Dear All,
I am running an instrumental variable regression on a small sample size of 83. My KP F-stat is 13. I am performing the weak IV test using the 'weakiv' package, but I keep encountering an unsupported estimator error when clustering the standard errors. When using the first option of ivreg2, I get the Anderson-Rubin Wald test which shows that construction2009 affects lannual_avg_no2, even if my instrument (lHubDist) might be weak. When I use robust standard errors, the weak IV command works.
In the paper "A Practical Guide to Weak Instruments" by Keane and Neal, the authors advocate for the use of cluster-robust F statistics when dealing with panel data and the use of heteroskedasticity-robust standard errors when dealing with cross-sectional data. I have cross-sectional data, but I am clustering the data at the district level.
My intuition is that the first option automatically provides the AR test value, and there is no need to use the weak IV command.
I have attached all the output I am receiving. Additionally, I have used the Montiel-Pflueger robust weak instrument test. This test shows that my IV estimates might be biased between 20%-30%. Any help and guidance would be greatly appreciated.
I am running an instrumental variable regression on a small sample size of 83. My KP F-stat is 13. I am performing the weak IV test using the 'weakiv' package, but I keep encountering an unsupported estimator error when clustering the standard errors. When using the first option of ivreg2, I get the Anderson-Rubin Wald test which shows that construction2009 affects lannual_avg_no2, even if my instrument (lHubDist) might be weak. When I use robust standard errors, the weak IV command works.
In the paper "A Practical Guide to Weak Instruments" by Keane and Neal, the authors advocate for the use of cluster-robust F statistics when dealing with panel data and the use of heteroskedasticity-robust standard errors when dealing with cross-sectional data. I have cross-sectional data, but I am clustering the data at the district level.
My intuition is that the first option automatically provides the AR test value, and there is no need to use the weak IV command.
I have attached all the output I am receiving. Additionally, I have used the Montiel-Pflueger robust weak instrument test. This test shows that my IV estimates might be biased between 20%-30%. Any help and guidance would be greatly appreciated.
Code:
ivreg2 lannual_avg_no2 (construction2009 = lHubDist) manufacturing2009 tfp lelevation_mean lvcf_mean2013 ldmsp_mean_light2013 lyear2013 lprec2013 ltmean2013 i.state_id2, cl(district_id) first
First-stage regressions
-----------------------
First-stage regression of construction2009:
Statistics robust to heteroskedasticity and clustering on district_id
Number of obs = 83
Number of clusters (district_id) = 71
--------------------------------------------------------------------------------------
| Robust
construction2009 | Coefficient std. err. t P>|t| [95% conf. interval]
---------------------+----------------------------------------------------------------
lHubDist | -.0184343 .0050494 -3.65 0.001 -.0285346 -.008334
manufacturing2009 | -.0080146 .0687827 -0.12 0.908 -.1456005 .1295713
tfp | -.0248488 .0107343 -2.31 0.024 -.0463207 -.003377
lelevation_mean | .0130909 .0094243 1.39 0.170 -.0057606 .0319423
lvcf_mean2013 | -.0117367 .0127732 -0.92 0.362 -.0372868 .0138135
ldmsp_mean_light2013 | .0085817 .0107857 0.80 0.429 -.0129928 .0301563
lyear2013 | -.0135505 .0056428 -2.40 0.019 -.0248377 -.0022633
lprec2013 | .0033559 .0148407 0.23 0.822 -.0263299 .0330417
ltmean2013 | .194862 .2849136 0.68 0.497 -.37505 .764774
|
state_id2 |
07 | -.0977399 .0344553 -2.84 0.006 -.1666608 -.028819
08 | -.0197922 .0367808 -0.54 0.592 -.0933648 .0537804
09 | -.0071806 .0349712 -0.21 0.838 -.0771334 .0627722
10 | .0352983 .0451267 0.78 0.437 -.0549685 .1255652
19 | -.0996996 .0405225 -2.46 0.017 -.1807566 -.0186426
21 | -.0852802 .0509004 -1.68 0.099 -.1870961 .0165357
23 | -.0398631 .0561977 -0.71 0.481 -.1522752 .0725491
24 | -.1207808 .0476104 -2.54 0.014 -.2160157 -.0255459
27 | -.0969799 .0440684 -2.20 0.032 -.1851297 -.00883
28 | -.1074932 .053704 -2.00 0.050 -.2149171 -.0000692
29 | -.0927427 .0385901 -2.40 0.019 -.1699344 -.015551
32 | .0427553 .0485485 0.88 0.382 -.0543561 .1398667
33 | -.0533523 .0569229 -0.94 0.352 -.1672151 .0605105
|
_cons | -.3434168 .9726428 -0.35 0.725 -2.288992 1.602159
--------------------------------------------------------------------------------------
F test of excluded instruments:
F( 1, 70) = 13.33
Prob > F = 0.0005
Sanderson-Windmeijer multivariate F test of excluded instruments:
F( 1, 70) = 13.33
Prob > F = 0.0005
Summary results for first-stage regressions
-------------------------------------------
(Underid) (Weak id)
Variable | F( 1, 70) P-val | SW Chi-sq( 1) P-val | SW F( 1, 70)
construction | 13.33 0.0005 | 18.48 0.0000 | 13.33
NB: first-stage test statistics cluster-robust
Stock-Yogo weak ID F 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 i.i.d. errors only.
