

 

 

variable y-shock Ap -shock (R-Ap)-shock .1
C 0.86 -0.0028 0.0033 l
i 1.12 0.0024 -0.0028 1
y 1.00 0.00 o. 00
III-JP 1.66 -0.002 -0.013
AJp 6.31 1.00 0. 00
R 7 _ f _35_. 32 _ 0.14 _ 1. 00

 

 

24

TABLE 5

Long-Run Multipliers in Alternative Ordering

 

 

 

 

 

 

 

 

variable y-shock A p -shock (R- A p) -shock ,
C 1.00 -0.0036 -0.0025
1 1.00 -0.0036 -0.0086
y 1.00 -0.0036 -0.0058
m-p 1.197 -0.017 -0.016
‘ Ag 0.00 1.00 -0.2796
‘ R 0.00 1.00 ,_. “0.72 _
TABLE 6

 

 

Variance-Covariance Matrix in KPSW Model

 

 

 

0.00005

 

 

   

 

0.00031

0.10073

  

 

 

 

-0.00205

 

-0.09792

TABLE 7

 

 

    

0.35017

Correlations between Shocks in KPSW Model

 

 
 

0.13954

 

 

 

-0.49393

 

 

  

-0.52138

 

   

 

25

TABLE 8

H Matrix in KPSW Model

 

 

 

 

 

 

 

 

TABLE 9

Variance-Covariance Matrix in Alternative Ordering

 

 

 

 

   

 

 

 

 

(R—Ap) Ap
(R-Ap) 0. 35017 -
Ap -0. 09792 0 . 10073
y -0. 00205 0 . 00031 0 . 00005
TABLE 10

Correlations between Shocks in Alternative Ordering

 

-0.52138
-0.49393 0.13954

 

 

 

 

TABLE 11
H Matrix in Alternative Ordering

(R-Ap) AP

(R-Ap) 1. 00 -
Ap -0.28 1.00

 

 

 

 

 

 

 

 

 

Y' '0.01 0.0

 

26

TABLE 12

Variance-Covariance Matrix with Stationary M2-Velocity

 

0.46434
-0.16221 0.13700
-0.00489 0.00165

 

 

 

 

 

 

 

TABLE 13

Correlations Between Shocks with Stationary M2-Velocity

 

 

 

 

(R-Ap) Ap
.Ap -0.64313 -
y' -0.72480 0.44922 }
TABLE 14

ID Matrix with Stationary M2-Velocity

 

 

 

 

 

 

 

TABLE 15

Variance-Covariance Matrix in Two Trend Model

 
   
   

 

0.18204
-0.00101

 

 

 

   

27

TABLE 16

Correlations Between Shocks in Two Trend Model

 

AL) I

 

 

y -.35288 I

TABLE 17

H Matrix in Two Trend Model

 

 

 

 

 

 

 

 

 

Ap y
Ap 1.00 -
V -0.01 1.00
TABLE 18

Percentage of Forecast-Error Variance Attributed
to the Balanced-Growth Shock in Alternative Model

 

 

 

 

Period

1 4 8 12 16 20 24 120
19 27 26 29 38 52 58 85
0 12 14 11 11 14 17 38
70 40 26 25 27 30 33 31
10 30 36 33 36 41 47 67
33 19 18 15 13 11 11 4

l 1 2 3 3 2 2

 

 

28

TABLE 19

Percentage of Forecast-Error Variance Attributed
to the Inflation Shock in the Alternative Model

 

 

 

1 -1 3s ,,_1_ Period IL 7777 7 ,

w 1 4 8 12 16 20 24 120
w c 3 5 4 7 7 7 5 3 :
l 1' 34 52 39 25 22 21 20 10
w m-p 0 1 8 10 11 12 12 13
y 11 26 21 16 13 12 11 4
; Ap 43 44 48 55 52 52 52 65 i
R 6 26 25 25 28 28 28 28 i

TABLE 20

Percentage of Forecast-Error Variance Attributed
to the Real-Interest Shock in the Alternative Model

 

 

 

 

29

TABLE 21

Percentage of Forecast-Error Variance Attributed to the
Balanced-Growth Shock with Stationary MZ-Velocity Assumption

Period

 

 

 

TABLE 22

Percentage of Forecast-Error Variance Attributed to the
Inflation Shock with Stationary M2-velocity Assumption

 

 

 

30

TABLE 2 3

Percentage of Forecast-Error Variance Attributed to the
Real-Interest Shock with Stationary MZ-Velocity Assumption

 

 

 

TABLE 2 4

Percentage of Forecast-Error Variance Attributed to the
Balanced-Growth Shock in Two-Trend Model

 

 

s, _ WW _ __ ____Pd_- __ W l _ I .-

1 4 8 12 16 20 24 120 *
c 16 23 23 31 4o 47 55 82
1 0 5 17 15 16 16 18 51
m-p 72 43 36 41 40 39 41 37
‘ y 19 35 39 37 42 46 51 79
Ap 38 26 22 13 10 3
R 3 4 6 8 7 7 1

 

31

TABLE 2 5

Percentage of Forecast-Error Variance Attributed to the

Inflation Shock in Two-Trend Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Period
1 4 8 12 16 20 24 120
C 2 3 2 7 13 15 12
i 0 15 22 23 23 29 30 21
m-p 11 23 13 10 17 25 29 58
Y 3 3 7 13 12 14 13 12
Ap 23 26 31 56 66 71 73 91
R 21 11 8 21 35 41 48 91
TABLE 26
Percentage of the Forecast-Error Variance
Attributed to Transitory Shocks in Each Model
12 Quarters 120 Quarters
I II III IV I II III IV
C 38 40 28 44 4 5 3 6
27 27 31 37 13 13 11 28
y 18 17 24 50 4 3 4 9
Model I = Original KPSW Model
Model II = KPSW Model Under Alternative Ordering
Model III = Model II With Stationary M2-Velocity Assumption

Model IV

Model With Two Common Trends

 

 

32

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I? 70 II ICC 111

FIGURE 1: Consumption in Response to a One-Standard Deviation
Balanced-Growth Shock in KPSW

 

 

 

 

 

 

 

 

 

 

 

41 .1 .1 71 II II 10‘ 111

FIGURE 2: Investment in Response to a One-Standard Deviation
Balanced-Growth Shock in KPSW

33

 

 

 

 

1.1: .
II
I I
I h.
I \
I \
I I‘ \
III A 1’ -‘%
1 ' ‘ . i i I, \‘ -------------------
I \ / “"
. V"
I
I
I
I
j
I OI I
I

\
<

 

 

~..l\“~:""‘

 

 

 

 

 

 

 

I II N N H I. .7 7. I. I0. III

FIGURE 3: Output in Response to a One-Standard Deviation
Balanced-Growth Shock in KPSW

 

 

 

 

 

 

 

 

 

 

 

 

 

I.I \
O I \
\/
UV /\
\ \\/ ~
'I
I
I
‘1 A
I... I \/ \/\/—\
I
I
I
I
I
I
I - 2-1
'u' ‘ I"\‘ ’7 \
HIV I \ / ‘\ -----------
III I \ , \ ...........
"I I' ‘\ /’
‘I I. \\"I
J. l
1.: I I
I I
I I
I I
I I
I I
I I
I!
: 4 ii
II
II
II
.'
. e j I t I T I I T I T T I
I II II II 4I II II II OI OI IOI III

FIGURE 4: Net Exports in Response to a One-Standard Deviation
Balanced-Growth Shock in KPSW

 

 

 

 

 

 

 

 

 

 

 

 

0 CI. f‘
I I
I I \
I / \
I I \
\ I \
‘. z x
\ -------------
I I ---------
I I \--‘
LOII I, ,7
I I
I I
I I
I I
I I
\I I
\\ / 1/\\
\
0 0.. V
F‘
\
I \'n A
0 CI. [
,J
. ." T f I I I I I I I I I
I I. I. 8‘ C. I. .7 I. O. IO. III

FIGURE 5: Consumption in Response to a One-Standard Deviation
Real-Interest-Rate Shock in KPSW

 

 

 

 

 

 

 

 

 

 

 

 

I .00
I1
II
I I
I I
I l
I I
I I
I I
0.01. I
I
I
I
I
I
I ~
I II I \
I I I
0 OI. I l \
I I \\
I I \
“ I \\ .........
\ I \ 1’ """""""
\ I ‘~——’
I I
I
\ ’_/\\/’\“
. ./
\ 4’
0 CI. \v/ ‘\a’
0....
. ." I I I ’I’ I I I I I I I
I II I. 80 II I. .7 I. .0 IO. III

FIGURE 6: Investment in Response to a One-Standard Deviation
Real-Interest-Rate Shock in KPSW

35

 

 

 

 

0 on 7r
II
II
II
II
II
I I
I
I
I
0.0!. 1
I
I
I
I
I
'I I’\
l “\\
0.010 I‘ [I .....................
\ I
\

 

 

 

 

 

 

 

1 18 I. 30 CI ll 07 10 0. 10. 111

FIGURE 7: Output in Response to a One-Standard Deviation
Real-Interest-Rate Shock in KPSW

 

 

 

 

 

 

 

 

 

0....
0.080
IA
/. \\.
’ \
/ .“\//
70‘ _ /'\ AV
0.... , \
/ \
I \\
I \ I .......
I | / ‘ .................
I I /
I \ I
I \ /
I \ /
I \ I
I \ I
I \ I
I v
I
0 08‘ . '
| I
I I
‘1'
'u
I
. .'. I T f T I I 1 I I I Y
1 I! I. .0 H H 01 70 CI 100 111

FIGURE 8: Net Exports in Response to a One-Standard Deviation
Real-Interest-Rate Shock in KPSW

36

 

 

 

 

\
0.0.6. ‘

 

l

A

0.000.
/
I
k ./

 

 

 

 

 

 

 

 

-...II. V
....'.. I I I I T fi I f T r
I I. I: U. I. I. 'I 7. U. I.. III

FIGURE 9: Consumption in Response to a One-Standard Deviation
Inflation Shock in KPSW

 

 

 

 

 

 

 

 

 

 

 

0.000
A
II
II
II
II
II
II
II
I I
0.000 71
I I
I I
I I
I I
l l r\
II \
II I
II I
I\' 'I
0.010 T .
'I /" \ ........................
I I \~"
II
\I
0.000 ]\ \/
4.0" V
...... I I I I T I I I T I I
I u u u u u n H n III III

FIGURE 10: Investment in Response to a One-Standard Deviation
Inflation Shock in KPSW

37

 

 

 

 

 

0.0!.
I
M
II
II
II
II
I
1
0.010 I
I A
I H
I III
I n I
I \
".
0 0|. ‘\
I I ./ \\ ........
\ --------------
II \ r/ \\\\
J I I
I I
\I
I
0.006

 

 

 

 

 

 

 

 

 

 

 

0.0..
/ W
-I.O|O I \f/ \/
. . . . ' . I I I If 1 I I f I I I
I II II I. ll II I? I. I. IO. III

FIGURE 11: Output in Response to a One-Standard Deviation
Inflation Shock in KPSW

 

 

 

: “Um
/ \dmv
1 I /\ A

 

 

 

 

 

 

 

 

I \ v r \-—
O 000 , v \ I
I \ I
I \ 'l
.'
I
1
I on II
I I I
| A I
:II/
I I’
I on ‘ I
I I
II
II
II
II
I]
0.0.. II
II
II
H
II
II
. .‘. T l I I T I I I I I I
I I! I. 84 II II 07 10 I. 100 III

FIGURE 12: Net Exports in Response to a One-Standard Deviation
Inflation Shock in KPSW

38

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I . I .
."\
I \.
I \
I \
‘l ‘V
I .. ; \
x ...................
lI \ ......
r/
J
:1
1.2. {V
I'
l
I
I
I... ,J
I
I
I
I
..I. ij/f
.... l/K/
I“
..l. j//
. a . . f‘\.v”r
. .. 77 T7 7 V T T r T r 1’ I
I I. 8. I. .. .. .7 I. .. IO. 11]

FIGURE 13: Consumption in Response to a One-Standard Deviation
Balanced-Growth Shock with Alternative Ordering

 

 

 

 

 

 

 

 

 

 

 

/ \ M
/ \_ 4/

.o. I V

. . }//\\\\/

I II II .I .I .I .I II .I .I I.I III

FIGURE 14: Investment in Response to a One-Standard Deviation
Balanced-Growth Shock with Alternative Ordering

