--- title: "Comparison of conditional F-statistics" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Comparison of conditional F-statistics} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r, include=FALSE} # Only run code chunks if Suggests packages available suggestsavailable <- sapply(c("lfe", "haven"), requireNamespace, quietly = TRUE) evalcond <- all(suggestsavailable) knitr::opts_chunk$set( collapse = TRUE, comment = "#>", eval = evalcond ) ``` ```{r setup} library(haven) library(ivreg) library(lfe) library(OneSampleMR) ``` ## Run fsw() on ivreg() model object ```{r} url <- "http://fmwww.bc.edu/ec-p/data/wooldridge/mroz.dta" dat <- haven::read_dta(url) mod <- ivreg(lwage ~ educ + exper | age + kidslt6 + kidsge6, data = dat) summary(mod) fsw(mod) ``` ## Comparison with F-statistic from lfe package ```{r} modst2 <- felm(lwage ~ 1 | 0 | (educ | exper ~ age + kidslt6 + kidsge6), data = dat) summary(modst2) t(sapply(modst2$stage1$lhs, function(lh) { waldtest(modst2$stage1, ~ age | kidslt6 | kidsge6, lhs = lh) })) condfstat(modst2, quantiles = c(0.025, 0.975)) ``` ## Comparison with output from ivreg2 Code run using Stata version 16.1. ``` stata 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), first ``` ``` First-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 ------------------------------------------------------------------------------ ```