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)=11.74 P-val=0.0006
Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic 17.72
Kleibergen-Paap Wald rk F statistic 13.33
Stock-Yogo weak ID test critical values for K1=1 and L1=1:
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.
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(1,70)= 13.43 P-val=0.0005
Anderson-Rubin Wald test Chi-sq(1)= 18.61 P-val=0.0000
Stock-Wright LM S statistic Chi-sq(1)= . P-val= .
NB: Underidentification, weak identification and weak-identification-robust
test statistics cluster-robust
Number of clusters N_clust = 71
Number of observations N = 83
Number of regressors K = 23
Number of endogenous regressors K1 = 1
Number of instruments L = 23
Number of excluded instruments L1 = 1
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on district_id
Number of clusters (district_id) = 71 Number of obs = 83
F( 22, 70) = 241.16
Prob > F = 0.0000
Total (centered) SS = 19.09128377 Centered R2 = 0.6885
Total (uncentered) SS = 810.8011231 Uncentered R2 = 0.9927
Residual SS = 5.947878021 Root MSE = .2677
--------------------------------------------------------------------------------------
| Robust
lannual_avg_no2 | Coefficient std. err. z P>|z| [95% conf. interval]
---------------------+----------------------------------------------------------------
construction2009 | 5.682213 1.56244 3.64 0.000 2.619886 8.744541
manufacturing2009 | .0545445 .434132 0.13 0.900 -.7963386 .9054277
tfp | .197584 .0646678 3.06 0.002 .0708374 .3243305
lelevation_mean | -.042575 .0633236 -0.67 0.501 -.1666869 .081537
lvcf_mean2013 | .1089546 .0650508 1.67 0.094 -.0185426 .2364517
ldmsp_mean_light2013 | .1503779 .0623716 2.41 0.016 .0281318 .2726241
lyear2013 | .0840521 .0487457 1.72 0.085 -.0114878 .179592
lprec2013 | -.1540445 .1267045 -1.22 0.224 -.4023807 .0942917
ltmean2013 | -2.112641 2.35731 -0.90 0.370 -6.732883 2.507601
|
state_id2 |
07 | .8731768 .3254068 2.68 0.007 .2353911 1.510963
08 | .3533654 .3874195 0.91 0.362 -.4059629 1.112694
09 | .3033463 .3266158 0.93 0.353 -.3368089 .9435014
10 | .495316 .4479777 1.11 0.269 -.3827041 1.373336
19 | 1.245583 .3559856 3.50 0.000 .5478636 1.943302
21 | .4229356 .4275996 0.99 0.323 -.4151443 1.261015
23 | .3273937 .4020913 0.81 0.416 -.4606908 1.115478
24 | .5723936 .4079419 1.40 0.161 -.2271578 1.371945
27 | .8046118 .376948 2.13 0.033 .0658072 1.543416
28 | .3735878 .4637364 0.81 0.420 -.5353188 1.282494
29 | -.1430758 .3879087 -0.37 0.712 -.903363 .6172113
32 | -.9978864 .4648677 -2.15 0.032 -1.90901 -.0867624
33 | .3270571 .4880919 0.67 0.503 -.6295854 1.2837
|
_cons | 8.155018 7.66243 1.06 0.287 -6.863069 23.1731
--------------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 11.741
Chi-sq(1) P-val = 0.0006
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 17.724
(Kleibergen-Paap rk Wald F statistic): 13.328
Stock-Yogo weak ID test critical values: 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.
------------------------------------------------------------------------------
Warning: estimated covariance matrix of moment conditions not of full rank.
overidentification statistic not reported, and standard errors and
model tests should be interpreted with caution.
Possible causes:
number of clusters insufficient to calculate robust covariance matrix
singleton dummy variable (dummy with one 1 and N-1 0s or vice versa)
partial option may address problem.
