R: Overview. Linear Group Fixed Effects

lfe-package {lfe} | R Documentation

## Overview. Linear Group Fixed Effects

### Description

The package uses the Method of Alternating Projections to estimate linear models with multiple group fixed effects. A generalization of the within estimator. It supports IV-estimation with multiple endogenous variables via 2SLS, with conditional F statistics for detection of weak instruments. It is thread-parallelized and intended for large problems. A method for correcting limited mobility bias is also included.

### Details

This package is intended for linear models with multiple group fixed effects, i.e. with 2 or more factors with a large number of levels. It performs similar functions as `lm`, but it uses a special method for projecting out multiple group fixed effects from the normal equations, hence it is faster. It is a generalization of the within estimator. This may be required if the groups have high cardinality (many levels), resulting in tens or hundreds of thousands of dummy variables. It is also useful if one only wants to control for the group effects, without actually estimating them. The package may optionally compute standard errors for the group effects by bootstrapping, but this is a very time- and memory-consuming process compared to finding the point estimates. If you only have a single huge factor, the package plm is probably better suited. If your factors don't have thousands of levels, `lm` or other packages are probably better suited. lfe is designed to produce the same results as `lm` will do if run with the full set of dummies.

Projecting out interactions between continuous covariates and factors is supported. I.e. individual slopes, not only individual intercepts. Multiple left hand sides are supported.

The package does not support non-linear models. For GLMs with many dummies there is a package alpaca which uses similar methods to project them out.

The estimation is done in two steps. First the other coefficients are estimated with the function `felm` by centering on all the group means, followed by an OLS (similar to lm). Then the group effects are extracted (if needed) with the function `getfe`. This method is described by Gaure (2013), but also appears in Guimaraes and Portugal (2010), disguised as the Gauss-Seidel algorithm.

There's also a function `demeanlist` which just does the centering on an arbitrary matrix or data frame, and there's a function `compfactor` which computes the connected components which are used for interpreting the group effects when there are only two factors (see the Abowd et al references), they are also returned by `getfe`.

For those who study the correlation between the fixed effects, like in Abowd et al. (1999), there are functions `bccorr` and `fevcov` for computing limited mobility bias corrected correlations and variances with the method described in Gaure (2014b).

Instrumental variable estimations are supported with 2SLS. Conditional F statistics for testing reduced rank weak instruments as in Sanderson and Windmeijer (2015) are available in `condfstat`. Joint significance testing of coefficients is available in `waldtest`.

The centering on the means is done with a tolerance which is set by `options(lfe.eps=1e-8)` (the default). This is a somewhat conservative tolerance, in many cases I'd guess `1e-6` may be sufficient. This may speed up the centering. In the other direction, setting `options(lfe.eps=0)` will provide maximum accuracy at the cost of computing time and warnings about convergence failure.

The package is threaded, that is, it may use more than one cpu. The number of threads is fetched upon loading the package from the environment variable LFE_THREADS, OMP_THREAD_LIMIT, OMP_NUM_THREADS or NUMBER_OF_PROCESSORS (for Windows), and stored by `options(lfe.threads=n)`. This option can be changed prior to calling `felm`, if so desired. Note that, typically, lfe is limited by memory bandwidth, not cpu speed, thus fast memory and large cache is more important than clock frequency. It is therefore also not always true that running on all available cores is much better than running on half of them.

Threading is only done for the centering; the extraction of the group effects is not threaded. The default method for extracting the group coefficients is the iterative Kaczmarz-method, its tolerance is also the `lfe.eps` option. For some datasets the Kaczmarz-method is converging very slowly, in this case it may be replaced with a conjugate gradient method by setting the option `options(lfe.usecg=TRUE)`. Various time-consuming parts of lfe may print progress reports, the minimum interval in seconds is `options(lfe.pint=1800)`.

The package has been tested on datasets with approx 20,000,000 observations with 15 covariates and approx 2,300,000 and 270,000 group levels (the `felm` took about 50 minutes on 8 cpus, the `getfe` takes 5 minutes). Though, beware that not only the size of the dataset matters, but also its structure, as demonstrated by Gaure (2014a).

