TFT
Reputation: 231
2SLS standard errors with ivreg and plm in R
Could someone please confirm whether ivreg is calculating correct 2SLS standard errors by default or do I still have to manually correct them? I have an instrumental variable Z1 in my regression.
library(ivreg)
ivreg1 <- ivreg(log(Y) ~ log(X) + W1 + W2 + W3 | W1 + W2 + W3 + Z1, data = lending)
I then continue to combine IV with fixed effects. Do I have to manually correct the standard errors here? I need robust standard errors for sure.
library(plm)
IVpan <- plm(log(Y) ~ log(X) + W1 + W2 + W3 | W1 + W2 + W3 + Z1, model = "within", data = lending, index = c("countryIdentifier","year"))
In case a correction is needed, I guess I would have calculated the robust standard errors just like this:
covIVpan1 <- vcovHC(IVpan, type = "HC1")
robust_seIVpan1 <- sqrt(diag(covIVpan1))
Upvotes: 1
Views: 3490
Answers (1)
Helix123
Reputation: 3687
Your assumption about plm and IV models estimated by it are correct. The conventional approach in R is to have the model estimation and the robust standard error estimation split in two different steps. Typically, summary methods for model objects will accept a vcov argument with other than the usual standard errors or a function to estimate them (typically also called vcov with varying arguments).
See below for a panel IV example with plm.
For ivreg, the typicall approach applies as well. See below (for a slightly extended) example from ?ivreg::ivreg making also use of pkg sandwich.
Example for plm::plm with panel IV model:
library(plm)
data("Crime", package = "plm")
FE2SLS <- plm(lcrmrte ~ lprbarr + lpolpc + lprbconv + lprbpris + lavgsen +
ldensity + lwcon + lwtuc + lwtrd + lwfir + lwser + lwmfg + lwfed +
lwsta + lwloc + lpctymle + lpctmin + region + smsa + factor(year)
| . - lprbarr - lpolpc + ltaxpc + lmix,
data = Crime, model = "within")
summary(FE2SLS, vcov = vcovHC)
#> Oneway (individual) effect Within Model
#> Instrumental variable estimation
#>
#> Note: Coefficient variance-covariance matrix supplied: vcovHC
#>
#> Call:
#> plm(formula = lcrmrte ~ lprbarr + lpolpc + lprbconv + lprbpris +
#> lavgsen + ldensity + lwcon + lwtuc + lwtrd + lwfir + lwser +
#> lwmfg + lwfed + lwsta + lwloc + lpctymle + lpctmin + region +
#> smsa + factor(year) | . - lprbarr - lpolpc + ltaxpc + lmix,
#> data = Crime, model = "within")
#>
#> Balanced Panel: n = 90, T = 7, N = 630
#>
#> Residuals:
#> Min. 1st Qu. Median 3rd Qu. Max.