39

 

 

 

I...
n

I II F-

I II ,/ \

II III\ I \\

II I \r' \ I -

1| 1 1 .v , ------
I... II I \I ‘s ’r’

I I I \-'

III

I II

I II

I II

I II

f U
I II I

I

 

 

 

 

 

 

 

 

 

I II 8. I. l. I. .7 7. .. 1.. III

FIGURE 15: Output in Response to a One-Standard Deviation
Balanced-Growth Shock with Alternative Ordering

 

 

 

 

 

 

 

 

 

 

/ .
\\\ /. \W
\\’//
A A
i
I
I
I
I
I. I I
: "§‘\
I I II / \ ________ __
In I\ / ~ --------------
I I \ I
‘I I, \ II
I.. I .l \ I
I
I
I
I

 

 

 

 

I II II .I .I .I .I II .I .l I.I III

FIGURE 16: Net Exports in Response to a One-Standard Deviation
Balanced-Growth Shock with Alternative Ordering

4O

 

I..III

 

.
I..III I

’
'1

cu-—
~ a---—~ ‘-—- —
\--” ‘----"

I"
4—-'
s..-

 

III \\ '/\/\/
\v

i’-
,’
\
\‘-‘

 

 

 

 

 

 

\

 

-I.IIII w

 

 

 

....‘.' I I T I I I I T

I I. I. I. I. II II I. I. III III

FIGURE 17: Consumption in Response to a One-Standard Deviation
Real-Interest-Rate Shock with Alternative Ordering

 

 

 

 

 

 

 

 

 

 

 

 

I....
{I
I .8. I
‘I
I
I
I
a
I II. I / \
‘I / \
I I \
\ I \
‘\‘ [IA \\\ ---------------------
. ... \\‘\ ll/ \\\\\L;l/;;/”-\\\~__—',——--__
I II. \ A‘ ,/‘\\
\V/ \\// pm
I .II \ /
I..II \\/l
. ... If I I I f I I I I T
I I. .I II II I. I, I. I. II. III

FIGURE 18: Investment in Response to a One-Standard Deviation
Real-Interest-Rate Shock with Alternative Ordering

41

 

 

 

I I
l
I....

0.01! i
n
H
I
I
I
I
l

0.01! I
I
I
I
I
I
I
I
A

0.... \ {4 \\
I I ‘\
'\ ,’ .....................
\ I

 

 

 

~I..II

\ I’m-y
.w’
~I..II

 

 

 

 

 

II II. III

FIGURE 19: Output in Response to a One-Standard Deviation
Real-Interest-Rate Shock with Alternative Ordering

 

 

 

I.II. i
n
'I
I
I
I
I
l
I..II I
I
I
I
I
I
'\ I
I
e
0.... I {D \\
I I \\
k / -----------
.........
\ I ‘
\ I
I....

 

 

\Uf\\v/\V_
\ /

 

 

 

 

 

 

FIGURE 20: Net Exports in Response to a One-Standard Deviation
Real-Interest-Rate Shock with Alternative Ordering

42

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I II I! 80 II I. 01 70 00 II. III

FIGURE 21: Consumption in Response to a One-Standard Deviation
Inflation Shock with Alternative Ordering

 

 

 

 

 

 

 

 

 

 

 

 

 

0....
9‘
II
II
II
II
II
1 I
O .0. l I
I I
I I
I I
I I
I I
' I
11'.
0 .0. \‘
I
I
I
I
I
I1
0 .8. \ /\ r\
"X I, \
"I I \ .................
\ I \ ““““““““
A \.I 5’
M
/ ‘J‘
O .8. I\ J
0 .0. U
. ... I I I I I I I I I
I I. I. .0 C. I. .7 I. I. I0. III

FIGURE 22: Investment in Response to a One-Standard Deviation
Inflation Shock with Alternative Ordering

43

 

 

---lh-----

 

’
a
“
-Ab'
___. -—--
’,—

 

>..

 

 

 

 

 

 

 

 

 

 

I It I. 80 II II .7 I. H II. III

FIGURE 23: Output in Response to a One-Standard Deviation
Inflation Shock with Alternative Ordering

 

 

Z?
,r‘
/

 

 

g

 

 

 

F'

-
.
.
.
\
K
‘s
1’)
\
\
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

 

 

a--. '--
0"-
-------q---

 

 

 

‘
u.
'
.
O
O
O
O
O
C
O
O
Q
Q
C
O
.

IO. III

FIGURE 24: Net Exports in Response to a One-Standard Deviation
Inflation Shock with Alternative Ordering

44

REFERENCES

Crowder, W. J., and Hoffman, D. L. (1992), "Is There a Long
Run Relationship Between Nominal Interest Rates and
Inflation: The Fisher Equation Revisited," Working
Paper.

Darby, M. R. (1975), "The Financial and Tax Effects of
Monetary Policy on Interest Rates," Economic Inquiry, 13,
266-269.

Dornbusch, Rudiger, "Expectations and Exchange Rate

Dynamics," Journal of Political Economy, December 1976,
84, 1161-1174.

Fisher, I. (1930), The Theory of Interest Rates, New York:
Macmillan, 1930.

Friedman, M. (1970) , "A Theoretical Framework for Monetary

Analysis," Journal of Political Economy, 78, 139-238.

Hallman, J., Porter, R., and Small, D., "Is the Price Level
Tied to the M2 Monetary Aggregate in the Long Run?"

American Economic Review, 81:4, 841-858.

King, R. G., Plosser, C. I., and Rebelo, S. (1988),
"Production, Growth, and Business Cycles: II, New

Directions," Journal of Monerary Economics, 21, 309-342.

King, R. G., Plosser, C. 1., Stock, J. H. and Watson, M. W.
(1987), "Stochastic Trends and Economic Fluctuations,"
NBER (Cambridge, MA) Discussion Paper No. 2229.

 

, , , and (1991), "Stochastic Trends and
Economic Fluctuations," American Economic Review, 81,
819-840.

Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., and.Shin, Y.C.
(1991), "Testing the Null Hypothesis of Stationarity
Against the Alternative of a Unit Root: How Sure are we
That Economic Time Series Have a Unit Root?" Jggrgg1_gfi

W. f orthcoming.

Kydland, F. and Prescott, C. I. (1982), "Time to Build and
Aggregate Fluctuations," Econometrica, 50, 1345-70.

Mishkin, F. (1992), "Is the Fisher Effect for Real?," lQQIDQl
of Monerary Economics, 30, 195-215.

Phillips, P.C.B., and Perron, P. (1988), "Testing for a Unit
Root in Time Series Regression," W, 75, 335-346.

45

Sachs, J. (1981) , "The Current Account and Macroeconomic

Adjustment in the 1970's," Brookings Papers 9n Economic
Activity, VOl. 1, 201-282.

Solow, R. M. (1970), Growtn Theory: An Exposition, Oxford:

Clarendon Press, 1970.

III: STOCHASTIC TRENDS IN A LARGE OPEN ECONOMY

CHAPTER III
STOCHASTIC TRENDS IN A LARGE OPEN ECONOMY

1. INTRODUCTION

With the exception of Mellander, Vredin, and Warne
(1992), who examine a small open economy, The importance of
open-economy variables is largely ignored in the empirical
literature regarding the causes of economic fluctuations.
Though such factors are likely to play a significant role in
explaining the economic fluctuations in smaller countries, it
is commonly assumed that these effects are minimal in larger
countries. This chapter extends the closed-economy model of
King, Plosser, Stock and Watson (1991) in order to examine
economic fluctuations in an open-economy, Vector Error-
Correction model (VECM) of the United States.

The organization of the chapter is as follows: (1) a
theoretical basis for the long-run restrictions is outlined;
( 2) long-run properties of the data are examined for both
univariate series and linear combinations of certain series
(cointegrating vectors); (3) results are presented for
estimated impulse response functions and forecast-error
variance decompositions; ( 4) exports are included in the model
and the results are contrasted with the model excluding
exports; (5) conclusions are drawn, and further extensions are

outlined.

46

47
2. THEORETICAL BACKGROUND

Since the structural model is identified by imposing
restrictions of the reduced-form (i.e., the VECM), it is
necessary to justify theoretically the use of the certain
restrictions and the omission of other potential restrictions.
This section outlines the theoretical justifications of the
underlying restrictions which will be used throughout this
study.

The models estimated in this chapter will maintain the
restrictions implied by the Solow growth model, which were
presented in Chapter II.1 In addition, KPSW’s long-run money
demand function used in Chapter II will also be employed in
this analysis. For the reasons outlined in section 3.2 in

Chapter II, the long-run relationship between the nominal

 

1Stock and Watson’s (1993) Dynamic OLS technique to
estimate to coefficient on per capita real private output
yields,

ct-yt - -.065 + 0.04yt
(-.39) (1.00)

it-yt - -1.42 + 0.03yt
(-5.20) (0.53)

Investment here is defined as "gross private investment
(gpi82) . The estimates in the investment equation are not
sensitive to the definition of investment. When investment is
defined as "gross fixed investment" (gif82), the results are
quantitatively similar,

it-yc - -1.45 + 0.03yt
(-6.68) (0.66)

These estimates are consistent with the theory of balanced-
growth, since the coefficient on output is not significantly
different from 1.00.

48
interest rate and inflation specified by Darby (1975) will be

assumed. That is,

Rt-.r;+-1.30Apt (1)

Using Johansen's estimator,2 Crowder and Hoffman (1992) have
found that a long-run (cointegrating) relationship exists

between the rate of inflation and the nominal interest rate,

Rc-1.30Apc-et; ec—'I(0) (2)

Therefore, in the long run all movements in the nominal
interest rate are due to movements in inflation“ That is, the
after-tax real interest rate, equation (1), is stationary.
In particular, the analysis in this chapter examines the
long-run properties of the external sector. Theoretically,
the demand for real imports is a positive function of real
income and a negative function of the relative price of
imports. The derived-demand for U.S. real exports is a
positive function of "rest-of-the-world" income, and a
negative function of the relative price of U.S. exports.
However, by including a foreign variable representing "rest-
of-the-world" income, the issue of the international
transmission of economic fluctuations is introduced, Backus,
Kehoe, and Kydland (1992). The issue of the international

transmission of business cycles will be explored in a later

 

2Crowder and. Hoffman (1992) estimated the inflation
coefficient using both Stock and Watson’s (1993) DOLS
technique, and Johansen's (1988) method. Consistent with
their findings, I found the DOLS estimate to be 0.77.

49

chapter.
3. LONG-RUN TIME SERIES PROPERTIES

3.1 THE DATA

Vector autoregressions are performed over the period
1954:1 to 1988:4, with 6 lags of autoregression. The data
used are all quarterly, seasonally adjusted, observations
covering 1951:4 to 1988:4. The data are as follows: log of
per capita real consumption (c), log of per capita private
gross real investment (1)3, log of per capita private real
GNP (y), log of per capita real imports (im), log of per
capita real exports (ex), the three-month U.S. Treasury bill
(R), log of per capita real M2 money supply (m-p), and the
log of the (multilateral) U.S real effective exchange rate
(q). The price deflator was obtained by dividing nominal
private GNP by real GNP. The inflation rate (Ap) is the
first difference in the log of the deflator. With the
exception of M2 from 1951:4 to 1958:4, which was constructed
frmm flanking and Monetary Etnristics i251-127 , all of the
‘variables are from.Citibaseu The U.S. real exchange rate, vis

a vis the G-7‘, is constructed by using the Federal Reserve

 

3The baseline model estimated in this chapter will use
this definition. However, the alternative 9-variable model
also estimated in this chapter will use real "gross private
fixed" investment per capita. The difference is that the
"gross private investment" includes changes in inventories.

‘Since Citibase does not include Yen/S nominal exchange
rate prior to 1957, the real exchange rate prior to this date
excludes Japan.

50
Board’s trade-weighted index (1972-76), and is defined as

5

foreign currency per dollar; Therefore, an increase in the

real exchange rate is a real appreciation of the dollar.