------------------------------------------------------------------------------
Instrumented: construction2009
Included instruments: manufacturing2009 tfp lelevation_mean lvcf_mean2013
ldmsp_mean_light2013 lyear2013 lprec2013 ltmean2013
3.state_id2 4.state_id2 5.state_id2 6.state_id2
7.state_id2 8.state_id2 9.state_id2 10.state_id2
11.state_id2 12.state_id2 13.state_id2 14.state_id2
15.state_id2
Excluded instruments: lHubDist
------------------------------------------------------------------------------
weakiv ivreg2 lannual_avg_no2 (construction2009 = lHubDist) manufacturing2009 tfp lelevation_mean lvcf_mean2013 ldmsp_mean_light2013 lyear2013 lprec2013 ltmean2013 i.state_id2, cl(district_id)
Estimating model for Wald tests using ivreg2...
type mismatch
# Using robust option
ivreg2 lannual_avg_no2 (construction2009 = lHubDist) manufacturing2009 tfp lelevation_mean lvcf_mean2013 ldmsp_mean_light2013 lyear2013 lprec2013 ltmean2013 i.state_id2, robust first
First-stage regressions
-----------------------
First-stage regression of construction2009:
Statistics robust to heteroskedasticity
Number of obs = 83
--------------------------------------------------------------------------------------
| Robust
construction2009 | Coefficient std. err. t P>|t| [95% conf. interval]
---------------------+----------------------------------------------------------------
lHubDist | -.0184343 .0047659 -3.87 0.000 -.0279676 -.0089011
manufacturing2009 | -.0080146 .0681988 -0.12 0.907 -.1444325 .1284033
tfp | -.0248488 .0106259 -2.34 0.023 -.0461038 -.0035939
lelevation_mean | .0130909 .0090265 1.45 0.152 -.0049649 .0311466
lvcf_mean2013 | -.0117367 .0120301 -0.98 0.333 -.0358004 .0123271
ldmsp_mean_light2013 | .0085817 .0101256 0.85 0.400 -.0116724 .0288359
lyear2013 | -.0135505 .0055968 -2.42 0.019 -.0247457 -.0023553
lprec2013 | .0033559 .0144947 0.23 0.818 -.0256378 .0323496
ltmean2013 | .194862 .2837048 0.69 0.495 -.3726321 .7623561
|
state_id2 |
07 | -.0977399 .0327464 -2.98 0.004 -.1632425 -.0322373
08 | -.0197922 .0360276 -0.55 0.585 -.091858 .0522737
09 | -.0071806 .0343292 -0.21 0.835 -.0758493 .0614881
10 | .0352983 .0444134 0.79 0.430 -.0535416 .1241383
19 | -.0996996 .039216 -2.54 0.014 -.1781433 -.0212559
21 | -.0852802 .0499134 -1.71 0.093 -.1851218 .0145614
23 | -.0398631 .0558556 -0.71 0.478 -.1515909 .0718648
24 | -.1207808 .0467 -2.59 0.012 -.2141948 -.0273669
27 | -.0969799 .0435774 -2.23 0.030 -.1841477 -.009812
28 | -.1074932 .052825 -2.03 0.046 -.2131588 -.0018275
29 | -.0927427 .0378263 -2.45 0.017 -.1684066 -.0170789
32 | .0427553 .0480659 0.89 0.377 -.0533909 .1389015
33 | -.0533523 .0562508 -0.95 0.347 -.1658707 .059166
|
_cons | -.3434168 .9686871 -0.35 0.724 -2.28108 1.594246
--------------------------------------------------------------------------------------
F test of excluded instruments:
F( 1, 60) = 14.96
Prob > F = 0.0003
Sanderson-Windmeijer multivariate F test of excluded instruments:
F( 1, 60) = 14.96
Prob > F = 0.0003
Summary results for first-stage regressions
-------------------------------------------
(Underid) (Weak id)
Variable | F( 1, 60) P-val | SW Chi-sq( 1) P-val | SW F( 1, 60)
construction | 14.96 0.0003 | 20.70 0.0000 | 14.96
NB: first-stage test statistics heteroskedasticity-robust
Stock-Yogo weak ID F 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 i.i.d. errors only.
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)=14.94 P-val=0.0001
Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic 17.72
Kleibergen-Paap Wald rk F statistic 14.96
Stock-Yogo weak ID test critical values for K1=1 and L1=1:
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.
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(1,60)= 15.63 P-val=0.0002
Anderson-Rubin Wald test Chi-sq(1)= 21.62 P-val=0.0000
Stock-Wright LM S statistic Chi-sq(1)= . P-val= .
