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st: Multiple endogenous regressors: weak instrument robust test statistic for individual coefficients (xtivreg2)?
From
Matthias Flückiger <[email protected]>
To
[email protected]
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
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