Calculate Durbin-Wu-Hausman endogeneity test after ivreg
ivendog [varlist]
ivendog is for use after ivreg or ivreg2; see help ivreg or help ivreg2 (if installed). The test is not valid with pweights, nor with the robust or cluster options of the original estimator, and will not be performed in these circumstances.
Description
ivendog computes a test for endogeneity in a regression estimated via instrumental variables (IV), the null hypothesis for which states that an ordinary least squares (OLS) estimator of the same equation would yield consistent estimates: that is, any endogeneity among the regressors would not have deleterious effects on OLS estimates. A rejection of the null indicates that endogenous regressors' effects on the estimates are meaningful, and instrumental variables techniques are required. The test was first proposed by Durbin (1954) and separately by Wu (1973) (his T4 statistic) and Hausman (1978). This "Durbin-Wu-Hausman" (DWH) test is numerically equivalent to the standard "Hausman test" obtained using hausman with the sigmamore option, in which both forms of the model must be estimated. Under the null, it is distributed Chi-squared with m degrees of freedom, where m is the number of regressors specified as endogenous in the original instrumental variables regression.
The ivendog output also contains another test statistic: the "Wu-Hausman" T2 statistic of Wu (1973). Hausman (1978) showed that the test could be calculated straightforwardly through the use of auxiliary regressions. The test statistic, under the null, is distributed F(m,N-k), where m is the number of regressors specified as endogenous in the original instrumental variables regression. A rejection indicates that the instrumental variables estimator should be employed. See Davidson and MacKinnon (1993, p. 237-240) and Wooldridge (2000, p. 483-484).
If the constant was excluded from ivreg or ivreg2, it will be excluded from the auxiliary regression.
As Davidson and MacKinnon (1993, p. 241-242) discuss, the test may be applied to a subset of the endogenous variables, maintaining those not specified as endogenous. In this form, the varlist contains those variables which are to be tested, and the degrees of freedom for the test refer to the number of variables listed.
These tests may also be computed by the orthog option of ivreg2. Although ivendog may not be applied to robust nor cluster estimates, ivreg2 may also be used to perform a heteroskedasticity-robust form of the test in either context, as well as in the GMM context.
The underlying computations for these tests are described in much greater detail in Baum, Schaffer, and Stillman (2003).
Examples
. use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz, clear . ivreg lwage exper expersq (educ = motheduc fatheduc) . ivendog
. ivreg lwage (exper educ = motheduc fatheduc huseduc) . ivendog . ivendog exper
References
Baum, C. F., Schaffer, M. E., Stillman, S., 2003, Instrumental variables and GMM: Estimation and testing. Stata Journal, Vol. 3, No. 1, pp. 1-31. Available as Working Paper no. 545, Boston College Department of Economics. http://fmwww.bc.edu/ec-p/WP545.pdf
Davidson, R. and MacKinnon, J., Estimation and Inference in Econometrics, 1993, New York: Oxford University Press.
Durbin, J., Errors in Variables, 1954, Review of the International Statistical Institute, Vol. 22, pp. 23-32.
Hausman, J., Specification Tests in Econometrics, 1978, Econometrica, Vol. 46, No. 6, pp. 1251-1271.
Wooldridge, J., Introductory Econometrics: A Modern Approach, 2000, New York: South-Western College Publishing.
Wu, D., 1973, Alternative Tests of Independence Between Stochastic Regressors and Disturbances, Econometrica, Vol. 41, No. 4, pp. 733-750.
Acknowledgements
We are grateful to Ronna Cong, Vince Wiggins, David Drukker, and an anonymous reviewer for critical review of this module. Errors remaining are our own.
Authors
Christopher F Baum, Boston College, USA baum@bc.edu
Mark E. Schaffer, Heriot-Watt University, UK M.E.Schaffer@hw.ac.uk Steven Stillman, New Zealand Department of Labour Steven.Stillman@lmpg.dol.govt.nz
Also see
Manual: [R] ivreg, [R] hausman On-line: help for ivreg, ivreg2 (if installed); hausman