essays on income inequality exchange rate and policy coordination

At the same time, Hong Kong should steadily increase its government expenditure and China should keep a stable money growth.. Figure 2.2: Hong Kong’s Government Expenditure It is obvious

Copyright

by Xiaojun Yang

2003

The Dissertation Committee for Xiaojun Yang Certifies that this is the

approved version of the following dissertation:

Essays on Income Inequality, Exchange Rate,

and Policy Coordination

Committee:

David A Kendrick, Supervisor

Li Gan Vince Geraci William Glade Hong Yan

Essays on Income Inequality, Exchange Rate,

and Policy Coordination

by Xiaojun Yang, B.A., M.I.A., M.S

Dissertation

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements for the Degree of

Doctor of Philosophy

The University of Texas at Austin

May 2003

UMI Number: 3116243

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Acknowledgements

I am deeply indebted to my supervisor Professor David A Kendrick for his kind guidance, advice and encouragement Under his consistent, conscientious and patient supervision, I have gained insight about macroeconomics and computational economics, importantly how to approach academic research I will continue to value his friendship

I also owe thanks to the other member of the dissertation committee: Dr

Li Gan, Dr Vince Geraci, Dr William Glade, Dr Hong Yan, for their valuable discussions and suggestions, and for their generosity and kindness Also, I would like to express my appreciation to Seung-Rae Kim and Marco Tucci for their intellectual and technical advice

Finally, I express my special thanks to my parents for their lasting support and love

Essays on Income inequality, Exchange Rate,

and Policy Coordination

Publication No. _

Xiaojun Yang, Ph.D

The University of Texas at Austin, 2003

Supervisor: David A Kendrick

The goal of this dissertation is to develop and to use computational methods to study issues in policy coordination, exchange rates and income inequality

The topic of policy formulation among interdependent economies has received much attention in the literature In the first essay a two-country model is used to illustrate the interdependence of China’s and Hong Kong’s economies Not surprising, we find that the policy effect is asymmetric, due to difference in size Shocks to the Chinese economy will affect Hong Kong’s stable economic growth In order for Hong Kong to keep a stable growth, both governments must act in certain ways Particularly, by importing more China can help Hong Kong’s economy, especially during the financial crisis years We find that fiscal policy is

more effective than monetary policy in affecting economic activities in this model

In the second essay, we develop a model to study the behavior of the Yuan/Dollar exchange rate The parameter values estimated for the model are such that when China increases its relative money supply, the exchange rate appreciates, which is different than the conventional result Also the parameter values indicate that in order for China to have a higher level of GDP, China has to increase its money supply; and for a stable exchange rate, China either decreases its money supply then increases it or increases its money supply during the entire period The right policy hinges on the desired path for the exchange rate Since the model is simple in essence, the results should be interpreted with caution

The third essay analyses the contribution of different factors to the determination of income inequality The questions regarding whether greater income inequality is conducive to China's growth and the role of degree of reform for growth and inequality have been studied in the paper We find a positive correlation between income inequality and growth, that reform plays a dominant role in determining growth and income inequality, and that steady growth can not

be emphasized too much, otherwise the reform process will be reversed, which is not practical Finally, the tradeoff between income inequality and growth is analyzed

Table of Contents

Chapter One: Introduction 1

Chapter Two: Economic Interaction and Policy Coordination Between China and Hong Kong 3