3.2 UNIVARIATE CHARACTERISTICS

Nelson and Plosser (1982) show that most macroeconomic
time series are characterized by non-stationarity (1(1)).
Tables 1 and 2 summarize the univariate characteristics of
each of the variables in the model. Using the test proposed
by Phillips and Perron (1988) under the null hypothesis of
non-stationarity, or 1(1), the null cannot be rejected for any
of the variables except real per capita consumption in the
presence of an intercept and a time trend. The Kwiatkowski-
Phillips-Schmidt-Shin test ( 1991) under the null hypothesis of
stationarity, 1(0), supports the finding of non-stationarity
for all of the variables. The null of stationarity is
rejected at the 5% in the presence of a trend for all of the
variables, except for real per capita exports and the real
exchange rate, where the null is rejected at the 10% level in
the presence of a trend, and.nominal interest rates, where the

null of stationarity cannot be rejected at standard levels.

3.3 MULTIVARIATE CHARACTERISTICS
Though the univariate series are characterized by non-
stationarity, economic theory suggests that the paths of two

or more of these 1(1) variables be related in the long-run.

 

5W. August 1978. pq 700.

51
Following Engle and Granger (1987), a vector of variables is
said to be cointegrated if each variable is individually non-
stationary, but a linear combination of the variables is
stationary. If two variables are cointegrated, then their
long-run paths are not independent.

In addition to the Solow balanced-growth restrictions and
the Darby-Fisher restriction, the remaining theoretical
relationships discussed in section 2 need to be estimated.
Point estimates of the cointegrating vectors are found using
Stock.and.Watson's (1993) Dynamic OLS technique over 1954:1 to
1987:3 with five leads and lags. The estimated cointegrating

vectors and their t-statistics are,6

m—pt - 0.65 + 1.199y. - 0.01312, (3)
(2.00) (17.08) ('3.11)
1121,. - 4.69 + 2.726yt + 0.117(1),- (4)

(4.57) (8.34) (0.305)

imt--2.67 +0.007t+l.13yt+0.103qt (5)
(-1.44) (4.10) (2.73) (0.609)

Equation (3) represents the money-demand equation. Since
the nominal interest rate is significant in the equation, I

conclude that it should be included in the long-run money-

 

‘As Stock and Watson (1993) show, the "distributions of
the t-ratios tend to be spread out relative to the normal
distribution, suggesting that the usual confidence intervals
will overestimate precision." Therefore, the t-statistics
reported in parentheses below have been adjusted to be
”standard normal", so that the standard critical values are
appropriate.

52
demand function, as opposed to the specification suggested by
Hallman, Porter and Small (1991). Equations (4) and (5) both

7 Equation (4)

represent the derived-demand for real imports.
is the estimate of cointegration in the absence of a time
trend. Equation (5) is the estimate of cointegration in the
presence of a time trend.

Since the 'theoretical restrictions implied. by Solow
growth models were not rejected,8 it is sufficient to test
whether the variables c-y and i-y are stationary. This is
reported in Tables 1 and 2. For c-y and i-y the null of non-
stationarity using the Phillips-Perron test is rejected.at the
5% level. Using the Kwiatkowski-Phillips-Schmidt-Shin test,
the null of stationarity cannot be rejected at the 10% level
for i-y. However, stationarity of c-y is rejected at the 5%
level.

Crowder and Hoffman's (1992) finding that the Darby-
Fisher equation (2) is stationary is also tested. The
Phillips-Perron test confirmed the finding of stationarity,
since the null was rejected at the 1% level.’ Using the

Kwiatkowski-Phillips-Schmidt-Shin test, the null cannot be

 

7The import-demand equations were also estimated with a
dummy included to represent the exchange-rate regime shift in
1973. In neither of the equations (11) or (12) was the dummy
significant at standard levels.

”See footnote 1.

9KPSW (1991) found that there was no evidence of
cointegration between the nominal interest rate and the
inflation rate, and concluded that the real interest rate was
non-stationary. However, they did not consider the
possibility that the Fisher equation is correctly depicted by
equation (4), the Darby equation.

53
rejected at the 10% level.

In order to test the estimated vectors (3), (4) and (5)
for the presence of cointegration, the residuals from each of
the estimated vectors are tested for stationarity. If the
residuals are 1(0) , then the variables in the vector are
cointegrated. Table 3 summarizes the tests for stationarity
of the residuals from each of the three vectors. Shin (1992)
has provided a set of critical values for a residual-based
test of cointegration which is based upon the Kwiatkowski-
Phillips-Schmidt-Shin test under the null hypothesis of
cointegration. If the residuals of the estimated vector are
stationary, or 1(0), then the variables are cointegrated.
For the long-run money-demand equation (3) , the null of
cointegration cannot be rejected at the 10% level. The null
is rejected at the 5% level for import demand equation (4).
However, in the presence of a time trend, equation (5), the
null cannot be rejected at the 10% level. This suggests that
a stable long-run relationship exists between real per capita
imports, private income, and the real exchange rate in the
presence of a deterministic trend. This finding is supported
by Rose and Yellen (1989), though Rose (1989) failed to find
such a relationship. However, both of these studies use only
post-Bretton Woods data, and examine bilateral relationships,

where the present study uses multilateral data.

54

4. EMPIRICAL RESULTS

4.1 AN OPEN-ECONOMY COMMON TRENDS MODEL

The open-economy Vector-Error Correction Model10 is
estimated from 1954:1 to 1988:4 with 6 lags and five error
correction terms.11 It consists of three permanent
stochastic shocks to the system: an inflation shock, a real-
exchange-rate shock, and a real balanced-growth shock. The
cointegrating vectors described in equations (1), (2), (5),
(6), and (12) are used to restrict the matrix of long-run
multipliers.12 11 is given in Table 6 for the 8-variable
model, and the estimated long-run multipliers for the

permanent innovations in the model are reported in Table 10.

4.2 IMPULSE RESPONSE FUNCTIONS

Impulse response functions with respect to a one-
standard-deviation shock in the three common trends are
estimated for consumption, investment, output, imports and net
exports. The one-standard deviation of the balanced-growth
shock is .79%, the real-exchange-rate shock is .73%, and the
inflation shock is .66%. Selected mean impulse responses

(solid line), along with their respective 95% confidence

 

10See Chapter 11, section 2 for an overview of the
methodology.

11Following Sims (1980) , Likelihood Ratio tests were
performed in order to determine the appropriate number of lags
of autoregression. When AR(8) is unrestricted, the
restriction of AR(6) is not rejected at the 5% level. When
AR(6) is unrestricted, the restriction of AR(4) is rejected at
the 1% level.

12For a more complete exposition, see Appendix.

55
intervals (dashed lines), are show in Figures 1-15.

A. positive balanced-growth shock leads to the
proportional permanent increases in output, consumption, and
investment as predicted by Solow growth theory. The negative
initial effect of the balanced-growth shock on investment in
Figure 2 is contrary to theoretical predictions. However,
this is not significant at the 95% level. Figure 3 shows that
the initial response of imports to the positive balanced-
growth shock is to decrease. In the long run, however, the
response of imports is significantly positive. IFigure 5 shows
that the short-run response of net exports to the balanced-
growth shock is consistent with intertemporal theories of
current account behavior. Intertemporal theories of the
current account such as Sachs (1981) predict that.positive net
exports are procyclical. However, they also predict that net
exports will not be affected by a balanced-growth shock in the
long run. After about 20 quarters, the response of net
exports to the balanced-growth shock is significantly
negative.

Though changes in real exchange rates can, theoretically,
have significant effects on consumption and investment, there
is no evidence that this is the case for the United States.
In Figures 6 and 7 the responses of consumption and investment
are never significantly different from zero. Given the fact
that the United States is a large open economy, this result is
not surprising. Furthermore, Figure 8 shows that imports are

not significantly affected by the real-exchange-rate shock,

56
either. Rather, the only permanent shock which affects
imports is the balanced-growth shock. Figure 10 shows the
response of net exports to the real-exchange-rate shock.
Though the mean response appears to follow the so-called J-
curve, the response to insignificantly different from zero.13
This is consistent with recent work.by Rose and Yellen (1989),

who find no reliable evidence of either a short-run or a long-

run J-curve .

4.3 VARIANCE DECOMPOSITIONS

Forecast-error variances given in Tables 12-14 show the
relative importance of the common trends in accounting for
unpredicted variability in the eight variables up to 120
quarters.

One-sector Real Business Cycle models predict that the
balanced-growth shock is capable of explaining both short-run
and long-run variation. However, examining the forecast-error
variance decompositions in Table 12, the balanced-growth shock
is relatively unimportant over the short-run. Although it
accounts for 68% of the error-variance in imports after only
1 quarter, it accounts for only 11% of the error-variance in
consumption, 9% of investment error-variance, and 0% of output
error-variance. At 12 quarters, it accounts for 30% of the

error-variance in output. At 120 quarters, while the

 

‘BMost commonly, the J-curve refers to a short-run
worsening of the current account in response to an exchange
rate doprociation, while in the long run, there is a permanent
improvement in the current account. However, the exchange-
rate shock here is an appreciation.

57
balanced-growth shock explains only 33% of the error-variance
in investment, it explains 87% of the error-variance in
consumption, 78% in output and 53% in imports. These
estimates are broadly consistent with closed-economy estimates
in King, Plosser, Stock, and Watson (1991).

Permanent innovations in inflation do not account for the
majority of unpredicted variation in the real flow variables
in the short run, either. After 1 quarter, the inflation
shocks explain 12% of the error-variance in output, 1% of the
error-variance in consumption, 13% of the error-variance in
investment, and only 1% of the error-variance in imports. At
4 quarters, it accounts for 47% of investment variance and 35%
of output variance. After 12 quarters, however, it only
explains 25% of investment variance and 15% of output
variance. Clearly, investment is the most sensitive to
changes in inflation of any of the variables.

It is not surprising that the real-exchange-rate shock
does not explain a large proportion of the variation in the
real flow variables. It explains 10% of the error-variance in
consumption, 6% of the error-variance in investment, 7% of the
error-variance in output, and 11% of the error-variance in
imports at 12 quarters. The fact that the real-exchange-rate
shock does not account.for much of the variation in imports is
consistent with the fact that it is an insignificant
determinant of the long-run demand for imports, equation (11)

and (12).

58

Table 19 summarizes the percentage of the variance which
is accounted for by the transitory shocks. Since the
transitory shocks are not uniquely identified, it is not
possible to assign the relative importance to any specific
factors. Generally speaking, these can be thought of as
temporary aggregate demand shifts. Over the course of the
three-year horizon, these transitory shocks account for the
majority of the variance in the real flow variable (though
permanent shocks account for 52% of output variance at 12
quarters). This is different from the conclusions of KPSW
(1991), Blanchard and Quah (1989), Gali (1992), and Mellander,
Vredin, and.Warne (1992). The main.reason for the discrepancy
between these estimates and those of KPSW (1991) is that they
modelled the real interest rate as non-stationary, as one of

their permanent innovations.

4.4 AN OPEN-ECONOMY MODEL WITH EXPORTS

The baseline model does not explicitly account for real
per capita exports. Rather, it is left as the residual term.
As argued in the theoretical section, it is not possible to
model the long-run properties of exports without introducing
"rest-of-the-world" income. Exports can, however, be added to
the model by assuming that they are a fourth common trend,
which is not present in any of the cointegrating vectors, and
therefore have no long-run effects on anything except for
exports itself. If this is done, the results in the previous

sections will be tested for their sensitivity to another

 

59
permanent innovation.“
Forecast-error variance decompositions for the 9-Variable
model (the baseline model + exports as a fourth trend) are
summarized in Tables 15-18. The real-exchange-rate shock now
accounts for 30% of the forecast-error variance in output
after 1 quarter (versus 5% in the baseline model) and 29%
after 12 quarters (versus 7% in the baseline model). In
addition after 12 quarters, the real-exchange-rate shock
accounts for 34% of the error-variance in consumption, 31% of
the error-variance in investment, and 41% of the error-
variance in imports. It is also noteworthy that after 120
quarters, 30% of the error-variance in imports is still
explained by the real-exchange-rate shock. Moreover, this
increase in the importance of the real-exchange-rate shock
does not depend upon a large correlation between the real-

5 However, it may

exchange-rate and balanced-growth shocks.1
be the result of the large correlation between the real-
exchange-rate and real export shocks.

It is also important to note the effect of the inclusion
of exports in the VECM on the relative importance of the other

permanent innovations. The balanced-growth shock actually

explains more of the 4 and 8 quarter variance in output in the

 

1"In order to include exports in the VECM, the residual
in the national income identity becomes "changes in
inventories". That is, investment is now defined as "gross
fixed investment".

15The H for the 9-variable model is reported in Table 9.

