Perform Ramsey/Pesaran-Taylor/Pagan-Hall RESET specification test after IV/GMM/ > OLS estimation
ivreset [, polynomial(#) rform cstat small ]
ivreset is for use after ivreg2 and regress.
Description
ivreset performs various flavors of Ramsey's regression error specification test (RESET) as adapted by Pesaran and Taylor (1999) and Pagan and Hall (1983) for instrumental variables (IV) estimation. The RESET test is sometimes called an "omitted variables test" but probably is best interpreted as a test of neglected nonlinearities in the choice of functional form (Wooldridge 2002, pp. 124-5). Under the null that there are no neglected nonlinearities, the residuals should be uncorrelated with low-order polynomials in y-hat, where the y-hats are the "forecast values" of the dependent variable (see below). The test flavors vary according to the polynomial terms (square, cube, 4th power of y-hat), the choice of forecast values (Pesaran-Taylor optimal forecasts or Pagan-Hall reduced form forecasts), test statistic (Wald or GMM-distance), and large vs. small sample statistic (chi-squared or F-statistic). The test statistic is distributed with degrees of freedom = number of polynomial terms. The default is the Pesaran-Taylor version using the square of the optimal forecast of y and a chi-squared Wald statistic with one degree of freedom.
If the original ivreg2 or regress estimation was heteroskedastic-robust, cluster-robust, autocorrelation-consistent (AC), or heteroskedastic and autocorrelation-consistent (HAC), the RESET test reported will be as well.
ivreset can also be used after OLS or HOLS regression with regress or ivreg2, when there are no endogenous regressors. In this case, a standard Ramsey RESET test using fitted values of y is reported.
Options
rform requests the Pagan-Hall (1983) version of the RESET test for IV regression instead of the default Pesaran-Taylor (1999) version. The Pagan-Hall version uses the reduced form forecast y-hat of the dependent variable y, as opposed to the default Pesaran-Taylor version that uses an "optimal forecast" (see below).
polynomial(#) requests a second, third, or fourth-order polynomial in y-hat. The default is a second-order polynomial, i.e., y-hat squared.
cstat requests a C-test statistic, also known as a "GMM-distance" or "difference-in-Sargan" test statistic (see below), instead of the default Wald statistic.
small requests a small-sample F statistic instead of the default chi-squared statistic.
Remarks
The Ramsey (1969) RESET test is a standard test of neglected nonlinearities in the choice of functional form (sometimes, perhaps misleadingly, also described as a test for omitted variables; see ovtest and Wooldridge (2002), pp. 124-5). The principle is to estimate y=X*beta+W*gamma+u and then test the significance of gamma. The Ws in a RESET test can either be powers of X or, as implemented here, powers of the forecast values of y.
As Pagan and Hall (1983) and Pesaran and Taylor (1999) point out, a RESET test for an IV regression cannot use the standard IV predicted values X*beta-hat, because X includes endogenous regressors that are correlated with u. Instead, the RESET test needs to be implemented using "forecast values" of y that are functions of the instruments (exogenous variables) only.
Denote the full set of instruments by Z (possibly including exogenous regressors also in X).
In the Pagan-Hall version of the test, the forecast values y-hat are the reduced form predicted values of y, i.e., the predicted values Z*pi-hat from a regression of y on the instruments Z.
In the Pesaran-Taylor version of the test, the forecast values y-hat are the "optimal forecast" values. The optimal forecast (predictor) y-hat is defined as X-hat*beta-hat, where beta-hat is the IV estimate of the coefficents and X-hat consists of the exogenous regressors in X and the reduced form predicted values of the endogenous regressors in X. The latter are the predicted values Z*pi-hat from regressions of the endogenous Xs on the instruments Z. Note that if the equation is exactly identified, the optimal forecasts and reduced form forecasts coincide, and the Pesaran-Taylor and Pagan-Hall tests are identical.
