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IMPORTANT TESTS FOR PANEL DATA MODELLING
Hausmann test: Comparing the RE and FE estimates, if the estimates are statistically different, then the RE assumption is probably invalid. In this case FE has to be used. Otherwise, RE is more efficient. Breusch and Pagan test: This is to test the hypothesis that there are no random effects
THE SAMPLE PROBLEMS
The determinants of FDI inflows in India:
Dependent variable: FDI
Independent variables: Power; Education; Health; Transport; Research and Development; Domestic Investment; Profit; Risk
THE MODELLING PROCESS
The general framework of panel data model is as follows:
jit i it
p
Yit 1 j 2 jX t
The fixed effects regression model is of three different forms: within-group fixed effect model, first difference fixed effect model and least square dummy variable (LSDV) fixed effects model.
The within-group fixed effects model is in following form:
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Yit Yi j p 2 j Xjit Xji ( t t ) it i
This is known as the within groups regression model because it is explaining the variations about the mean of the dependent variable in terms of the variations about the means of the explanatory variables for the group of observations relating to a given individual.
The first difference fixed effect model is as follows:
2 jit it it 1
p
Yit j j X
Here the unobserved effect is eliminated by subtracting the observations for the previous time period from the observation for the current time period, for all time periods.
The LSDV regression model is as follows:
i it
n jit i i
p
Yit 1 j 2 jX t 1 Z
Here, the unobserved effect is brought explicitly into the model. Zi is considered as dummy variable, where it is equal to 1 in the case of an observation relating to individual I and 0 otherwise. Formally, the unobserved effect is being treated as the coefficient of the individual- specific dummy variable. The weight of αi Zi represents the fixed effect on the dependent variable Yi for individual i.
It is to be noted that when the variables of interest are constant for each individual, a fixed effects regression is not an effective tool because such variables cannot be included. So the alternative approach is the use of random effect regression model. It has two conditions. First, Zi should be drawn randomly from a given distribution> This may well be the case if the individual
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**Results of Panel Data Model
Test Statistics Fixed Effect Model Random Effect Model ========================================================================**
Intercept 0.51 [0.58] 0.33 [0.31] PWR 0.03 [0.02] 0.004 [0.01] EDU -1.00 [0. 8] -0.01 [0.33] HEA 1.42 [0.24] -0.188 [0.13] TRA 0.52 [0.44] 0.834 [0.65] R&D -0.56 [0.8] 3.04 [0.71] DOI 0.01 [0.00] 0.01 [0.00] PRO 0.03 [0.02] 0.024 [0.01] RIS -0.06 [0.06] -0.053 [0.03] R^2 (within) 0.20 0. R^2 (between) 0.001 0. R^2 (overall) 0.0001 0. HFR 5. BPL 6. ========================================================================
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REFERENCES FOR FURTHER READING:
Montgomery, D. C., Peck, E. A., and G. G. Vining: Introduction to Linear Regression Analysis , Wiley India, New York, 2006.
Dielman, Terry E.: Applied Regression Analysis for Business and Economics, PWS-Kent, Boston, 1991.
Draper, N. R., and H. Smith: Applied Regression Analysis, 3d ed., John Wiley & Sons, New York, 1998.
Frank, C. R., Jr.: Statistics and Econometrics, Holt, Rinehart and Winston, New York, 1971.
Goldberger, Arthur S.: Introductory Econometrics, Harvard University Press, 1998.
Graybill, F. A.: An Introduction to Linear Statistical Models , vol. 1, McGraw- Hill, New York,
Greene, William H.: Econometric Analysis, 4th ed., Prentice Hall, Englewood Cliffs, N. J., 2000.
Griffiths, William E., R. Carter Hill and George G. Judge: Learning and Practicing Econometrics, John Wiley & Sons, New York, 1993.
Gujarati, Damodar N.: Essentials of Econometrics, 2d ed., McGraw-Hill, New York, 1999.
Hill, Carter, William Griffiths, and George Judge: Undergraduate Econometrics, John Wiley & Sons, New York, 2001.
Johnston, J.: Econometric Methods, 3d ed., McGraw-Hill, New York, 1984.
Katz, David A.: Econometric Theory and Applications, Prentice Hall, Englewood Cliffs, N.J.,
Koop, Gary: Analysis of Economic Data, John Wiley & Sons, New York, 2000.
Koutsoyiannis, A.: Theory of Econometrics, Harper & Row, New York, 1973.
Maddala, G. S.: Introduction to Econometrics, John Wiley & Sons, 3d ed., New York, 2001.
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a) FEM and REM estimators differ substantially b) FEM and REM estimators differ do not substantially c) FEM and REM estimators are equal to zero d) FEM and REM estimators are not equal to zero e) None of the above
- Hausman test statistics follows a) Normal distribution b) T distribution c) Chi‐square distribution d) F distribution e) None of the above
SELF EVALUATION TESTS/ QUIZZES
- In 1985, neither Florida nor Georgia had laws banning open alcohol containers in vehicle passenger compartments. By 1990, Florida had passed such a law, but Georgia had not. a) Suppose you can collect random samples of the driving-age population in both states, for 1985 and 1990. Let arrest be a binary variable equal to unity if a person was arrested for drunk driving during the year. Without controlling for any other factors, write down a linear probability model that allows you to test whether the open container law reduced the probability of being arrested for drunk driving. Which coefficient in your model measures the effect of the law? b) Why might you want to control for other factors in the model? What might some of these factors be?
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- What is meant by an error components model (ECM)? How does it differ from FEM? When is ECM appropriate? And when is FEM appropriate?
- In order to determine the effects of collegiate athletic performance on applicants, you collect data on applications for a sample of Division I colleges for 1985, 1990, and 1995. a) What measures of athletic success would you include in an equation? What are some of the timing issues? b) What other factors might you control for in the equation? c) Write an equation that allows you to estimate the effects of athletic success on the percentage change in applications. How would you estimate this equation? Why would you choose this method?
- Suppose that, for one semester, you can collect the following data on a random sample of college juniors and seniors for each class taken: a standardized final exam score, percentage of lectures attended, a dummy variable indicating whether the class is within the student’s major, cumulative grade point average prior to the start of the semester, and SAT score. a) Why would you classify this data set as a cluster sample? Roughly how many observations would you expect for the typical student? b) If you pool all of the data together and use OLS, what are you assuming about unobserved student characteristics that affect performance and attendance rate? What roles do SAT score and prior GPA play in this regard? c) If you think SAT score and prior GPA do not adequately capture student ability, how would you estimate the effect of attendance on final exam performance?
