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Masters in International Economics and Finance Faculty of Economics,

Chulalongkorn University, Phayathai Road, Bangkok-10330,Thailand.Tel: (662) 218 6295, (662) 218 6218,Fax:(662) 218 6295,

E-mail: [email protected], http://www.econ.chula.ac.th/programme/ma_inter.html

Paper#1

Application of Regression models and Estimation problems

2940605: Quantitative Methods in Economic Analysis

BY SK. ASHIQUER RAHMAN

ID#4585974929

A Thesis Submitted In Partial Fulfillment of the Requirement for the Degree of Masters in International Economics and Finance

TO, DR.BANGORN TUBTIMTONG

ASSISTANT PROFESSOR

A Paper On

A relation between the number of wilsdcats drilled and three key factors: price at the wellhead, domestic

output and GNP constant dollars.

Wilsdcats Activities 2002

ii

Letter of Transmittal June 1, 2002

Dr.Bangorn Tubtimtong

Assistant Professor,

Masters in International Economics and Finance

Faculty of Economics,

Chulalongkorn University,

Phayathai Road, Bangkok, Thailand

Subject: Letter of Transmittal.

Dear Madam,

Here is my paper on "A relation between the number of wilsdcats drilled and three key factors:

price at the wellhead, domestic output and GNP constant dollars.” that I was assigned. It was a

great opportunity for me to acquire practical knowledge of the Quantitative Methods in Economic

Analysis and forecasting

I have concentrated my best effort to achieve the objectives of the report and hope that my

endeavor will serve the purpose.

I believe that the knowledge and experience I have gathered during my paper preparation will

immensely help me in my professional life. I will be obliged if you kindly approve this effort.

Sincerely yours

Sk. Ashiquer Rahman

Id#4585974929


Bangkok, Thailand


iii

Preface Any institutional education would not be completed if it were confined within theoretical aspects.

Every branch of education has become more competed by their practical application and

accomplishment of full knowledge. We shall be benefited by our education if we can effectively

apply the institutional education in practical fields. Hence, we all need practical education to apply

theoretical knowledge in real world. By considering this importance “faculty of economics”

arranges the Quantitative Methods in Economic Analysis courses for the students of Masters in

International Economics and Finance. As a part of this program my topic was selected as “A

relation between the number of wilsdcats drilled and three key factors: price at the wellhead,

domestic output and GNP constant dollars.”)”

I tried my best to conduct an effective study by arrange and analysis data. There may be some

mistakes, which are truly unintentional. So, I would request to look at the matter with merciful

mind.

Sk. Ashiquer Rahman Id#4585974929 Chulalongkorn University Masters in International Economics and Finance Bangkok, Thailand


iv

Acknowledgement First, all praises go to almighty Allah, the most gracious, the most merciful to give me the ability for

all these I have done.

Then I would like to thank Ms. Wanwadee Wongmongkol. Now I would like to thank

Dr.Bangorn Tubtimtong Assistant Professor, Chulalongkorn University, Phayathai Road,

Bangkok,Thailand to give me the opportunity to do this project.

I would also like to thank Professor. Paitoon Wiboonchutikula, Ph.D ,Associate professor and

Chairperson of Faculty of Economics, Chulalongkorn University & Professor Salinee. Secretatery

international economics and finance. My striking thanks go to honorable sir Dr. MN.Sirker who

has helped me in all aspect to prepare the report.

I would like to thank lab incharge Ms. Mink . Last but not the least I wish to thank my

friends, William Lloyed ,Nakarin and Athipat, for their very helpful discussions.



v

Table of Content

Title Page

Letter of Transmittal ii

Preface iii

Acknowledgement iv

Table Of Content v

Statement Of The Problem 1-1

Literature Review 1-1

Formulation Of General Model 1-2

Data Sources &Description 2-5

Model Estimation And Hypothesis Testing 6-10

Interpretation Of The Results And Conclusions 11-11

Limitations Of The Study And Possible Extensions 11-12

References 11-12

wildcats Activities

1

The Statement of the Problem:

Recently, oil becomes more influence to almost every economics sector as a

key material. As can be seen from news, when there are some changes in an oil price or OPEC announces a new strategy, its effect spreads to every part of economy directly and indirectly. That’s a reason why people always observe the oil price and try to forecast the changes of it. The most important factor affecting to the price is its supply that is determined by the number of wildcats drilled. Therefore, study in relation between the number of wellheads and other economic variables may give us some understanding of the mechanism indicated the amount of oil supplies.

In this paper, we will consider a relation between the number of wellheads and three key factors: price of the wellhead, domestic output and GNP constant dollars. We also add trend variable in the models due to the consumption of oil varies from time to time.

Moreover, this paper will use an econometrics method to estimate parameters in the model, apply some tests to verify the result we acquire and then conclude the model

Formulation of a General Model

Practically, the number of wildcats drilled depends on many factors such as

demand for oil, 0 ,̀ner energy's price and OPEC policy etc. If demand for oil is high, the oil

production and its supply

Increase. In the paper, we will focus on four main factors: price at the wellhead,

domestic output, GNP, time trend and vices versa. The simple single-equation model is:

Y = the number of wildcats drilled

XZ = price at the wellhead in the previous period

(In constant dollar, 1972 = 100)

X3 = domestic output

X4 = GNP constant dollars (1972 = 100)

XS = trend variable, 1948 = 1, 1949 = 2,..., 1978 = 31

wildcats Activities

2

According to the model, there are four exogenous variables in the equation:

oil price, domestic output. GNP and trend variable.. thus we can predict directions of

the results before estimating the model. Firstly, if the oil price rise, it can be inferred

that there is an increase in demand for oil. As a result, manufactures have to adapt

their oil production to response rising demand, that is, coefficient of X2 is expected to

be positive since change in Y moves in the same direction as X2 change.

Secondly, in the case of domestic output, which demonstrates a condition of

production? The more domestic outputs are, the more amount of oil is used to produce

those outputs. Thus, coefficient of X3 should be positive as well.Thirdly, when national

income or GNP increases, it is a sign that people have more purchasing power. Hence,

demand for oil will grow directly via consumption of oil and indirectly via consumption

of other goods which use oil as a raw material. The relation is predicted to be positive

as well. Finally, in the term of time variables showing the change in oil production over

the time. The expected coefficient of this trend variable is positive because from time to

time, there are new machine created everyday so the usage of oil as a source of energy is

more and more

Data Source and Description

Data and model are obtained from Damodar N. Gujaeati, Basic Econometrics,

MaGraw-Hill, fourth edition, 2003.

The data is annual time-series of oil production from 1948 to 1978. There

are five variables ~ our model: Y, X1 , X2 , X3 , X4 and X5. Here is the table of the

definitions of variables.

Variables Definitions Units of measurement

Y The number of wildcats drilled Thousands of wildcats

XZ Price at the wellhead in the Per barrel price,

X3 Domestic output Millions of barrels per d

X4 GNP constant dollars Constant $ billion

X5 Trend variable - Table 1 Definitions of variables

wildcats Activities

3

Descriptive statistics of each variable:

wildcats Activities

4

wildcats Activities

5

Model Estimation and Hypothesis Testing

1. Parameter Estimation

we apply the ordinary least square method and the output is show below:

Dependent Variable: Y Method: Least Squares Date: 10/18/09 Time: 18:30 Sample: 1 31 Included observations: 31

Variable Coefficient Std. Error t-Statistic Prob.

C -9.798930 8.931248 -1.097151 0.2826 X2 2.700179 0.698589 3.865190 0.0007 X3 3.045134 0.941113 3.235673 0.0033 X4 -0.015994 0.008212 -1.947619 0.0623 X5 -0.023347 0.273410 -0.085394 0.9326

R-squared 0.578391 Mean dependent var 10.63742 Adjusted R-squared 0.513529 S.D. dependent var 2.355480 S.E. of regression 1.642889 Akaike info criterion 3.977479

wildcats Activities

6

Sum squared resid 70.17616 Schwarz criterion 4.208767 Log likelihood -56.65093 F-statistic 8.917142 Durbin-Watson stat 0.938545 Prob(F-statistic) 0.000113

Table 2 Parameter estimated by ordinary least square method

Estimated equation with t statistic in the parentheses:

Yt = - 9.798930+2.700179X2t+ 3,456X3t -0.015994X4t - 0.0237Xu

(-1.11) (3.88) (3.26) (-1.96) (-0.08)

R2=058 SE =1.636

2. Hypothesis Testing

Three of five. coefficients are insignificant at the 5 percent level (accept H0: βi= 0)

because their t statistics are less than 2.052 (from t distribution table, df = 27) in

absolute value and the rest are significant. In addition, it is obvious that R2 value

is only 0.58, which means that the explanatory variables in the right hand side can

explain 58% of the movement in Y. Therefore, verification, and adjustment will be

needed to improve the equation.

3. Multicollinearity

3.1) Test for Multicollinearity

From table 2, it is obvious that although R2 value is quite moderate, there are only two

significant t ratios. Thus, it may have a relationship among explanatory variables in this

model. To ensure the existence of multicollinearity, we will use a correlation matrix to

consider the pair-wise

Y X2 X3 X4 X5

Y 1.000000 0.135193 0.426595 0.557392 -0.529881

X2 0.135193 1.000000 0.305424 0.182018 0.160882

X3 0.426595 0.305424 1.000000 0.827147 0.848050

wildcats Activities

7

X4 -0.557392 0.182018 0.827147 1.000000 0.990589

X5 0.529881 0.160882 0.848050 0.990589 1.000000

Table 3 Correlation matrix

As can be seen from the table 3, several of these pair-wise correlations are

quite high. For instance, correlation between X, and X5 is 0.990589, between X3 and

X, is 0.827147 and between X3 and XS is 0.848050, respectively. It indicates that there

is a collinearity problem in our model.

3.2) Correction for Multicollinearity

According to table 3, there is a strong relationship among X3 , X4 and XS leading to the

multicollinearity in our equation. To correct the model, we will drop a variable

owing to we can't find more information to add or poll in the model. We decide to drop

X4 because of two reasons:

1. X3(domesic output) and X4(GNP) are quite similar. Hence, using only one of them

would be better for the model

2. From the correlation matrix in table 3, it manifests a strong relationship among

X3,X4 and X5. So if we drop one of them, it may improve out model. especially,

correlation between X4 and X5 is close to one so it may be good to drop X4 or X5

instead of X3

After drop X4 and Conduct the OLS Method over the model again, the regression results are as follow:

Dependent Variable: Y Method: Least Squares Date: 10/19/09 Time: 10:40 Sample: 1 31 Included observations: 31


C -16.90701 8.562803 -1.974471 0.0586

X2 2.655855 0.733446 3.621066 0.0012 X3 3.172020 0.986224 3.216328 0.0034 X5 -0.508888 0.117925 -4.315345 0.0002

R-squared 0.516882 Mean dependent var 10.63742 Adjusted R-squared 0.463202 S.D. dependent var 2.355480

wildcats Activities

8

S.E. of regression 1.725778 Akaike info criterion 4.049147 Sum squared resid 80.41438 Schwarz criterion 4.234178 Log likelihood -58.76178 F-statistic 9.628973 Durbin-Watson stat 0.659223 Prob(F-statistic) 0.000171

Table 4 Parameter estimated by OLS method. Estimated equation with t statistic in the parentheses:

Yt = -16.9922 + 2.6565X, + 3.1870X, - 0.5103X, (2) (-1.99) (3.63) (3.24) (-4.34)

R2 = 0.52 SE = 1.721 Almost coefficients are significant at the 5 percent level (reject Ho: Rt=0

because their t are greater than or equal to 2.048 in absolute value).

Except only coefficient of constant term but its t statistic is close to 2 so we

will ignore its insignification. This equation is considerably better than

uncorrected equation and the multicollinearity is already eliminated from

our model.

4_A.uiocorrelation 4_1) Test for autocorrelation

wildcats Activities

9

From Fig. 1, residual line has a pattern indicating that there is a positive autocorrelation. To ensure that this problem exists, we will exert Durbin-Watson test

According to table 4, Durbin-Watson statistic is equal to 0.653 and from Durbin-Watson d statistic table at 5 percent level : dL= 1.229 and dU = 1.650

Positive No autocorrelation

Autocorrelation Negative autocorrelation

0 4 dL= 1.229 dU = 1.650 4- dL 4- dU 0 653

We will find that Durbin-Watson statistic falls in positive autocorrelation

region. As a result, we reject null hypothesis (H. : P= 0), that is, there is

autocorrelation in our model surely.

4.2. Correction on for Autocorrelaion

We Reestimate the equation by using Corchrane-Orcutt procedure and a

serial correlation is eliminated. The regression results are:

Dependent Variable: Y

Method: Least Squares Date: 06/02/02 Time-. 10:28 Sample(adjusted): 2 31 Included observations: 30 after adjusting endpoints Convergence achieved after 9 iterations

Variable Coefficient

Std. Error t-Statistic Prob.

C X2 X3 X5

AR(1)

5.095206 1.137359 0.942234

-0.351872 0.710037

5.260470 0.442307 0.608573 0.092804 0.093735

0.968584 2.571423 1.548268

-3.791557 7.574928

0.3420 0.0165 0.1341 0.0008 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.878218 0.858733 0.879268

19.32782 -35.97337

1.832106

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

10.73400 2.339377 2.731558 2.965091 45.07108 0000000

Inverted AR Roots 71

wildcats Activities

10

Table5.Parameter estimated by OLS Method.