2.1 Introduction 3

2.2 The Model 4

2.3 The Optimal Control Theory 10

2.4 The Model with Price Variables 32

2.4.1 The Model Equations… 32

2.4.2 Simulations 39

2.4.2.1 Historical Simulation 39

2.4.2.2 Policy Simulation 43

2.4.2.2.1 Fiscal Expansion 43

2.4.2.2.2 Monetary Expansion 49

2.5 The Model with Price Variables in the Control Theory Framework 50

Chapter Three: Yuan - Dollar Exchange Rate Model 62

3.1 Introduction 62

3.2 Developments of China's Foreign Exchange System 63

3.3 The Model 71

3.3.1 The Model Equations… 72

3.3.2 Data 74

3.3.3 Estimation 75

3.3.4 Policy Simulation 77

3.4 The Control 82

3.4.1 The Control Framework 82

3.4.2 Results and Experiments 86

3.5 Conclusion 95

Chapter Four: Reform, Inequality, and Growth 96

4.1 Introduction 96

4.2 Factor Consideration 97

4.3 The Model 102

4.4 Control and Sensitivity Analyses 112

4.4.1 The Control Framework 112

4.4.2 Sensitivity Analysis 117

4.4.2.1 Sensitivity Analysis from 1991 to 1998 119

4.4.2.2 Sensitivity Analysis from 1998 to 2010 132

4.4.2.2.1 Caring More about Income Inequality 135

4.4.2.2.2 Caring More about Growth Rate 140

4.4.2.2.3 Greater Difficulty to Further Reform 144

4.4.2.2.4 Inequality verse Growth 149

4.5 Conclusion 152

Appendix A-1 Historical Simulation 154

Appendix A-2 Simulation Results for China's Fiscal Expansion 158

Appendix A-3 Duali Input File 1 162

Appendix A-4 Duali Input File 2 179

Appendix B-1 Comparison of Different Money Supply 198

Appendix B-2 Duali Input File 199

Appendix C-1 Constant Inequality, Growth and Inflation 204

Appendix C-2 Duali Input File 206

Appendix D-1 Data-China 212

Appendix D-2 Data-Hong Kong 220

Appendix D-3 Data-US 226 Bibliography 228 Vita 231

Chapter 1: Introduction

The topic of policy formulation among interdependent economies has received much attention in the literature China and Hong Kong are economically closely linked Policy initiatives in one economy may influence the evolution of economics variables in the other In the first essay a two-country model is used to illustrate the interdependence of these two economies Not surprisingly, we found that the policy effects are asymmetric, due to differences in size China’s economic policies have a big effect on Hong Kong, but the reverse is not true However, China and Hong Kong’s economies are intertwined A shock to the Chinese economy will affect Hong Kong’s stable economic growth In order for Hong Kong to keep a stable growth, both governments must act in certain ways Particularly, by importing more China can help Hong Kong’s economy, especially during financial crisis years In doing so, China has to have higher government expenditure and Hong Kong has to have higher money growth At the same time, Hong Kong should steadily increase its government expenditure and China should keep a stable money growth Fiscal policy is more effective than monetary policy

in affecting economic activities in this model

In the second essay, we develop a model to study the behavior of the Yuan/Dollar exchange rate We connect the exchange rate with China and America’s income, money supply, interest rate, and current account The parameter values estimated for the model are such that when China increases its

relative money supply, the exchange rate appreciates Also the parameter values indicate that in order for China to have a higher level of GDP, China has to increase its money supply; and for a stable exchange rate, China can either decrease its money supply then increases it or increase its money supply during the entire period The correct policy depends on the desired path of the exchange rate Since the model is simple in essence, the results should be interpreted with caution

The reform and open-door policies in China have liberated people’s work incentive and enthusiasm Important aspects of this change are that people have more job choices and more opportunities, and that income inequality has increased The final chapter analyses the contribution of different factors in the determination of income inequality The questions regarding whether income inequality is conducive to China's growth and the role of degree of reform for growth and inequality have been studied in the paper A two-period model with two-group households—rural and urban—is introduced to illustrate factors that should be considered in income distribution and growth Based on this framework, equations are developed for urban income inequality, rural income inequality, growth and inflation Contradicting a popular view regarding East Asian countries, a positive correlation between income inequality and growth was found The other findings are that reform plays a dominant role in determining growth and income inequality, and that steady growth can not be emphasized too much, otherwise the reform process will be reversed, which is not practical Finally, the tradeoff between income inequality and growth is analyzed