NB: Underidentification, weak identification and weak-identification-robust
test statistics heteroskedasticity-robust
Number of observations N = 83
Number of regressors K = 23
Number of endogenous regressors K1 = 1
Number of instruments L = 23
Number of excluded instruments L1 = 1
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity
Number of obs = 83
F( 22, 60) = 245.03
Prob > F = 0.0000
Total (centered) SS = 19.09128377 Centered R2 = 0.6885
Total (uncentered) SS = 810.8011231 Uncentered R2 = 0.9927
Residual SS = 5.947878021 Root MSE = .2677
--------------------------------------------------------------------------------------
| Robust
lannual_avg_no2 | Coefficient std. err. z P>|z| [95% conf. interval]
---------------------+----------------------------------------------------------------
construction2009 | 5.682213 1.533766 3.70 0.000 2.676088 8.688339
manufacturing2009 | .0545445 .4264853 0.13 0.898 -.7813513 .8904404
tfp | .197584 .0626455 3.15 0.002 .0748011 .3203668
lelevation_mean | -.042575 .0618594 -0.69 0.491 -.1638171 .0786672
lvcf_mean2013 | .1089546 .061616 1.77 0.077 -.0118106 .2297197
ldmsp_mean_light2013 | .1503779 .0594219 2.53 0.011 .0339131 .2668428
lyear2013 | .0840521 .0481032 1.75 0.081 -.0102285 .1783327
lprec2013 | -.1540445 .1207354 -1.28 0.202 -.3906815 .0825925
ltmean2013 | -2.112641 2.343997 -0.90 0.367 -6.70679 2.481508
|
state_id2 |
07 | .8731768 .3240291 2.69 0.007 .2380915 1.508262
08 | .3533654 .3832305 0.92 0.356 -.3977527 1.104483
09 | .3033463 .3242123 0.94 0.349 -.3320981 .9387906
10 | .495316 .4407528 1.12 0.261 -.3685436 1.359176
19 | 1.245583 .347189 3.59 0.000 .5651047 1.92606
21 | .4229356 .4193161 1.01 0.313 -.3989089 1.24478
23 | .3273937 .3991721 0.82 0.412 -.4549693 1.109757
24 | .5723936 .4013948 1.43 0.154 -.2143258 1.359113
27 | .8046118 .3749752 2.15 0.032 .069674 1.53955
28 | .3735878 .4596281 0.81 0.416 -.5272667 1.274442
29 | -.1430758 .3859589 -0.37 0.711 -.8995414 .6133898
32 | -.9978864 .4594633 -2.17 0.030 -1.898418 -.0973549
33 | .3270571 .4847485 0.67 0.500 -.6230325 1.277147
|
_cons | 8.155018 7.626706 1.07 0.285 -6.79305 23.10309
--------------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 14.940
Chi-sq(1) P-val = 0.0001
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 17.724
(Kleibergen-Paap rk Wald F statistic): 14.961
Stock-Yogo weak ID test critical values: 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.
------------------------------------------------------------------------------
Warning: estimated covariance matrix of moment conditions not of full rank.
overidentification statistic not reported, and standard errors and
model tests should be interpreted with caution.
Possible causes:
singleton dummy variable (dummy with one 1 and N-1 0s or vice versa)
partial option may address problem.
------------------------------------------------------------------------------
Instrumented: construction2009
Included instruments: manufacturing2009 tfp lelevation_mean lvcf_mean2013
ldmsp_mean_light2013 lyear2013 lprec2013 ltmean2013
3.state_id2 4.state_id2 5.state_id2 6.state_id2
7.state_id2 8.state_id2 9.state_id2 10.state_id2
11.state_id2 12.state_id2 13.state_id2 14.state_id2
15.state_id2
Excluded instruments: lHubDist
------------------------------------------------------------------------------
weakiv ivreg2 lannual_avg_no2 (construction2009 = lHubDist) manufacturing2009 tfp lelevation_mean lvcf_mean2013 ldmsp_mean_light2013 lyear2013 lprec2013 ltmean2013 i.state_id2, robust first
Estimating model for Wald tests using ivreg2...
Estimating confidence sets over 100 grid points
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
.................................................. 100
Weak instrument robust tests and confidence sets for linear IV
H0: beta[lannual_avg_no2:construction2009] = 0
------------------------------------------------------------------------------
Test | Statistic p-value | Conf. level Conf. Set
------+---------------------------------+-------------------------------------
AR | chi2(1) = 12.66 0.0004 | 95% [ 3.07083, 10.1155]
------+---------------------------------+-------------------------------------
Wald | chi2(1) = 13.73 0.0002 | 95% [ 2.67609, 8.68834]
------------------------------------------------------------------------------
Confidence sets estimated for 100 points in [-.330038, 11.6945].
Number of obs N = 83.
Method = lagrange multiplier (LM).
Tests robust to heteroskedasticity.
Wald statistic in last row is based on ivreg2 estimation and is not robust to weak instruments.