Y. = 50952 - 1' 373x, Y 3.1870X3t - 0.5103X5t (3)

R2- =0.88 SE=0.879

DW = 1.823

Now Durbin-Watson statistic is equal to 1.823, so it falls into no autocorrelation region. Therefore, we accept null hypothesis, in the other word, there is no statistically significant evidence of autocorrelation, positive or negative. Besides, the equation is greately better than the prior one because R2 value rises from 0.52 to 0.88.

5. Heteroscedasticity

Test for Heteroscedasticity

White test with no cross term,

White Heteroskedasticity Test:

F -statistic Obs`R-squared

1.257117 7.408680

Probability Probability

0.315129 0.284699

Table 6 no cross term white test 2) White test with cross term,

White Heteroskedasticity Test: F-statistic 0.955024 Probability 0.502733 Obs'R-squared 9.017470 Probability 0.435663

Table 7 white test with cross term

Value of nR2 from both tests are less than critical chi-square value

at 5 percent level of significant (df = 3): )2 = 9.815 . Thus, we can accept null

hypothesis (Ho : (XI = 0 where OC is a coefficient in auxiliary equation) . We can

conclude that there is no heteroscedasticity in our model.

wildcats Activities

11

Interpretation of the Results and Conclusions

The final results of the regression (equation 3) show that the explanatory

variables on the rtght hand side can explain 88% of movement in change of the number of wildcats drilled. The remained variables which substantially influence to the dependent variable is 3 variables, we drop X4 in the correcting process. As we predicted the direction of the results before estimation, we expected the coefficient of X4 should be positive. But after estimated original data, we found that it is negative. Therefore, it is possible that XQ or GNP may not a proper variable for this model.

At last, we obtain the final results:

Yt = 5.0952 + 1.1373X, + 3.1870X3t - 0.5103X,

It shows that domestic output (X) has a strong and positive effect

on the number of wildcats as we predicted earlier. The price at the wellhead (X)

also has the expected positive impact whereas time trend has negative effect on

the number of wildcats.

Limitation of the Study and Possible Extensions

There are some drawbacks in the paper, especially in the part of

review of literature that is -o; cited at all. Moreover, our model is based on only 31 observations and data-collecting time is outof-date which is from time period 1948 to 1978. Therefore, if apply their results to a current situation, it may not absolutely correct. It is recommended that larger and more update observation should be considered. In addition, to improve the model, we ought to observe other variables having effects to the number of wildcats drills such as the decision of OPEC committees about the quantity of world oil. Either added or omitted variables may increase Rz value of the model as well

wildcats Activities

12

(VII). References

1).Gujarati, Damodar N., Basic Econometrics, Mcgrawhill, 2003

2).Pindyck, Robert S., and Daniel L. Rubinfeld, Econometric Models And Economic Forecasts, Mcgrawhill,

1998 3.).Cobham, David, Macroeconomic Analysis an intermediate text, Longman, 1998

Appendix

Thousands of

wildcats, (Y)

Per barrel price

constant $

(X2)

Domestic output

(millions of barrels per day),

(X3)

GNP, Constant $ billions,

(X4)

TIME (X5)

8.01 4.89 5.52 487.67 1948 = 1 9.06 4.83 5.05 490.59 1949 = 2 10.31 4.68 5.41 533.55 1950 = 3 11.76 4.42 6.16 576.57 1951 = 4 12.43 4.36 6.26 598.62 1952 = 5 13.31 4.55 6.34 621.77 1953 = 6 13.10 4.66 6.81 613.67 1954 = 7 14.94 4.54 7.15 654.80 1955 = 8 16.17 4.44 7.17 668.84 1956 = 9 14.71 4.75 6.71 681.02 1957 = 10 13.20 4.56 7.05 679.53 1958 = 11 13.19 4.29 7.04 720.53 1959 = 12 11.70 4.19 7.18 736.86 1960 = 13 10.99 4.17 7.33 755.34 1961 = 14 10.80 4.11 7.54 799.15 1962 = 15 10.66 4.04 7.61 830.70 1963 = 16 10.75 3.96 7.80 874.29 1964 = 17 9.47 3.85 8.30 925.86 1965 = 18 10.31 3.75 8.81 980.98 1966 = 19 8.88 3.69 8.66 1,007.72 1967 = 20 8.88 3.56 8.78 1,051.83 1968 = 21 9.70 3.56 9.18 1,078.76 1969 = 22 7.69 3.48 9.03 1,075.31 1970 = 23 6.92 3.53 9.00 1,107.48 1971 = 24 7.54 3.39 8.78 1,171.10 1972 = 25 7.47 3.68 8.38 1,234.97 1973 = 26 8.63 5.92 8.01 1,217.81 1974 = 27 9.21 6.03 7.78 1,202.36 1975 = 28 9.23 6.12 7.88 1,271.01 1976 = 29 9.96 6.05 7.88 1,332.67 1977 = 30 10.78 5.89 8.67 1,385.10 1978 = 31

Source: Energy Information Administration, 1978 Report to Congress.




Paper#2

Application of Dummy Variable models



ID#4585974929



ASSISTANT PROFESSOR

A Paper On

Relationship Between Hourly Compensation in Manufacturing and Unemployment Rate in the United States, Canada and the United Kingdom

UNEMPLOYMENT RATE AND COMPENSATION 2002

ii









Dear Madam,

Here is my paper on "Relationship between Hourly Compensation in Manufacturing and

Unemployment Rate in the United States, Canada and the United Kingdom” that I was

assigned. It was a great opportunity for me to acquire practical knowledge of the Quantitative

Methods in Economic Analysis and forecasting





Sincerely yours,



iii







International Economics and Finance. As a part of this program my topic was selected as

“Relationship between Hourly Compensation in Manufacturing and Unemployment Rate in

the United States, Canada and the United Kingdom.”



mind.



iv














v

Table of Content

Title Page


Preface iii

Acknowledgement iv

Table Of Content v

List Of Tables vi

List Of Figures vii

Acronyms And Abbreviation/ Contraction/Symbols viii








References 17-17

Appendix 18-19


vi

Title Page

Table 1. Descriptive Statistics 2

Table 2. Least Squares Regressions Results 13

Table 3 ML-ARCH Regressions Results 13

List of Tables


vii

Title Page

Fig:1: Compensation in Canada 3

Fig:2: Compensation in UK 3

Fig:3: Compensation in USA 4

Fig:4: Unemployment in Canada 4

Fig:5: Unemployment in UK 5

Fig:6: Unemployment in USA 5

List of Figure


viii

Title Page

Graph:1: Compensation in Canada 6

Graph :2: Compensation in UK 6

Graph :3: Compensation in USA 7

Graph :4: Unemployment in Canada 7

Graph :5: Unemployment in UK 8

Graph :6: Unemployment in USA 8

Graph :7. Residual, Actual, Fitted 14

Graph: 8. Pooled Result 15

List of Graph


ix

Title Page

Chat:1: Compensation in Canada 9

Chat :2: Compensation in UK 9

Chat :3: Compensation in USA 10

Chat :4: Unemployment in Canada 10

Graph :5: Unemployment in UK 11

Chat :6: Unemployment in USA 11

List of Chat

Unemployment Rate and Compensation Page 1

Statement of the Problem

This paper studies the relationship between hourly compensation in manufacturing

and unemployment rate in the United States, Canada and the United Kingdom. Since each

country provides only 20 observations, the parameters from the regression may not be valid.

I further study whether the method of pooling data can be applied to this case by using

dummy variable technique to test the difference of intercepts and slopes in each country.

Literature Review

In Branson (1989), the compensation should negatively correlated with

unemployment rate because if (inns pay more compensation, labors will have more

incentive to continue working, so unemployment rate is low. But when firms reduce

compensation for labors, unemployment rate will be higher because labors have little

incentive continuing their jobs.

Formulation of General Model:

The linear regression model is set as follows

Yit = β1+ β2 Xit+ Uit (1)

Where Y;t is civilian unemployment rate, and X;t is manufacturing hourly compensation

in U.S. dollars (index, 1992 = 100). i denotes country-the United States, Canada and

the United Kingdom and t denotes time period. In this case, i = 3 and t = 20.


Data Sources and Description

I used an annual data from 1980 to 1999 of the United States, Canada and the

United Kingdom. There are 20 observations for each country, so 60 observations in total.

The data was from Gujarati 2002 (See Appendix) and its descriptive statistics is presented

in here

Table 1. Descriptive Statistics


Histogram and Stats

Fig: 2: Compensation in UK

Fig:1: Compensation in Canada


Fig:3: Compensation in USA

Fig:4: Unemployment in Canada


Fig:5: Unemployment in UK

Fig:6: Unemployment in USA


Graph1. Compensation in Canada

Graph :2: Compensation in UK


Graph3: Compensation in USA

Graph :4: Unemployment in Canada


Graph :5: Unemployment in UK

Graph :6: Unemployment in USA


Chat 1. Compensation in Canada

Chat :2: Compensation in UK


Chat 3: Compensation in USA

Chat :4: Unemployment in Canada


Chat :5: Unemployment in UK

Chat :6: Unemployment in USA


Model Estimation and Hypothesis Testing

The usual OLS was assigned to estimate equation (1) and 60 observations are

pooled disregarding the space and time dimensions. The results are as follows

Ŷ = 12.439 - 0.053X (2) Se (0.818) (0.010)

t (15.202) (-5.424)

Rz = 0.3366, d = 0.4806

n=60, df=58

Clearly, compensation is negatively correlated with unemployment rate as

expected and t statistic is statistically significant but RZ value is quite low. Also

Durbin-Watson statistic suggests that perhaps there is autocorrelation in the data. However`,

there are highly restricted assumption in equa t ion (1) because the differences across each

country's data, such as intercept and slope, are not considered. So, the regression results in

(2) may not capture the different characteristics between the cross-sectional unit. If this is to

be the case, maybe each country's data cannot be pooled


One way to take into account the individuality of each country is to let the

Table 2. Least Squares Regressions Results

Table 3 ML-ARCH Regressions Results


intercept and slope coefficients vary across countries. So the fixed effects model (FEM) is

set by using dummy variables as in equation (3) to test whether the intercepts and slope

Cefficients are statistically different.

Yit = α1+ α2D2i+ α3D3i β Xit+ γ1(D2i Xit)+ γ2(D3i Xit)+ Uit (3)

Where D2i = 1 if the observation belongs to Canada, 0 otherwise and D3i = 1 if the

observation belongs to the United Kingdom, 0 otherwise. Therefore, the United States is

the comparison country. The results of estimating equation (3) are as follows

Ŷ= 11.524-- 2.181 D2i + 1.029D3i -0.056X;tt + 0.049(D2i Xit) + 0.009(D3i Xit) (4)

se (1.510) (2.173) (1.778) (0.016) (0.025) (0.020) t (7.627) (-1.004) (0.578) (-3.400) (1.951) (0.463)

As you can see from the model above, all t statistics of the dummy variables added are

not statistically significant at( 0.05) level of significance suggesting that, the intercepts and

slope coefficients of Canada and the/ United Kingdom are not statistically different

from the United States.

R2 = 0.5582, d = O.6764 n = 60, df = 54

Graph :7. Residual, Actual, Fitted


If the comparison country is changed, regression model (3) will yield different

results. Let D2i = 1 if the observation belongs to the United States, 0 otherwise and D3i

= I if the observation belongs to the United

Kingdom

, 0 otherwise; i.e. Canada is a

Then let D2i = 1 if the observation belongs to the United States, 0 otherwise and D3;

-1 if the observation belongs to Canada, 0 otherwise; i.e. the United Kingdom is a

comparison country, the estimation is as follows

Y= 12.554 – 1.029D2i - 3.211D3i - 0.046Xit - 0.009(D2i Xit t) + 0.040(D3i Xit) (6)

se (0.938) (1.778) (1.822) (0.012) (0.020) (0.022) t (-0.578) (-1.762) (-3.847) (-0.463) (1.758)

R2 = 0.5582, d = 0.6764 n = 60, df = 54

Y= 9.342 - 2.181 D2i + 3.211D3- 0.006X;t- 0.049(D2i Xit) - 0.040(D3i Xit) (5)se (1.561) (2.173) (1.82 (0.019) ( 0.025) (0.022) t (5.981) (1.004) (1.76 (-0.341) (-0.463) (-1.758) R'= 0.5582, d = 0.6764 n = 60, df = 54

Graph: 8. Pooled Result


All t statistics for dummy variables in both (5) and (6) are statistically insignificant

as in model (4). It can be concluded that the intercepts and slopes of the three countries

are not statistically different suggesting that they can be pooled. However, the RZ value

from model (2) is very low compared with model (4). To do a formal test whether

model (4) is better, F statistic is calculated as follows

(R2UR-R2

R)/q (0.5582-0.336)/4

F = = =6.771 (7)

(1-R2UR)/n-k (1-0.5582)/54

Where q is the number of parameter restrictions. The critical value of F with 4 numerator

df and 54 denominator df is 3.16, so F= 6.7713 exceeds the critical value. This proves

Fig:7. Pooled Result


that model (4) can explain the variation in unemployment rate better than model (2),

although coefficients of dummies are statistically insignificant.

Interpretation of the Results and Conclusions

If we accept that all data sets from the three countries can be pooled and using

regression (2), it can be concluded that if an hourly compensation in manufacturing

increases US$ 1, the unemployment rate will reduce 0.053 percent. But the interpretation

here is subject to some limitations since RZ is very low. However, if we consider model (4)

with higher R2 value, it would yield similar conclusions except that the unemployment

rate will decrease 0.056 percent when there is a US$1 rise in hourly compensation. This

time, the intercepts and slopes from different country will change, but these coefficients

are statistically insignificant. For example, if there is a US$ 1 increase in compensation,

the unemployment rate will drop 0.056, 0.007 and 0.047 percent in the United States,

Canada and the United Kingdom, respectively.