Chapter 2: Economic Interaction and Policy Coordination

Between China and Hong Kong

2.1 INTRODUCTION

The economic reforms that took place in mainland China in the late 1970s began a new process that fundamentally changed the economic relationship between mainland China and Hong Kong In the 1960s and 1970s, Hong Kong’s economic growth rate reached, on average, almost 10 percent per year However

by the early 1980s high land rents and wages began to erode Hong Kong’s international competitiveness that had been the basis of its success Coincidentally, the emergence of such pressures coincided with China’s open-door policies Thus a mutual benefit situation arose between the two and the forging of much closer economic relations began We want to know how the two economies interact, how policy interaction can increase their welfare, and what policy instrument is more effective in affecting the economies In this paper a two-country model is used to illustrate the interdependence of these two economies and also answer those questions We found the policy effect is asymmetric, due to different size China’s economic policies have a big effect on Hong Kong, but the reverse is not true However, China and Hong Kong’s economies are intertwined The shock of the Chinese economy will affect Hong Kong’s stable economic growth In order for Hong Kong to keep a stable growth, both governments must act in certain ways China can help Hong Kong

Fiscal policy is more effective than monetary policy in affecting economic activities

The chapter is organized as follows Section 2 describes the model The optimal control theory is presented in section 3, where we describe the quadratic linear problem, give the solution process for the system, and associate the dynamic optimization method with our problem In section 4, the price variables are added to the model to see the role of monetary policy, where we also present policy simulations Section 5 puts the expanded model in the control theory framework and gives a sensitivity analyse

2.2 THE MODEL

2.2.1 The Model Setup

The model consists of the GDP identity and functions for each of its components Specifically, for the Chinese economy we have:

For the Hong Kong economy we have:

of the model to the data

Since all the endogenous variables are interrelated between China and Hong Kong as well as within each economy, we use two-stage least squares to estimate the model We use all the relevant variables as the instrumental variables When the Durbin-Watson statistic indicates a first-order serial correlation, we use the Cochrane-Orcutt technique to correct it

The following is the estimation result1:

For the Chinese economy:

CYt+1 = CCt+1 + CIt+1 + CGt+1 + CXt+1 – CMt+1

The standard errors are in parentheses All the signs meet our expectation The interaction of the two economies is represented by the export functions: China’s export is a function of Hong Kong’s GDP, and Hong Kong’s export is a function of China’s GDP

2.2.2 The Estimation Technique 2

This section describes a consistent estimator of a simultaneous-equations model in which there is a lagged dependent variable and serial correlation Consider the following equations (in deviation form):

t 1 t 3 t

2

q = + − + ε (1)

t 1

t

ε − (2)

t t

t 1 t 3 1

t t 2 1

t

q − ρ − = − ρ − + − − ρ − + (4)

Since ρ is not known, the estimate of the serial correlation coefficient, r, may not

equal ρ Then (4) becomes

] ) ( v [ ) rq q

( a ) rp p ( a

2

p = γ + γ − + γ − + γ − + (6)

and get the predicted values pˆt.

Stage two: estimate the equation

] wˆ a )

( v [

) rq q

( a ) rp pˆ ( a rq

q

t 2 1 t t

2 t 1 t 3 1 t t 2 1

t

t

+ ε

− ρ +

+

− +

Figure 1.1 Actual verse Prediction

64 66 68 70 72 74 76 78 80 82 84 86

Panel d: Hong Kong's Consum ption

actual predicted

2.3 OPTIMAL CONTROL THEORY 3

Many problems in economics are formulated as dynamic models Control theory is a dynamic optimization method, in which controls are used to move an economic system over time from a less desirable to a more desirable state The basic idea of control theory is that an objective function is optimized subject to a set of state or system equations The objective function of a model depends on the decision maker’s objectives Variables in the system are separated into two groups: state and control variables The state of the economic system at any point

in time is represented by the state variables Controls represent policy variables, that can be altered by decision makers The application of optimal control in economics normally centers on a class of control problems called quadratic linear tracking problems The goal in the quadratic linear tracking problem is to cause the state variables and control variables to follow their desired paths as closely as possible That is also the model we use in this study

