References—191
Dependent Variable: CS
Method: Least Squares
Date: 08/10/09 Time: 16:46
Sample (adjusted): 1947Q2 1995Q1
Included observations: 192 after adjustments
Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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|
C |
-1413.901 |
130.6449 |
-10.82247 |
0.0000 |
GDP |
5.131858 |
0.472770 |
10.85486 |
0.0000 |
CS(-1) |
0.977604 |
0.018325 |
53.34810 |
0.0000 |
CS1F |
-7.240322 |
0.673506 |
-10.75020 |
0.0000 |
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|
|
R-squared |
0.999836 |
Mean dependent var |
1962.779 |
|
Adjusted R-squared |
0.999833 |
S.D. dependent var |
854.9810 |
|
S.E. of regression |
11.04237 |
Akaike info criterion |
7.661969 |
|
Sum squared resid |
22923.56 |
Schwarz criterion |
7.729833 |
|
Log likelihood |
-731.5490 |
Hannan-Quinn criter. |
7.689455 |
|
F-statistic |
381618.5 |
Durbin-Watson stat |
2.260786 |
|
Prob(F-statistic) |
0.000000 |
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The fitted values are again statistically significant and we reject model H2 .
In this example, we reject both specifications, against the alternatives, suggesting that another model for the data is needed. It is also possible that we fail to reject both models, in which case the data do not provide enough information to discriminate between the two models.
References
Andrews, Donald W. K. (1993). “Tests for Parameter Instability and Structural Change With Unknown Change Point,” Econometrica, 61(4), 821–856.
Andrews, Donald W. K. and W. Ploberger (1994). “Optimal Tests When a Nuisance Parameter is Present Only Under the Alternative,” Econometrica, 62(6), 1383–1414.
Breusch, T. S., and A. R. Pagan (1979). “A Simple Test for Heteroskedasticity and Random Coefficient Variation,” Econometrica, 48, 1287–1294.
Brown, R. L., J. Durbin, and J. M. Evans (1975). “Techniques for Testing the Constancy of Regression Relationships Over Time,” Journal of the Royal Statistical Society, Series B, 37, 149–192.
Davidson, Russell and James G. MacKinnon (1989). “Testing for Consistency using Artificial Regressions,” Econometric Theory, 5, 363–384.
Davidson, Russell and James G. MacKinnon (1993). Estimation and Inference in Econometrics, Oxford: Oxford University Press.
Engle, Robert F. (1982). “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation,” Econometrica, 50, 987–1008.
Glejser, H. (1969). “A New Test For Heteroscedasticity,” Journal of the American Statistical Association, 64, 316–323.
Godfrey, L. G. (1978). “Testing for Multiplicative Heteroscedasticity,” Journal of Econometrics, 8, 227– 236.
192—Chapter 23. Specification and Diagnostic Tests
Godfrey, L. G. (1988). Specification Tests in Econometrics, Cambridge: Cambridge University Press.
Hansen, B. E. (1997). “Approximate Asymptotic P Values for Structural-Change Tests,” Journal of Business and Economic Statistics, 15(1), 60–67.
Harvey, Andrew C. (1976). “Estimating Regression Models with Multiplicative Heteroscedasticity,” Econometrica, 44, 461–465.
Hausman, Jerry A. (1978). “Specification Tests in Econometrics,” Econometrica, 46, 1251–1272.
Johnston, Jack and John Enrico DiNardo (1997). Econometric Methods, 4th Edition, New York: McGrawHill.
Koenker, R. (1981). “A Note on Studentizing a Test for Heteroskedasticity,” Journal of Econometrics, 17, 107–112.
Longley, J. W. “An Appraisal of Least Squares Programs for the Electronic Computer from the Point of View of the User,” Journal of the American Statistical Association, 62(319), 819-841.
Ramsey, J. B. (1969). “Tests for Specification Errors in Classical Linear Least Squares Regression Analysis,” Journal of the Royal Statistical Society, Series B, 31, 350–371.
Ramsey, J. B. and A. Alexander (1984). “The Econometric Approach to Business-Cycle Analysis Reconsidered,” Journal of Macroeconomics, 6, 347–356.
White, Halbert (1980).“A Heteroskedasticity-Consistent Covariance Matrix and a Direct Test for Heteroskedasticity,” Econometrica, 48, 817–838.
Wooldridge, Jeffrey M. (1990). “A Note on the Lagrange Multiplier and F-statistics for Two Stage Least Squares Regression,” Economics Letters, 34, 151-155.
Wooldridge, Jeffrey M. (2000). Introductory Econometrics: A Modern Approach. Cincinnati, OH: SouthWestern College Publishing.