financial econometrics ver1

8/6/2019 Financial Econometrics Ver1

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Short-run and Long-run relationship between Producer Price Index (PPI) and Consumer

Price Index (CPI)

(An Individual Assignment)

By

J.B.A. Ravinath Niroshana (2009/MBA/WE/71)

Semester III First Half

January 2011

Course: MBAFI 616 - Financial Econometrics

Lecturer: Dr. Prabath Jayasinghe

Postgraduate & Mid-Career Development Unit

Faculty of Management & Finance

University of Colombo

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Time Series

Consumer Price Index (CPI) for all urban consumers and Producer Price Index (PPI) for all

commodities in U.S.A, have been used for analyze the long-run and short-run relationship

between the two variables. The source for above data is

U.S. Department of Labor: Bureau of Labor Statistics and I have used monthly data from year

1913 to year 2010 for perform this analysis.

Augmented Dickey Fuller (ADF) test as a Stationery Test

Unit root test for CPI With 0 differences, no trend and no intercept

Null Hypothesis: CPI has a unit rootExogenous: Constant

Lag Length: 11 (Automatic - based on SIC, maxlag=22)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic 4.072955 1.0000

Test critical values: 1% level -3.4358065% level -2.863837

10% level -2.568044

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(CPI)Method: Least Squares

Sample (adjusted): 1914M01 2010M01Included observations: 1153 after adjustments

R-squared 0.421991 Mean dependent var 0.179260Adjusted R-squared 0.415907 S.D. dependent var 0.379788

S.E. of regression 0.290256 Akaike info criterion 0.375107

Sum squared resid 96.04362 Schwarz criterion 0.432047

Log likelihood -203.2491 Hannan-Quinn criter. 0.396598

F-statistic 69.35730 Durbin-Watson stat 2.018762Prob(F-statistic) 0.000000

Figure: 1 ADF test EViews output for the

regression

Since the computed ADF test-statistics (4.072955) is greater thanthe critical values at 1%, 5%, 10% significant level), we cannot

reject Ho and conclude unit root exists. Hence CPI is a non-

stationary series. Figure: 2 Graph for the regression

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0

40

80

120

160

00

40

PPI

By introducing trend and intercept also the series did not become stationary with 0 differences.

Further now Durbin-Watson Stat is 2.018762 and it is approximately equal to 2 and hence we

can trust the regression results.

Unit root test for PPI With 0 differences, no trend and no intercept

According to figure 3(Refer Annexure 2) we can observe that

computed ADF test-statistics ( 4.773238) is greater than

the critical values at 1%, 5% and 10% significant level,

respectively, we cannot reject Ho . Hence conclude unit

root exists and PPI is a non-stationary series. By

introducing trend and intercept also the series did not

become stationary with 0 differences. . Further now

Durbin-Watson Stat is 1.981003 and it is approximately

equal to 2 and hence we can trust the regression results.

Figure: 4

Transforming from non-stationary to stationary

Difference-Stationery Process (DSP) has been used to transform above non stationary data series

to stationary data series.

Transforming from non-stationary to stationary CPI

By using level one difference and introducing trend and intercept the CPI series become

stationary

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Figure: 5

The

computed

ADF test-

statistic (-

4.463067) is

smaller than the critical values at 10%, 5%, 1% significant

level, respectively, therefore we reject Ho. It means the CPI series is a stationary series at 1%,

10% and 5% significant level and it is an I (1) series.

Figure: 6 Stationary Graphs

Transforming from non-stationary to stationary PPI

As per the figure 7(Refer annexure 3) the computed ADF

test-statistic (-15.24086) is smaller than the critical values

at 10%, 5%, 1% significant level, respectively, thereforewe reject Ho. It means the Wages series is a stationary

series at 1%, 10% and 5% significant level and it is a I (1)

series.

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Null Hypothesis: D(CPI) has a unit root

Exogenous: Constant


t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -4.463067 0.0002

Test critical values: 1% level -3.435811

5% level -2.863840

10% level -2.568045



Dependent Variable: D(CPI,2)

Method: Least Squares

Sample (adjusted): 1914M02 2010M01

Included observations: 1152 after adjustments

R-squared 0.293248 Mean dependent var 0.000641

Adjusted R-squared 0.285802 S.D. dependent var 0.344938




F-statistic 39.38317 Durbin-Watson stat 1.993260


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Therefore it can be concluded that both series are in same Figure 8 Stationary Graphs

order as they become stationary at first difference.

Regression Analysis

Regression analysis is performed for observe the relationship between two series PPI and CPI.

Dependent Variable: PPI


Sample: 1913M01 2010M01

Included observations: 1165

Variable Coefficient Std. Error t-Statistic Prob.

CPI 0.785172 0.003226 243.3735 0.0000

C 7.437830 0.288092 25.81759 0.0000







Prob(F-statistic) 0.000000

Figure 9

As shown in below EViews output the residuals are non stationary at level 0.

Null Hypothesis: RESID01 has a unit root

Exogenous: None


t-Statistic Prob.*



5% level -1.941097

10% level -1.616515



Dependent Variable: D(RESID01)








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Durbin-Watson stat 1.986633

Figure 10

The computed ADF test-statistic (-2.457178) is greater than the critical values (-4.07 -3.37 -3.03)

according to EG tables, we dont reject Ho. It means the residual series is a non stationary series

at 1%, 10% and 5% significant level which is not I (0). However series become stationary at

level 1.

Since the residuals are not stationary at level 0, there is no long term relationship between two

series PPI and CPI.

However we can observe a short run relationship between two variables.

The regression line

PPI= 1.69CPI -0.15

According to the regression line, for every unit increase in CPI will increase 1.69 units in PPI. At

the same time PPI=(-0.15), even the CPI is 0.

As R- squared is a 0.98 we can say that 98% of the changes PPI can be described by the CPI.

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References & Bibliography

Gujarati, D.N, & Sangetha. (2010). Basic Econometrics: McGraw Hill

Hirschey, M (2009), Managerial Economics: An integrative

Approach,Cengage Learning, India.

Lipsey, R.G. (1968),An Introduction to Positive Economics,LPE India edition

Lipsey, R.G. & Cheristal,K.A. (2009) Economics, Oxford university press,

Oxford.

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Annexure:2

Null Hypothesis: DPPI has a unit root

Exogenous: Constant


t-Statistic Prob.*



5% level -2.863824

10% level -2.568037



Dependent Variable: D(DPPI)




R-squared 0.336401 Mean dependent var 0.003279Adjusted R-squared 0.333523 S.D. dependent var 0.958080





Prob(F-statistic) 0.000000

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Figure: 3 ADF test EViews output for the regression

Annexure:3

Null Hypothesis: PPI has a unit root

Exogenous: None


t-Statistic Prob.*

Augmented Dickey-Fuller test statistic 4.773238 1.0000


5% level -1.941097

10% level -1.616515



Dependent Variable: D(PPI)









Durbin-Watson stat 1.981003

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Figure: 7 ADF test EViews output for the regression

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