Effects on inference of pretesting the exogeneity of a regressor

Ka-Fu, Wong

doi:10.1016/s0165-1765(97)00172-9

Cited by 9 publications

(13 citation statements)

References 6 publications

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“…Selection of a final estimator based on the results of a preliminary test is known as a pretest procedure. Inference based on the standard errors of the final selected estimator alone may be misleading; however, bootstrap techniques which include the model selection step can circumvent this problem (Wong, 1997).…”

Section: Comparison To Alternative Estimatorsmentioning

confidence: 99%

On the Fixed-Effects Vector Decomposition

Breusch

Ward²,

Nguyen³

et al. 2011

Polit. anal.

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This paper analyses the properties of the fixed-effects vector decomposition estimator, an emerging and popular technique for estimating time-invariant variables in panel data models with unit effects. This estimator was initially motivated on heuristic grounds, and advocated on the strength of favorable Monte Carlo results, but with no formal analysis. We show that the three-stage procedure of this decomposition is equivalent to a standard instrumental variables approach, for a specific set of instruments. The instrumental variables representation facilitates the present formal analysis which finds: (1) The estimator reproduces exactly classical fixed-effects estimates for time-varying variables. (2) The standard errors recommended for this estimator are too small for both time-varying and time-invariant variables. (3) The estimator is inconsistent when the time-invariant variables are endogenous. (4) The reported sampling properties in the original Monte Carlo evidence are incorrect. (5) We recommend an alternative shrinkage estimator that has superior risk properties to the decomposition estimator, unless the endogeneity problem is known to be small or no relevant instruments exist.

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Section: Comparison To Alternative Estimatorsmentioning

confidence: 99%

On the Fixed-Effects Vector Decomposition

Breusch

Ward²,

Nguyen³

et al. 2011

Polit. anal.

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show abstract

“…In these cases, negligible amounts of endogeneity may be difficult to detect with our test. This can lead to poor size properties when conducting inference using OLS estimates of the β j parameters as discussed by Wong (1997) and Guggenberger (2010) who study this issue in the context of linear models and use of the Hausman test to determine exogeneity. Monte Carlo results presented in Online Appendix B suggest caution when using OLS estimates for inference -even if our test fails to reject exogeneity -if the instruments are relatively weak.…”

Section: And Letmentioning

confidence: 99%

“…In an analogous context with a linear relationship between the outcome variable and endogenous regressor, Wong (1997) and Guggenberger (2010) We also report average point estimates and their standard deviations for OLS and 2SLS estimators from the mis-specified linear-in-schooling model, as well as the re-weighted OLS estimates from the more general model that allows for varying grade-specific effects. The next column reports the fraction of cases in which we reject the null hypothesis of equality between the IV and re-weighted OLS estimates using the exogeneity test given in Theorem 1 (.05 significance level).…”

Section: Inference In a Two Stage Approachmentioning

confidence: 99%

“…In these cases, the researcher is likely to conclude from our test that schooling is exogenous, which then suggests that the OLS estimates of the β j parameters from equation (2) are consistent. However, as Wong (1997) and Guggenberger (2010) point out (when using the standard Hausman test in the first stage), inference using the OLS estimates is likely to have poor size properties. Even a negligible amount of endogeneity (too small to cause our test to reject exogeneity) is likely to lead one to reject plimB = B when using the OLS estimates.…”

Section: Inference In a Two Stage Approachmentioning

confidence: 99%

“…6 Specifically, Wong (1997) and Guggenberger (2010) provide simulation evidence (in a linear regression model like equation 1) for the null rejection probability of a simple hypothesis test conditional on a standard Hausman pretest for exogeneity not rejecting. Their findings indicate that when regressor endogeneity is small, the null rejection probability of the hypothesis test may be substantially higher than the nominal size if the instruments are not sufficiently strong.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimating and Testing Models with Many Treatment Levels and Limited Instruments

Lochner

Moretti

2011

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Many empirical microeconomic studies estimate econometric models that assume a single finite-valued discrete endogenous regressor (for example: different levels of schooling), exogenous regressors that are additively separable and enter the equation linearly; and coefficients (including per-unit treatment effects) that are homogeneous in the population. Empirical researchers interested in the causal effect of the endogenous regressor often use instrumental variables. When few valid instruments are available, researchers typically estimate restricted specifications that impose uniform per-unit treatment effects, even when these effects are likely to vary depending on the treatment level. In these cases, ordinary least squares (OLS) and instrumental variables (IV) estimators identify different weighted averages of all per-unit effects, so the traditional Hausman test (based on the restricted specification) is uninformative about endogeneity. Addressing this concern, we develop a new exogeneity test that compares the IV estimate from the restricted model with an appropriately weighted average of all per-unit effects estimated from the more general model using OLS. Notably, our test works even when the true model cannot be estimated using IV methods as long as a single valid instrument is available (e.g. a single binary instrument). We re-visit three recent empirical examples that examine the role of educational attainment on various outcomes to demonstrate the practical value of our test.

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The Hausman pretest estimator

Chmelarova

Hill

2010

Economics Letters

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Effects on inference of pretesting the exogeneity of a regressor

Cited by 9 publications

References 6 publications

On the Fixed-Effects Vector Decomposition

On the Fixed-Effects Vector Decomposition

Estimating and Testing Models with Many Treatment Levels and Limited Instruments

The Hausman pretest estimator

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