The objective function in the quadratic linear tracking problem is

)

~()

~(2

N N N N

−+

1N

u u u

u x x W x

and the system equations are in the structural form used by Pindyck (1973), i.e

t t t t

u~ = desired path for the control vector

z t = purely exogenous variable vector of period t

A0, A1, B1, and C1 are the coefficient matrices and vectors

To specify, in our model we have:

u , z t =[Const]

Since we are going to represent this model in Duali software written by Amman and Kendrick (1999), and Duali software does not allow variables in concurrent

terms, we introduce Lead CG t and Lead HG t, where

Lead CG t = CG t+1 Lead HG t = HG t+1

0000000004

0

000074.000000

000041.000000

11

11000000

00000000007

0

00003.000000

00000000046

0

00000000048

0

0000011110

0

A

0

0042.005.000000

0005.0000000

0000000000

0000075.00000

00000

09.0000

00000

0065.0035

0

0000000085.04

0

00000

00000

1

C

The desired paths of all the state variables are computed using their average growth value the same growth rate from 1987 to 2000 except for the control variables which are from 1988 to 2000, for example, China’ GDP in 1987 and

2000 are 359 billion and 815 billion US dollars (both in 1990 price) respectively The growth rate of GDP during this period is 6.5 percent per year The desired

path of China’s GDP then is calculated according the growth rate of 6.5% each year The desired paths are shown in Table 2.1

Table 2.1: Desired Paths for the State and Control Variables

559 mean of i

W i =

Where 559 is the average for China’s GDP

i: state variables or control variables

For example, China’s consumption average from 1987 to 2000 is 277 billion dollars The penalty weight for China’s consumption is 559 divided by

277, and which is about two 559 is China’s GDP average, which is the largest

average value among all variables We chose 559, since we want the penalty weights to be greater than one

Since variables in our model have different units, this normalization will give the same importance on each variable Sometimes the weights are normalized with different methods, for example, normalized with squares Fonseca (1999) gave a detailed description about different normalization approaches Here we follow Shih (1997)’s method This normalization is simple

to calculate and also it achieves normalization goal The following table lists the penalty weights

Table 2.2: Penalty Weights on State and Control Variable

CY CC CI CX CM HY HC HI HX HM CG HG

1 2 2.7 5.5 5.6 6.6 11.3 24 4.8 5 7.9 80.5

In fact the quadratic linear tracking problem can be transformed to the quadratic linear problem (QLP), as described in Kendrick (1981, page 6-8) The quadratic linear problem (QLP) is to obtain the solution paths for all the relevant variables by optimizing a quadratic objective function subject to system equations and a given initial condition The variables in the model are separated into two groups: state and control variables Kendrick (1981) states the QLP as to find

' '

' '

'

' '

2

12

12

1

N k

k k k k k k k k k k k k k

N N N N

N

u u

u u F x x w x W x

x w x

W

x

J

λ (2.1)

subject to the system equations

k k k k k

A , B and k c = coefficient matrices and vectors k

Thus the problem is to find the time paths for the m control variables in

each period for the time periods from 0 to N-1 to minimize the quadratic form

(2.1) given x and following (2.2) 0

Solution Process

The problem (2.1) to (2.2) can solved by the method of dynamic programming to obtain the feedback-control solution The derivation of the solution for this model is described in detail in Chapter 2 of Kendrick (1981) The

cost-to-go at time k is defined as

' ' '

' '

2

12

12

1

)

(

N k t

t t t t t t t t t t t t t

N N N N N

k

u u u u F x x w x W x

x w x W

x

x

f

λ (2.3)

Which is the summation of the objective function from period k to the terminal

12

1

)

1 '

' '

' '

+ +

++

Λ++

' 1 1

*

1

2

1)