Limitations of the Study and Possible Extensions

Since RZ value from the regression (2) is very low suggesting an invalidity of the

model, the assumption that the data from 3 countries can be pooled, which is proved by

FEM, may have to be relaxed. Another method to test whether we can use the panel data

should be considered, for example, use random effects model (REM) or allow all

coefficients vary over individuals as well as time

References:

Branson, William H. (1989). Macroeconomic Theory and Policy. Third edition,

Harper & Row. Gujarati, Domadar N. (2002). Basic Econometrics. Fourth edition, McGraw-Hill. p 6


Appendix

Unenrplolvuent rate (UNEM) and hourly compensation in manufacturing (COMP) in the United States, Canada and the United Kingdom, 1980-1999

Obs UNEM? COMP?

-US-1980 7.100000 55.600000

-US-1981 7.600000 61.100000

-US-1982 9.700000 6700000

-US-1983 9.600000 68.800000

-US-1984 7.500000 71.200000

-US-1985 7.200000 75.100000

-US-1986 700000 78.500000

-US-1987 6.200000 80.700000

-US-1 988 5.500000 8400000

-US-1989 5.300000 86.600000

-US-1990 5.600000 90.800000

-US-1 991 6.800000 95.600000

-US-1992 7.500000 10000000

-US-1993 6.900000 102.700000

-US-1994 6.100000 105.600000

-US-1995 5.600000 107.900000

-US-1996 5.400000 109.300000

-US-1997 4.900000 111.400000

-US-1998 4.500000 117.300000

-US-1 999 4.000000 123.200000 CAN-1980 7.200000 4900000

-CAN-1981 7.300000 54.100000

-CAN-1982 10.60000 59.60000

-CAN-1983 11.500000 63.900000

-CAN-1984 10.900000 64.300000

_CAN-1985 10.200000 63.500000

-CAN-1 986 9.200000 63.300000

-CAN-1 987 8.400000 6800000

-CAN-1988 7.300000 7600000

-CAN-1989 700000 84.100000

-CAN-1 990 7.700000 91.500000

-CAN-1991 9.800000 100.100000


-CAN-1992 10.600000 10000000

-CAN-1993 10.700000 95.500000

-CAN-1994 9.400000 91.700000

-CAN-1995 8.500000 93.300000

-CAN-1996 8.700000 93.100000

-CAN-1997 8.200000 94.400000

-CAN-1998 7.500000 90.600000

-CAN-1999 5.700000 91.900000

-UK-1980 7.000000 43.700000

-UK-1981 10.500000 44.100000

-UK-1982 11.300000 42.200000

-UK-1983 11.800000 3900000

-UK-1 984 11.70000 37.200000

_UK-1985 11.200000 3900000

_UK-1986 11.200000 47.800000

_UK-1987 10.300000 60.200000 UK-1988 8.600000 68.300000 UK-1989 7.200000 67.700000 UK-1990 6.900000 81.700000

UK-1991 8.800000 90.500000

UK-19992 10.100000 10000000

UK-1993 10.500000 88.700000

U K-1994 9.700000 92.300000

UK-1995 8.700000 95.900000

UK-1996 8.200000 95.600000

UK-1997 7.000000 103.300000

UK-1998 6.300000 109.800000

UK-1999 6.100000 112.200000




Paper#3

Application of Qualitative response regression models



ID#4585974929



ASSISTANT PROFESSOR

A Paper On

Voting for a School Budget (Application of Qualitative Response Regression Models)

Voting for a school budget 2002

ii









Dear Madam,

Here is my paper on “Voting for a School Budget (Application of Qualitative Response Regression

Models) ” that I was assigned. It was a great opportunity for me to acquire practical knowledge of

the Quantitative Methods in Economic Analysis and forecasting





Sincerely yours,



iii







International Economics and Finance. As a part of this program my topic was selected as “Voting

for a School Budget (Application of Qualitative Response Regression Models)”



mind.



iv














v

Table of Content

Title Page


Preface iii

Acknowledgement iv

Table Of Content v

List Of Tables vi

List Of Figures vii

Acronyms And Abbreviation/ Contraction/Symbols viii








References 18-18


vi

Title Page

Table 1. variables and definition 2

Table 2. Data set 13

Table 3 Comparing the values of YESVM and the probabilities from three models

13

List of Tables


vii

Title Page

Fig:1: loginc 6

Fig:2: ptcon 3

Fig:3: Linear Probability Model 11

Fig:4: logit Model 4

Fig:5: probit 5

List of Figure


viii

Title Page

Graph:1: loginc 7

Graph :2: ptcon 8

Graph :3: group 10

Graph: 4. Residual, Actual, Fitted 11-14

Graph: Result 18

List of Graph


ix

Title Page

Chat:1: loginc 7

Chat :2: ptcon 8

Chat :3: group 10

List of Chat

Voting for a school budget

1

STATEMENT OF THE PROBLEM

I have studied the problem about voting for a school budget. The questions I ask are whether each of the following independents variables: level of annual household income, amount of property taxes, number of years of residency, number of children in public and private school, the status of being employed as a teacher (public or private), has effect on the probability of voting for a school budget or not. The hypothesis I have test is there is no relationship between one of such variables with the probability of voting for a school budget. The results, derived from the test of statistical significance, that support to the rejection of this hypothesis lead us to the conclusion that the probability of voting for a school budget cal be explained by these variables.

REVIEW OF LITERATURE

When children are of school age, households are most likely to be aware of the costs and benefits associated with a vote for higher school taxes. The presence of at least one child in public school is expected and does have a significant positive impact on the probability of yes vote. The presence of additional school-age children does not increase the probability of a yes vote until beyond the fifth child the marginal gain of reallocating the household budget toward private expenditures outweighed the gain from the public expenditures and the probability of a yes vote decline.The number or years in residence is also included as explanatory variable in the model. As the time of residence increases, voters tend to vote no, either in criticism of the educational system or possibly in opposition to the growing burden of taxes.The school variable is included to account for the fact that the sample of respondents is overrepresented by schoolteachers and their spouses. Schoolteachers are more likely to vote yes in the election relative to individual with otherwise similar attributes.On the assumption that local school education is a normal good, we expected, other things being equal, that income and the demand for public schools will be positively correlated.As price of schooling (property tax payments) rises, other things being equal, we expected that the quantity of educational expenditures per pupil demand will fall, as will the probability of voting yes in the election.

The yes probability of voting for a school budget function is

+ ---- ---- + Yes probability = (income Property taxes, Years of residency, Number of children in public –

---- + School, number of children in private school, the status of being employed as a teacher)

FORMULATION OF A GENERAL MODEL

I use three following models in my study:


2

LINEAR PROBABILITY MODEL

LOGIT MODEL

PROBITY MODEL

DATA SOURCES AND DESCRIPTION

Table‐1 Variables Definition

E (Yi / Xi) probability of yes LOGINC log of annual household income ($) PTCON log of property taxed ($) YEARS the number of years of residency (year) PUB12 1 if 1 or 2 children attend public school

0, otherwise

PUB34 1 if 3 or 4 children attend public school 0, otherwise

PUBS I if 5 or more children attend public school 0, otherwise

PRIV 1 if I or more children attend private schoo 0, otherwise

SCHOOL 1 if being employed as a teacher (public or private) 0, otherwise

E (Yi / Xi)= β0+ β1LOGINCi+ β2 PTCONi + β3YEARSi + β4PUB12i + β5PUB34i + β6 PUB5i + β7PRI i + β8 SCHOOLi + εi

Prob(yes) LOG = β0+ β1 LOGINC i+β2 PTCON i+β3 YEARSj +β4 PUB12i +β5PUB34i 1 - Prob (yes)

+β6 PUBS; +β7 PRIi +β8 SCHOOLi+ εi

Pi = F(βD +β1LOGINC; + β2PTCON; + β3 YEARS, + β4 PUB12 + β5PUB34, + β6PUB5; + β7PRI; +

β8SCHOOL; )


3

DATA SET IS AS FOLLOWS:

Table‐2

obs YESVM LOGINC PTCON YEARS PUB12 PUB34 PUB5 PRIV SCHOOL

1 1.000000 9.770001 7.047500 10.00000 0.000000 1.000000 0.000000 0.000000 1.000000

2

0.000000 10.02100 7.047500 8.000000 0.000000 1.000000 0.000000 0.000000 0.000000

3

1.000000 10.02100 7.047500 4.000000 1.000000 0.000000 0.000000 0.000000 0.000000

4

0.000000 9.433500 6.396900 13.00000 0.000000 1.000000 0.000000 0.000000 0.000000

5

1.000000 10.02100 7.279200 3.000000 0.000000 1.000000 0.000000 0.000000 1.000000

6

0.000000 10.46300 7.047500 5.000000 1.000000 0.000000 0.000000 0.000000 0.000000

7

0.000000 10.02100 7.047500 4.000000 0.000000 0.000000 0.000000 0.000000 0.000000

8

1.000000 10.02100 7.279300 5.000000 0.000000 1.000000 0.000000 0.000000 0.000000

9

0.000000 10.22200 7.047500 10.00000 1.000000 0.000000 0.000000 0.000000 0.000000

10

1.000000 9.433500 7.047500 5.000000 0.000000 1.000000 0.000000 0.000000 0.000000

11

1.000000 10.02100 7.047500 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

12

0.000000 9.770001 6.396900 30.00000 1.000000 0.000000 0.000000 0.000000 0.000000

13

1.000000 9.770001 6.745200 1.000000 1.000000 0.000000 0.000000 0.000000 0.000000

14

1.000000 10.02100 7.047500 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

15

1.000000 10.82000 6.745200 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

16

1.000000 9.770001 6.745200 42.00000 0.000000 1.000000 0.000000 0.000000 0.000000

17

1.000000 10.22200 7.047500 5.000000 0.000000 1.000000 0.000000 0.000000 1.000000

18

0.000000 10.02100 7.047500 10.00000 1.000000 0.000000 0.000000 0.000000 0.000000

19

1.000000 10.22200 7.047500 4.000000 1.000000 0.000000 0.000000 0.000000 0.000000

20

1.000000 10.22200 6.745200 4.000000 1.000000 0.000000 0.000000 0.000000 0.000000

21

1.000000 10.46300 7.047500 11.00000 0.000000 1.000000 0.000000 0.000000 1.000000

22

1.000000 10.22200 7.047500 5.000000 0.000000 0.000000 0.000000 0.000000 0.000000

23

1.000000 9.770001 6.745200 35.00000 0.000000 1.000000 0.000000 0.000000 0.000000

24

1.000000 10.46300 7.279300 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

25

1.000000 10.02100 6.745200 16.00000 1.000000 0.000000 0.000000 0.000000 0.000000

26

0.000000 10.46300 7.047500 7.000000 0.000000 0.000000 0.000000 1.000000 0.000000

1.000000 9.770001 6.745200 5.000000 1.000000 0.000000 0.000000 0.000000 1.000000


4

27

28 0.000000 9.770001 7.047500 11.00000 1.000000 0.000000 0.000000 0.000000 0.000000

29

0.000000 9.770001 6.745200 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

30

1.000000 10.22200 7.047500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

31

1.000000 10.02100 6.745200 2.000000 0.000000 1.000000 0.000000 0.000000 0.000000

32

0.000000 9.433500 6.745200 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

33

0.000000 8.294000 7.047500 2.000000 0.000000 1.000000 0.000000 0.000000 1.000000

34

1.000000 10.46300 7.047500 4.000000 0.000000 0.000000 0.000000 0.000000 0.000000

35

1.000000 10.02100 7.047500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

36

0.000000 10.22200 7.279300 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

37

1.000000 10.22200 7.047500 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

38

1.000000 10.22200 7.495500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

39 0.000000 10.02100 7.047500 10.00000 0.000000 1.000000 0.000000 0.000000 1.000000

40 1.000000 10.22200 7.047500 2.000000 0.000000 0.000000 0.000000 0.000000 0.000000

41

0.000000 10.02100 7.047500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

42

0.000000 10.82000 7.495500 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

43

1.000000 10.02100 7.047500 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

44

1.000000 10.02100 7.047500 3.000000 1.000000 1.000000 0.000000 0.000000 0.000000

45

1.000000 10.02100 6.745200 6.000000 0.000000 0.000000 0.000000 0.000000 1.000000

46

1.000000 10.02100 7.047500 2.000000 1.000000 1.000000 0.000000 0.000000 0.000000

47

0.000000 9.770001 6.745200 26.00000 0.000000 0.000000 0.000000 0.000000 0.000000

48

0.000000 10.22200 7.495500 18.00000 1.000000 0.000000 0.000000 0.000000 0.000000

49

0.000000 9.770001 6.745200 4.000000 0.000000 0.000000 0.000000 0.000000 0.000000

50

0.000000 10.02100 7.047500 6.000000 0.000000 0.000000 0.000000 0.000000 0.000000

51

1.000000 10.02100 6.745200 12.00000 0.000000 0.000000 0.000000 0.000000 0.000000

52

1.000000 9.433500 6.745200 49.00000 0.000000 0.000000 0.000000 0.000000 0.000000

53

1.000000 10.46300 7.279300 6.000000 1.000000 0.000000 0.000000 0.000000 0.000000

54

0.000000 9.770001 7.047500 18.00000 1.000000 0.000000 0.000000 0.000000 0.000000

55

1.000000 10.02100 7.047500 5.000000 0.000000 0.000000 0.000000 0.000000 0.000000

56

1.000000 9.770001 5.991500 6.000000 1.000000 0.000000 0.000000 0.000000 0.000000

0.000000 9.433500 7.047500 20.00000 1.000000 0.000000 0.000000 0.000000 0.000000


5

57

58 1.000000 9.770001 6.396900 1.000000 1.000000 0.000000 0.000000 1.000000 1.000000

