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
Lag Length: 11 (Automatic - based on SIC, maxlag=22)
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
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
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
S.E. of regression 0.291508 Akaike info criterion 0.383722
Sum squared resid 96.78872 Schwarz criterion 0.440702
Log likelihood -208.0240 Hannan-Quinn criter. 0.405229
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
Method: Least Squares
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
R-squared 0.980743 Mean dependent var 57.62412
Adjusted R-squared 0.980726 S.D. dependent var 49.46171
S.E. of regression 6.866729 Akaike info criterion 6.692968
Sum squared resid 54837.74 Schwarz criterion 6.701656
Log likelihood -3896.654 Hannan-Quinn criter. 6.696245
F-statistic 59230.66 Durbin-Watson stat 0.010407
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
Lag Length: 5 (Automatic - based on SIC, maxlag=22)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.457178 0.0136
Test critical values: 1% level -2.566959
5% level -1.941097
10% level -1.616515
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(RESID01)
Method: Least Squares
Sample (adjusted): 1913M07 2010M01
Included observations: 1159 after adjustments
R-squared 0.171635 Mean dependent var 0.006521
Adjusted R-squared 0.168043 S.D. dependent var 0.701988
S.E. of regression 0.640295 Akaike info criterion 1.951389
Sum squared resid 472.7047 Schwarz criterion 1.977560
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Log likelihood -1124.830 Hannan-Quinn criter. 1.961264
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
Lag Length: 4 (Automatic - based on SIC, maxlag=22)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -15.24086 0.0000
Test critical values: 1% level -3.435777
5% level -2.863824
10% level -2.568037
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(DPPI)
Method: Least Squares
Sample (adjusted): 1913M07 2010M01
Included observations: 1159 after adjustments
R-squared 0.336401 Mean dependent var 0.003279Adjusted R-squared 0.333523 S.D. dependent var 0.958080
S.E. of regression 0.782157 Akaike info criterion 2.351642
Sum squared resid 705.3712 Schwarz criterion 2.377813
Log likelihood -1356.777 Hannan-Quinn criter. 2.361517
F-statistic 116.8989 Durbin-Watson stat 1.976273
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
Lag Length: 5 (Automatic - based on SIC, maxlag=22)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 4.773238 1.0000
Test critical values: 1% level -2.566959
5% level -1.941097
10% level -1.616515
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(PPI)
Method: Least Squares
Sample (adjusted): 1913M07 2010M01
Included observations: 1159 after adjustments
R-squared 0.230367 Mean dependent var 0.146678
Adjusted R-squared 0.227029 S.D. dependent var 0.886584
S.E. of regression 0.779474 Akaike info criterion 2.344769
Sum squared resid 700.5394 Schwarz criterion 2.370939
Log likelihood -1352.793 Hannan-Quinn criter. 2.354644
Durbin-Watson stat 1.981003
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Figure: 7 ADF test EViews output for the regression
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