Hausman tests

Lag periods Fixed-effect model Random-effect model Hausman test... 

Results based on both fixed effects and random effects, with P-values from the Hausman tests, are shown in Table 13.2. The Hausman tests indicated that, in this context, a random-effect framework was more appropriate. 

The Hausman test was used to test the null hypothesis that the coefficients estimated by the efficient random-effect model are the same as the ones estimated by the consistent fixed-effect model. If this null hypothesis cannot be rejected (insignificant P-value in general, it is larger than 0.05), then the random-effect model is more appropriate. 

The consumption function used in Example 5.3 is a very simple specification. One might wonder if the meager specification of the model could help explain the finding in the Hausman test. The data set used for the example are given in Table F5.1. Use these data to carry out the test in a more elaborate specification... 

In the panel data models estimated in Example 21.5.1, neither the logit nor the probit model provides a framework for applying a Hausman test to determine whether fixed or random effects is preferred. Explain. (Hint Unlike our application in the linear model, the incidental parameters problem persists here.) Look at the two cases. Neither case has an estimator which is consistent in both cases. In both cases, the unconditional fixed effects effects estimator is inconsistent, so the rest of the analysis falls apart. This is the incidental parameters problem at work. Note that the fixed effects estimator is inconsistent because in both models, the estimator of the constant terms is a function of 1/T. Certainly in both cases, if the fixed effects model is appropriate, then the random effects estimator is inconsistent, whereas if the random effects model is appropriate, the maximum likelihood random effects estimator is both consistent and efficient. Thus, in this instance, the random effects satisfies the requirements of the test. In fact, there does exist a consistent estimator for the logit model with fixed effects - see the text. However, this estimator must be based on a restricted sample observations with the sum of the ys equal to zero or T muust be discarded, so the mechanics of the Hausman test are problematic. This does not fall into the template of computations for the Hausman test. 

Results of the computations are shown below. The Hausman statistic is 25.1 and the t statistic for the Wu test is -5.3. Both are larger than the table critical values by far, so the hypothesis that least squares is consistent is rejected in both cases. 

Corr[v(i,t),v(i, s)] = Lagrange Multiplier Test vs. Model ( 1 df, prob value = 0.000000) Fixed vs. Random Effects (Hausman)... 

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