Calculate tests of overidentifying restrictions after ivreg, ivreg2, ivprobit, > ivtobit, reg3
overid [, chi2 dfr f all depvar(varname)]
overid may be used after IV estimation with aweights, fweights and iweights; see help weights.
Description
+-----------------------------------+ ----+ Instrumental variables regression +--------------------------------
overid computes versions of Sargan's (1958) and Basmann's (1960) tests of overidentifying restrictions for a regression estimated via instrumental variables in which the number of instruments exceeds the number of regressors: that is, for an overidentified equation. These are tests of the joint null hypothesis that the excluded instruments are valid instruments, i.e., uncorrelated with the error term and correctly excluded from the estimated equation. A rejection casts doubt on the validity of the instruments.
For single-equation (limited-information) instrumental variables regression (as implemented in ivreg or ivreg2), write the full set of instruments as Z and the residuals from the IV estimation as u, let P represent the "projection matrix" Z*inv(Z'Z)*Z', and let M=I-P, where I is the identity matrix. N is the number of observations, L the number of instruments, K the number of regressors, and L-K the number of overidentifying restrictions. Then
Sargan's (1958) statistic = u'Pu / (u'u/N)
Basmann's (1960) statistic = u'Pu / (u'Mu/(N-L))
The statistics share the same numerator. The denominators can be interpreted as two different estimates of the error variance of the estimated equation, both of which are consistent (see Davidson and MacKinnon (1993), pp. 235-36).
Both statistics are distributed as chi-square with L-K degrees of freedom. Both can be calculated via an artificial regression of the residuals of the IV estimation regressed on the full set of instruments; the Sargan statistic is N * the uncentered R-sq from this regression. See, e.g., Davidson and MacKinnon (1993), p. 236 and Wooldridge (2002), p. 123.
If there are no overidentifying restrictions (i.e., in the case of exact identification, where the number of excluded instruments equals the number of right-hand endogenous variables), an error message is printed.
The version of this test that is robust to heteroskedasticity in the errors is Hansen's J statistic; under the assumption of conditional homoskedasticity, Sargan's statistic becomes Hansen's J (see Hayashi (2000), p. 227-28), and hence the two statistics are sometimes referred to as the Hansen-Sargan statistic. Robust overidentification statistics are available via ivreg2. overid will not produce a result if either the robust or cluster options are employed in the preceding IV regression. ivreg2 also provides "diff-Sargan" or "C" tests for the endogeneity of a subset of instruments; see help ivreg2 (if installed) for details.
The test will fail to run if N<L. For Z'Z to be of full rank, N>L.
+-----------------------------------------+ ----+ Instrumental variables probit and Tobit +--------------------------
overid will report an overidentification statistic after estimation by ivprobit and ivtobit with the twostep option. These Stata commands request Newey's (1987) minimum-distance (or minimum-chi-squared) IV probit and IV Tobit estimators, respectively. Lee (1992) shows that the minimized distance for these estimators provides a test of overidentifying restrictions. Like Sargan and Basmann single-equation statistics, the test statistic is distributed as Chi-squared with (L-K) degrees of freedom under the null that the instruments are valid. The test statistic is available after twostep estimation only.
+---------------------------+ ----+ Three-stage least squares +----------------------------------------
overid will report an overidentification statistic after system estimation with reg3. As Davidson and MacKinnon (2004, p.532) indicate, a Hansen-Sargan test of the overidentifying restrictions is based on the 3SLS criterion function evaluated at the 3SLS point and interval parameter estimates. Under the null hypothesis, the statistic is distributed Chi-squared wih (G*L - K) degrees of freedom, where G is the number of simultaneous equations. The procedure will take proper account of linear constraints on the parameter vector imposed during estimation.
+------------------+ ----+ General comments +-------------------------------------------------
The command displays the test statistics, degrees of freedom and P-value, and places values in the return array. return list for details.
A full discussion of these computations and related topics can be found in Baum, Schaffer, and Stillman (2003) and Baum, Schaffer and Stillman (2006). A version of this routine by Schaffer and Stillman that works in the context of panel data is available as xtoverid.