In both the Pesaran-Taylor and Pagan-Hall versions of the RESET test, the augmented equation is y=X*beta+W*gamma+u, where the Ws are the powers of y-hat. The default is squares of y-hat, but 3rd and 4th powers of y-hat can be requested. This equation is estimated by IV, and the default test statistic is a Wald test of the significance of gamma. Under the null that there are no neglected nonlinearities and the equation is otherwise well-specified, the test statistic is distributed as chi-squared with degrees of freedom equal to the number of powers of y-hat.
Alternatively, Godfrey has suggested that a C-test statistic (also known as a "GMM-distance" or "difference-in-Sargan" test) be used to test whether the powers of y-hat can be added to the orthogonality or moment conditions that define the IV or OLS estimator (see Pesaran and Taylor, pp. 262-63). This test can be requested with the cstat option. Under the null that the equation is well-specified and has no neglected nonlinearities, J-J1 is distributed as chi-squared with degrees of freedom equal to the number of powers of y-hat, where J1 is the Sargan-Hansen statistic for the original IV estimation and J is the Sargan-Hansen statistic for the IV estimation using the additional orthogonality conditions provided by the powers of y-hat. For a general discussion of this test, see help ivreg2 (if installed) and Hayashi (2000), pp. 218-22 and pp. 232-34.
If the equation was estimated using OLS or HOLS (heteroskedastic OLS - see help ivreg2), and there there are no endogenous regressors, ivreset reports a standard Ramsey RESET test using the fitted values of y, i.e., X*beta-hat. Note that if the original estimation was OLS or HOLS, the excluded instruments (if any) are ignored by ivreset.
If the original equation was estimated using robust, cluster, or bw, so is the augmented equation, and the RESET test statistic will be heteroskedastic-, cluster-, and/or autocorrelation-robust, respectively.
Saved results
ivreset saves the value of the test statistic, its p-value, and the degrees of freedom of the test. See return list.
Examples
. use http://fmwww.bc.edu/ec-p/data/hayashi/griliches76.dta
(Wages of Very Young Men, Zvi Griliches, J.Pol.Ec. 1976)
. ivreg2 lw s expr tenure rns smsa (iq=med kww)
(Default: 2nd-order polynomial in y-hat, Pesaran-Smith optimal forecast, Wald c > hi-squared statisic)
. ivreset
(If estimation is heteroskedastic-robust, so are RESET tests) . ivreg2 lw s expr tenure rns smsa (iq=med kww), robust
(4th order polynomial, Pagan-Hall reduced form forecast, Wald F-statistic)
. ivreset, poly(4) rf small
(3rd order polynomial, Pesaran-Smith optimal forecast, C (GMM-distance) chi-squ > ared statistic)
. ivreset, poly(3) cstat
References
Baum, C. F., Schaffer, M. E., Stillman, S., 2003. Instrumental variables and GMM: Estimation and testing. The Stata Journal, Vol. 3, No. 1, pp. 1-31. Unpublished working paper version: Boston College Department of Economics Working Paper No. 545. http://fmwww.bc.edu/ec-p/WP545.pdf
Hayashi, F. Econometrics. 2000. Princeton: Princeton University Press.
Pagan, A.R. and Hall, D. 1983. "Diagnostic Tests as Residual Analysis." Econometric Reviews, Vol. 2, No. 2, pp. 159-218.
Pesaran, M.H. and Taylor, L.W. 1999. "Diagnostics for IV Regressions." Oxford Bulletin of Economics and Statistics, Vol. 61, No. 2, pp. 255-81.
Ramsey, J.B. 1969. "Tests for Specification Errors in a Classical Linear Least Squares Regression Analysis." Journal of the Royal Statistical Society B, Vol. 31, pp. 350-71.
Wooldridge, J.M. 2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press.
Author
Mark E Schaffer, Heriot-Watt University, UK m.e.schaffer@hw.ac.uk
Also see
Manual: [R] regression diagnostics On-line: help for ivreg2, ivhettest, ivendog (if installed)