60
alternative model, 32% and 35% (versus 13% and 20% in the
baseline model). The inflation shock explains less of the 4
and.8 quarter variance in output in the alternative model, 18%
and 18% (versus 35% and 25% in the baseline model). Table 19
shows that the majority of short-run forecast-error variance
for each of the variables discussed is explained by permanent
innovations, not the transitory innovations. This is in
contrast with results from the model without exports.
Furthermore, the increased relative importance of the
permanent innovations in accounting for the forecast-error
variances is almost entirely accounted for by the output and

real-exchange-rate shocks.

5. CONCLUSION

This study has found that there is evidence that a stable
long-run relationship exists between per capita real imports,
the multilateral real effective exchange rate, and per capita
real private output. However, the real exchange rate is not
significant at standard levels in this vector. The evidence
suggests that there is a significant deterministic trend in
the long-run import-demand.function, perhaps the result of the
liberalization of trade policies since the Kennedy round of
GATT negotiations in the 1960's. When exports are introduced
into the model, shocks to the real-exchange-rate have
surprisingly' large short-run. effects on. the variance in
output, especially for a large open-economy. Furthermore, the

permanent stochastic trends account for the majority of both

61
the short-run and long-run forecast-error variance in output.
This conclusion does not depend upon the interpretation of the
real interest rate as possessing a non-stationary component.

Though the central result of this study is surprising,
the models estimated in this chapter should be considered to
be :reasonable open-economy ‘models of the ‘United States.
Impulse responses show that none of the domestic real
‘variables examined are significantly affected by shocks to the
real exchange rate. Therefore, the relative importance of
real-exchange-rate shocks in accounting for forecast-error
variances does not seem to be the result of any unreasonable
restrictions. Furthermore, with the exception of the real
export shock, which is affected by the real-exchange-rate
shock, the permanent innovations are uniquely identified. As
in closed-economy models, the balanced-growth shock, as well
as the inflation shock, fails to account for the majority of
the short-run variance in output.

The inclusion of the export shock in the model presented
here suggests that, in order to explain the behavior of an
open-economy, the long-run demand for exports should be
explicitly modelled. In doing so, the importance of the real
exchange rate may be better defined, since it is not a
significant determinant of long-run import demand. In
modelling the long-run demand for exports, it is necessary to
introduce yet another permanent shock to the model.
Theoretically a long-run relationship should exist between

real exports, the real exchange rate and "rest-of-the-world"

62
income. ZBy adding an additional shock.representing the impact
of other countries' income on the domestic variables, the
issue of the international transmission of real business

cycles, along the lines of Backus, Kehoe, and Kydland (1992),

is introduced.

63

TABLE 1

Phillips-Perron Test for Non-Stationarity of
Univariate Time Series: 1951:4 - 1988:4

 

 

 

 

Series Zta th
c -4.35 -o.97

i -o.92 -l.69
m-p -2.54 -O.36
y' -2.78 -o.72
Ap -1.25 -3.25
R -o.44 -1.86
im -3.34 -0.65
ex -2.34 -o.2o

q -1.01 -1.19
c-y3 - -3.3o
i-y‘J - -3.33
i-yl3 - -3.56
R-1.3Ap3 - -4.os

 

Lags of truncation is 6
Critical values :
Phillips-Perron (Ho: 1(1)):

Ztu: 1% = -3.96, 5% = -3.41
Ztr: 1% = -3.43, 5% = -2.86

Zt,: tests the null of 1(1) with intercept and.time trend
Ztr: tests the null of 1(1) with intercept only

 

1gross fixed investment
2gross private investment

31954:1 - 1988:4

64

TABLE 2

Kwiatkowski-Phillips-Schmidt-Shin Test for
Stationarity of Univariate Time Series: 1951:4 - 1988:4

 

 

 

 

.-.. ...=.=.=.=. . =.===.......
Series Trend No Trend
c .367 2.173
1 .166 1.794
m-p .223 2.041
y .341 2.152
Ap .262 1.002
R .099 1.537
im .166 2.192
ex .134 1.176
g .131 1.476
c-y3 - .513
i-y“3 - .047
i-yL3 - .089
R-1.3Ap3 - .285 _J

 

 

Lags of Truncation is 6
Critical values:
KPSS (Ho: 1(0)):

NO Trend: 1% = .739, 5% = .463, 10% = .347
Trend: 1% = .216, 5% = .146, 10% = .119

 

1gross fixed investment
2gross private investment

31954:1 - 1988:4

 

65

TABLE 3

Shin (1992) Residual-Based Cointegration Tests
of Vectors: 1954:1-1987:3

 

 

Estimated Vectors KPSS: KPSS:
No Trend Trend
m—pt - 0.65 + 1.1993,, - 0.01311; .091 -
1m, - 4.69 + 2.726yt + 0.117qc .342 -
imc--2.67 +0.007t+1.13yc+0.103qt - .079

 

 

 

Lags of truncation for both KPSS tests is 6
Critical Values (Shin 1992):
KPSS (Ho: 1(0)):

No Time Trend:

1 Regressor: 5% = .314, 10% = .231

2 Regressors: 5% = .221, 10% = .163
Time Trend:

2 Regressors: 5% = .101, 10% = .081

TABLE 4

Variance-Covariance Matrix of Permanent Shocks
in Baseline Model

 

 

 

Ap q y
Ap 0.09266 - ..
q 0.00238 0.00030 -

 

.Y -0.00015 0.00001 0.00003

 

 

 

 

 

 

66

TABLE 5

Correlations between the Permanent Shocks
in the Baseline Model

 

 

 

 

 

TABLE 6

H in Baseline Model

 

 

 

 

 

 

 

 

= r
I Ar: q .Y
I Ap 1.00 - -
q 0.0257 1.00 -
y -0.0016 0.0634 1.00
TABLE 7

Variance-Covariance Matrix of Permanent Shocks
in the 9-Variable Model

 

 
 

 

  

 

  

 

  

 

I AL) q ex

I AP 0. 10565 - - -
q 0.00099 0.00064 - -
ex -0.00020 -0.00020 0.00025 -
Y' -0.00063 0.00001 0.00002 0.00003

 

 

 

 

    

    

67

TABLE 8

Correlations Between the Permanent Shocks

in the 9-Variable Model

 

 

 

 

[AP q ex
q 0.1204 " "
6X “0.0389 0.5000 '-

 

 

 

 

TABLE 9

0.0722

 

 

 

 

 

 

 

 

 

 

 

 

 

 

q 0.0095 1.00 -

ex -0.0019 -O.3127 1.00

Y -0.0059 0.0302 0.1019
TABLE 10

Long-Run Multipliers in Response to Changes

 

 

in the

 

Three Common Trends (order: Ap, q, y, with AR(6))

variable ‘AP q

c 0.00 0.06
.i 0.00 0.06
m-P -0.02 0.08
im 0.00 0.17
R 1.30 0.00
y 0.00 0.06
AP 1.00 0.00
q 0.03 1.00

 

 

 

 

68

TABLE 1 1

Long-Run Multipliers in Response to Changes in the
Four Common Trends (order: Ap, q, ex, y, with AR(6))

I variable Ap q ex y

I c 0.00 0.03

i 0.00 0.03
m-p -0.02 0.04
.im 0.00 0.14
R 1.30 0.00
y -0.01 0.03
Ap 1.00 0.00
q 0.01 1.00
ex 0.00 -0.31

 

 

 

 

 

 

 

TABLE 12

Percentage of Forecast-Error Variance Attributed
to the Balanced-Growth Shock in the Baseline Model

Period

 

 

 

 

 

69

TABLE 13

Percentage of Forecast-Error Variance Attributed
to the Real-Exchange-Rate Shock in the Baseline Model

 

 

 

TABLE 14

Percentage of Forecast-Error Variance Attributed
to the Inflation Shock in the Baseline Model

Period

 

12
2

 

 

 

TABLE 15

Percentage of Forecast-Error Variance Attributed to the
Balanced-Growth Shock in the 9-Variable Model

Period

 

 

 

70

TABLE 16

Percentage of Forecast-Error Variance Attributed to the
Real-Exchange-Rate Shock in the 9-Variable Model

 

 

 

 

 

 

Period
I 1 4 8 12 16
c 28 34 28
1' 20 31 30
y 30 22 24 29 27
im 9 29 41 40
L63: 7 19 18 24 31

TABLE 17

Percentage of Forecast-Error Variance Attributed to the
Inflation Shock in the 9-Variable Model

 

 

 

 

Period
r 1 4 8 12 16
C 1 7 5 3 8
1' 7 33 32 12 14
Y 3 18 18 14 13
I'm 3 10 13 10 11
I ex 3 3 6 12 13

 

 

71

TABLE 18

Percentage of Forecast-Error Variance Attributed to the
Export Shock in the 9-Variable Model

 

 

 

 

 

 

Period
1 4 8 12 16 20 24 120
c 2 3 3 5 9 8
1’ 1 1 2 4 5
Y 1 1 3 4 8 II
1:12 0 8 5 3 3 3 6
ex 51 51 51 43 38 38 40 63
TABLE 19

Iaercentage of the Forecast-Error Variance Attributed to
Transitory Shocks in Each Model

 

8 Variables 9 Variables 8 Variables 9 Variables
12 Periods 12 Periods 120 Periods 120 Period

51 24 7 4 I
I

 

 

58 29 43 19
48 26 13 8

66 37 28 17 I

 

 

 

 

 

 

 

72

 

 

 

 

 

 

I 1 I
H 1.1 H!

 

 

FIGHURE 1: Consumption in Response to a One-Standard Deviation
Balanced-Growth Shock

 

 

 

 

 

 

 

 

1 I I 1
II II I" ‘11

 

 

FIGURE 2: Investment in Response to a One-Standard Deviation
Balanced-Growth Shock

73

 

 

 

 

 

 

 

 

 

 

 

 

it \
II \
I, \
V \J A
An 1 w
0.. 4' \v/l,
1.8 fi‘gj
I.‘ {
08..
‘ . I I I I I I I I I I I I
‘1 8' .I 6‘ '1 0‘ 7' .1 0‘ '0‘ '1‘

FIGURE 3: Imports in Response to a One-Standard Deviation
Balanced-Growth Shock

 

 

 

 

 

 

 

 

 

 

 

 

\ //
I... \\j/
0... J
1 .. I I I I I I I I I I I
II I. 84 4| II I? ’0 0| 1.. III

FIGURE 4: Output in Response to a One-Standard Deviation
Balanced-Growth Shock

74

 

 

 

W
van—— b—O""---‘
a"
p
I

 

 

 

 

 

 

 

 

I ‘1 II I! I! I1 I1 1| II II III 111

FIGURE 5: Net Exports in Response to a One-Standard Deviation
Balanced-Growth Shock

 

 

 

 

 

I.II
1“
I I. I \
I \
I \
I \
I \
I \
I \
I \
I L.
I II I \
‘\
II ‘ ...........................
' \ \\\\\
' .......
I
u I
I l A
I.1I \ I
\ I’
| P
I I
N
I.II '

 

A\ //\\‘ A.
-I.II [\V/ \V/

I H II II 4I II I? 7| II

 

 

 

 

 

FIGURE 6: Consumption in Response to a One-Standard Deviation
Real-Exchange-Rate Shock

75

 

 

 

 

 

 

 

 

 

 

 

I II II II II II II II II II III III

FIGURE 7: Investment in Response to a One-Standard Deviation
Real-Exchange-Rate Shock

 

I.II Ffl\
\

 

I
I
I
I
I
I \
I
L
I
I
I

 

I
I
I
I I
I I
I I \
‘ ' \ --------
.......
i ‘I \_ _____
I
I.
I
\

 

 

 

 

 

 

 

 

 

 

I II II II II II II II II III III

FIGURE 8: Imports in Response to a One-Standard Deviation
Real-Exchange-Rate Shock

76

 

 

 

 

 

 

 

 

 

 

FIGURE 9:

Output in Response to a One-Standard Deviation
Real-Exchange-Rate Shock

 

 

 

 

 

 

 

 

 

 

 

FIGURE 10: Net Exports in Response to a One-Standard Deviation
Real-Exchange-Rate Shock

77

 

 

I.III
I“\
II / \
I V
0.01: I , \
I I \
I I \
I I‘. I \
I I \ I \
I I \ l \ --------------------
II \I ‘\ ............
\/ \ .....
0....