+----------+ ----+ Citation +---------------------------------------------------------
overid is not an official Stata command. It is a free contribution to the research community, like a paper. Please cite it as such: Baum, C.F., Schaffer, M.E., Stillman, S., Wiggins, V. 2006. overid: Stata module to calculate tests of overidentifying restrictions after ivreg, ivreg2, ivprobit, ivtobit, reg3. http://ideas.repec.org/c/boc/bocode/s396802.html
Options
Options chi2, dfr, f and all only pertain to use of overid after ivreg or ivreg2.
chi2 requests Sargan's and Basmann's chi-squared statistics; this is the default.
dfr is equivalent to chi2 except that the the Sargan statistic has a small-sample correction: u'Pu / (u'u/(N-K))
f requests the pseudo-F test versions of the Sargan and Basmann statistics. Sargan pseudo-F = u'Pu/(L-K) / (u'u/(N-K)) Basmann pseudo-F = u'Pu/(L-K) / (u'Mu/(N-L))
all causes all five statistics to be reported.
depvar must be used after ivprobit, version 1.1.8 or earlier, to specify the dependent variable of the estimated equation.
Examples
. sysuse auto
. ivreg price mpg (weight turn=length displacement gear_ratio trunk)
. overid
. overid, all
. ivprobit foreign displacement (mpg=length weight turn), twostep
. overid, depvar(foreign)
. ivtobit gear_ratio displacement (mpg=length weight turn) [fw=rep78], twostep ll(2.2)
. overid
. webuse klein
. constraint define 1 [consump]wagepriv = [consump]wagegovt
. constraint define 2 [consump]govt = [wagepriv]govt
. reg3 ( consump wagepriv wagegovt govt invest) ( wagepriv consump govt capital1 taxnetx)
. overid
. reg3 ( consump wagepriv wagegovt govt invest) ( wagepriv consump govt capital1 taxnetx), c(1 2)
. overid
Acknowledgements
We are grateful to Austin Nichols for providing a better version of the reg3 code which greatly reduces memory use. Martin Weiss was also helpful in pointing out a recent bug in official ivtobit which was causing overid to fail.
References
Basmann, R.L., On Finite Sample Distributions of Generalized Classical Linear Identifiability Test Statistics. Journal of the American Statisical Association, Vol. 55, Issue 292, December 1960, pp. 650-59.
Baum, C. F., Schaffer, M. E., Stillman, S., Instrumental variables and GMM: Estimation and testing. Stata Journal, Vol. 3, 2003, pp. 1-31. Available as Working Paper no. 545, Boston College Department of Economics. http://fmwww.bc.edu/ec-p/WP545.pdf
Baum, C. F., Schaffer, M. E., Stillman, S., 2006. Enhanced routines for instrumental variables/GMM estimation and testing. Unpublished working paper, forthcoming.
Davidson, R. and MacKinnon, J., Estimation and Inference in Econometrics. 1993. New York: Oxford University Press.
Davidson, R. and MacKinnon, J., Econometric Theory and Methods. 2004. New York: Oxford University Press.
Hayashi, F., Econometrics. 2000. Princeton: Princeton University Press.
Lee, L., Amemiya's Generalized Least Squares and Tests of Overidenfication in Simultaneous Equation Models with Qualitative or Limited Dependent Variables. Econometric Reviews, Vol. 11, No. 3, 1992, pp. 319-328.
Newey, W.K., Efficient Estimation of Limited Dependent Variable Models with Endogeneous Explanatory Variables". Journal of Econometrics, Vol. 36, 1987, pp. 231-250.
Sargan, J.D. The Estimation of Economic Relationships Using Instrumental Variables. Econometrica, Vol. 26, 1958, pp. 393-415.
Wooldridge, J.M., Econometric Analysis of Cross Section and Panel Data. 2002. Cambridge, MA: MIT Press.
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, Motu, New Zealand stillman@motu.org.nz Vince Wiggins, Stata Corporation, USA vwiggins@stata.com
Also see
Manual: [R] ivreg, [R] ivprobit, [R] ivtobit, [R] reg3 On-line: help for ivreg; ivreg2 (if installed); ivprobit; ivtobit; reg3; xtoverid (if installed)