59

1.000000 10.02100 6.745200 3.000000 1.000000 0.000000 0.000000 0.000000 0.000000

60

0.000000 10.46300 7.047500 5.000000 1.000000 0.000000 0.000000 0.000000 0.000000

61

1.000000 10.02100 7.047500 2.000000 1.000000 0.000000 0.000000 1.000000 0.000000

62

0.000000 10.82000 7.279300 5.000000 1.000000 0.000000 0.000000 0.000000 0.000000

63

0.000000 9.433500 6.745200 18.00000 0.000000 0.000000 0.000000 0.000000 0.000000

64

1.000000 9.770001 5.991500 20.00000 1.000000 0.000000 0.000000 0.000000 1.000000

65

0.000000 8.922700 6.396900 14.00000 1.000000 0.000000 0.000000 0.000000 0.000000

66

0.000000 9.433500 7.495500 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

67

0.000000 9.433500 6.745200 17.00000 0.000000 0.000000 0.000000 0.000000 0.000000

68

0.000000 10.02100 7.047500 20.00000 1.000000 0.000000 0.000000 0.000000 0.000000

69

1.000000 10.02100 7.047500 3.000000 1.000000 1.000000 0.000000 0.000000 0.000000

70

1.000000 10.02100 7.047500 2.000000 0.000000 1.000000 0.000000 0.000000 0.000000

71

1.000000 10.22200 7.047500 5.000000 0.000000 0.000000 0.000000 0.000000 1.000000

72

1.000000 9.770001 7.047500 35.00000 0.000000 0.000000 0.000000 0.000000 0.000000

73

0.000000 10.02100 7.279300 10.00000 1.000000 1.000000 0.000000 0.000000 0.000000

74

1.000000 9.770001 7.047500 8.000000 0.000000 1.000000 1.000000 1.000000 0.000000

75

0.000000 9.770001 7.047500 12.00000 0.000000 0.000000 0.000000 0.000000 0.000000

76

1.000000 10.22200 6.745200 7.000000 1.000000 1.000000 0.000000 0.000000 0.000000

77

1.000000 10.46300 6.745200 3.000000 0.000000 0.000000 0.000000 0.000000 1.000000

78

0.000000 10.22200 6.745200 25.00000 1.000000 1.000000 1.000000 0.000000 0.000000

79

1.000000 9.770001 6.745200 5.000000 0.000000 0.000000 0.000000 1.000000 1.000000

80

1.000000 10.22200 7.047500 4.000000 1.000000 1.000000 0.000000 0.000000 0.000000

81

1.000000 10.02100 7.279300 2.000000 0.000000 0.000000 0.000000 0.000000 0.000000

82

1.000000 10.46300 6.745200 5.000000 1.000000 1.000000 0.000000 0.000000 0.000000

83

0.000000 9.770001 7.047500 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

84

1.000000 10.82000 7.495500 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000

85

0.000000 8.922700 5.991500 6.000000 1.000000 0.000000 0.000000 1.000000 0.000000

86

1.000000 9.770001 7.047500 3.000000 0.000000 0.000000 0.000000 1.000000 0.000000


6

87

1.000000 9.433500 6.396900 12.00000 1.000000 0.000000 0.000000 0.000000 0.000000

88

1.000000 9.770001 6.745200 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

89

1.000000 10.02100 7.047500 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

90

1.000000 10.02100 6.745200 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

91

1.000000 10.22200 7.279300 3.000000 0.000000 0.000000 0.000000 0.000000 0.000000

92

1.000000 10.02100 7.047500 3.000000 1.000000 1.000000 0.000000 1.000000 1.000000

93

1.000000 10.02100 7.047500 5.000000 0.000000 0.000000 0.000000 0.000000 0.000000

94

1.000000 8.922700 5.991500 35.00000 0.000000 0.000000 0.000000 1.000000 1.000000

95

0.000000 10.46300 7.495500 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000

Number of observations

Log income ($)


7

The mean of log income is 9.97 $ per year. Seen from the above information, the values of log


8

income range from 8.29 to 10.82, with a standard deviation of 0.411. The median is 10.021. The skewness of - 0.89 tell us that the lower tail of the distribution is slightly thicker, with more observation than the upper tail. The kurtosis of 5.62 is much greater than 3, telling as that the distribution of log income has tail that is higher and longer than normal. The JB statistic of 39.85 is more than the critical value of the chi-square distribution with 2 df, that is 5.99. Therefore, the null hypothesis that the log income values are normally distributed can be rejected.

Log Property Taxes


9

The mean of log property taxes is 6.93 $ per year. Seen from the above information, the values of log property taxes range from 5.99 to 7.49, with a standard deviation of 0.31. The median is 7.047. The skewness of 0.31 tell us that the upper tail of the distribution is slightly thicker, with more observation than the lower tail. The kurtosis of 4.68 is much greater than 3, telling us that the distribution of log property taxes has tail that is higher and longer than normal. The JB statistic of 26.81 is more than the critical value of the chi-square distribution with 2 df, that is 5.99. Therefore, the null hypothesis that the log propert; taxes values are normally distributed can be rejected.


10


11

MODEL ESTIMATION AND HYPOTHESIS TESTING

The regression results of Linear Probability Model are:


12


13


14

The hypothesis I have tested is: H0: β1= β2 =β3 =β4 = β5 = β6 =β7 =β8 = 0 H0: β1≠ β2 ≠β3 ≠β4 ≠ β5 ≠ β6 ≠β7 ≠β8 ≠ 0

In the results of three models, only )3t and 132 are significant at 95% level of confidence, as their probabilities are less the 5%. However, in the results of Linearity probability Model, F-statistic of 2.21 with less than 5% probability (3.35%) tells that there is overall significance of the model, i.e., all explanatory variables together have effect on probability of voting yes for a school budget. In Logit and Probit models, LR statistics (8 df) are 19.46 and 19.78 respectively. Comparing these values to the 5% critical chi-square value with 8 df of 15.5073, the null hypothesis that all the slope coefficients are simultaneous equal to zero is rejected, i.e., all explanatory variables together have effect on probability of voting yes for a school budget.

INTERPRETATION OF THE RESULTS AND CONCLUSION

The regression results of Linearity Probability Model are as follows:

E(Yi / Xi) = - 0.38 + 0.37 LOGINCi - 0.41 PTCON i - 0.005 YEARS i + 0.106 PUB12 i + 0.216

PUB34 i +

se = (1.48) (0.14) (0.18) (0.005) (0.14) (0.16)

t = (-0.26) (2.68) (-2.24) (-1.003) (0.72) (1.33)

0.101 PUB5 i - 0.067 PRI i + 0.31 SCHOOL i + ε

i

(0.26) (0.16) (0.15)

(0.38) (-0.40) (1.97

The intercept of -0.38 gives the probability that zero value of log income, log property taxes and the numb 3r of years of residency will vote yes for a school bidget. Since this value is negative, and since probability cannot be negative, we treat this value as zero, which is sensible in the present instance. The slope values of 0.37, -0.41 and -0.005 mean that for a unit change in log income ($), log property taxes ($) and year of residency (year), on average, the probability of voting yes for a school budget increases by 37%, decreases by 41% and decreases by 0.5% respectively. The number of children in the public school increase the yes probability by 10.6%, 21.6% and 10.1% for 1 or 2, 3 or 4 and 5 or more children in the public school respectively, while one or more children in the private school decrease the yes probability by 6.7%. The status of being employed as a teacher (public and private) increases the yes probability by 31 %.

THE REGRESSION RESULTS OF LOGIT MODEL ARE AS FOLLOWS:


15

Log rob(yes) = 5.19 + 2.18 LOGlNCi- 2.39 PTCONi - 0.026 YEARSi + 0.58 PUB12i + 1 - Prob

se = (7.55) (0.78) (1.08) (0.026) (0.68) z = (-0.68) (2.77) (-2.21) (-0.96) (0.84)

1.12 PUB34 i + 0.52 PUB5 i -0.34 PRI i + 2.62 SCHOOL i + ε i (0.76) (1.26) (0.78) (1.41)

(1.46) (0.41) (-0.43) (1.86)

The 2.18 coefficient of log income means, with other variables held constant, that if log income increases by a unit, on average the estimated logit increases by about 2.18 units. For log property taxes, if it increases by a unit, the estimated logit decreases by 2.39 units. Increasing in years of residency by a unit cause the estimated logit to decrease by 0.026 unit. For the number of children, 1 or 2, 3 or 4 and 5 or more children in the public school increase the estimated logit by 0.58, 1.12 and 0.52 unit respectively, while 1 or more children in the private school decrease it by 0.34 unit. The estimated logit can increase by 2.62 unit as to the status of being employed as a teacher (public or private).

THE REGRESSION RESULTS OF PROBIT MODEL ARE AS FOLLOWS:

Pi = F( -2.95 + 1.31 LOGING- 1.46 PTCON; - 0.015 YEARS; + 0.36 PUB12; +0.69 PUB34; +0.29 PUB5;

se = (4.50) (0.46) (0.64) 0.015) (0.42) (0.47) (0.75) z = (-0.65) (2.83) (-2.28) (-1.03) (0.85) (1.46) (0.38)

- 0.21 PRI; + 1.58 SCHOOL)

(0.48) (0.82) (-0.43) (1.92)

The 1.31 coefficient of log income means, with other variables held constant, that if log income increases by a unit, on average the estimated probit increases by about 1.31 units. For log property taxes, if it increases by a unit, the estimated probit decreases by 1.46 units. Increasing in years of residency by a unit cause the estimated probit to decrease by 0.015 unit. For the number of children, 1 or 2, 3 or 4 and 5 or more children in the public school increase the estimated probit by 0.36, 0.69 and 0.29 unit respectively, while 1 or more children in the private school decrease it by 0.21 unit. The estimated logit can increase by 1.58 unit as to the status of being employed as a teacher (public or private).

COMPARING THE VALUES OF YESVM AND THE PROBABILITIES FROM THREE MODELS.

Table‐3 obs YESVM LMP PROBIT LOGIT

1 1.000000 0.795538 0.851226 0.860401

2 0.000000 0.713714 0.729725 0.738597


16

3 1.000000 0.501486 0.490557 0.488591

4 0.000000 0.721922 0.749317 0.745865

5 1.000000 0.837365 0.875463 0.883210 6 0.000000 0.665035 0.694005 0.698059 7 0.000000 0.597170 0.604833 0.609235 8 1.000000 0.637445 0.637049 0.651473 9 0.000000 0.545291 0.552493 0.553740 10 1.000000 0.505538 0.472957 0.476612 11 1.000000 0.506999 0.496729 0.494920 12 0.000000 0.522635 0.550823 0.538072 13 1.000000 0.543054 0.545345 0.537934 14 1.000000 0.741278 0.754696 0.762297 15 1.000000 1.167924 0.981167 0.969127 16 1.000000 0.551309 0.570284 0.574279 17 1.000000 0.995988 0.953308 0.946590 18 0.000000 0.468410 0.453627 0.450761 19 1.000000 0.578367 0.588930 0.590914 20 1.000000 0.699402 0.734418 0.732170 21 1.000000 1.055092 0.970142 0.961527 22 1.000000 0.668538 0.691065 0.696811 23 1.000000 0.589898 0.612331 0.616947 24 1.000000 0.817532 0.823271 0.829942 25 1.000000 0.556367 0.576168 0.571597 26 0.000000 0.886284 0.870345 0.877349 27 1.000000 0.709857 0.794735 0.801792 28 0.000000 0.366892 0.329155 0.323192 29 0.000000 0.532028 0.533060 0.525323 30 1.000000 0.589393 0.600924 0.603099 31 1.000000 0.867825 0.865691 0.861590 32 0.000000 0.408832 0.375421 0.362307 33 0.000000 0.275081 0.254924 0.266120 34 1.000000 0.766231 0.791677 0.794642 35 1.000000 0.512512 0.502901 0.501252 36 0.000000 0.725351 0.735650 0.748299 37 1.000000 0.583880 0.594938 0.597021 38 1.000000 0.410024 0.367238 0.371222 39 0.000000 0.891543 0.911809 0.911722 40 1.000000 0.685076 0.707222 0.712618 41 0.000000 0.512512 0.502901 0.501252 42 0.000000 0.633241 0.649721 0.663198 43 1.000000 0.506999 0.496729 0.494920 44 1.000000 0.645595 0.655346 0.662751 45 1.000000 0.896033 0.920332 0.915147 46 1.000000 0.651107 0.661026 0.668388 47 0.000000 0.500918 0.506645 0.502160 48 0.000000 0.321819 0.278693 0.282483 49 0.000000 0.622199 0.639469 0.637792 50 0.000000 0.586144 0.592870 0.597112 51 1.000000 0.674102 0.706620 0.706700