 

 

 

,.L“’\/\J

-I.III I

 

 

 

 

 

....I. f I I I I I I I I I I

I II II II II II II II II III III

FIGURE 11: Consumption in Response to a One-Standard Deviation
Inflation Shock

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I.III I
II
II
II
I
1‘.
0.100 I|
I
I
I.I7I
I
AI
I
I.III [\I
I
| f\
II \
II \
II I
v ‘.
I.III \ ,v\
\ l “-
\r \\
x
\ -
4/\\ ._ \ """"""""""
I III // \J/ \ ,/ <‘7
I".
A 'l
I
I III \/ \ '
\v/
I III
. .7. I Ti I I I I I I I I T
I II II II II II II II II III III

FIGURE 12: Investment in Response to a One-Standard Deviation
Inflation Shock

'78

 

 

 

I.III
I
I
I
II
II
:I
fix
I.III . I
I I
I I
I I
' i
I
I
I
| rrrrr
I J] \\
I III . I \ I \
I I I I \
II I J \
:ll I\’I \\ .......
\ ---------------------
v V “““““
A A

 

 

 

 

 

I III I I \ /
l \_
\/
I III ' Y I I I I I I I I Y
I II II II II II I? II II III III
FIGURE 13: Imports in Response to a One-Standard Deviation

Inflation Shock

 

 

 

 

 

 

 

 

 

 

 

0.0:.
I
I
II
II
II
II
II
I on: {I
II
II
II
I I
I I
I I
l
l
0.0:. I
I A
I II
I I I
II I
II I
{\II I
- \ .....
I I ‘_
o no. I \ I \\
\ --------
a on. \/ \\_~_’,»—-___
P
I
/\
/\ ,.-——-.~.
I coo
...'. I I T 1 T I T I I I r
I II a: on 40 II or I. no III 1:1

FIGURE 14: Output in Response to a One-Standard Deviation
Inflation Shock

79

 

 

I
n
n
0|
1|
II
II
:1
II I \
v\ I \
l \
.-.. '\ g \
0 \a \
\v \a \
\0 it \
\l \l \
\g V \\ .............
|l .................
\n
\I A
O I. V

 

 

 

 

 

 

 

t 11 I. Id ‘0 I. I? 70 II IO. I11

FIGURE 15: Net Exports in Response to a One-Standard Deviation
Inflation Shock

APPENDIX

80

APPENDIX

AN OPEN-ECONOMY (S VARIABLE) COMMON TRENDS MODEL

A. 1 . REDUCED-PORN ANALYSIS
The reduced-form is represented by a Wold decomposition

of the series in first differences

AXt-wqws t (A. 1)

where Xt - (c,.i,m-p,im,y,Ap,R,q)’ and st is the vector of one-

step-ahead.forecast errors in X}, given information on lagged
values of Xt. Xc is 1(1), and is cointegrated with the 4

cointegrating vectors, given by the 8x4 matrix B . Then,

p’cu) - o, where C(l) -; cj, and
-o

o o 1.0 o -1.199 0 .013 o

, 1.0 o o o -1.0 .0033 -.0033 o

p ' o 1.0 o o -1.0 -.007 .007 o
o o o 1.0 -1.13 o o -.103

A. 2 . CONNON TRENDS TRENDS REPRESENTATION

If 2 series are cointegrated, then they must share a
common stochastic trend, since they have a common integrated
component. KPSW's model can be viewed as a multivariate
extension of Beveridge and Nelson (1981). They show thatX;
can be written as a linear function of a permanent component

and a transitory component

81

X, -X0 +Att+D(L)ec (1.2)

where 1.". - y + 1b1 + n c. A must be orthogonal to [3’ (B’A-O) in

order to preserve the cointegrating properties of X, . Since.“ 8

is I(1), and D(L)¢!t is 1(0), then Atc is the "common trends"

in Xt.

A.3. IDENTIFICATION OF THE COMMON TRENDS

Since 1: ,3 follows a random walk, then At t follows a random

walk. So, the problem of identification becomes a problem of
identifying tt and 11, when k>1. Since A and ct are only

identified up to an arbitrary transformation by a nonsingular

kxk matrix, define A - .5011. A0 reflects a priori restrictions

about which permanent shock affects which variables.

1 -.0033 .0033 0
1 .007 -.007 0
1.199 0 -.013 0

A _ 1.13 0 0 .103
° 1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

 

 

In order to "name" the shocks, A; - AGO , where

82
says that the inflation shock is ordered first, the interest-
rate shock is second, the real-exchange-rate shock is third,
and the balanced-growth shock is forth. The model is also
estimated using an alternative ordering, where the interest-
rate shock is first, the inflation shock is second, the real-
exchange-rate shock is third, and the balanced-growth shock is

forth.

So, A}, - A001 is given by

0 .0033 0 1
0 -.007 0 1

-.013 -.013 0 1.199

A“ _ 0 0 .103 1.13
° 0 0 0 1
1 0 0 0
1 1 0 0
. 0 0 1 0

 

 

where the first column represents the long-run impact of the
first shock on each of the variables,

c, 1', m-p, im, y, Ap, R, q.

A.4. ESTIMATION

The reduced-form (A.1) is estimated to get CK13., C(i),

and ;ej. From equation (A.2),
-0

Axc - XOIIAn , + D(L)Aec . (It-3)

83

In the long-run, (A.1) implies that

'0

and equation (A.3) implies that

AX: - XOHIK

since Em C - 11,, and Etc, - €t_1.

Therefore,

'0

where,

.003
.013
.007
.004
.006

1

-.002

.-.028

 

.004
.014
.021
.003
.007

0
1

.045

.065
.065
.078
.018
.065
0
0
l

l

1
1.197
1.130

1

0
0
0

 

(A.4)

(A.5)

(A.6)

and II - 2:": , where the covariance matrix of the permanent

innovations E", - E(n1'f|1) .

84

REFERENCES

Backus, D., Kehoe, P. and Kydland, F. (1992), "International

Real Business Cycles," Jounnal of Political Economy,
100:4, 745-775.

Blanchard, O. and Quah, D. (1989), "The Dynamic Effects of
Aggregate Supply' and Demand Disturbances," Amenignn

EQQDQELQ_B§¥i§!r 79: 555' '573-

Board of Governors of the Federal Reserve System, Banking and
Monetary Statistics i941-i970, Washington, D.C.: Board

of Governors of the Federal Reserve System, 1976.

"Index of the Weighted-Average Exchange Value of
the U.S. Dollar: Revision," era es ve u ti
August 1978, 700.

 

DeLoach, S. B. (1993), "Chapter II: Stochastic Trends and
Economic Fluctuations: Some Further Analysis , "
unpublished dissertation, Michgan State University.

Engle, R. P., and.Granger, C.‘W..J. (1987), "Cointegration and
Error-Correction: Representation, Estimation, and
Testing," Econometnica, 55, 251-276

Fisher, 1. (1930), The Theory of Interest Rates, New York:
Macmillan, 1930.

Friedman, M. (1970) , "A Theoretical Framework for Monetary

Analysis," Jouznai of Egiiticai Ecgngny, 78, 139-238.

Gali, J. (1992), "How Well Does the IS-LM Model Fit Postwar
U.S. Data?" Qnantegiy JounnaJ= of Econgni cs, May, 709-738.

Hallman, J., Porter, R., and Small, D., "Is the Price Level
Tied to the M2 Monetary Aggregate in the Long Run?"

AEQIi§§fl_§QQDQEiQ_B§_i§E 81: 4: 341' 353.

King, R. G., Plosser, C. 1., and Rebelo, S. (1988),
"Production, Growth, and Business Cycles: II, New

Directions, " Jgngngi 9f Monetgzy Eggnonics, 21, 309-342.

King, R. G., Plosser, C. 1., Stock, J. H. and Watson, M. W.
(1987), "Stochastic Trends and Economic Fluctuations,"
NBER (Cambridge, MA) Discussion Paper No. 2229.

, , and (1991), "Stochastic Trends and
Economic Fluctuations," e 'c co 0 'c ev' , 81,
819-840.

 

85

leiatkowski, D., Phillips, P.C.B., Schmidt, P., and.Shin, Y.C.
(1991), "Testing the Null Hypothesis of Stationarity
Against the Alternative of a Unit Root: How Sure are we
That Economic Time Series Have a Unit Root?" J9n;nnl_gfi

Econonetgics, forthcoming.

Kydland, F. and Prescott, C. I. (1982), "Time to Build and
Aggregate Fluctuations," Econometrica, 50, 1345-70.

Mellander, E., Vredin, E. and Warne, A. (1992), "Stochastic
Trends and Economic Fluctuations in a Small Open
Economy," Journal of A lied Eco omics, 7, 369-394.

Nelson, C. and Plosser, C. ( 1982) , "Trends and Random Walks in
Economic Time Series: Some Evidence and Implications,"

Jounnal of Monetary Ecgnomics, 10, 139-162.

Phillips, P.C.B., and Perron, P. (1988), "Testing for a Unit
Root in Time Series Regression," Bi onetri ca, 75, 335-346.

Rose, A. (1989), "The Role of Exchange Rates in a Popular
Model of International Trade: IDoes the "Marshall-Lerner
Condition" Hold?," Mimeo.

Rose, A., and Yellen, J. (1989), "Is there a J-Curve?,"
Jougnal of Monetary Economics, 24:1, 53-68.

Sachs, J. (1981) , "The Current Account and Macroeconomic

Adjustment in the 1970's," Brogkings Enners 9n Econgnic
Activity, vol. 1, 201-282.

Shin, Y. (1992), "A Residual-Based Test of the Null Of
Cointegration Against the Alternative of No
Cointegration," Mimeo.

Sims, C. (1980), "Macroeconomics and.Reality," Eggngnggnign,
48 , 1-48 .

Solow, R. M. (1970), Gnowth Theory: An Exposition, Oxford:

Clarendon Press, 1970.

Stock, J. H. and Watson, M. W. (1993), "A Simple Estimator of
Cointegrating Vectors an Higher Order Integrated

Systems," Ecgngnetzica, 61:4, 783-820.

 

IV: THE EFFECT OF STOCHASTIC TRENDS IN FOREIGN OUTPUT

ON ECONOMIC FLUCTUATIONS IN THE UNITED STATES

CHAPTER IV

TEE EFFECT OF STOCHASTIC TRENDS IN FOREIGN OUTPUT
ON ECONOMIC FLUCTUATIONS IN THE UNITED STATES

1. INTRODUCTION

This chapter extends the open-economy Vector Error-
Correction Model (VECM) in Chapter III to introduce a
permanent shock to foreign productivity in a model explaining
business cycles in the United States. By affecting domestic
net exports, changes in foreign income may have effects on
domestic output. Backus, Kehoe, and Kydland (1992) have
recently extended standard one-sector Real Business Cycle
models to introduce. a foreign. productivity shock as an
additional real permanent shock which is capable of accounting
for domestic economic fluctuations. They suggest that foreign
productivity may affect domestic economic fluctuations in two
additional important ways. First, through international
financial markets, increases in foreign productivity attract
capital to the foreign country, and may lead to short-run
decreases in domestic investment. This effect could also lead
to increases in net exports.in'the domestic country if capital
account deficits are matched be current account surpluses.
Second, positive technological spillovers between countries
imply that increases in foreign productivity may lead to
increases in domestic productivity in the long run, and
consequently increases in domestic output, consumption, and

investment.

86

87

The organization of this chapter is as follows: (1) a
theoretical basis for the long-run restriction on export-
demand is outlined; (2) long-run properties of the data are
examined; ( 3) results are presented for estimated impulse
response functions and forecast-error variance decompositions
of the open-economy model; ( 4) sensitivity tests are performed
with regard to the model specification; (5) conclusions are

drawn.

2 . THEORETICAL BACKGROUND

The open-economy model presented in this chapter will
maintain the assumptions regarding the Solow balanced-growth
hypothesis, the money-demand specification, the Fisher-Darby
equation, and the import-demand equation which were outlined
in Chapter III.1 The analysis in Chapter III abstracted from
the effects of foreign output on U.S. exports. The purpose of
this chapter is to examine this issue. By including foreign
output in the VECM, another permanent shock is introduced.
Furthermore, it may be possible to identify a long-run
relationship representing the demand for exports.
Theoretically, the derived-demand for U.S. real exports is a
positive function of "rest-of-the-world" income, and a

negative function of the real exchange rate, defined as

 

1Since the sample period is different from that used in
Chapter III, the theoretical long-run restrictions are
estimated and tested for the relevant time period. Estimates
for the long-run money-demand and import-demand are reported
in Tables 3 and 4, along with the tests of cointegration, The
tests for stationarity of the balanced-growth relationships,
and the Fisher-Darby effect are reported in Tables 1 and 2.