#> -0.7209110 -0.0682207 -0.0041115 0.0759381 0.5661659
#>
#> Coefficients:
#> Estimate Std. Error z-value Pr(>|z|)
#> lprbarr -0.5755058 0.7884162 -0.7300 0.4654
#> lpolpc 0.6575270 0.8624838 0.7624 0.4458
#> lprbconv -0.4231446 0.4998464 -0.8465 0.3972
#> lprbpris -0.2502550 0.2755415 -0.9082 0.3638
#> lavgsen 0.0090987 0.0550200 0.1654 0.8687
#> ldensity 0.1394120 0.9959261 0.1400 0.8887
#> lwcon -0.0287308 0.0381071 -0.7539 0.4509
#> lwtuc 0.0391292 0.0281711 1.3890 0.1648
#> lwtrd -0.0177536 0.0337546 -0.5260 0.5989
#> lwfir -0.0093443 0.0240168 -0.3891 0.6972
#> lwser 0.0185854 0.0368987 0.5037 0.6145
#> lwmfg -0.2431684 0.4342518 -0.5600 0.5755
#> lwfed -0.4513372 0.5134606 -0.8790 0.3794
#> lwsta -0.0187458 0.3083631 -0.0608 0.9515
#> lwloc 0.2632585 0.2924827 0.9001 0.3681
#> lpctymle 0.3511166 1.0707877 0.3279 0.7430
#> factor(year)82 0.0378562 0.0641333 0.5903 0.5550
#> factor(year)83 -0.0443801 0.0425536 -1.0429 0.2970
#> factor(year)84 -0.0451868 0.0610387 -0.7403 0.4591
#> factor(year)85 -0.0209411 0.0789048 -0.2654 0.7907
#> factor(year)86 0.0063234 0.1178049 0.0537 0.9572
#> factor(year)87 0.0435055 0.2002534 0.2173 0.8280
#>
#> Total Sum of Squares: 17.991
#> Residual Sum of Squares: 11.537
#> R-Squared: 0.44364
#> Adj. R-Squared: 0.32442
#> Chisq: 228.359 on 22 DF, p-value: < 2.22e-16
sqrt(diag(vcovHC(FE2SLS)))
#> lprbarr lpolpc lprbconv lprbpris lavgsen
#> 0.78841618 0.86248381 0.49984636 0.27554147 0.05501995
#> ldensity lwcon lwtuc lwtrd lwfir
#> 0.99592612 0.03810713 0.02817113 0.03375456 0.02401682
#> lwser lwmfg lwfed lwsta lwloc
#> 0.03689867 0.43425180 0.51346057 0.30836311 0.29248269
#> lpctymle factor(year)82 factor(year)83 factor(year)84 factor(year)85
#> 1.07078768 0.06413330 0.04255357 0.06103873 0.07890485
#> factor(year)86 factor(year)87
#> 0.11780486 0.20025343
summary(FE2SLS, vcov = vcovHC)
#> Oneway (individual) effect Within Model
#> Instrumental variable estimation
#>
#> Note: Coefficient variance-covariance matrix supplied: vcovHC
#>
#> Call:
#> plm(formula = lcrmrte ~ lprbarr + lpolpc + lprbconv + lprbpris +
#> lavgsen + ldensity + lwcon + lwtuc + lwtrd + lwfir + lwser +
#> lwmfg + lwfed + lwsta + lwloc + lpctymle + lpctmin + region +
#> smsa + factor(year) | . - lprbarr - lpolpc + ltaxpc + lmix,
#> data = Crime, model = "within")
#>
#> Balanced Panel: n = 90, T = 7, N = 630
#>
#> Residuals:
#> Min. 1st Qu. Median 3rd Qu. Max.
#> -0.7209110 -0.0682207 -0.0041115 0.0759381 0.5661659
#>
#> Coefficients:
#> Estimate Std. Error z-value Pr(>|z|)
#> lprbarr -0.5755058 0.7884162 -0.7300 0.4654
#> lpolpc 0.6575270 0.8624838 0.7624 0.4458
#> lprbconv -0.4231446 0.4998464 -0.8465 0.3972
#> lprbpris -0.2502550 0.2755415 -0.9082 0.3638
#> lavgsen 0.0090987 0.0550200 0.1654 0.8687
#> ldensity 0.1394120 0.9959261 0.1400 0.8887
#> lwcon -0.0287308 0.0381071 -0.7539 0.4509
#> lwtuc 0.0391292 0.0281711 1.3890 0.1648
