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 N1 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
Rsquared
=
.2451121


Adjusted Rsquared
=
.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.
.674093E01 
 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
Rsquared
=
.9054373


Adjusted Rsquared
=
.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]
=
.235188D01


Var[u]
=
.137422D+00


Corr[v(i,t),v(i,s)] =
.853867

 Lagrange Multiplier Test vs. Model (3) = 4352.48 
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 Fall '11
 WillamGreene
 Random effects model, random effects, effects model, Wooldridge

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