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st: RE: Multiple endogenous regressors: weak instrument robust test statistic for individual coefficients (xtivreg2)?
From
"Schaffer, Mark E" <[email protected]>
To
"[email protected]" <[email protected]>
Subject
st: RE: Multiple endogenous regressors: weak instrument robust test statistic for individual coefficients (xtivreg2)?
Date
Tue, 14 Jan 2014 10:26:24 +0000
Matthias,
> -----Original Message-----
> From: [email protected] [mailto:owner-
> [email protected]] On Behalf Of Matthias Flückiger
> Sent: 13 January 2014 20:25
> To: [email protected]
> Subject: st: Multiple endogenous regressors: weak instrument robust test
> statistic for individual coefficients (xtivreg2)?
>
> 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.
Unless I misunderstand what you are looking for, it's in the xtivreg2 output you provided:
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
--Mark
>
> 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
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