#> lwtrd -0.0177536 0.0337546 -0.5260 0.5989
#> lwfir -0.0093443 0.0240168 -0.3891 0.6972
#> lwser 0.0185854 0.0368987 0.5037 0.6145
#> lwmfg -0.2431684 0.4342518 -0.5600 0.5755
#> lwfed -0.4513372 0.5134606 -0.8790 0.3794
#> lwsta -0.0187458 0.3083631 -0.0608 0.9515
#> lwloc 0.2632585 0.2924827 0.9001 0.3681
#> lpctymle 0.3511166 1.0707877 0.3279 0.7430
#> factor(year)82 0.0378562 0.0641333 0.5903 0.5550
#> factor(year)83 -0.0443801 0.0425536 -1.0429 0.2970
#> factor(year)84 -0.0451868 0.0610387 -0.7403 0.4591
#> factor(year)85 -0.0209411 0.0789048 -0.2654 0.7907
#> factor(year)86 0.0063234 0.1178049 0.0537 0.9572
#> factor(year)87 0.0435055 0.2002534 0.2173 0.8280
#>
#> Total Sum of Squares: 17.991
#> Residual Sum of Squares: 11.537
#> R-Squared: 0.44364
#> Adj. R-Squared: 0.32442
#> Chisq: 228.359 on 22 DF, p-value: < 2.22e-16
## same:
sqrt(diag(vcovHC(FE2SLS)))
#> lprbarr lpolpc lprbconv lprbpris lavgsen
#> 0.78841618 0.86248381 0.49984636 0.27554147 0.05501995
#> ldensity lwcon lwtuc lwtrd lwfir
#> 0.99592612 0.03810713 0.02817113 0.03375456 0.02401682
#> lwser lwmfg lwfed lwsta lwloc
#> 0.03689867 0.43425180 0.51346057 0.30836311 0.29248269
#> lpctymle factor(year)82 factor(year)83 factor(year)84 factor(year)85
#> 1.07078768 0.06413330 0.04255357 0.06103873 0.07890485
#> factor(year)86 factor(year)87
#> 0.11780486 0.20025343
# with HC1 small sample correction
summary(FE2SLS, vcov = function(x) vcovHC(x, type="HC1"))
#> Oneway (individual) effect Within Model
#> Instrumental variable estimation
#>
#> Note: Coefficient variance-covariance matrix supplied: function(x) vcovHC(x, type = "HC1")
#>
#> Call:
#> plm(formula = lcrmrte ~ lprbarr + lpolpc + lprbconv + lprbpris +
#> lavgsen + ldensity + lwcon + lwtuc + lwtrd + lwfir + lwser +
#> lwmfg + lwfed + lwsta + lwloc + lpctymle + lpctmin + region +
#> smsa + factor(year) | . - lprbarr - lpolpc + ltaxpc + lmix,
#> data = Crime, model = "within")
#>
#> Balanced Panel: n = 90, T = 7, N = 630
#>
#> Residuals:
#> Min. 1st Qu. Median 3rd Qu. Max.
#> -0.7209110 -0.0682207 -0.0041115 0.0759381 0.5661659
#>
#> Coefficients:
#> Estimate Std. Error z-value Pr(>|z|)
#> lprbarr -0.5755058 0.8025535 -0.7171 0.4733
#> lpolpc 0.6575270 0.8779493 0.7489 0.4539
#> lprbconv -0.4231446 0.5088093 -0.8316 0.4056
#> lprbpris -0.2502550 0.2804823 -0.8922 0.3723
#> lavgsen 0.0090987 0.0560065 0.1625 0.8709
#> ldensity 0.1394120 1.0137844 0.1375 0.8906
#> lwcon -0.0287308 0.0387904 -0.7407 0.4589
#> lwtuc 0.0391292 0.0286763 1.3645 0.1724
#> lwtrd -0.0177536 0.0343598 -0.5167 0.6054
#> lwfir -0.0093443 0.0244475 -0.3822 0.7023
#> lwser 0.0185854 0.0375603 0.4948 0.6207
#> lwmfg -0.2431684 0.4420385 -0.5501 0.5822
#> lwfed -0.4513372 0.5226676 -0.8635 0.3878
#> lwsta -0.0187458 0.3138925 -0.0597 0.9524
#> lwloc 0.2632585 0.2977273 0.8842 0.3766
#> lpctymle 0.3511166 1.0899883 0.3221 0.7474
#> factor(year)82 0.0378562 0.0652833 0.5799 0.5620