88
foreign currency per dollar.

By including a foreign variable representing "rest-of-
the-world" income, the possibility of international real
business cycles is introduced. Backus, Kehoe, and Kydland
(1992) model international real business cycles as resulting
from "technological spillovers". They argue that foreign
productivity shocks actually leads to permanent innovations in
domestic productivity. If this is true, the permanent
innovation in domestic output is a linear combination of a
foreign productivity shock plus a domestic productivity shock.
This has implications for the econometric model which will be

discussed in Section 4.1.

3. LONG-RUN TIME SERIES PROPERTIES

3.1 THE DATA

Vector autoregressions are performed over the period
1959:2 to 1988:4, with 6 lags of autoregression. The data
used are all quarterly, seasonally adjusted, observations
covering 1957:2 to 1988:4. All of the definitions for the
variables used in Chapter III are the same, except that
investment is now defined as the log of per capita gross
private fixed investment. Univariate characteristics are
reported in Tables 1 and 2.

Foreign output is defined as the log of per capita real
private foreign output (y‘). The proxy was constructed by

constructing a trade-weighted per capita real private GNP (or

GDP) for the G-7 countries, using the Federal Reserve Board’s

89
trade-weighted index (1972-76). The foreign data was taken
from the integnational Financial Statistics. Each country’s
private per capita GNP (GDP) was then converted to U.S.
equivalent dollars. At this point the trade-weighted index of
G-7 countries was constructed. In order to express foreign
output in foreign currency, the index was multiplied by the
trade-weighted real exchange rate (foreign currency per
dollar). Univariate tests of foreign output, reported in

Tables 1 and 2, suggest that foreign output is non-stationary.

3.2 MULTIVARIATE CHARACTERISTICS

The assumptions with regards to the Solow balanced-growth
restrictions and the Fisher-Darby effect outlined in Chapter
III, section 2 can be tested using standard univariate
techniques, since the right-hand-side theoretically consists
of only a constant and a random error. These are reported in
Tables 1 and 2. INon-stationarity, Table 1, is rejected at the
5% level for both the investment-output ratio and the Fisher-
Darby equation. However, at the 5% level non-stationarity of
the consumption-output ratio cannot be rejected. However, in
Table 2, the null of stationarity (cointegration) cannot be
rejected at the 5% level for each of the relationships.

Point estimates of the cointegrating vectors are found
using Stock and Watson's (1993) Dynamic OLS technique over
1959:2 to 1987:3 with five leads and lags. The cointegrating
vectors used throughout Chapter III, the money-demand and

import-demand vectors, were estimated for the new sample

90
period. There estimates are reported in Tables 3 and 4.2 The
estimated cointegrating vectors for the export-demand equation

are3

ex, - -11.02 + 0.946y; - 0.259q, (1)
(—8.31) (11.45) (-1.27)

ex, - -6.71 + 0.006t + 0.33734 - 0.496qt (2,
(-5.74) (4.25) (2.28) (~4.72)

Table 3 summarizes the tests for stationarity of the
residuals from each of the vectors in the absence of a
deterministic (time) trend. The null of cointegration cannot
be rejected at the 5% level for the long-run money-demand
function. However, the null is rejected at the 5% level for
the long-run import-demand equation with the real exchange
rate as an explanatory variable, and at the 10% level for the
import-demand equation without the real exchange rate as an
explanatory variable. The null is also rejected at the 5%
level for the export-demand equation (1) . In Table 4 the
presence of a time trend, the null cannot be rejected at the
5% level for the export-demand equation (2), or either of the
import-demand equations. These results strongly suggest that

both long-run import and export-demand functions contain a

 

2The difference in the point estimates in Tables 3 and 4
from those in Chapter III are the result of the different time
periods covered. The differences are not statistically
significant.

3The t-statistics reported in parentheses below are the
adjusted statistics. See Footnote 6, Chapter III.

91

significant deterministic trend.‘

4. EMPIRICAL RESULTS

4 . 1 AN OPEN-ECONOMY COMMON TRENDS MODEL

The open-economy Vector-Error Correction Model5 is
estimated from 1959:2 to 1988:4 with 6 lags of
autoregression.6 The cointegrating vector representing
export-demand, equation (2), and the theoretical restrictions
specified in section 2, are used to identify the matrix of
long-run multipliers. These include the "great ratios", the
long-run money demand equation, the long-run import and export
demand equations, and the Fisher-Darby assumption. The
permanent shocks in the model are ordered as (1) an inflation
shock, (2) a real-exchange-rate shock, (3) a foreign
productivity shock, and (4) a domestic productivity shock.
The ordering allows for the possibility that technological
progress from foreign countries may "spillover" onto domestic
productivity. The II matrix for the baseline model is
reported in Table 7, and the matrix of long-run multipliers is

reported in Table 11. Table 7 shows that the spillover effect

 

"Furthermore, the import and export-demand equations were
estimated with a dummy variable representing the exchange-rate
regime shift in 1973. In the presence of a deterministic
trend the structural dummy was insignificant in both demand
equations.

5See Chapter II, section 2 for an overview of the
methodology.

6The Appendix gives a complete exposition of the
identification of the baseline common trends model estimated
in this paper; For further details, see King, Plosser, Stock,
and Watson (1987).

92
from foreign productivity to domestic productivity is
estimated to be 0.02, since 1:,3 = 0.02. However, it will
become obvious when the impulse response functions are
estimated that this is not significantly different from zero.
Therefore, the model estimated here finds no statistically
reliable evidence for the existence of significant positive
foreign technological spillovers on the U.S. productivity.
That is, foreign productivity has no significant long-run

effects on productivity in the United States.

4.2 IMPULSE RESPONSE FUNCTIONS

Impulse response functions with respect to a one-
standard-deviation shock in the four common trends are
estimated for consumption, investment, imports, exports,
output and net exports. The one-standard deviation domestic
productivity shock is .86%, the foreign productivity shock is
.78%, the real-exchange-rate shock is .72%, and the inflation
shock is .66%. Mean impulse responses (solid line), along
with their respective 95% confidence intervals (dashed lines),
are shown in Figures 1-24.

Figures 7-12 show how the domestic variables respond to
innovations in foreign productivity. None of the domestic
impulse responses estimated are significantly affected by the
foreign productivity shock in the long run, not even exports
(Figure 10). However, exports, investment and output are
significantly affected in the short run. Between 10 and 12
quarters, the responses of both investment (Figure 8) and

output (Figure 11) are significantly’ negative. Exports

 

93
(Figure 10) show a positive response between 4 and 6 quarters.
Since an increase in foreign. productivity increases the
marginal product of capital.in the foreign country, an outflow
of capital from the U.S. to the foreign country is likely to
occur. The resulting negative capital flow may in turn lead
to decreases in investment and output with some lag.

As shown in Figures 6 and 12, the size of the response of
net exports to the domestic and foreign productivity shocks
are quite different. The foreign productivity shock does not
significantly affect net exports either in the short run or
the long run. On the other hand, the domestic productivity
shock has significant negative effects on net exports in the
short run. This is different from.the results in Chapter III,
where there were significant positive short-run responses. In
the long run, the response of net exports with respect to the
domestic productivity shock seems to by significantly
negative. However, since the response of net exports has not
stabilized after 120 periods, it is not definite that the
long-run response is negative.7

Theoretically, there are several ways in which the real
exchange rate can affect domestic variables. Most obviously,
it may affect net exports. Figure 18 shows that an increase
in the real exchange rate (a real appreciation of the dollar)

leads to a significant decrease in net exports in the short

 

7However, in the open-economy model estimated in Chapter
III, the response of net exports with respect to the domestic
productivity shock was significantly negative in the long run.

94
run. There is no evidence of positive responses of net
exports in the short run. That is, there is no evidence of a
J-curve effect. In the long-run, since exports are more
sensitive to changes in the real exchange rate than imports,
the real appreciation of the dollar leads to a permanent,
significant worsening of the current account.

Shocks to real exchange rates can have direct effects of
consumption and investment as well. If imports and
domestically-produced consumption goods are imperfect
substitutes, then changes in the relative prices of these
goods may increase the total level of consumption in the
economy. That is, the appreciation of the real exchange rate
would lead to positive wealth effects. Since investment
depends on international capital flows, innovations in the
real exchange rate can have a significant effect on investment
as well. In these cases, one would expect the responses of
consumption and investment to be positive at some point.
However, the responses of consumption (Figure 13) and
investment (Figure 14) are never significantly positive. In
fact both have significant negative responses between 6 to 12
quarters. Also, output (Figure 17) is not significantly
affected by the real-exchange-rate shock.

Responses of consumption, investment, imports and output
with respect to shocks in domestic productivity (Figures 1-6)
and inflation (Figures 19-24) are consistent the theories
discussed in Chapter II, as well as the responses from models

estimated in Chapters II and III. A positive inflation shock

95
has no significant effects on the real flow variables in
either the short run or the long run. The productivity shock
significantly increases all of the variables over the short

run and the long run.

4.3 VARIANCE DECOMPOSITIONS

Forecast-error variances given in Tables 13-20 show the
relative importance of the common trends in accounting for
unpredicted variability in the five real flow variables up to
120 quarters.

Table 14 shows the extent to which changes in foreign
productivity account for forecast-error variances of the real
domestic flow variables. As explained in Section 4.2,
investment may be affected by innovations in foreign
productivity in the short run through changes in international
capital flows. After 12 quarters 9% of the forecast-error
variance is explained by the foreign productivity shock.
Though the foreign productivity shock accounts for an
estimated 27% of the 1 quarter variance in investment, this
result is suspicious. Even if capital flows are affected
instantaneously by the increase in foreign productivity,
investment would only respond to capital flows with a
significant lag. As would be suggested by the impulse
responses, the foreign productivity shock does not play a
large role in explaining exports. It only accounts for 12% of
the variance after 12 quarters, and only 4% after 120 periods.

After 12 quarters, it accounts for 9% of the variance in

96
consumption, 9% of the variance in investment, 7% of the
variance in imports, and a surprisingly large 13% of the
variance in output after 12 quarters.

The effect of permanent real-exchange-rate shocks on
consumption, investment and output is surprisingly large.
After 12 quarters it accounts for 22% of consumption variance,
15% of investment variance, and 17% of output variance.
Furthermore, the real exchange rate is the dominant shock
driving changes in U.S. exports, not the foreign balanced-
growth shock. After 120 quarters, the real-exchange-rate
shock accounts for 63% of the variance in exports. Only 4% of
the variance in U.S. exports is due to permanent shocks to
foreign income. However, imports are due mostly to changes in
income in the long run, while real-exchange-rate shocks only
account for 7% of import variance after 120 periods.

Results of the variance decomposition of output are
generally favorable to explanations of business cycles like
those argued by Real Business Cycles theorists. The real
productivity shocks (the combination of the domestic and
foreign shocks) account for the majority of the variance in
domestic consumption and output after 4 quarters. In fact at
the 4 and 8 quarter intervals, the domestic productivity shock
explains the majority of output variance by itself. After 12
quarters, the two real productivity shocks account for a
combined 57% of output variance. On the other hand,
investment is explained more by permanent inflation and real-

exchange-rate shocks. As in the model with exports in Chapter

 

97
III, the permanent shocks account for the majority of economic

fluctuations in both the short and long run.

4.4 SENSITIVITY ANALYSIS

Since the real exchange rate is insignificant.at standard
levels in the long-run import-demand equation, the model is
also estimated without the real exchange rate as an
explanatory variable in the long-run import demand equation.
This may decrease the degree to which innovations in the real
exchange rate explain forecast-error variances of the real
flow variables. It may have an effect on the relative
importance of other permanent shocks.

The estimates of the cointegrating vectors in this case

are

imt - 5.68 + 2'83yt (3)
(5.07) (10.75)

imt--0.57 +0'0054t+1'49yt (4)
(-0.16) (1.82) (1.94)

Tables 3 shows that the residual of equation (3) is not
stationary, and therefore equation (3) is not a cointegrating
vector. However, Table 4 shows that the residual in equation
(4), with the time trend included as an explanatory variable,
is stationary. Equation ( 4) will be substituted for the
import-demand equation with the real exchange rate as an
additional explanatory variable. Consequently, in the

alternative model, per capita real imports have only one

98
permanent component, domestic productivity.

