Comparison of conditional F-statistics
Source:vignettes/f-statistic-comparison.Rmd
f-statistic-comparison.RmdRun fsw() on ivreg() model object
url <- "http://fmwww.bc.edu/ec-p/data/wooldridge/mroz.dta"
dat <- haven::read_dta(url)
mod <- ivreg(lwage ~ educ + exper | age + kidslt6 + kidsge6, data = dat)
summary(mod)
#>
#> Call:
#> ivreg(formula = lwage ~ educ + exper | age + kidslt6 + kidsge6,
#> data = dat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.04973 -0.30711 0.05531 0.38952 2.27672
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.360182 1.033416 -0.349 0.728
#> educ 0.105836 0.080982 1.307 0.192
#> exper 0.016153 0.007595 2.127 0.034 *
#>
#> Diagnostic tests:
#> df1 df2 statistic p-value
#> Weak instruments (educ) 3 424 4.466 0.00421 **
#> Weak instruments (exper) 3 424 55.044 < 2e-16 ***
#> Wu-Hausman 2 423 0.004 0.99609
#> Sargan 1 NA 1.168 0.27976
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.669 on 425 degrees of freedom
#> Multiple R-Squared: 0.1482, Adjusted R-squared: 0.1442
#> Wald test: 3.034 on 2 and 425 DF, p-value: 0.04917
fsw(mod)
#>
#> Model sample size: 428
#>
#> Sanderson-Windmeijer conditional F-statistics for first stage model:
#> F value d.f. Residual d.f. Pr(>F)
#> educ 6.69425 2 424 0.001373 **
#> exper 81.81237 2 424 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comparison with F-statistic from lfe package
modst2 <- felm(lwage ~ 1 | 0 | (educ | exper ~ age + kidslt6 + kidsge6),
data = dat)
summary(modst2)
#>
#> Call:
#> felm(formula = lwage ~ 1 | 0 | (educ | exper ~ age + kidslt6 + kidsge6), data = dat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.04973 -0.30711 0.05531 0.38952 2.27672
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.360182 1.033416 -0.349 0.728
#> `educ(fit)` 0.105836 0.080982 1.307 0.192
#> `exper(fit)` 0.016153 0.007595 2.127 0.034 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.669 on 425 degrees of freedom
#> (325 observations deleted due to missingness)
#> Multiple R-squared(full model): 0.1482 Adjusted R-squared: 0.1442
#> Multiple R-squared(proj model): 0.1482 Adjusted R-squared: 0.1442
#> F-statistic(full model):3.034 on 2 and 425 DF, p-value: 0.04917
#> F-statistic(proj model): 3.034 on 2 and 425 DF, p-value: 0.04917
#> F-statistic(endog. vars):3.034 on 2 and 425 DF, p-value: 0.04917
t(sapply(modst2$stage1$lhs,
function(lh) waldtest(modst2$stage1,
~ age | kidslt6 | kidsge6, lhs = lh)))
#> p chi2 df1 p.F F df2
#> educ 3.849465e-03 13.39851 3 4.210326e-03 4.466172 424
#> exper 1.429780e-35 165.13309 3 4.561549e-30 55.044363 424
condfstat(modst2, quantiles = c(0.025, 0.975))
#> educ exper
#> iid F 6.710039 82.00533
#> attr(,"df1")
#> [1] 2
#> attr(,"quantiles")
#> 2.5% 97.5%
#> educ -0.0808003007 0.25850072
#> exper 0.0008784942 0.03091819
#> attr(,"quantiles")attr(,"q")
#> [1] 0.025 0.975
#> attr(,"quantiles")attr(,"samples")
#> [1] 100Comparison with output from ivreg2
Code run using Stata version 16.1.