Substituting the system equation (2.2) for x in equation (2.5) to express k+1

the optimal value in terms of x , we get: k

++

++

= x A P A x A P c A p x x A P B u

x

u k B k P k B k u k B k P k c k B k p k 'u k

1 ' '

1

' 1

Plugging (2.6) into (2.4) and taking the first order condition with respect

to u , we get the optimal solution: k

k k k

u* = + (2.7) where

][

]

1 ' 1 1

'

k k k k k k k k

][

]

1 ' 1

1

'

+ +

(2.7) is called a feedback rule, which says that if the economy is in state x at k, k

the best policy is *

2

1)

where

k k k k k k k k k k k k k k

1

' 1

'

++

++

= k k k k+ k k+ k k k k+ k k

1 ' ' 1

' 1 '

)(

k k k k k k k k k k k

1 ' ' + + + + Λ + (2.12) Equations (2.11) and (2.12) are the Riccati equations for the problem The Riccati equations dictate the backward relationships in the time dimension and P and k k

p are functions of P and k+1 p k+1 That means if we have the terminal values for

N

P and p , then we can solve N P and k p by integrating the Riccati equations k

backward in time P and N p can be obtained from the minimization of the N

terminal period cost-to-go

N n N N N N

2

1)

we get

Because the objective function at N is constant in terms of the control vector u N

and thus is the same as its optimal value

Results and Experiment

If we apply the desired paths and penalty weights above and use the Duali software written by Amman and Kendrick (1999), we get the optimal values for each variable, and also this is our base case value for each variable in the following experiment The experiments here are a warm up, they set the stage for the second model with prices

Experiment one: lower government expenditure

Due to the relative size of the two economies, China’s policy change will have a substantial effect on the Hong Kong economy, but not vice versa For example, if China should decide to lower government expenditure to slow inflation, the effect on Hong Kong would be substantial However if Hong Kong should cut government expenditure, the effect on China’s GDP would be

expenditure be 80% of its previous level each year, which is reflected in “low1” case in Figures 2.1 – 2.4 Then we restore Chinese government expenditure to its initial level and let Hong Kong government expenditure be 80% of its previous level, which is reflected in “low2” case in those Figures 2.1 – 2.4 “low1” and

“low2” stand for optimal solutions for all variables under the reduced China and Hong Kong’s government expenditure respectively Figures 2.1 and 2.2 reflect what happens to China and Hong Kong’s government expenditure after the change respectively

Figure 2.1: China’s Government Expenditure

Figure 2.2: Hong Kong’s Government Expenditure

It is obvious, from Figure 2.1, that China’s government expenditure is lower under “low1” than in the base case which reflects optimal solutions for all variables before making any change, and from Figure 2.2, Hong Kong’s Government expenditure is lower under “low2” than the base case At the same time, the reduction of China’s government expenditure has a big effect on Hong Kong’s government expenditure, see Figure 2.2 “low1” case Hong Kong’s government expenditure is increased substantially over the base path in order to offset the loss of income which comes from the decrease in exports to China However the reverse in not true – China’s government expenditure under “low2”

is almost the same as the base case, see Figure 2.1 The reduction of China’s government expenditure also has a big effect on Hong Kong’s export Figures 3 below reflect the optimal paths for Hong Kong’s export From Figure 2.3, Hong

Kong’s export path is apparently lower than the base level So the Hong Kong government must greatly increase expenditure to offset the loss in exports caused

by a decrease in government expenditure in China but the reverse is not true

Not surprisingly, Hong Kong’s government expenditure change has a negligible effect on China’s export, see Figure 2.4 under “low2” case