Results for the alternative model are summarized in
Tables 17-20. The results are quantitatively similar to those
of the baseline model, except for the degree to which shocks
to the real exchange rate account for unpredicted variance of
the real flow variables. The real-exchange-rate shock now
only accounts for 18% of the 1 quarter variance in output, not
25%. Its importance at longer intervals is not significantly
affected. In fact, it now accounts for 34% of the 12 quarter

variance in imports, versus 26% in the baseline model.

5. CONCLUSION

This chapter focussed on the role of a permanent.shock to
foreign productivity in accounting for economic fluctuations
in the United States. When this shock is added to an open-
economy model of the U.S. , the combined effects of the
domestic and foreign productivity shocks explain the majority
of both the short-run and long-run variance in output and
consumption. The long-run variation in exports is primarily
the result of permanent shocks to real exchange rates, not
foreign income. However, as is the case in models without a
foreign productivity shock (Chapter III), investment is
dominated in the short-run by permanent inflation shocks and
other transitory factors, such as temporary changes in real
interest rates. In addition, permanent shocks account for the
majority’of the short and long-run forecast-error variances of

the real flow variables.

99

There are a number of findings here which are not
consistent with predictions of the open-economy one-sector
Real Business Cycle model of Backus, Kehoe, and Kydland
(1992). The existence of a significant positive spillover
effect of foreign productivity on domestic productivity is not
found. Therefore, the foreign productivity shock appears to
impact the domestic economy only through changes in the
current and capital accounts. IFurthermore, net exports do not
respond significantly to the foreign productivity shocks.
However, some of the results are consistent with their model.
The domestic productivity shock has negative effects on net
exports in the short run. 'This is consistent with their model
in that current account surpluses (deficits) may be counter-
cyclical (procyclical) . This is contrary to the results
obtained in the less explicit models of Chapter III._, In
addition, after a lag, the response of investment to the
foreign productivity shock is significantly negative for a
short period, which is consistent with the idea that

international capital flows affect investment.

100

TABLE 1

Phillips-Perron Test Non-Stationarity Test of

Univariate Time Series 1957:2 - 1988:4

 

 

i
r

?
I

Series Zta Ztv

c -1.74 -0.60

i -2.75 -1.29
m-p -1.90 -1.22
Y -2.20 -0.77
Ap -2.68 -2.46

R -2.49 -1.89
im -2.29 -0.06
ex -3.04 0.14
y~ -1.13 -2.10
q -2.04 -1.31
cz-y’1 - -2.76
i-y‘ - -3.05
R-l 3Ap'l - -3.07

LH,__1____1“_H___ ____mwww_m__i_

Lags of truncation is 6

Critical Values :
Phillips-Perron (Ho: I(1)):

Zt.: 1% = -3.96, 5% = -3.41
Zt,.: 1% = -3.43, 5% = -2.86

Ztg: tests the null of I(1) with intercept and time trend
Ztyq tests the null of I(1) with intercept only

 

11959:2 - 1988:4

101
TABLE 2

Kwiatkowski-Phillips-Schmidt-Shin Stationarity Test of
Univariate Time Series 1957:2 - 1988:4

Series Trend No Trend I

 

c .299 1.872
1 .167 1.552
m-p .268 1.631
y .306 1.780
Ap .314 0.722
R .117 1.180
im .161 1.844
ex .186 1.866
y‘ .450 1.873
q .160 1.097
c-y‘ - 0.341
i-y‘ - 0.085

 

I R—1.3.Ap1 - 0.359

Lags of Truncation is 6

 

Critical values:
KPSS (Ho: I(0)):

NO Trend: 1% = .739, 5% = .463, 10% = .347
Trend: 1% = .216, 5% = .146, 10% = .119

 

11959:2 - 1988:4

102

TABLE 3

Residual-Based Cointegration Tests of Vectors
Without a Time Trend: 1959:2-1987:3

 

 

 

 

 

Estimated Vectors KPSS: No
Trend
m—p, - .72 + 1.211y, - 0.01412, .150
im,-S.30-+2.89y,+-0.131q, .308
im,-S.68+2.83y, .238
ex, - -11.02 + 0.946y; - 0.259q, ~257
TABLE 4

Residual-Based Cointegration Tests of Vectors
With a Time Trend: 1959:2-1987:3

    
 
 
 

Estimated Vectors

 

Trend
im,--1.94 +0.006t+1.29y,+0.101q, .101
im,--.57 +0.0054t+1.49y, .103

 

ex, - -6.71 + 0.006t + 0.337y; — 0.497q,

 

Lags of truncation for KPSS tests is 6

Critical Values (Shin 1992) KP88 (11,: 1(0)):

Without Trend:

1 Regressor : 5% = .314, 10% = .231

2 Regressors: 5% = .221, 10% = .163
With Trend:

1 Regressor : 5% = .121, 10% = .097

2 Regressors: 5% = .101, 10% = .081

103

TABLE 5

Variance-Covariance Matrix of Permanent Shocks
in the Baseline Model

 

 

 

 

 

 

 

 

 

   

 

I .Ap g y‘ (y
I Ap 0. 18453 - - -
I q 0.00073 0.00030 — ..
3" -0.00123 -0.00002 0.00004 -
Y -0. (£200 -0. 00001 1.00001 0. 00005
TABLE 6

Shocks in the Baseline Model

Correlations between the Four Permanent

 

 

 

  

 

 

 

 

 

 

 

        

I AP 9 y‘
(1 0.09811 - -
y’ -0.45273 -O.18257 -
y -0.65843 -0.08165 0.22361
_ _
TABLE 7

In Matrix in the Baseline Model

 

 

 

 

 

 

 

 

 

104

TABLE 8

Variance-Covariance Matrix of Permanent Shocks
in the Alternative Model

 

 

  

 

  

 

  

 

   

 

 

 

Correlations between the Four Permanent

TABLE 9

 

 

T
AP ‘1 y‘ y
Ap 0. 18595 - - -
0 0.00110 0.00032 - -
y‘ -0.00129 -0.00003 0.00005 -
-0.00214 -0.00002 0.00002 0.00006

 

Shocks in the Alternative Model

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

     

 

 

 

 

 

 

 

 

 

AP 0
q 0.14260 - -
y‘ -0.42306 -0.23717 -
.Y -0.64068 -0.14434
:— — __7, e 77' -1,
TABLE 10
:0 Matrix in the Alternative Model
m 1
(AP g y‘
AP 1.000 0.000
g 0.006 1.000
I y‘ -0.007 -0.075
I Y' -0.012 -0.020

 

105

TABLE 11

Long-Run Multipliers in the Baseline Model in
Response to Changes in the Four Common Trends

 

C

i
m-p
im

 

TABLE 12

Long-Run Multipliers in the Alternative Model in
Response to Changes in the Four Common Trends

 

 

106

TABLE 13

Percentage of Forecast-Error Variance Attributed to
the Domestic Balanced-Growth Shock in the Baseline Model

 

 

 

  
  
  
  
 

 

 

 
 

Period
P= J 1 fl 4» _ " _.‘
1 4 8 12 16 20 24 120
C 32 65 57 48 44 40 44 6O
1 31 29 21 20 18 16 43
y 11 60 58 44 44 42 41 59
ex 22 15 14 6
L111) 39 21 17

 

 

TABLE 14

Percentage of Forecast-Error Variance Attributed to
the Foreign Productivity Shock in the Baseline Model

 

 

 

 

107

TABLE 1 5

Percentage of Forecast-Error Variance Attributed to
the Real-Exchange-Rate Shock in the Baseline Model

 

 

 

 

Period
" 1 4 8 12 16 20 24 120
C 3 2 19 22 19 14 10
O 2 9 15 15 15 14
y 25 9 13 l7 16 14 12
ex 10 6 20 37 38 42 41 63
im 6 14 18 26 24 20 17 7
TABLE 16

Percentage of Forecast-Error Variance Attributed to
the Inflation Shock in the Baseline Model

Per199_

 

 

 

 

 

108

TABLE 17

Percentage of Forecast-Error Variance Attributed to
the Domestic Balanced-Growth Shock in the Alternative Model

Period

I 1 4 8 12 16 20 24 120
i 48
22
46
6
14

 

 

 

TABLE 18

Percentage of Forecast-Error Variance Attributed to
the Foreign Productivity Shock in the Alternative Model

Period

12 16
7

 

 

 

 

109
TABLE 19

Percentage of Forecast-Error Variance Attributed to
the Real-Exchange-Rate Shock in the Alternative Model

 

 

 

 

 

Period
============== e=====1
1 4 8 12 16 20 24 120
C 5 4 22 26 23 16 12
1 1 1 9 17 17 16 14 6
Y' 18 7 12 18 17 15 13
ex 12 7 18 35 37 41 40 65
in) 11 10 22 34 32 25 21 5
TABLE 20

Percentage of Forecast-Error Variance Attributed to
the Inflation Shock in the Alternative Model

 

 

 

 

 

 

 

 

 

 

 

 

 

_ Period
fl 1 4 8
II c 4 2 2
i 3 37 36
Y' 6 10 11
ex 6 12 11
£===£=.=9_1=§3=
TABLE 21
Percentage of the Forecast-Error Variance
Attributed to the Transitory Shocks in Each Model
(‘ _ —'r‘—”‘ . :_ ._ . 1 iii _, _ _ 1
I Baseline Alternate , IBasel1ne Alternate
12 Periods 12 Periods { 120 Periods 120 Period
1 c 18 17 3 1 '
1 1‘ 22 23 ‘ 14 14
[L y 15 16 i 4 3 i
It ex E as 1. 1 1. 1. +
‘ i 39 ,_ 37 j 16 11 ‘

 

 

 

131(3

 

 

 

 

S", 1.:
\}
l

 

 

 

 

 

 

 

I.II i ' "'

o u I W
/\ // \

. ‘. ‘ i j I V V I t T T I
I II :I H u :I H II II 01 HI III

FIGURE 1: Consumption in Response to a One-Standard Deviation
Domestic Productivity Shock

 

 

 

 

 

4 . O
5
II
"I
I A
I I I
I I I
I I I
I I I
I
I . O | , ‘
I I I
I I I
I I I
I I I
I I I
‘I i ‘I
1 l l
I . O I. 'l I‘
f—‘\
‘\ II ‘I ” ~~~~
\
| l ‘ / ...............
“ / \ , r’
0 ’§ O---
I| ’I \a’ ‘‘‘‘‘ ’
I I
T l
I I
\
\

 

 

 

 

 

 

' 1| H H 41 .1 CI 71 H .1 101 1”

FIGURE 2: Investment in Response to a One-Standard Deviation
Domestic Productivity Shock

111

 

 

 

 

4. l
I \
I \
l \
I \
A \
I . 4 I 1
I \
l \
I \
l \\
I I
I l \\
:1 1 A x , -1
I I I \ ’ ‘~ ~
I I I \ / .........
I 1 I \ /
I I I \‘ l
I A l J A
N \4 I
I \ I
I \ I
.' I I \
I I

 

 

 

 

 

 

 

 

1 11 I1 41 41 41 41 71 41 .1 101 111

FIGURE 3: Imports in Response to a One-Standard Deviation
Domestic Productivity Shock

 

 

 

3..
A
II
II
11
I I
I l
2.0 III I
III I
III I
II I
I I' I
I I I / “‘ ‘
a“. ‘ ll ........
1.0 ........ II‘ I- \\ ...........
III I’ ---------
II I
II I
I
O

 

 

 

 

 

 

 

 

1 11 II .1 41 41 41 11 41 I1 141 111

FIGURE 4: Exports in Response to a One-Standard Deviation
Domestic Productivity Shock

112

 

 

 

I. I
I A
II ‘
I ' MI I I
'1 I \
I I \
I I I
I I \
I I I
..........
-~--
I I I” -‘.. --------
II \ /’~\ 1
1 I III I \ ~~~~~~~~~
III I
III I
II I
\ I
k I
\ I
\ I
\ I
I I
‘3
V

 

 

 

 

 

 

 

 

 

1 11 I1 .1 61 .1 II II .1 .1 1.1 111

FIGURE 5: Output in Response to a One-Standard Deviation
Domestic Productivity Shock

 

 

”ion-I-" ""
'5
j
7’---
\
\
\
I
I
I
I
I

\-----—--“‘
\ -o.--------—--.
\~ ——“'
- ‘—-

 