use http://fmwww.bc.edu/ec-p/data/wooldridge/mroz.dta, clear
// ssc install ivreg2
ivreg2 lwage (educ exper = age kidslt6 kidsge6) if !missing(lwage, educ, exper, age, kidslt6, kidsge6), firstFirst-stage regressions
-----------------------
First-stage regression of educ:
Statistics consistent for homoskedasticity only
Number of obs = 428
------------------------------------------------------------------------------
educ | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0185412 .0163449 -1.13 0.257 -.0506683 .0135859
kidslt6 | .6984283 .2966854 2.35 0.019 .1152709 1.281586
kidsge6 | -.222821 .0906154 -2.46 0.014 -.4009324 -.0447096
_cons | 13.64009 .7644499 17.84 0.000 12.13751 15.14268
------------------------------------------------------------------------------
F test of excluded instruments:
F( 3, 424) = 4.47
Prob > F = 0.0042
Sanderson-Windmeijer multivariate F test of excluded instruments:
F( 2, 424) = 6.69
Prob > F = 0.0014
First-stage regression of exper:
Statistics consistent for homoskedasticity only
Number of obs = 428
------------------------------------------------------------------------------
exper | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .3948754 .0496446 7.95 0.000 .2972953 .4924555
kidslt6 | -.7469412 .9011267 -0.83 0.408 -2.518173 1.024291
kidsge6 | -1.430306 .2752275 -5.20 0.000 -1.971286 -.8893254
_cons | -1.500019 2.321874 -0.65 0.519 -6.063837 3.063798
------------------------------------------------------------------------------
F test of excluded instruments:
F( 3, 424) = 55.04
Prob > F = 0.0000
Sanderson-Windmeijer multivariate F test of excluded instruments:
F( 2, 424) = 81.81
Prob > F = 0.0000
Summary results for first-stage regressions
-------------------------------------------
(Underid) (Weak id)
Variable | F( 3, 424) P-val | SW Chi-sq( 2) P-val | SW F( 2, 424)
educ | 4.47 0.0042 | 13.51 0.0012 | 6.69
exper | 55.04 0.0000 | 165.17 0.0000 | 81.81
Stock-Yogo weak ID F test critical values for single endogenous regressor:
5% maximal IV relative bias 13.91
10% maximal IV relative bias 9.08
20% maximal IV relative bias 6.46
30% maximal IV relative bias 5.39
10% maximal IV size 22.30
15% maximal IV size 12.83
20% maximal IV size 9.54
25% maximal IV size 7.80
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Sanderson-Windmeijer F statistic.
Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Anderson canon. corr. LM statistic Chi-sq(2)=13.10 P-val=0.0014
Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic 4.46
Stock-Yogo weak ID test critical values for K1=2 and L1=3:
10% maximal IV size 13.43
15% maximal IV size 8.18
20% maximal IV size 6.40
25% maximal IV size 5.45
Source: Stock-Yogo (2005). Reproduced by permission.
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(3,424)= 2.08 P-val=0.1025
Anderson-Rubin Wald test Chi-sq(3)= 6.29 P-val=0.0983
Stock-Wright LM S statistic Chi-sq(3)= 6.20 P-val=0.1023
Number of observations N = 428
Number of regressors K = 3
Number of endogenous regressors K1 = 2
Number of instruments L = 4
Number of excluded instruments L1 = 3
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics consistent for homoskedasticity only
Number of obs = 428
F( 2, 425) = 3.03
Prob > F = 0.0492
Total (centered) SS = 223.3274513 Centered R2 = 0.1482
Total (uncentered) SS = 829.594813 Uncentered R2 = 0.7707
Residual SS = 190.2315236 Root MSE = .6667
------------------------------------------------------------------------------
lwage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ | .1058361 .0806975 1.31 0.190 -.0523281 .2640003
exper | .0161527 .007568 2.13 0.033 .0013197 .0309858
_cons | -.3601821 1.029787 -0.35 0.727 -2.378528 1.658164
------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 13.101
Chi-sq(2) P-val = 0.0014
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 4.463
Stock-Yogo weak ID test critical values: 10% maximal IV size 13.43
15% maximal IV size 8.18
20% maximal IV size 6.40
25% maximal IV size 5.45
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 1.168
Chi-sq(1) P-val = 0.2798
------------------------------------------------------------------------------
Instrumented: educ exper
Excluded instruments: age kidslt6 kidsge6
------------------------------------------------------------------------------