fevcov {lfe}

Compute limited mobility bias corrected covariance matrix between fixed effects

Description

With a model like y = X\beta + D\theta + F\psi + \epsilon, where D and F are matrices with dummy encoded factors, one application of lfe is to study the variances var(D\theta), var(F\psi) and covariances cov(D\theta, F\psi). However, if we use estimates for \theta and \psi, the resulting variances are biased. The function fevcov computes a bias corrected covariance matrix as described in Gaure (2014).

Usage

fevcov(
  est,
  alpha = getfe(est),
  tol = 0.01,
  robust = !is.null(est$clustervar),
  maxsamples = Inf,
  lhs = NULL
)

Arguments

est

an object of class '"felm"', the result of a call to ⁠[felm](keepX=TRUE)⁠.

alpha

a data frame, the result of a call to getfe().

tol

numeric. The absolute tolerance for the bias-corrected correlation.

robust

logical. Should robust (heteroskedastic or cluster) residuals be used, rather than i.i.d.

maxsamples

integer. Maximum number of samples for expectation estimates.

lhs

character. Name of left hand side if multiple left hand sides.

Details

The tol argument specifies the tolerance. The tolerance is relative for the variances, i.e. the diagonal of the output. For the covariances, the tolerance is relative to the square root of the product of the variances, i.e. an absolute tolerance for the correlation. If a numeric of length 1, tol specifies the same tolerance for all variances/covariances. If it is of length 2, tol[1] specifies the variance tolerance, and tol[2] the covariance tolerance. tol can also be a square matrix of size length(est$fe), in which case the tolerance for each variance and covariance is specified individually.

The function performs no checks for estimability. If the fixed effects are not estimable, the result of a call to fevcov is not useable. Moreover, there should be just a single connected component among the fixed effects.

alpha must contain a full set of coefficients, and contain columns 'fe' and 'effect' like the default estimable functions from efactory().

In the case that the felm()-estimation has weights, it is the weighted variances and covariance which are bias corrected.

Value

fevcov returns a square matrix with the bias corrected covariances. An attribute 'bias' contains the biases. The bias corrections have been subtracted from the bias estimates. I.e. vc = vc' - b, where vc' is the biased variance and b is the bias.

Note

Bias correction for IV-estimates are not supported as of now.

Note that if est is the result of a call to felm() with keepX=FALSE (the default), the biases will be computed as if the covariates X are independent of the factors. This will be faster (typically by a factor of approx. 4), and possibly wronger. Note also that the computations performed by this function are non-trivial, they may take quite some time. It would be wise to start out with quite liberal tolerances, e.g. tol=0.1, to get an idea of the time requirements.

If there are only two fixed effects, fevcov returns the same information as bccorr(), though in a slightly different format.

References

Gaure, S. (2014), Correlation bias correction in two-way fixed-effects linear regression, Stat 3(1):379-390, 2014. doi:10.1002/sta4.68

See Also

varvars() bccorr()

Examples

x <- rnorm(5000)
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 <- runif(nlevels(firm))
foo.eff <- rchisq(nlevels(foo), df = 1)
## left hand side
id.m <- id.eff[id]
firm.m <- firm.eff[firm]
foo.m <- foo.eff[foo]
# normalize them
id.m <- id.m / sd(id.m)
firm.m <- firm.m / sd(firm.m)
foo.m <- foo.m / sd(foo.m)
y <- x + 0.25 * x2 + id.m + firm.m + foo.m + rnorm(length(x), sd = 2)
z <- x + 0.5 * x2 + 0.7 * id.m + 0.5 * firm.m + 0.3 * foo.m + rnorm(length(x), sd = 2)
# make a data frame
fr <- data.frame(y, z, x, x2, id, firm, foo)
## estimate and print result
est <- felm(y | z ~ x + x2 | id + firm + foo, data = fr, keepX = TRUE)
# find bias corrections, there's little bias in this example
print(yv <- fevcov(est, lhs = "y"))
## Here's how to compute the unbiased correlation matrix:
cm <- cov2cor(yv)
structure(cm, bias = NULL)