Cointegration of Consumption and Income 3

8/14/2019 Cointegration of Consumption and Income 3

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The co-interaction of consumption and income

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=1+2YD t+ t

Where:Ct(GC)= Consumption Expenditure

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 long- run relationship

between two variables

Data sources and description

Due to time and scope, quarterly time series data from 1954.1 to 1995.21


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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.

Descriptive statistics of each variable:

Date:11/15/09

Time: 12:22Sample: 1954:1 1995:2

GC GYD

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

Jarque-Bera 23.62498 22.38407Probability 0.000007 0.000014

Observations

166 166


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GYD

Model Estimation

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

ADF Test Statistic 9.623256

1% CriticalValue*

-3.4713

5% Critical Value -2.879110% Critical Value -2.5760

*MacKinnon critical values for rejection of hypothesis of aunit root.

Augmented Dickey-Fuller Test EquationDependent Variable: D(GC)

Method: Least SquaresDate: 11/15/09 Time: 13:01Sample(adjusted): 1954:3 1995:2Included observations: 164 after adjusting endpoints

Variable Coefficient

Std. Error t-Statistic Prob.

GC(-1) 0.014044

0.001459 9.623256 0.0000

D(GC(-1)) 0.02290 0.079927 0.286596 0.7748


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738.0990

1

Durbin-Watsonstat

1.912886

Prob(F-statistic) 0.000000

Vector Error Correction Estimates:

Date: 11/15/09 Time: 13:16Sample(adjusted): 1954:4 1995:2Included observations: 163 afteradjusting

endpointsStandard errors & t-statistics inparentheses

CointegratingEq: CointEq1

D(GC(-1)) 1.000000

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

(-25.5512)

C 0.825001

ErrorCorrection:

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 0.710258Adj. R-squared

0.451293 0.704791

Sum sq.resids

41319.57 51269.99

S.E. equation 16.12053 17.95697


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F-statistic 45.41319 129.9214Log likelihood -682.4173 -700.0025Akaike AIC 8.422298 8.638068Schwarz SC 8.498218 8.713988Meandependent

0.408840 0.087730

S.D.dependent

21.76252 33.04977

Determinant ResidualCovariance

72079.53

Log Likelihood -1374.194Akaike InformationCriteria

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


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equation model.

Acknowledgement

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

contribution and his moral assistance.

References.

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

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


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Appendix


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Cointegration of Consumption and Income 3

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