#> factor(year)83 -0.0443801 0.0433166 -1.0246 0.3056
#> factor(year)84 -0.0451868 0.0621332 -0.7273 0.4671
#> factor(year)85 -0.0209411 0.0803197 -0.2607 0.7943
#> factor(year)86 0.0063234 0.1199173 0.0527 0.9579
#> factor(year)87 0.0435055 0.2038442 0.2134 0.8310
#>
#> Total Sum of Squares: 17.991
#> Residual Sum of Squares: 11.537
#> R-Squared: 0.44364
#> Adj. R-Squared: 0.32442
#> Chisq: 220.384 on 22 DF, p-value: < 2.22e-16
## same:
sqrt(diag(vcovHC(FE2SLS, type="HC1")))
#> lprbarr lpolpc lprbconv lprbpris lavgsen
#> 0.80255354 0.87794930 0.50880927 0.28048230 0.05600654
#> ldensity lwcon lwtuc lwtrd lwfir
#> 1.01378441 0.03879045 0.02867628 0.03435982 0.02444747
#> lwser lwmfg lwfed lwsta lwloc
#> 0.03756031 0.44203851 0.52266760 0.31389248 0.29772729
#> lpctymle factor(year)82 factor(year)83 factor(year)84 factor(year)85
#> 1.08998834 0.06528329 0.04331662 0.06213323 0.08031972
#> factor(year)86 factor(year)87
#> 0.11991726 0.20384425
Example for ivreg::ivreg:
library(ivreg)
data("CigaretteDemand", package = "ivreg")
## model
m <- ivreg(log(packs) ~ log(rprice) + log(rincome) | salestax + log(rincome),
data = CigaretteDemand)
summary(m)
#>
#> Call:
#> ivreg(formula = log(packs) ~ log(rprice) + log(rincome) | salestax +
#> log(rincome), data = CigaretteDemand)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.611000 -0.086072 0.009423 0.106912 0.393159
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 9.4307 1.3584 6.943 1.24e-08 ***
#> log(rprice) -1.1434 0.3595 -3.181 0.00266 **
#> log(rincome) 0.2145 0.2686 0.799 0.42867
#>
#> Diagnostic tests:
#> df1 df2 statistic p-value
#> Weak instruments 1 45 45.158 2.65e-08 ***
#> Wu-Hausman 1 44 1.102 0.3
#> Sargan 0 NA NA NA
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.1896 on 45 degrees of freedom
#> Multiple R-Squared: 0.4189, Adjusted R-squared: 0.3931
#> Wald test: 6.534 on 2 and 45 DF, p-value: 0.003227
summary(m, vcov = sandwich::sandwich, df = Inf)
#>
#> Call:
#> ivreg(formula = log(packs) ~ log(rprice) + log(rincome) | salestax +
#> log(rincome), data = CigaretteDemand)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.611000 -0.086072 0.009423 0.106912 0.393159
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 9.4307 1.2194 7.734 1.04e-14 ***
#> log(rprice) -1.1434 0.3605 -3.172 0.00151 **
#> log(rincome) 0.2145 0.3018 0.711 0.47729
#>
#> Diagnostic tests:
#> df1 df2 statistic p-value
#> Weak instruments 1 45 47.713 1.4e-08 ***
#> Wu-Hausman 1 44 1.287 0.263
#> Sargan 0 NA NA NA
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.1896 on Inf degrees of freedom
#> Multiple R-Squared: 0.4189, Adjusted R-squared: 0.3931
#> Wald test: 2 on NA DF, p-value: NA
## same:
sqrt(diag(sandwich::sandwich(m)))
#> (Intercept) log(rprice) log(rincome)
#> 1.2194016 0.3604805 0.3018477
Upvotes: 2
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