17

52 1.000000 0.245415 0.225075 0.219959 53 1.000000 0.566715 0.572972 0.580202 54 0.000000 0.328302 0.290970 0.285689 55 1.000000 0.591657 0.598863 0.603189 56 1.000000 0.817255 0.850229 0.834224 57 0.000000 0.188568 0.159270 0.159878 58 1.000000 1.007951 0.956326 0.949031 59 1.000000 0.628034 0.652927 0.649672 60 0.000000 0.665035 0.694005 0.698059 61 1.000000 0.649103 0.644106 0.667167 62 0.000000 0.708777 0.739149 0.747091 63 0.000000 0.416311 0.391453 0.382057 64 1.000000 0.928930 0.944279 0.931382 65 0.000000 0.286753 0.250761 0.234186 66 0.000000 0.198599 0.149215 0.156535 67 0.000000 0.421824 0.397408 0.388053 68 0.000000 0.413282 0.393109 0.389160 69 1.000000 0.645595 0.655346 0.662751 70 1.000000 0.746791 0.759537 0.766856 71 1.000000 0.857392 0.897924 0.898345 72 1.000000 0.330268 0.300130 0.297924 73 0.000000 0.514198 0.493487 0.502289 74 1.000000 0.516035 0.490941 0.505392 75 0.000000 0.457062 0.433224 0.431748 76 1.000000 0.821459 0.838376 0.835563 77 1.000000 1.081633 0.977256 0.966534 78 0.000000 0.483965 0.509059 0.494608 79 1.000000 0.942131 0.929852 0.929411 80 1.000000 0.716963 0.736564 0.743385 81 1.000000 0.515388 0.495614 0.501400 82 1.000000 0.924665 0.906024 0.897696 83 0.000000 0.506677 0.488463 0.488303 84 1.000000 0.638754 0.655436 0.668831 85 0.000000 0.629760 0.637658 0.637297 86 1.000000 0.643268 0.630531 0.655566 87 1.000000 0.493156 0.496119 0.479104 88 1.000000 0.627712 0.645245 0.643621 89 1.000000 0.741278 0.754696 0.762297 90 1.000000 0.723717 0.752629 0.751632 91 1.000000 0.586756 0.587843 0.597164 92 1.000000 0.971040 0.937352 0.937777 93 1.000000 0.591657 0.598863 0.603189 94 1.000000 0.754427 0.832479 0.841011 95 0.000000 0.730970 0.739175 0.755652


18

LIMITATION OF THE STUDY AND POSSIBLE EXTENSIONS

There are many limitations of my study. First, I cannot understand the concept very well, so it may be difficult for me to develop the perfect study. Second, I face some difficulties in using the Eviews Program as the program is complicated and I am not quite well in using computer. Last, as the time is constraint, I cannot get more information I should have to do a perfect study.As the RZ is not meaningful in binary regressand model, one can use Count R2 tomeasure goodness of fit. The R2 can be computed as number of correct predictions divided by total number of observations. Also, in Linearity Probability Model, the hetroscedasticity exists, dividing the original equation by ~Wi can correct this problem, whereas ~wi is equal to aPi(1-Pi) .

References

• Damodar N. Gujarati, Basic Econometrics, New York: McGraw-Hill, 2000 • Karl E. Case and ray C. fair, Piinciples of Economics, New Jersey: Prentice-Hall, Inc.,

1996 • Robert S. Pindyck and Daniel L. Rubinfeld, Econometric Models Econometric

Forecasts NewYork: McGraw-Hill, 1997




Paper#4

Application of the simulation models



ID#4585974929



ASSISTANT PROFESSOR

A Paper On

“How Effectiveness of the Fiscal and Monetary Policy to the Growth Rate of National Income Expansion?”

Policy Effectiveness 2002

ii









Dear Madam,

Here is my paper on " How effectiveness of the fiscal and monetary.” that I was assigned. It was a great opportunity for me to acquire practical knowledge of the Quantitative Methods in Economic Analysis and forecasting





Sincerely yours

Sk. Ashiquer Rahman

Id#4585974929


Bangkok, Thailand


iii

Preface Any institutional education would not be completed if it were confined within theoretical aspects. Every branch of education has become more competed by their practical application and accomplishment of full knowledge. We shall be benefited by our education if we can effectively apply the institutional education in practical fields. Hence, we all need practical education to apply theoretical knowledge in real world. By considering this importance “faculty of economics” arranges the Quantitative Methods in Economic Analysis courses for the students of Masters in International Economics and Finance. As a part of this program my topic was selected as “how effectiveness of the fiscal and monetary. ”



mind.



iv














v

Table of Content

Title Page


Preface iii

Acknowledgement iv

Table Of Content v







References 15-15

1


(I). Statement of the Problems

Under the economic conceptual, namely the IS-LM framework, the government might increase the income by operate the fiscal expansion policy. The same gold also can occur from the monetary sector. The central bank might choose to increase the money supply level in order to expand the economic growth. However, the policy manipulation might not able to achieve the target since some of economic reason. Then, this paper tries to predict that how effectiveness of the fiscal and monetary.

(II) Reviews of literature and theoretical background:

One of the economic frameworks, which illustrate the relationship of the macroeconomic variables, is the IS-Lm framework. The IS-LM framework goes beyond the simple Keynesian cross model of national income determination by adding a monetary sector and allowing for the simultaneous interactions between investment, the interest rate and the demand for money, and between saving, income and the demand for money. It is therefore an extremely useful and versatile model, which can be used to discuss the effects of change in exogenous expenditure, fiscal policy, monetary policy, and so on. The IS curve shows all the combinations of income and interest rate at which the market for good and services is in equilibrium, in the sense that expenditure is equal to output. The consumption is assumed to be a function of measured income. It is positively related to the income.

C = a + by a > 0, 0<b<1 The investment is assumed to be partly autonomous and partly related to the interest rate by negatively related.

I = J + iR J>2, i>0 The LM curve is the locus of all the combinations of interest rate and real income at which the money market is in equilibrium that is the demand for money equal supply of money. It is assumed that the supply of money is fixed exogenous by the government, i.e. M, = M. At the equilibrium, it can get that;

Md/P = d+mY-iR

Ms= M. Ms =M Ms=Md

Then, it might be able to obtain R as a function of Y;

R=Pd-M+m.Y

2


Pi i Where

d, m, i are the constant term

Ms ,Md Supply of money and money demand, respectively From the above theoretical framework, one might able to analyst the effect of fiscal and money expansion to macroeconomic variables. For the instance, if the government chooses to increase the government expenditure, one may see that;

That is if the government increases the exogenous expenditure, the national income and the interest rate will rise up. Another scenario, the same target might also achieve by the expanding of monetary policy as follows;

Y

(III) Formulation of General Model:

According the IS-LM framework as illustrate above, one might able to setup the model as Follow; CSt = β0 + β1Yt + β2CSt-1 + ε1 t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ( 1 )

R0 y0

R

Y

R1

R2

Y1

3


It = β3 + β4(Yt-1 –Yt-1) +β5Yt+β6Rt-1+ ε2 t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ( 2 )

Rt = β7 + β8Yt +β9(Yt –Yt-1) + β10( MSt-MSt-1)+β11 (Rt-1 – Rt-2) + ε3 t - - - - - - ( 3 )

Yt = CSt + It + Gt ------------------------------------------------------------------------------------------------------------- (4)

W h er e CS = Real Aggregate Personal Consumption I = Real Gross Domestic Investment Y = Real GNP (Net of Export and Import) Real Government Spending G = Real Money Stock, Narrowly Defined (M1) MS = Treasury Bills R = Interest Rate on 3-Month Treasury Bills.

(IV)Data sources and Description

The equations are estimated using quarterly time-series data from 1950 thought the end of 1985 (Pindyck and Rubinfeld, 1998). The variables description is shown as follows.

4


(V). Model Estimation and Hypothesis Testing

(V.1). Identification Test

Since the problems of simultaneous equation is the identification problem. It need to know the type of the identification in order to choose the appropriate estimation method, otherwise, the estimator might face with the problems of bias and inconsistent.

The way to check the identification problem might classify into two categories. The first is The Order Condition, and the second is The Rank Condition. The first one is the necessary condition, but not sufficient. The second one is sufficient and also necessary. However, for the large simultaneous equation model, apply the rank condition is a formidable task. While Harvey notes that the order condition is usually sufficient to ensure identifiability. Hence, this paper will check the identification under the order condition.

5


The model consists of four endogenous variables (CS, I, Y, R), and seven predetermine

variables (CS, , t1',_, - Yt_, ) , Y,_, , G t , (MSt - MS ,_, ) , ( R t -t - R t-z By the order condition which state that K-k >_ m-1

Where K is number predetermined variables in the model including the intercept K is number of predeterniined variables in a given equation m is number of endogenous variables in a given equation

The result is;

Equation no. K-k m-1 Identified Estimation Methods

(1) 6 1 Overidentified 2SLS

(2) 5 1 Overidentified 2SLS

(3) ? ? Exactly identified OLS

However, the interest rate appears as an explanatory variable only in the investment equation, then, it need not worry about inconsistency in the OLS estimation of the coefficient of the interest rate equation (Recursive model).

In short, since two of three equations are over identified (equation (1) and (2)), then, the first two equation will be estimated under two-stage least squares (2SLS). However, the third equation will be estimated under OLS method. (V.2) Model Estimation I apply the two stage least square method in model (1) and model(2) because we can see model (1) and model(2) are ovridentified. So the outputs of these models are show below:

Dependent variable: cs Method : Two stage Least squares Date: 06/15/02 Time: 12.-02 Sample: 1950:1 1985:4 Included observations: 144 Instrument list: CS(-1 ) (Y(-1)-Y(-2) ) Y(-1) G (MS-MS(-1) ) (R(-1)-R(-2) )

R(-4) Variable Coefficie Std. Error t-Statistic Prob

C -3.622196 4.949340 -0.731854 0.4655Y 0.027667 0.018173 1.522411 0.1301

CS(-1) 0.965346 0.027151 35.55409 0.0000R-squared 0.999466 Mean dependent var 1411.162

6


Adjusted R-squared 0.999458 S. D. dependent var 486.7321S.E. of regression 11.32836 Sum squared resid 18094.79F-statistic 131920.0 Durbin-Watson stat 1.628630Prob(F-statistic) 0.000000

Dependent Variable: I Method: Two-Stage Least Squares Date: 06/15/02 Time: 12:29 Sample: 1950:1 1985:4 Included observations: 144 Instrument list: CS(-1) (Y(-1)-Y(-2) ) Y(-1) G (MS-MS(-1) ) (R(-1)-R(-2) ) R ( -4 )

Variable Coefficie Std. Error t-Statistic Prob.C -64.08308 8.167319 -7.846281 0.0000

Y(-1)-Y(-2) 0.178104 0.077128 2.309196 0.0224 Y 0.216422 0.005670 38.16637 0.0000

R4v4) -10.94074 1.225571 -8.927052 0.0000R-squared 0.967537 Mean dependent var 383.8354 Adjusted R-squared 0.966841 S. D. dependent var 131.0940S. E. of regression 23.87161 Sum squared resid 79779.56F-statistic 1381.824 Durbin-Watson stat 0.545257Prob(F-statistic) 0.000000 I apply the least squares method in model (3) because model (3) is exactly identified. So the output of the model (3) is show below: Dependent Variable: R Method: Least Squares Date: 06/15/02 Time: 13-.30 Sample: 1950:1 1985:4 Included observations: 144

Variable Coefficie Std. Error t-Statistic Prob.C Y

Y-Y(-1) MS-MS(-1}

-3.683841 0.003961 -0.012926 -0.099259

0.411369 -8.955067 0.000172 23.00733 0.005194 -2.488564 0.031588 -3.142259

0.0000 0.0000 0.0140 0.0020

R-squared 0.803749 Mean dependent var 5.15343Adjusted R-squared 0.798101 S. D. dependent var 3.26889S.E. of regression 1.468817 Akaike info criterion 3.64089

7


According the above tables, it may summarize that the result of estimation are; CS = -3.622196416 + 0.02766714557 Yt + 0.9653459803 CSc_1 ------------------------------------------------(1)

t-stat (-0.37) (1.52) (35.55)

R2-= 0.99 S.E. = 23.87 DW - 1.63 Durbin h -2.35

I = -64.08308199 + 0.1781044365 (Y,_, - Y, ) + 0.2164223566 Y, - 10.9407366 R,_., (2)

t-stat (-7.84) (2.31) (38.16) (-8.93)

R2- - 0.97 S.E. = 23.87 DW - 0.55

R = -3.683841135 + 0.003960784 Y, - 0.01292640826(Y, - Y" ) (3)

t-stat (-8.95) (23.00) (-249)

- 0.09925883596 (MS,-MS,, ) +0.2936927099(R,, - R,-,)

t-stat (-3.14) (1.59)

RZ = 0.80 S.E. = 1.47 DW = 0.51

Yt = CS, + It + (4)

(V.3). The Interpretation of the result According the result from equation, even though the current consumption should depend oil the income by the theory, however, this case, the consumption is just determined by lag consumption itself. Since the equation (1) is the autoregressive equation, then, the Durbin h statistic is constructed. From the h statistic, it implies that there is no autocorrelation problem in this model. By the way, the investment behavior follows as the theory state. It depends on the income level and

Sum squared resid 299.8820 Schwarz criterion 3.74401Log likelihood - F-statistic 142.318Durbin-Watson stat 0.513725 Prob(F-statistic) 0.00000

8


also has a negatively related with the interest rate. For the interest rate determinant, it can be explained by the current income, the rate of change rate of income, and the rate of change rate of money supply. However, it does not have any related with its lag value. Moreover, it might able to see the historical simulation of consumption, investment, interest rate, and income from the diagram as follow

‐‐‐‐‐‐‐CS‐‐‐‐‐‐‐‐CSSML1

‐‐‐‐‐‐‐I ‐‐‐‐‐‐‐‐ISML1

9


(V.4).Export Forecast: After we got the estimated result, then it might want to test the goodness of fit of model in the prediction .Hence, we make the export forecast], by using the date 1986:1to 1988:1.The result is show as:

10


11


According the above graph, the simulation model may able to forecast the movement of the

economic variables. Nevertheless, it seems that the power of the prediction is not quite good. Thus,

we might want to confirm the goodness of the model by calculating for the root mean square error,

12


mean absolute error, mean absolute percent error, and Theil Inequality Coefficient in order to

evaluate the goodness of model. The result shows as follows;

From the above information, most of the indicators show that the model is quite fit to actual data. Especially, the Theil inequality coefficient is quite low. It approaches to zero. Then, overall, the model is good for forecast.

