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From | Matthias Flückiger <bistgaun@gmail.com> |
To | statalist@hsphsun2.harvard.edu |
Subject | st: Multiple endogenous regressors: weak instrument robust test statistic for individual coefficients (xtivreg2)? |
Date | Mon, 13 Jan 2014 21:24:58 +0100 |
Dear all, I am estimating a IV-2SLS model with 2 endogenous regressors (x1, x2) and 2 excluded instruments (z1, z2) using the xtivreg2 command. Is there any way to obtain a weak instrument robust test satistic for the individual (a subset of) endogenous parameters? I.e., a Anderson-Rubin test statistic for x1 and x2, respectively. Any help would be greatly appreciated. Matthias The command and the corresponding output are: xtivreg2 y ( x1 x2 = z1 z2) , cluster(id ) fe first FIXED EFFECTS ESTIMATION ------------------------ Number of groups = 109 Obs per group: min = 2 avg = 5.8 max = 6 First-stage regressions ----------------------- First-stage regression of x1: FIXED EFFECTS ESTIMATION ------------------------ Number of groups = 109 Obs per group: min = 2 avg = 5.8 max = 6 OLS estimation -------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity and clustering on id Number of clusters (id) = 109 Number of obs = 636 F( 2, 108) = 4.33 Prob > F = 0.0155 Total (centered) SS = 56.34311291 Centered R2 = 0.0290 Total (uncentered) SS = 56.34311291 Uncentered R2 = 0.0290 Residual SS = 54.70817761 Root MSE = .3228 ------------------------------------------------------------------------------ | Robust x1 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- z1 | .3654952 .1258542 2.90 0.004 .1160303 .6149601 z2 | .1336675 .1063186 1.26 0.211 -.0770744 .3444094 ------------------------------------------------------------------------------ Included instruments: z1 z2 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 108) = 4.33 Prob > F = 0.0155 Angrist-Pischke multivariate F test of excluded instruments: F( 1, 108) = 8.64 Prob > F = 0.0040 First-stage regression of x2: FIXED EFFECTS ESTIMATION ------------------------ Number of groups = 109 Obs per group: min = 2 avg = 5.8 max = 6 OLS estimation -------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity and clustering on id Number of clusters (id) = 109 Number of obs = 636 F( 2, 108) = 2.27 Prob > F = 0.1083 Total (centered) SS = 40.33333333 Centered R2 = 0.0079 Total (uncentered) SS = 40.33333333 Uncentered R2 = 0.0079 Residual SS = 40.01470425 Root MSE = .2761 ------------------------------------------------------------------------------ | Robust x2 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- z1 | .0293852 .1057135 0.28 0.782 -.1801572 .2389276 z2 | -.2039007 .0972056 -2.10 0.038 -.396579 -.0112223 ------------------------------------------------------------------------------ Included instruments: z1 z2 ------------------------------------------------------------------------------ F test of excluded instruments: F( 2, 108) = 2.27 Prob > F = 0.1083 Angrist-Pischke multivariate F test of excluded instruments: F( 1, 108) = 3.49 Prob > F = 0.0645 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 2, 108) P-val | AP Chi-sq( 1) P-val | AP F( 1, 108) x1 | 4.33 0.0155 | 8.73 0.0031 | 8.64 x2 | 2.27 0.1083 | 3.53 0.0604 | 3.49 NB: first-stage test statistics cluster-robust Stock-Yogo weak ID test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Kleibergen-Paap rk LM statistic Chi-sq(1)=3.16 P-val=0.0755 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 1.75 Kleibergen-Paap Wald rk F statistic 1.55 Stock-Yogo weak ID test critical values for K1=2 and L1=2: 10% maximal IV size 7.03 15% maximal IV size 4.58 20% maximal IV size 3.95 25% maximal IV size 3.63 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(2,108)= 2.20 P-val=0.1161 Anderson-Rubin Wald test Chi-sq(2)= 4.44 P-val=0.1086 Stock-Wright LM S statistic Chi-sq(2)= 3.74 P-val=0.1540 NB: Underidentification, weak identification and weak-identification-robust test statistics cluster-robust Number of clusters N_clust = 109 Number of observations N = 636 Number of regressors K = 2 Number of endogenous regressors K1 = 2 Number of instruments L = 2 Number of excluded instruments L1 = 2 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics robust to heteroskedasticity and clustering on id Number of clusters (id) = 109 Number of obs = 636 F( 2, 108) = 1.38 Prob > F = 0.2549 Total (centered) SS = 40.33333333 Centered R2 = -0.6194 Total (uncentered) SS = 40.33333333 Uncentered R2 = -0.6194 Residual SS = 65.31571726 Root MSE = .352 ------------------------------------------------------------------------------ | Robust y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | -.5789745 .3461093 -1.67 0.094 -1.257336 .0993872 x2 | -.3621129 .6874695 -0.53 0.598 -1.709528 .9853026 ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 3.158 Chi-sq(1) P-val = 0.0755 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 1.755 (Kleibergen-Paap rk Wald F statistic): 1.553 Stock-Yogo weak ID test critical values: 10% maximal IV size 7.03 15% maximal IV size 4.58 20% maximal IV size 3.95 25% maximal IV size 3.63 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: x1 x2 Excluded instruments: z1 z2 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/