 

 

 

 

 

 

1 11 81 I1 61 I1 01 'I1 .1 .1 101 111

FIGURE 6: Net Exports in Response to a One-Standard Deviation
Domestic Productivity Shock

113

 

 

 

 

 

 

 

 

 

 

 

 

I II , ~~~~~~ ‘
\ ...............
/ \\ .............
I\Aq” \ \\\\\\
1‘. '
I.“ I' I I
I I
I I
I I
I I
I I
I 1
I.II ‘3; I
I I
I/
‘-’ /\
I 01 / \
‘ f/\/\/
0.1. \
//~\\
0... '
v ,,
/
1
/
J
I II \ /[
V
‘ .. I f r I I I I I I T I T
1 11 81 .1 ‘1 II .1 I1 .1 .1 1.1 111

FIGURE 7: Consumption in Response to a One-Standard Deviation
Foreign Productivity Shock

 

 

----------

O - -
...................
I

 

 

 

 

 

 

 

 

1 11 .1 II 61 II 01 ’1 01 .1 1.1 111

FIGURE 8: Investment in Response to a One-Standard Deviation
Foreign Productivity Shock

114

 

 

 

 

LI
I
j
I.I II
II
II
II
3“
’\
\
LI 3.
II
--
|n \ ..........
a
‘" ‘ I .........
I! \\ ’1 -
I ‘ -v’
; \ , '
I I '. s-’
II
II

(

 

 

 

 

E
\\
.><

 

 

 

 

 

\

 

 

 

I II II II II II II II II II III III

FIGURE 9 Imports in Response to a One-Standard Deviation

Foreign Productivity Shock

 

 

 

 

 

I.I
A
’\
. . I I
. I
f ‘
. \
I N
A r' \
M i ‘
l 1 l \\\ .............
' . I, I I, ‘ ---------
I I
II
II
/\.\ u //\v\'\
V
A M
0.0 I

 

 

 

c:
e‘\\\
Z

 

 

 

 

I II II II II II II II II II III III

FIGURE 10: Exports in Response to a One-Standard Deviation
Foreign Productivity Shock

115

 

 

 

 

 

 

 

 

 

 

 

 

 

I II V /--—-’ v
\ \ //
H \1
I II V V
‘ .. I I I I I I I I I I I I
I II II II II II II II II II III III

FIGURE 11: Output in Response to a One-Standard Deviation
Foreign Productivity Shock

 

 

 

I . I
I‘\
I \
I L
I . I I I
I \
I \
I I
I I
I \
I \
1 \
I I / '\\
I \\ ......
I
'I \\ I, ‘‘‘‘‘
N ~~~~~~~~
’\ I \‘ (I, .....
_______

 

 

.
-::: b
: -¢:'-'
:1:
-~ L

 

 

 

 

 

 

/
. . I I I I I I I I I I I I
I II II II II II II II II II III III

FIGURE 12: Net Exports in Response to a One-Standard Deviation
Foreign Productivity Shock

116

 

 

 

 

 

’a‘
I I I I; \\
J \ _______
I, \\ ’’’’’’
I \ ’1’ ..........
1 \‘ A,
I . I I r \ ,’
'I \ ‘‘‘‘
I I
I I
II I
II I
II I
A 5 l
I . I I I \ I
I I
I I
I l
I /
\ I
1 u Av A
I.II

 

 

 

 

 

1 II II II II II II II II II III III

FIGURE 13: Consumption in Response to a One-Standard Deviation
Real-Exchange-Rate Shock

 

 

 

 

 

 

 

 

 

 

 

I II II II I! II II II II II III 111

FIGURE 14: Investment in Response to a One-Standard Deviation
Real-Exchange-Rate Shock

117

 

 

 

 

 

I... '
I
I
H r’\
r. .' \
‘0
II I ‘
II I\ I \
II I l L
0 60 I | a: | I \
I I Hi I I \
l I H \.I \ ........
I I I \I \ r’ ‘\
I I. 'I \\ /’ ‘~_»\
I s
' ‘ \ I, .......
a g \ x
I... ‘ I \‘-" I
I I
I I
‘ J»p\Lf“/’/A\\\\
I I
I I
I
o." n/ .
‘
\A

 

 

 

 

 

 

 

 

 

I II II II II II II II II II IOI III

FIGURE 15: Imports in Response to a One-Standard Deviation
Real-Exchange-Rate Shock

 

 

 

 

 

 

 

 

 

 

 

/ W
1nd
0 n \ /,\’,v
1 u xfo//
‘ .‘ I I j I I I I I I I I f
I II II .I CI II II II .I OI IOI III

FIGURE 16: Exports in Response to a One-Standard Deviation
Real-Exchange-Rate Shock

I...
0.80 ’ i
I: Ir\\"_ I \ \\\\ \\\ -----------------------
o.” ‘ i‘ I!
o u I! I ”W
LII \\\///r‘\
f/"‘fl.-‘\\\~.”"_—“~—___________.
0.10 \ [ //
I... \f/
L
..‘. I I I I I I I I I I I I
I II II II II II II II II II III III
FIGURE 17: Output in Response to a One-Standard Deviation
Real-Exchange-Rate Shock
0.00
I. H I. Ill ’1" .\
\"\ .1”
"L ’\ I \
a." \r/\ V \ .............................................
0.80 V /1
\/ \\ A M
I.II
/ \ A
o." \ / \\_—/
1.00 /
\ [\/
1.“ V
I... T I I I I 1 y I T7 44T r’ '

FIGURE 18: Net Exports in Response to a One-Standard Deviation

118

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I II II II II II II II II II III III

Real-Exchange-Rate Shook

 

 

119

 

 

I.III
I
fl
’\
In I \
'I 1‘ I, ‘
I I I \\
I I I -----------------
' \ I -------
0.00! ' ‘ ' ..........
I \
I \ /
‘ ll
\ I
A ‘I
0.000 ‘

 

.0.III M41

 

 

\\ III/\'
1’ “
.I.III ‘I1///

FIGURE 19: Consumption in Response to a One-Standard Deviation

 

 

 

 

II II III III

Inflation Shock

 

 

 

 

 

 

 

 

 

I..II |
N
‘I
I
I
I
I
I
I
I
I
0.060 ‘3‘.
I
I
I
I
I
\
I
. I
L. I
0.01. g '| , \
I I I \
I I \
I I \
I I \
I I, \\
‘ I-‘~‘ \ ------------------------------
‘x/I -------------
4.0M \/ \ /
.I.ooo V V ‘ ‘ ‘ ‘ ' ' '
I II II II II II II

 

II II III III

FIGURE 20: Investment in Response to a One-Standard Deviation
Inflation Shock

120

 

 

 

I.III
I'
I.III I
II
II
II
M
I I
I I
I H
II ’I
R ‘n z \
. .I. II I l \
I I \
'. I’ \
I II \“
\
I I \
V

 

 

 

 

 

1/ \\k
. .I. I I, v
//
. /
\AV/
. ... I 17 I I I I T I I I j
I II II II II II II II II III III

FIGURE 21: Imports in Response to a One-Standard Deviation
Inflation Shock

 

 

 

 

 

 

 

 

 

 

I.III
I.III
I.III ‘\a\
V\
\
\\
\
\ .....................................
I on J' v
w
M // V’W
I III / v
I III ‘ V ' I I I I I I 1 l

I II II II II II II II II III III

FIGURE 22: Exports in Response to a One-Standard Deviation
Inflation Shock

121

 

 

 

 

 

Ail
I‘I
I I
II
I I
t 1
0.010 F \
I \
I \
I \
I I
I I
a L
0.01. g \
I I
I \ /\
I '. / \
JI"\ \. .I x .......................
0.0" ; '\ ,Y -
‘.,,-/
0.000 I \

 

 

A /\
,Mqv \//\_

:1: :3: \A
/\_\_fl/_~
\./

-0.0IO ‘

 

 

 

 

 

I. II. III

FIGURE 23: Output in Response to a One-Standard Deviation
Inflation Shock

 

 

 

 

 

 

 

 

 

0.071
A
I\
I \
I I
I \
I ‘\
1
I. on , ‘
I I
'I \
' W ~~~~~
I \
i \
I \
0.03I I \
I \
I \
I \
'I \
I ‘\ IIIIII
I \ 1’ \‘
: \ I \‘ - _"
7 ‘ I
o. no , \ /
: ‘ /
\ ' \"’l
\ a
\!U
0.... ”\u/
N I,
-O..I. /
/‘\/ V,
y
. ..... Y Y I I I I T I T I
I II II .4 ll I. .7 7. 0. IO. III

FIGURE 24: Net Exports in Response to a One-Standard Deviation
Inflation Shock

APPENDIX

122

APPENDIX

AN OPEN-ECONOMY COMMON TRENDS MODEL

A.1. REDUCED-FORM ANILYBIB
The reduced-form is represented by a Wold decomposition

of the series in first differences

Mrs-wane t (A1)

where X, - (c,i,m-p,im,ex,R,y‘,Ap,q,y)’ and e:c is the vector

of one-step-ahead forecast errors in KC, given information on
lagged values of xx. x, is I(1) , and is cointegrated with the

4 cointegrating vectors, given by the 8x4 matrix B . Then,

B’C(1) - 0, where C(l) - ; Cj, and
-o

 

 

o o 1.0 o o .014 o o o -1.21‘
1.0 o o o o o o o o -1.0
, o 1.0 o o o o o o o -1.0
B ' o o o 1 o o o o o -.101 -1.29
o o o o 1.0 o -.337 o .497 o
_o o o o o 1 o o -1 3 o o J

3.2. COMMON TRENDS REPRESENTATION

If 2 series are cointegrated, then they must share a
common stochastic trend, since they have a common integrated
component. KPSW’s model can be viewed as a multivariate

extension of Beveridge and Nelson (1981) . They show that X,

123
can be written as a linear function of a permanent component

and a transitory component

Xc-X0+A1:t+D(L)et (A2)

where 1,. - y + 1.4 + n c. A must be orthogonal to [3’ (B’A-O) in

order to preserve the cointegrating properties of Xc. Since
Att is I(1), and D(L)et is I(O), then Art is the "common

trends" in X..

L.3. IDENTIFICATION OF THE COMMON TRENDS

Since 1' c follows a random walk, then A1: t follows a random
walk. So, the problem of identification becomes a problem of
identifying 1:c and ‘1: when k>1. Since A and 1:, are only

identified up to an arbitrary transformation by a nonsingular

kxk matrix, define A - 5011. A0 reflects a priori restrictions

about which permanent shock affects which variables.

0 o o 1
o o o 1

o o o 1.21

o o .101 1.29
A _ .337 o -.497 0
° 0 1.3 o o
1 o o o
o 1 o o
o o 1 o

o o o 1 ,

 

 

124

In order to "name" the shocks, ITO - AOQ, where

0 O 1 O

1 O 0 0
O1-

0 1 0 O

0 0 O 1

says that the inflation shock is ordered first, the real-
exchange-rate shock is second, the foreign productivity shock

is third, and the domestic productivity shock is forth.

So, 50 - A001 is given by

0 o o 1 *
o o o 1
o o o 1.21
o 101 o 1.29
.. o -.497 .337 o
A° ' 1.30 o o o
o o 1 o
1 o o o
o 1 o o
o o o 1

 

 

where the first column represents the long-run impact of the

first shock on each of the variables,

c, i, m-p, im, ex, R, y’, Ap, g, y.

3.4. ESTIMATION

The reduced-form (11.1) is estimated to get C(I'D , C(i) ,

and ;ej. From equation (A.2),
-o

AX, - KoHAn c + D(L)Aet . (A3)

125

[In the long-run, (A.1) implies that
AX, - 63(1):)” (14)
-o
and equation (A.3) implies that
AX, - A'OIIIk (35)
since Ecn c - 11,, and Etc. - €c-1- Therefore,
0(1)::61 - £0111), - .1? (16)
-o

where,

;.01 .03 -.10 1
-.01 .03 -.10 1
-.03 .04 -.12 1.21
-.01 .14 -.12 1.29

 

 

A‘- 0 -.s35 .337 o
1.30 o o o
-.01 -.113 1 o

1 o o o
o 1 o o
_-.01 .03 -.1o 1

and II - 2:” , where the covariance matrix of the permanent

innovations 2‘1 - E(n1’n1). II for the lO-variable model is
reported in Table 10.

126

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"11111111111“