13


(V.5).Policy Analysis: Supposed that the government increase the exogenous expenditure by 3 percent, while also increase the money supply for 1 percent. The result show as follows

14


(V.6). Interpretation the policy Effectiveness According the graph which shown in the section (V.5), it illustrates the effectiveness of the government policy. In this case, we let the government increase the government expenditure and also expand the money supply. The result is consistent with the theoretical background.

We might interpret the result by combining the result in section (V.5) and the theoretical background in

section (V.6) together.

R

R10

R0

R1

A

B

Y0 Y01

LM0

C

Y

R IS0

Y1

IS1

LM1

15


The Fiscal Policy

At the beginning period of time, the autarky equilibrium stays at point A, income stay at ''+- , and interest rate at .

Then, the government injects the government expenditure amount 3 percent in to the economy. This might increase

the aggregate demand. The IS curve shift to the right. The economy moves to point B. At that time, the

consumption will increase to Y01(2650). The interest rate rise up from .(11%) to Rfll (12.75%). The investment

will also increase from 770 to 820. This evidence drive the national income from i,(4100) to Yol (4300).

The Monetary Policy

At the same time, the central bank also injects the money supply into the economy. The LM curve will shit to the

right. The economy moves from point B to C. The consumption level still rises up to 2700. However, the interest rate

will drop to 11.5. These events drive the national income up to 4400, eventually.

(VI). Conclusion

This paper tries to study the effectiveness of the government policy, both of fiscal policy and monetary policy. The

paper use the simulation model to capture the effect of the 3 percent increase in the government expenditure, and

the 1 percent increase un the money supply. By the simulation method, we might able to predict the changing

magnitude of the economic variable, such as consumption, interest rate, investment, and the national income. All

of the information is available in the interpretation part (V.6).

(VII). References

1).Gujarati, Damodar N., Basic Econometrics, Mcgrawhill, 2003

2).Pindyck, Robert S., and Daniel L. Rubinfeld, Econometric Models And Economic Forecasts, Mcgrawhill,

1998 3.).Cobham, David, Macroeconomic Analysis an intermediate text, Longman, 1998

16


APPRENDIX

17


18





Paper#5

Application of Cointegration and ECM



ID#4585974929



ASSISTANT PROFESSOR

A PAPER

ON COINTEGRATION OF CONSUMPTION AND INCOME

co-interaction of consumption and income 2002

ii









Dear Madam,

Here is my paper on " the co-interaction of consumption and income” that I was assigned. It was a

great opportunity for me to acquire practical knowledge of the Quantitative Methods in Economic

Analysis and forecasting





Sincerely yours

Sk. Ashiquer Rahman

Id#4585974929


Bangkok, Thailand


iii







International Economics and Finance. As a part of this program my topic was selected as “the co-

interaction of consumption and income”



mind.



iv














v

Table of Content

Title Page


Preface iii

Acknowledgement iv

Table Of Content v






Interpretation Of The Results And Conclusions 5--6


References 6-6

The co-interaction of consumption and income

1

Statement of the Problem

This paper studies the co-interaction of consumption and income. But the consumption expenditure is a

complex matter. It depends on the income. If income increases in a dollar, consumption increases by a

fraction of a dollar. This fraction is the marginal propensity to consume on the simplest ways to express

such a relation of dependency is as a linear function:

C=a+bY

Where C is the consumption expenditure, Y is the national income and "a" and "b" is constant.

In this paper, we will consider a relation between the consumption and the income. Moreover this paper

will use an econometric method to estimate parameters in the model, apply some test to verify the result we

acquire and then conclude the model.

General model:

C t =β 1 +β2Y D t +ε t

Where: Ct(GC)= Consumpt ion Ex pend i tu re

YDt(GYD)= Income

Before some testing process we have to establish random walks model because regressing one random walk

against another can lead to spurious results in that conventional significance tests will tend to indicate a

relationship between the two variables when in fact none exists. This is one reason why it is important to test

for random walks. If a test fails to reject the hypothesis of a random walk, one can difference the series

question before using it in regression. Since many economic time series seem to follow random walks, this

suggests that one will typically want to difference a variable before using it in regression. While this is

acceptable, differencing may result in a loss of information about the longrun relationship between t w o

variables

Data sources and description

Due to time and scope, quarterly time series data from 1954.1 to 1995.21 There are 166 observation.

The data has been collected from sheet. In addition with this purpose the book of (i) Econometric models

and Economic forecast ( by- Robert S. pindyck and Doniel L.), fourth edition, (ii) Basic Econometrics.

Domandar N. Gujrati. fourth edition, have been used. . After analysis the result, I'll attach a copy of data.


2

Descriptive statistics of each variable:

Date: 11/15/09 Time: 12:22

Sample: 1954:1 1995:2

GC GYD

Mean 1578.775 1726.075 Median 950.4500 1071.650 Maximum 4851.029 5201.000 Minimum 236.4000 258.6000 Std. Dev. 1388.838 1496.928 Skewness 0.878114 0.838759 Kurtosis 2.424395 2.350241

Jarque-Bera 23.62498 22.38407 Probability 0.000007 0.000014

Observations 166 166

GYD

Model Estimation


3

For the model estimation, we will do some test about the cointegration of consumption and income. Now we apply the least square method for the ADF test and output is show below:

ADF Test Statistic 9.623256 1% Critical Value* -3.4713

5% Critical Value -2.8791 10% Critical Value -2.5760

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(GC) Method: Least Squares Date: 11/15/09 Time: 13:01 Sample(adjusted): 1954:3 1995:2 Included observations: 164 after adjusting endpoints


GC(-1) 0.014044 0.001459 9.623256 0.0000 D(GC(-1)) 0.022907 0.079927 0.286596 0.7748

C 5.479646 1.914002 2.862926 0.0048

R-squared 0.613585 Mean dependent var 28.12152 Adjusted R-squared 0.608785 S.D. dependent var 25.13435 S.E. of regression 15.72083 Akaike info criterion 8.365973 Sum squared resid 39790.26 Schwarz criterion 8.422678 Log likelihood -683.0098 F-statistic 127.8253 Durbin-Watson stat 2.011854 Prob(F-statistic) 0.000000

ADF Test Statistic 9.692602 1% Critical Value* -3.4713 5% Critical Value -2.8791 10% Critical Value -2.5760

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(GYD) Method: Least Squares Date: 11/15/09 Time: 13:04 Sample(adjusted): 1954:3 1995:2 Included observations: 164 after adjusting endpoints


GYD(-1) 0.015977 0.001648 9.692602 0.0000 D(GYD(-1)) -0.157648 0.080974 -1.946904 0.0533

C 7.489210 2.671796 2.803062 0.0057

R-squared 0.468437 Mean dependent var 30.13659 Adjusted R-squared 0.461834 S.D. dependent var 29.98479 S.E. of regression 21.99678 Akaike info criterion 9.037792


4

Sum squared resid 77901.16 Schwarz criterion 9.094497 Log likelihood -738.0990 F-statistic 70.94031 Durbin-Watson stat 1.912886 Prob(F-statistic) 0.000000

Vector Error Correction Estimates:

Date: 11/15/09 Time: 13:16 Sample(adjusted): 1954:4 1995:2 Included observations: 163 after adjusting endpoints Standard errors & t-statistics in parentheses

Cointegrating Eq: CointEq1

D(GC(-1)) 1.000000

D(GYD(-1)) -0.949584 (0.03716) (-25.5512)

C 0.825001

Error Correction: D(GC,2) D(GYD,2)

CointEq1 -0.480847 1.265850 (0.11620) (0.12944) (-4.13802) (9.77945)

D(GC(-1),2) -0.338085 -0.242504 (0.09645) (0.10744) (-3.50512) (-2.25706)

D(GYD(-1),2) -0.278621 -0.053315 (0.06086) (0.06779) (-4.57800) (-0.78643)

C 0.643335 0.181223 (1.26298) (1.40686) (0.50938) (0.12881)

R-squared 0.461454 0.710258 Adj. R-squared 0.451293 0.704791 Sum sq. resids 41319.57 51269.99 S.E. equation 16.12053 17.95697 F-statistic 45.41319 129.9214 Log likelihood -682.4173 -700.0025 Akaike AIC 8.422298 8.638068 Schwarz SC 8.498218 8.713988 Mean dependent 0.408840 0.087730 S.D. dependent 21.76252 33.04977


5

Determinant Residual Covariance

72079.53

Log Likelihood -1374.194 Akaike Information Criteria 16.98398 Schwarz Criteria 17.17378

Result and conclusion

We have tested whether real consumption spending and real income are co-integrated, using quarterly data

from 1954:1 to 1952:2. we first test whether each variable is a random walk using the augmented Dickey-

Fuller test. Running this test, first for consumption and then for the income and case include logs for the

change in the variable, always yields test statistics that fail to reject the random walk h Hypothesis. Next run a

co-integrated regression of consumption C against income from the Durbin-Watson statistics. We can see it

value and comparing the critical value. We can reject the hypothesis at a random walk at the 5% level.

Running a Dickey-Fuller test on the residuals of the regression also leads to a rejection of the random walk

hypothesis at the 5% level.

Limitation of the study and possible extension

There is no limitation on getting the essential data and information. The data which are collected, I have

assumed the all information true and collected. I have some limitation from the span of time, besides I did

not get enough facility to use EVIEWs program for me. Notwithstanding these limitations, it is expected that it

will also contribute in a merger to have better under standing of the condition of the single equation model.

Acknowledgement

I am grateful to our beloved professor Dr. Bangorn Tubtimtong for his contribution and his moral

assistance.


6

References.

1.Damonder N. Gujarati , Basic Econometrics, McGraw-Hill, fourth edition.

2. Robert S Pindyck and Daniel L Rubinfeld, Econometric model and forecast


7

Appendix


8


9

Cointegration Tests of Purchasing Power Parity: the Case of the Thai Baht

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Co‐integration Tests of Purchasing Power Parity: the Case of the Thai Baht*

This paper will examine the validity of the purchasing power parity (PPP) hypothesis for the Thai baht visdvis the currencies of Thailand's key trading partners under the new exchange rate regime using the cointegration technique. The major conclusions obtained from this empirical analysis may be broadly summarized as follows. First, the empirical evidence, based on the DF and ADF statistics, seems to suggest that the nominal exchange rates and relative prices are well characterized as nonstationary 1(1) process. Second, the cointegration analysis provides no evidence in support of a longrun equilibrium relationship between bilateral nominal exchange rates for the Thai baht visdvis the currencies of Thailand's major trading partners and the correspdnding relative price ratios. This implies rejection of PPP for these countries. If this is the case, considerable care should competitiveness against Thailand's key trading partners, of shocks to the nominal exchange rate be taken in assessing the loner run implications for the real exchange rate, and thus.

1. Introduction In the pursuit of economic policy, monetary authorities in many developing countries have given increasing attention to the use of the exchange rate as a means of achieving and maintaining external competitiveness or as an anchor for domestic prices. This is particularly relevant in the case of Thailand where exchange rate policy has been regarded as an important instrument for correcting external disequilibrium problems (Wibulswasdi, 1987, p. 40), particularly after the switching of the exchange rate regime from pegging the US dollar to an undisclosed basket of currencies in November 1984. It has been surmised that, under this new exchange rate regime, the nominal exchange rate is adjusted continuously in order tc maintain the real exchange rate close to its long‐run equilibrium level as implied by the purchasing power parity (hereafter PPP) doctrine.' Although this new exchange rate regime has given the Thai monetary authorities more room to maneuver the exchange rate in response to developments prevailing at home and abroad, it still remains unclear whether such a continuous adjustment of the nominal exchange rate is reasonably consistent with a differential between domestic and foreign inflation rates as implied by a PPP doctrine. In view of this, an examination of the validity of the PPP hypothesis is important since it can serve as a useful guide for Thailand's policymakers in implementing exchange rate management .2Earlier empirical studies of the PPP hypothesis have been carried out mainly in the context of highly developed or advanced countries. The evidence obtained so far has been far from conclusive. Some recent empirical studies of PPP are unable to find evidence in support of a long‐run relationship between the exchange rate and the ratio of price levels. For example, Corbae and Ouliaris (1988) use the cointegration approach to test for PPP between the United States and her three major trading partners. They find little evidence in favour of PPP after 1973. Taylor (1988) finds no evidence supporting the long‐run relationship between the exchange rate and inflation differentials among five countries of interest, even with an allowance made for transaction costs and measurement errors. Mark (1990), employing a cointegration technique, is unable to find empirical evidence to support the presence of PPP between the United States and six industrial countries during the 1973‐1988 period. Similar findings, also using the technique of cointegration, are reported in empirical studies of other countries. For instance, Karfakis and Moschos (1989) observed that there is little evidence in support of the presencee of long‐run PPP between Greece and six of its major trading partners since the adoption of a man‐aged floating regime in 1975. Kim and Enders (1991) showed that there was little evidence in favour of the existence of long‐run PPP between Korea and the Pacific Rim nations over the 1973 to 1987 period. Contrary to the findings cited above, some other empirical studies have found some evidence in favour of the long‐run PPP hypothesis (i.e. Hakkio, 1984; Rush and Husted, 1985; Frankel, 1981; Huizinga, 1987; Abuaf and Jorion, 1990). On the other hand, some studies report mixed results regarding the validity of the PPP hypothesis (see, for example, Taylor and McMahon, 1988). Although the exchange rate has played an increasing role in macroeconomic management in Thailand, particularly since the mid‐1980s, little attention has been paid to explicitly modelling the behaviour of the exchange rate between the US dollar and the Thai baht in recent studies of macroeconometric modelling for Thailand such as Nijathaworn and Arya (1987) and Deeithinant


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(1988). The exception in this regard is the study by Warr and Nidhiprabha (1989).Against this background it is interesting to see whether, and to what extent, PPP is applicable to the case of Thailand from 1984.M1i to 1992.M6 when the management of the Thai baht became more flexible.' The validity of PPP is tested within the context of the bilateral nominal exchange rate‐price relationship between Thailand and its seven major trading partners: Japan, the USA, the UK, Germany, Hong Kong, Malaysia and Singapore. These countries are chosen on the ground that their currencies have been used in the present currency basket of Thailand. The econometric methodology used for this analysis is based on a cointegration approach developed by Engle and Granger (1987). The cointegration analysis is useful since the existence of long‐run relationships among the economic variables postulated by PPP theory can be tested for. The plan of this study is an follows. Section II provides a brief discussion of the theoretical framework of exchange rate determination based on the PPP approach and of some earlier empirical studies based on PPP. This is followed by a brief discussion of the econometric methodology employed in testing for the PPP hypothesis over the said period. Section III discusses empirical results.