The package will work with any number of grouping factors, but if more than two, their interpretation is in general not well understood, i.e. one should make sure that the group coefficients are estimable. A discussion of estimability, the algorithm used, and convergence rate are available in vignettes, as well as in the published papers in the citation list (`citation('lfe')`).

In the exec-directory there is a perl-script `lfescript` which is used at the author's site for automated creation of R-scripts from a simple specification file. The format is documented in `doc/lfeguide.txt`.

lfe is similar in function, though not in method, to the Stata modules `a2reg` and `felsdvreg`. The method is very similar to the one in the Stata module `reghdfe`.

### References

Abowd, J.M., F. Kramarz and D.N. Margolis (1999) High Wage Workers and High Wage Firms, Econometrica 67 (1999), no. 2, 251–333. doi: 10.1111/1468-0262.00020

Abowd, J.M., R. Creecy and F. Kramarz (2002) Computing Person and Firm Effects Using Linked Longitudinal Employer-Employee Data. Technical Report TP-2002-06, U.S. Census Bureau. https://www2.census.gov/ces/tp/tp-2002-06.pdf

Andrews, M., L. Gill, T. Schank and R. Upward (2008) High wage workers and low wage firms: negative assortative matching or limited mobility bias? J.R. Stat. Soc.(A) 171(3), 673–697. doi: 10.1111/j.1467-985X.2007.00533.x

Cornelissen, T. (2008) The stata command felsdvreg to fit a linear model with two high-dimensional fixed effects. Stata Journal, 8(2):170–189, 2008. https://econpapers.repec.org/RePEc:tsj:stataj:v:8:y:2008:i:2:p:170-189

Correia, S. (2014) REGHDFE: Stata module to perform linear or instrumental-variable regression absorbing any number of high-dimensional fixed effects, Statistical Software Components, Boston College Department of Economics. https://econpapers.repec.org/RePEc:boc:bocode:s457874

Croissant, Y. and G. Millo (2008) Panel Data Econometrics in R: The plm Package, Journal of Statistical Software, 27(2). https://www.jstatsoft.org/v27/i02/

Gaure, S. (2013) OLS with Multiple High Dimensional Category Variables. Computational Statistics and Data Analysis, 66:8–18, 2013 doi: 10.1016/j.csda.2013.03.024

Gaure, S. (2014a) lfe: Linear Group Fixed Effects. The R Journal, 5(2):104-117, Dec 2013. https://journal.r-project.org/archive/2013/RJ-2013-031/RJ-2013-031.pdf

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

Guimaraes, P. and Portugal, P. (2010) A simple feasible procedure to fit models with high-dimensional fixed effects. The Stata Journal, 10(4):629–649, 2010. https://www.stata-journal.com/article.html?article=st0212

Ouazad, A. (2008) A2REG: Stata module to estimate models with two fixed effects. Statistical Software Components S456942, Boston College Department of Economics. https://ideas.repec.org/c/boc/bocode/s456942.html

Sanderson, E. and F. Windmeijer (2014) A weak instrument F-test in linear IV models with multiple endogenous variables, Journal of Econometrics, 2015. https://www.sciencedirect.com/science/article/pii/S0304407615001736

### Examples

      oldopts <- options("lfe.threads")
      options(lfe.threads = 2)
      x <- rnorm(1000)
      x2 <- rnorm(length(x))
      id <- factor(sample(10,length(x),replace=TRUE))
      firm <- factor(sample(3,length(x),replace=TRUE,prob=c(2,1.5,1)))
      year <- factor(sample(10,length(x),replace=TRUE,prob=c(2,1.5,rep(1,8))))
      id.eff <- rnorm(nlevels(id))
      firm.eff <- rnorm(nlevels(firm))
      year.eff <- rnorm(nlevels(year))
      y <- x + 0.25*x2 + id.eff[id] + firm.eff[firm] +
             year.eff[year] + rnorm(length(x))
      est <- felm(y ~ x+x2 | id + firm + year)
      summary(est)

      getfe(est,se=TRUE)
    # compare with an ordinary lm
      summary(lm(y ~ x+x2+id+firm+year-1))
      options(oldopts)

[Package lfe version 2.8-7 Index]