When to use random effect estimator fixed effect estimator...

Name: when to use random effect estimator fixed effect estimator pooled ols estimator first difference estimator between estimator explain when to use these methods 53897
Uploaded: 2024-07-15T03:25:45-08:00
Duration: 1 min 26 s
Channel: Breanna Ollech
Description: when to use random effect estimator fixed effect estimator pooled ols estimator first difference estimator between estimator explain when to use these methods 53897

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Using your own words, explain how to choose between the Random effects and pooled Ordinary least squares approaches. State the weakness of the test you will use.

Breanna O.

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Consider the linear panel data model with individual-specific 'fixed' effects: yit = ̑i + ̒xit + uit Where i = 1,2, ..., N indexes individuals/firms/states/etc and t = 1, ..., T indexes time periods. Suppose that the error terms uit are "strictly exogenous for given i", i.e., E(uit|xi1, xi2, ..., xiT) = 0. a) Suppose we run a 'pooled OLS' regression, i.e., ignore ̑i and run a regression of yit on xit using the full sample of NT observations. Note that, if we do this, the 'error term' in this regression is vit = ̑i + uit. Show that the slope estimator ̒OLS is consistent if and only if Cov(̑i, xit) = 0. b) Define first differences as Δyit = yit − yit−1 (and similarly for Δxit and Δuit). Show that Δyit = ̒Δxit + Δuit, and that Cov(Δxit, Δuit) = 0. (So the slope estimate from regressing Δyit on Δxit is consistent). Consider the 'within transformation' ȳi = (1/T)Σt=1 to T yit, ȓi = (1/T)Σt=1 to T xit, ũi = (1/T)Σt=1 to T uit ÿit = yit − ȳi, ẉit = xit − ȓi, üit = uit − ũi As we said in class, the slope coefficient from a regression of ÿit on ẉit has become known in econometrics as ̒FE, the 'fixed effects estimator'. c) Using the definitions above, show that ȳi = ̑i + ̒ȓi + ũi. d) Explain why the 'between estimator', i.e. the slope coefficient ̒BE from a regression of ȳi on ȓi, has the same problem we saw for ̒OLS in part a). e) Show using the definitions above that ÿit = ̒ẉit + üit. In other words, by writing the model in terms of within-transformed y and x, we eliminate ̑i from the model. (This implies that ̒FE is consistent even when Cov(̑i, xit) ≠ 0!) f) Suppose that the original error terms uit are homoscedastic and serially uncorrelated, i.e. Var(uit|X) = σu^2, Cov(uit, uis|X) = 0 for any t ≠ s Again using the definitions above, what is Cov(üit, üis|X)? (Hint: It is not zero! This is why, when using fixed effects estimators, we always employ 'clustered' standard errors, which allow correlation across time periods within a given i.)

Sri K.

This question assumes that you have access to a statistical package that computes standard errors robust to arbitrary serial correlation and heteroskedasticity for panel data methods. (i) For the pooled OLS estimates in Table $14.1,$ obtain the standard errors that allow for arbitrary serial correlation (in the composite errors, $v_{i t}=a_{i t}+u_{i t} )$ and heteroskedasticity. How do the robust standard errors for educ, married, and union compare with the nonrobust ones? (ii) Now obtain the robust standard errors for the fixed effects estimates that allow arbitrary serial correlation and heteroskedasticity in the idiosyncratic errors, $u_{i r}$ . How do these compare with the nonrobust FE standard errors? (iii) For which method, pooled OLS or FE, is adjusting the standard errors for serial correlation more important? Why?

Transcript

00:01 The random effects model assumes that the individual effects are uncorrelated with the independent variables, while the pooled ordinary least squares approach assumes that there are no individual specific effects.

00:16 To choose between these two tests, we're going to use the hosman's test, and this test compares the the estimates.

00:25 If the estimates are significantly different, it suggests that the individual effects are correlated with the independent variables and thus the random effects test would be most appropriate.

00:40 If they are not statistically different, then it suggests that there are no specific effects in the pols model is more appropriate...

Question

when to use random effect estimator, fixed effect estimator, pooled ols estimator, first difference estimator, between estimator? explain when to use these methods?

Question

when to use random effect estimator, fixed effect estimator, pooled ols estimator, first difference estimator, between estimator? explain when to use these methods?

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