* The author would like to thank Dr Anthony. J. Phipps and Dr Costas L Karfakis for their detailed and valuable comments on earlier versions or the paper. Thanks are also due to anonymous referees for helpful comments and suggestions and to Dr Ammara Sripa}•ak and Dr Pichit Patrawimolporn for supplying part of the data for use in this study. Financial support from the Bank of Thailand is gratefully acknowledged. The views presented here are those of the author and do not necessarily coincide with the Bank of Thailand. 1. In a case where the exchange rate follows PPP, the real exchange rate will remain constant. To understand this, the bilateral real exchange rate (RER) of the Thai baht against a currency of one of Thailand's major trading partners is expressed algebraically as:

RER = EPf / P

where E represents the bilateral nominal (e.g. Thai baht/US dollar) exchange rate; P denotes the consumer price index (CPI) in Thailand: and P is the CPI in the USA. It follows from the above equation that if PPP prevails, then an increase in Thailand's price levels relative to the price levels of its corresponding trading partner would be compensated for or reflected in a proportionate fall in E. Accordingly, the RER would not be altered. See Dornbusch (1987) for more discussion on this.

2. Under the new exchange rate regime, the bahtUS dollar rate is the exchange rate which has been normally used by the monetary authorities as a basis for setting an appropriate level of the baht's external value against Thailand's six major remaining trading partners, namely Japan, the UK, Germany, Hong Kong, Malaysia and Singapore. The daily nominal exchange rate between the Thai baht and the US dollar appears to have been adjusted in response to three proximate factors, namely, (i) the movements of the exchange rates of major currencies in the international foreign exchange market; (ii) the patterns of selling and buying of foreign currencies in the domestic market; and (iii) the prevailing conditions and likely outlook of Thailand's economy (Wibulswasdi, 1988). Since the adjustments based on (i) and (ii) have been generally regarded as short term in nature, their effects on the rate setting seem to be minimal. Nevertheless, adjustments in the exchange rate following developments in these two factors have to be pursued constantly in order to shield the domestic economy from the adverse effects of fluctuations in the exchange rates of major currencies in the international foreign exchange market. Adjustments in exchange rate based on (iii), on the other hand, have constantly been implemented with the view to addressing a deterioration in competitiveness and in external debt as well as to protecting the balance of payments. This latter adjustment in exchange rates appears to be of particular importance at times when certain shocks, i.e. monetary or real shocks, can be identified 3. The evolution of exchange rate arrangements in Thailand can be broadly divided into five distinct phases: (i) the pre par value system (until 1963); (ii) the par value system (19631978); (iii) the daily fixed system (19781981); (iv) the de facto fixed system (19811984); and (v) The basket of currency system (1984present). Exchange rate regimes during the first four periods may be broadly characterized as fixed exchange rate systems. This is no longer the case in the fifth period during which the variability of the bilateral nominal exchange rates of the Thai baht visdvis the currencies of Thailand's seven prime trading partners has increased and the official exchange rate policy is regarded as an adjustable multicurrency peg regime. More detailed information on this can be found in Sakornratanakul and Patrawimolporn (1992)


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II. The PPP Approach to Exchange Rate Determination: Theoretical Considerations and Methodological Issues IL1 Theoretical Considerations Several alternative theoretical approaches to the determination of the exchange rate have been put forward in the literature.' One such .an approach is based on the notion of PPP. Although this approach has on occasions been criticized as being inappropriate on theoretical and empirical grounds, it has remained in use as an important building block in macroeconometric models and as guidance in choosing an appropriate long‐run exchange rate as reflected in the "monetary approach" to exchange rate determination. The theory of PPP asserts that the bilateral exchange rate between two countries is determined by their price ratio, measured by some form of aggregate price indices. This implies that prices of a similar consumption bundle between countries, when expressed in a common currency, should be equal in the absence of transaction costs and trade barriers. This theory emphasizes the law of one price by assuming that perfect commodity arbitrage acts as an error‐correction mechanism (ECM) to force the home price of a consumption bundle in line with the foreign price of a corresponding consumption bundle (Corbae and Ouliaris, 1988). There are two main versions of the PPP approach to exchange rate determination: one is the absolute version and the other is the relative version.The absolute version of PPP theory states that the equilibrium exchange rate between two currencies equals the ratio of two price levels (domestic price index to foreign price index). The estimating model based on such a version may be empirically formulated as:

et = a0+ a1t + ult (1)

where e, denotes the bilateral nominal spot exchange rate (the domestic currency price (baht) of a unit of foreign currency), and n, is the relative price level, defined as p, p*, between Thailand and each of its seven major trading partners, where p, stands for the domestic price level, p* represents the foreign price level and ul, is the disturbance term. All the lower case letters denote logarithms of the variables concerned. Testing the validity of this version is equivalent to testing whether ao = 0, a, = 1 and ul, is white noise. In the relative version of PPP, on the other hand, it is asserted that the rate of change of the nominal

exchange rate is determined by the inflation :ate differential between the two countries. Since inflation erodes a currency's purchasing power, a country with a higher inflation rate tends to have its currency depreciated relative to a country with a lower rate of inflation. The validity of this version can be empirically tested by testing whether aZ = 0 and a, = 1 in the following model:

Δet = a2 + a3 Δt + u2t (2)

IN Econometric Methodology In testing for the presence of a long‐run relationship between the exchange rate and the price ratio between the two countries such as those specified in Equations (1) and (2), several alternative testing methods have been used in the literature e.g. OLS, TSLQ and cointegration. Since a testing methodology based on the cointegration approach of Engle and Granger (1987) has been rapidly gaining in popularity in recent empirical studies of the PPP hypothesis, due to its appropriate treatment of endogeneity and non‐stationarity problems, it would be desirable to'•apply this testing procedure in this study.' The main idea underlying this cointegration analysis is that two (or more) non‐stationary 1(1) variables can be combined to form a stationary 1(0) variable even though each individual variable itself 4. for a detailed review of this see, for example,Mussa(1984);MacDonald and Tailor(1992) 5. It is worth noting that the issue concerning the appropriateness of using a cointegration technique in testing the PPP hypothesis has received increasing attention in recent empirical studies. As noted in the papers by several researchers such as Hakkio and Rush (1991), the application of the cointegration technique to test for the presence of longrun PPP relationships seems to be more appropriate in the case where the total sample length is long enough to capture the fluctuations in the variables concerned. In their view, the extension of the number of observations by the use of higher frequency data appeared to be of little help in increasing the power of the cointegration test. Mark (1990) also notes that some caution should be exercised in the interpretation of the empirical results based on the relatively short period of modern experience with flexible exchange rates (16 years). He has surmised that the issue of committing a socalled "type I error" would become more relevant if the "true" longrun were longer than 16 years. Contrary to this view, Isard (1983) argued that the adjustment toward longrun PPP can be fulfilled within two to five years. A similar argument to this is made in Manzur (1990) who finds that adjustment to longrun PPP can have full effect in five years.


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is non‐stationary. In the present context, although the two time series (e, and n) in equation (1) are individually non‐stationary or 1(1), they may be cointegrated if there exists a non‐zero constant (3 such that ul, = e, P'7<, is a stationary or 1(0) process. Then, e, and n, are said to be cointegrated with a cointegrating parameter β. In order to test for cointegratiorn between e, and it,, the Engle and Granger (1987) two‐step method is

applied in this study. In the "first step", it is necessary to establish that e, and n, in Equations (1) and (2) are integrated of the same order, i.e. a unit root or I(1) process. Note that this requirement must be fulfilled before proceeding to the second step since cointegration is a test for equilibrium between non‐stationary time series. Testing for the presence of a unit root employed here is based on the socalled Augmented Dicky‐Fuller (ADF) test as suggested in Dickey and Fuller (1979, 1981). The ADF test can be implemented by estimating the following equation:

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐(3) where x, stands for variables appearing in (1) (that is, e, and n) k is the number of lags chosen to ensure that the estimated estimated residuals, e„ are approximately white noise, C is a constant term and TT is a time trend. Notice that when k = 0, the statistic in (3) becomes known as the Dickey and Fuller (DF) test. The null hypothesis is Ho: x, is I(1) which is rejected in favour of 1(0) if a is found to be significantly negative. The test statistic is the usual t‐ratio for the estimate of a. Since the distribution of the DF and ADF t‐statistic associated with the coefficient a is~ asymptotical, the appropriate critical values for these statistics are tabulated in Fuller (1976, p. 373) and denoted as ti, tiµ and TT depending on whether a constant and/ or a constant and time trend are included in (3), respectively. After having established that e, and n,.are cointegrated of the same order, the "second step" in cointegration

tests is to test whether the time series in question are cointegrated. This can proceed by first regressing e, on 7r„ using OLS, and then examining whether the estimated residuals obtained from Equations (1) and (2) are stationary, 1(0), process using the integration test statistics, DF and ADF test statistics; reported in Dickey and Fuller (1981). If the residual terms in Equations (1) and (2) are stationary, the cointegrating vector among these variables is said to exist, implying that there is a stable long ‐run relationship among these variables.

This requires testing for HO: ‐y, = 0 in the regression:

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐(4) where u, are the residuals from the cointegrating regression. The t‐ratio statistics associated with the estimated residuals are then compared with those provided in Engle and Granger (1987) and Engle and Yoo (1987). The rejection of the null hypothesis of a unit root for the residuals from the cointegrating regression implies that e, and n, are cointegrated. The Cointegrating Regression Durbin‐Watson (CIRDW) test statistic ‐ the DW ratio in the OLS estimation of the 'cointegrating regression' of Equations (1) and (2) ‐ is also employed as an alternative test for the existence of cointegration. IIL Empirical Tests of the PPP Hypothesis IIL1 Data and Integration Analysis In this sectior., the null hypothesis that there is a long‐run equilibrium relationship between the exchange rate, e, and relative prices, n,, for Thailand and each of its seven major trading partners is tested against the alternative that there is no such relationship, using the econometric technique of cointegration discussed earlier. The estimation period is' from 1984.M11 to 1992.M6. The choice of sample period was dictated by the implementation of the new exchange rate regime in which the Thai baht was unpegged from the US dollar. The definitions and sources of data are provided in the Appendix. There are a number of issues that must be considered in conducting the PPP testing of Equations (1) and

(2) as noted by many researchers such as Boughton (1988) and Layton and Stark (1990). In this study, the following two related issues are addressed: (i) a suitable trading partner; and (ii) an appropriate price index. With regard to a suitable trading partner set, the following seven countries are selected: Japan, the USA, the UK, Germany, Hong Kong, Malaysia, and Singapore. These countries are selected on the grounds that their


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currencies are accounted for in the present system of Thailand's currency basket. As for the‐selection of appropriate price measures, the following two alternative definitions of the price index are utilized: the consumer price index (CPI) and the wholesale price index (WPI). The choice of these price indices in this study is dictated by their popularity in the literature on empirical studies of the PPP hyporthesis.b Before proceeding to test whether the exchange rates are cointegrated with the price ratios, it is necessary

first to test for the existence of unit roots in the stochastic processes of the exchange rates and price ratios. The results of these integration tests are reported in Table 1. As indicated Table 1 Unit Root Tests of Exchange Rates and Prices