Figure 2.3: Hong Kong's Export

Figure 2.4: China’s Export

From this experiment, we have seen that the size of an economy matters Since China’s economy size is bigger than Hong Kong’s, China’s economic policy has

a large effect on Hong Kong, but the reverse is not true

Experiment two: China has lower GDP growth

In this experiment, we want to see what happens to Hong Kong’s economy if China’s GDP growth is slower In order to mitigate this adverse effect on Hong Kong’s economy, what should both governments do? First we let the growth rate of China’s GDP be 4% each year, which is lower than the base

all variables From Figure 2.5 panel a and Figure 2.6 panel a, we can see both

China and Hong Kong have a lower optimal GDP path (lower than the base case) after the change Now we want China’s GDP growth rate still to be the lower level – 4% – each year, but at the same time, we want Hong Kong’s optimal GDP stays as almost the same level as the base case, the case where China’s GDP growth rate is 6.5% In order to achieve this, we increase Hong Kong GDP’s desired level – higher than the base case and “lowy1” case (Hong Kong’s GDP has same desired level under base and “lowy1” case) This is reflected in

“lowy2” in panel b of Figures 2.5 – 2.8 Panel a of figures 5 – 8 show base and

“lowy1” and panel b of Figures 2.5 – 2.8 then add “lowy2” Now we describe

this scenario As mentioned above, the optimal path for China’s GDP stays at

lower level under “lowy1”, as can be seen from Figure 2.5 panel a

Figure 2.5: China’s GDP

350 450 550 650 750 850

The shock of the Chinese economy also makes Hong Kong’s GDP stay at lower

level, as can be seen in Figure 6 panel a under “lowy1”

Figure 2.6: Hong Kong’s GDP

In order to reduce this adverse effect on Hong Kong’s economy, we increase Hong Kong GDP’s desired path, that is the “lowy2” case Under “lowy2”, the optimal path of Hong Kong’s GDP is almost the same as that in the base case, as

can be seen in Figure 2.6 panel b The higher growth rate of Hong Kong’s GDP

helps China’s growth in the presence of the adverse shock We can see the optimal path of China’s GDP is higher under “lowy2” than under “lowy1”, as can

be seen in Figure 2.5 panel b That means under “lowy2” both Hong Kong and

China gain In order to achieve this, what should the governments do? The

b

China and Hong Kong’s government expenditure respectively Comparing the optimal paths under “lowy1” with that under “lowy2”, we can see after the shock

of the Chinese economy, in order for Hong Kong to avoid the adverse effect, China should reduce its government expenditure initially, then increase their expenditure thereafter, and Hong Kong should increase its government

expenditure significantly, as can be seen from Figures 2.7 and 2.8 panel b

Figure 2.7: China’s Government Expenditure

88 90 92 94 96 98 2000

b

Figure 2.8 Hong Kong’ Government Expenditure

Experiment three: Hong Kong has a lower government expenditure

In this experiment, we want to see how much China can help Hong Kong with its economic growth, when Hong Kong has to cut its government expenditure We let Hong Kong’s government desired expenditure be 80% of its

previous level each year Figure 2.9 panel a reflects what happens to Hong Kong

government’s expenditure after the change It is obvious that Hong Kong government’s expenditure is lower than the base case “lowg1” in the figure reflects this change “lowg1” stands for optimal solutions for all variables under

the reduced government expenditure Panel a in Figures 2.9 – 2.11 show the

optimal path under the base case and the “lowg1” case

Figure 2.9: Hong Kong’s Government Expenditure

b

“lowg2” is the case that we let Hong Kong ‘s GDP track its desired path as closely as possible after Hong Kong government expenditure reduction Hong Kong’s GDP weight under “lowg2” case is as large as 10 times the previous

weights Panel b of Figure 2.9 – 2.11 add the “lowg2” case From Figure 2.10 panel b, we can see Hong Kong’s GDP is closer to its desired path under

“lowg2” At the same time, Hong Kong’s government expenditure also stays at

lower level, as can be seen in Figure 2.9 panel b

Figure 2.10: Hong Kong’s GDP

Under “lowg2”, Hong Kong has both stable economic growth and lower

30 50 70 90 110 130 150 170

Figures 2.11 and 2.12, we can see the reduction of government expenditure in Hong Kong and stable economic growth have little effect on China