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PanelDataProblemSet2

# PanelDataProblemSet2 - Department of Economics Econometric...

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Econometric Analysis of Panel Data Assignment 2 Part I. Interpreting Regression Results The results below show OLS, fixed effects and random effects estimates for a reduced version of the model analyzed in Assignment 1 (using the Cornwell and Rupert data). 1. Test the hypothesis of ‘no effects’ vs. ‘some effects’ using the results given below. 2. Explain in precise detail the difference between the fixed and random effects models. 3. Carry out the Hausman test for fixed effects against the null hypothesis of random effects and report your conclusion. Carefully explain what you are doing in this test. 4. In the context of the fixed effects model, test the hypothesis that there are no effects – i.e., that all individuals have the same constant term. (The statistics you need to carry out the test are given in the results.) 5. Using the fixed effects estimator, test the hypothesis that all of the coefficients in the model save for the constant term are zero. Show all computations, and the appropriate degrees of freedom for F . 6. Discuss the impact of adding the individual dummy variables to the model – in terms of the substantive change (or lack of) in the estimated results. Part II. Fixed Effects Normalization Some researchers (such as your professor) prefer to fit the conventional fixed effects model (estimator) by having exactly one dummy variable in the model for each individual. In some other cases, the researchers prefer to have a single overall constant and a set of N-1 individual dummy variables, i.e., dropping one of the individual constants to avoid the collinearity problem. A third way to proceed is to include an overall constant and the full set of dummy variables, but constrain the dummy variable coefficients to sum to zero. How does this manipulation of the dummy variable coefficients affect the least squares estimates of the other coefficients in the model and the fit of the equation, i.e., R 2 ? Department of Economics

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+----------------------------------------------------+ | OLS Without Group Dummy Variables | | LHS=LWAGE Mean = 6.676346 | | Standard deviation = .4615122 | | Model size Parameters = 5 | | Degrees of freedom = 4160 | | Residuals Sum of squares = 669.5138 | | Standard error of e = .4011743 | | Fit R-squared = .2451121 | | Adjusted R-squared = .2443862 | +----------------------------------------------------+ +----------------------------------------------------+ | Panel Data Analysis of LWAGE [ONE way] | | Unconditional ANOVA (No regressors) | | Source Variation Deg. Free. Mean Square | | Between 646.254 594. 1.08797 | | Residual 240.651 3570. .674093E-01 | | Total 886.905 4164. .212994 | +----------------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ OCC -.36608081 .01346550 -27.187 .0000 .51116447 UNION .11154686 .01402315 7.954 .0000 .36398559 MS .32218316 .01629572 19.771 .0000 .81440576 EXP .00805812 .00057594 13.991 .0000 19.8537815 Constant 6.40050047 .01785232 358.525 .0000 +----------------------------------------------------+ | Least Squares with Group Dummy Variables | | Model size Parameters = 599 | | Degrees of freedom = 3566 | | Residuals Sum of squares = 83.86816 | | Standard error of e = .1533585 | | Fit R-squared = .9054373 | | Adjusted R-squared = .8895796 | +----------------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ OCC -.02406298 .01384128 -1.738 .0821 .51116447 UNION .03515301 .01502985 2.339 .0193 .36398559 MS -.03226210 .01909579 -1.689 .0911 .81440576 EXP .09672164 .00119030 81.258 .0000 19.8537815 +--------------------------------------------------+ | Random Effects Model: v(i,t) = e(i,t) + u(i) | | Estimates: Var[e] = .235188D-01 | | Var[u] = .137422D+00 | | Corr[v(i,t),v(i,s)] = .853867 | | Lagrange Multiplier Test vs. Model (3) = 4352.48 |
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PanelDataProblemSet2 - Department of Economics Econometric...

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