Variable e Level(s) nc rzw Ae

First Difference(s) 471w

USA ‐3.18(2) ‐1.73(0) ‐2.17(0) ‐ ‐8.13(0) ‐ (20.28] [1833] [12.68] [17.00 [19.15] [S.SO] UK ‐2.61(0) ‐2.56(0) ‐1.92(0) ‐ ‐8.39(0) ‐ [S.BSJ [17.40] [18.80] [6.401 [16.50] [10.95] Japan ‐1.51(0) ‐4.41(0) ‐0.96(0) ‐ ‐10.95(1) ‐ [20.51] [18.90] [10.62] [13.68 [17.18] [13.98] Germany ‐1.44(0) ‐2.92(0) ‐1 07(0) ‐ ‐7.62(0) ‐ [16.05] [1630] [11.45] [11.13 (18.4‐i] [8.09] Singapore ‐2.28(1) ‐3.40(0) ‐3.62(0) ‐ ‐9.39(1) ‐ [18.12] [21.09] [17.69] [16.15 [17.71] [19.77] Malaysia ‐1.52(1) ‐3.34(1) ‐2.87(0) ‐ ‐8.70(1) ‐ [18.38] [2035] [10.23] [18.66

J[14JS] [11.09J

Notes: Figures in round parentheses represent the number of lagged dependent variables used in the autoregression to ensure the white noise in residual terms. The selection between zero and non‐zero lags was based on the Lagrange multiplier (LM) test for twelfth‐order serial correlation of the residuals. Figures in square brackets refer to the values of the LM(12) statistic. The rest of the entries are the reported DF and ADF statistics (T,) The critical value at the 5% significant level is ‐3.45 for N = 100 (Fuller 1976, p. 373). Rejection of the null hypothesis that the series in question are /(1) requires r, <‐3.45. The calculations of DF (ADF) statistics are base on Equation (3) in the text.

by the DF (ADF) statistics, the null hypothesis of non‐stationarity cannot be rejected for the `levels' of the variables. Using data in `first differences', by contrast, has resulted in the rejection of the null hypothesis of nonstationarity for all the series concerned, as the DF (ADF) statistics are now significantly negative. The results of this seem to suggest,that the exchange rates and most of the ratios of price levels are integrated of order one. The exceptions in this regard are the log level of 7tc (the price ratio expressed in terms of CPI) in the case of Thailand and Japan and the log levels of ntv (the price ratio in terms of WPI) in the case of Thailand and Singapore where the unit root null hypothesis can be rejected. This implies from the outset that there is no cointegration in these cases, and these country pairs are excluded from further cointegration tests. 6. Since data series on CPI and WPI for Hong Kong are not available from the IFS tape, testing for the existence of a cointegrating relationship between exchange rate and the relative price levels for this country is therefore left out in the subsequent empirical analysis.

7. The finding that PPP does not hold for Thailand during 19841992 seems to be inconsistent with the views contained in Akrasanee et al. (1991) and Wibulswasdi (1987) who claimed that the real exchange rate was from time to time depreciated as part of exchange ratemanagement by the Thai authorities in correcting external disequilibrium and in promoting exportled growth.


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H1.2 Testing for Cointegration: Bilateral Exchange Rates of the Thai Baht and Relative Prices Since most of the data series of concern are integrated of order one, it is therefore legitimate to apply Engle and Granger's txvo‐step estimation procedure for testing the existence of the cointegration relationship. The evidence from the DF (ADF) tests reported in Table 2 indicates that the Table 2 Cointegration Tests: Nominal Exchange Rates and Relative Prices `

Consumer Price Differential Wholesale Price DF(ADF) CIRDW DF(ADF) CIRD

USA ‐1.43(0) 0.09 ‐2.83(4) 0.21 (20.121 [15.28]

UK ‐2.69(0) 0.21 ‐2.16(0) 0.09 (4.581 [5.20]

Japan ‐ ‐ ‐1.93(0) 0.05 (13.81)

Germany ‐1.65(0) 0.05 ‐2.01(0) 0.08 [16.83] 116.921

Singapore 1.38(0) 0.06 ‐ ‐ [13.61]

Malaysia ‐0.76(0) 0.09 ‐2.27(0) 0.15 [20.92] (12.731

Notes: See notes to Table 1. The critical values of the DF (ADF) and CIRDW tests at the 5% level of significance are ‐3.37 (‐3.17) and 0386 respectively for sample sizes in the vicinity of 100 (Engle and Granger, 1987).

nominal bilateral exchange rates (between the Thai baht and the currencies of Thailand's key trading partners) are not cointegrated with the ratio of price differentials, when either nc or nw are used. As is evident from Table 2, the values of the DF or ADF test statistics (1‐statistics) are such that the null hypothesis of a unit root for the residuals from the cointegrating regression cannot be rejected in any case at the 5% significance level. A similar conclusion of no cointegration of the exchange rates and corresponding sponding price ratios is obtained from the CIRDW test statistics. The results of this appear to suggest that a simple notion of PPP did not hold between Thailand and its key trading partners during the period under review.' This implies that the nominal bilateral exchange rates for the Thai baht, visavis the currencies of Thailand's major trading partners, and the corresponding price ratios, drifted apart from each other following shocks to the balance of payments. That is, any variation in real exchange rates is regarded as being permanent and the real exchange rate is not expected to return to the equilibrium PPP value.Although the empirical results reported here seem to provide no support for cointegration, these results should be viewed as being preliminary and hence be interpreted with considerable caution. However, the results may be explained in the following ways. First, the failure of a simple PPP approach to model exchange rate determination may reflect the omission of some important variables as additional regressors from a model.' As noted by many researchers, a variety of factors, such as changes in monetary and/or fiscal policies, differential changes in productivity growth or terms of trade shock, may justify the departure of the exchange rate movements from PPP (see, inter alia, Frankel, 1981; Adler and Lehmann. 1983; Edison, 1987). Second, the results may be explained by the relatively short sampling period (approximately eight years) used in this study. Such a period may be too short to detect any significant movements of exchange rates to return to PPP following a shock to the economy. However, data over a longer sampling period with no switching of exchange rate regimes are not readily available. Extension of the data set backwards seems to be inappropriate, as the econometric technique used here cannot deal with changes in exchange rate regimes. As noted by many researchers, for example, Mussa (1984) and Mark (1990), the behaviour of real and nominal exchange rates has differed significantly across periods of fixed and flexible nominal exchange rate regimes and, in particular, the variance of the changes is much larger under floating exchange rates. Third, the unfavourable results of the PPP version of exchange rate determination may be


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attributed to the limited variability of the rate of inflation in Thailand during the period under. review. As claimed by many researchers (see, for example. Kim 1990), PPP is unlikely to hold when country pairs experience small differentials in price movements. Finally, from a technical point of view, the finding of no cointegration in PPP may be associated with the following two technical issues.' The first issue is related to the power of the Dickey-Fuller unit root test. As claimed by many researchers (see, inter alia, Schwert, 1987, Lo and MacKinlay, 1989), the power of the Dickey-Fuller unit root test is quite low in the sense that it tends to fail to reject the null hypothesis of a unit root against relevant trend stationarity alternatives, especially in the case of testing against the local alternative of a root close to, but below unity. In view of this, the non-rejection of the null hypothesis that the variables of interest are difference stationarity or I(1) may be due to two reasons. One reason is that the null is, in fact, true. The other is that, although the null is false. the data do not contain sufficient information to allow the test to statistically reject it. The second related issue is concerned with the formulation of an appropriate testing hypothesis in unit root tests. It has been claimed that the traditional formulation of the testing hypothesis in unit root tests is more favourable for the null hypothesis (see Kwiatkowski et al., 1992, among others). As can be seen, the rejection of the null hypothesis that the variables in question do not contain a unit root requires overwhelming evidence against it. It is possible that the conclusions obtained in this study would be different if the null and alternative hypotheses were to be reversed.9

8. I think a referee of this journal for directing my attention to these issues.

9. For more detailed discuss a new approach to testing for a unit root, see Maddala(1992),among others


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Appendix: Definitions of Variables and Sources of Data Data on exchange rate series (the baht price of foreign currencies) employed in

this study are obtained from the Department of Economic Research, the Bank of Thailand (BOT). Data series on price indices ‐ the consumer price index (CPI) and the wholesale price index (WPI) ‐ are taken from the IMF's International Financial Statistics (IFS) tape, lines 63 and 64 respectively. Note that price indices appearing in line 64 represent some form of wholesale or producer price indices. All data series cover 1984.M11 to 1992.M6, except that of Malaysia's WPI which is available from 1986.M1 onwards. The variables used in this study are all measured monthly and defined empirically as follows:

e The bilateral nominal spot exchange rate of the Thai "baht" against the currencies of Thailand's seven major trading partners, namely the US dollar, the Japanese yen, the UK pound stering, the deutschmark, the Hong Kong dollar, the Malaysian ringgit, and the Singapore dollar. All data are expressed in logarithms. An increase in the exchange rate depicts a nominal depreciation of the Thai baht rate. The data on exchange rates are monthly average values and are obtained from the BOT. pc The log of Thailand's consumer price index. pw log of Thailand's wholesale price index_ pcf The log of the consumer price index of Thailand's key trading partners, ners, respectively. Pwf The log of the wholesale price index of Thailand's key trading partners, respectively. ' c The log of the ratio of Thailand's CPI to the respective CPI of Thailand's major trading partners, defined as pc pcf. w The log of the ratio of Thailand's WPI to the respective WPI of Thailand's major trading partners, defined as pw = pw~

References

Abuaf, N. and Jorion, P., 1990, Purchasing power parity in the lone‐run. The Journal of Finance, XLV, pp. 157174.

Adler, M. and Lehman, B., 1983, Deviations from purchasing power paritv in the long run. The Journal of Finance, XXXVIII, pp. 14711487.

Akrasanee, N., Jansen, K. and Pongpisanupichit, J., 1991, International Capital Flows and Economic Adjustment in Thailand. Thailand Development Research Institute, Bangkok.

Boughton, J. M., 1988, The monetary approach to exchange rates: what now remains? Essay in International Finance, No. 171, October, Department of Economics, Princeton University.

Corbae, P. D. and Ouliaris, S., 1988, Co‐integration and tests of purchasing power parity Review of Economic and Statistics, 70, pp. S08‐S11.

Deeithinant, T., 1988, A Macroeconomic Model for the Thai Economy: with Special Emphasis on Some Current Issues. Ph.D. dissertation, submitted to the Washington University, St Louis, MO.

Dickey, D. A. and Fuller, W. A., 1979, Distribution of the estimators for auto‐regressive time series with a unit root. Journal of the American Statistical Association, 74, pp. 427‐431

Dickey, D. A. and Fuller, W. A., 1981, Likelihood ratio statistics for autoregressive time series with a unit root. Econontetrica, 49(4), pp. 1057‐1072.

Dornbusch, R, 1987, Purchasing power parity. In Eatwell, J., Milgage, M. and Newman, P., Eds., The New Palgrave: A Dictionary of Economics, vol. 3. Macmillan, London, pp1075‐1085.

Edison, H. J., 1987, Purchasing power parity in the long run: a test of the dollar/pound exchange rate (1890‐1978). Journal of Money, Credit and Banking, 19, pp. 376‐387.

Engle, R. F. and Granger, C. W. J., 1987, Co‐integration and error correction: representation, estimation, and testing. Econometrica, 55, pp. 251‐276. Engle, R. F., and Yoo, S., 1987, Forecasting and testing in cointegrated systems. Journal of Econometrics, 35, pp. 143‐159. Frankel, J. A., 1981, Flexible exchange rate, prices, and the role of news: lessons from the 1980s. Journal of Political Economy, 89, pp. 665‐705.


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Fuller, W. A., 1976, Introduction to Statistical Time Series. John Wiley, New York. Hakkio, C. S., 1984, A re‐examination of purchasing power parity. Journal of International

Economics, 17, pp. 265‐277. Hakkio, C. S., and Rush, M., 1991, Co‐integration: how short is the long run?. Journal of International Money

and Finance, 10, pp. 571‐581. Hataiseree, R. and Supapongse, M., 1991, Monetary Policy in Thailand: An Update. Paper presented at the

SEACEN‐IMF Seminar, 17‐19 December, 1990, Kuala Lumpur. Huizinga, J., 1987, An empirical investigation of the long‐run behaviour of real exchange

rates. In CarnegieRochester Conference Series on Public Policy, vol. 27, pp. 149‐214. Isard. P., 1983, An accounting framework and some issues in modelling how exchange rates respond to news.

In Frenkel, J. A., Ed., Exchange Rates and International Macroeconomics. University of Chicago Press, Chicago, pp. 19‐65.

Karfakis, C. and Moschos, D., 1989, Testing for long‐run purchasing power parity: a time series analysis for Greek drachma. Economics Letters, 30, pp. 243‐248.

Kim. J. O. and Enders, W., 1991, Real and monetary causes of real exchange rate rnovements in the Pacific rim. Southern Economic Journal, 57(4), pp. 1061‐1070.

Kwiatkowski, D., Peter, C. B., Phillips, Peter S. and Yongcheol, S., 1992, 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?. Journal of Econometrics, 54, pp. 159‐78.

Layton, A. and Stark, J. P., 1990, Co‐integration as an empirical test of purchasing power parity. Journal of Macroeconomics, winter, 12(1), pp. 125‐136.

Lo. A. and Craig, M., 1989, The size and power of the variance ratio test in finite samples a Monte Carlo investigation. Journal of Econometrics, 40, pp. 203‐238.

Lo, A. W. and MacKinlay, A. C., 1989, The size and power of the variance ratio test in finite samples: a Monte Carlo investigation. Journal of Econometrics, 40, pp. 203‐238.

MacDonald, R. and Taylor, M. P., 1992, Exchange rate economics: a survey. IMF Staff Papers, 39(1), pp. 1‐57.

Maddala, G. S., 1992, Introduction to Econometrics, 2nd edn. Macmillan, New York.

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