Compute the variance of the fixed effect variance estimate
Compute the variance of the fixed effect variance estimate
varvars(est, alpha = getfe(est), tol = 0.01, biascorrect = FALSE, lhs = NULL)
est |
an object of class '"felm"', the result of a call to
|
alpha |
a data frame, the result of a call to |
tol |
numeric. The absolute tolerance for the bias-corrected correlation. |
biascorrect |
logical. Should the estimates be bias corrected? |
lhs |
character. Name of left hand side if multiple left hand sides. |
With a model like y = Xβ + Dθ + Fψ + ε, where D and
F are matrices with dummy encoded factors, one application of lfe is
to study the variances var(Dθ), var(Fψ) and covariances
cov(Dθ, Fψ). The function fevcov computes bias corrected
variances and covariances. However, these variance estimates are still
random variables for which fevcov only estimate the
expectation. The function varvars estimates the variance of these
estimates.
This function returns valid results only for normally distributed residuals.
Note that the estimates for the fixed effect variances from
fevcov are not normally distributed, but a sum of chi-square
distributions which depends on the eigenvalues of certain large matrices. We
do not compute that distribution. The variances returned by varvars
can therefore not be used directly to estimate confidence intervals,
other than through coarse methods like the Chebyshev inequality. These
estimates only serve as a rough guideline as to how wrong the variance
estimates from fevcov might be.
Like the fixed effect variances themselves, their variances are also biased upwards. Correcting this bias can be costly, and is therefore by default switched off.
The variances tend to zero with increasing number of observations. Thus, for large datasets they will be quite small.
varvars returns a vector with a variance estimate for each
fixed effect variance. I.e. for the diagonal returned by
fevcov.
The tol argument specifies the tolerance as in
fevcov. Note that if est is the result of a call to
felm with keepX=FALSE (the default), the variances will
be estimated as if the covariates X are independent of the factors. There
is currently no function available for estimating the variance of the
covariance estimates from fevcov.
The cited paper does not contain the expressions for the variances computed
by varvars (there's a 10 page limit in that journal), though they can
be derived in the same fashion as in the paper, with the formula for the
variance of a quadratic form.
Gaure, S. (2014), Correlation bias correction in two-way fixed-effects linear regression, Stat 3(1):379-390, 2014.
x <- rnorm(500) x2 <- rnorm(length(x)) ## create individual and firm id <- factor(sample(40,length(x),replace=TRUE)) firm <- factor(sample(30,length(x),replace=TRUE,prob=c(2,rep(1,29)))) foo <- factor(sample(20,length(x),replace=TRUE)) ## effects id.eff <- rnorm(nlevels(id)) firm.eff <- rnorm(nlevels(firm)) foo.eff <- rnorm(nlevels(foo)) ## left hand side id.m <- id.eff[id] firm.m <- 2*firm.eff[firm] foo.m <- 3*foo.eff[foo] y <- x + 0.25*x2 + id.m + firm.m + foo.m + rnorm(length(x)) # make a data frame fr <- data.frame(y,x,x2,id,firm,foo) ## estimate and print result est <- felm(y ~ x+x2|id+firm+foo, data=fr, keepX=TRUE) alpha <- getfe(est) # estimate the covariance matrix of the fixed effects fevcov(est, alpha) # estimate variances of the diagonal varvars(est, alpha)
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