This package estimates linear models with high dimensional categorical variables and/or instrumental variables.
The package is registered in the
General registry and so can be installed at the REPL with
] add FixedEffectModels.
using DataFrames, RDatasets, FixedEffectModels df = dataset("plm", "Cigar") reg(df, @formula(Sales ~ NDI + fe(State) + fe(Year)), Vcov.cluster(:State), weights = :Pop) # ===================================================================== # Number of obs: 1380 Degrees of freedom: 32 # R2: 0.803 R2 Adjusted: 0.798 # F Statistic: 13.3382 p-value: 0.001 # R2 within: 0.139 Iterations: 6 # Converged: true # ===================================================================== # Estimate Std.Error t value Pr(>|t|) Lower 95% Upper 95% # --------------------------------------------------------------------- # NDI -0.00526264 0.00144097 -3.65216 0.000 -0.00808942 -0.00243586 # =====================================================================
A typical formula is composed of one dependent variable, exogeneous variables, endogeneous variables, instrumental variables, and a set of high-dimensional fixed effects.
dependent variable ~ exogenous variables + (endogenous variables ~ instrumental variables) + fe(fixedeffect variable)
High-dimensional fixed effect variables are indicated with the function
fe. You can add an arbitrary number of high dimensional fixed effects, separated with
+. You can also interact fixed effects using
For instance, to add state fixed effects use
fe(State). To add both state and year fixed effects, use
fe(State) + fe(Year). To add state-year fixed effects, use
fe(State)&fe(Year). To add state specific slopes for year, use
fe(State)&Year. To add both state fixed-effects and state specific slopes for year use
reg(df, @formula(Sales ~ Price + fe(State) + fe(Year))) reg(df, @formula(Sales ~ NDI + fe(State) + fe(State)&Year)) reg(df, @formula(Sales ~ NDI + fe(State)&fe(Year))) # for illustration only (this will not run here) reg(df, @formula(Sales ~ (Price ~ Pimin)))
To construct formula programatically, use
reg(df, Term(:Sales) ~ Term(:NDI) + fe(Term(:State)) + fe(Term(:Year))
Standard errors are indicated with the prefix
Vcov.robust() Vcov.cluster(:State) Vcov.cluster(:State, :Year)
weightsspecifies a variable for weights
weights = :Pop
subsetspecifies a subset of the data
subset = df.State .>= 30
savecan be set to one of the following:
:residualsto save residuals,
:feto save fixed effects,
trueto save both. You can access the result with
methodcan be set to one of the following:
:gpu(see Performances below).
contrastsspecifies particular contrasts for categorical variables in the formula, e.g.
df.YearC = categorical(df.Year) reg(df, @formula(Sales ~ YearC); contrasts = Dict(:YearC => DummyCoding(base = 80)))
reg returns a light object. It is composed of
- the vector of coefficients & the covariance matrix (use
vcovon the output of
- a boolean vector reporting rows used in the estimation
- a set of scalars (number of observations, the degree of freedoms, r2, etc)
- with the option
save = true, a dataframe aligned with the initial dataframe with residuals and, if the model contains high dimensional fixed effects, fixed effects estimates (use
feon the output of
Methods such as
residuals are still defined but require to specify a dataframe as a second argument. The problematic size of
glm models in R or Julia is discussed here, here, here here (and for absurd consequences, here and there).
You may use RegressionTables.jl to get publication-quality regression tables.
The package has support for GPUs (Nvidia) (thanks to Paul Schrimpf). This can make the package an order of magnitude faster for complicated problems.
First make sure that
using CuArrays works without issue. Then, estimate a model with
method = :gpu.
When working on the GPU, it is encouraged to set the floating point precision to
double_precision = false, since it is usually much faster.
using FixedEffectModels df = dataset("plm", "Cigar") reg(df, @formula(Sales ~ NDI + fe(State) + fe(Year)), method = :gpu, double_precision = false)
Denote the model
y = X β + D θ + e where X is a matrix with few columns and D is the design matrix from categorical variables. Estimates for
β, along with their standard errors, are obtained in two steps:
y, Xare regressed on
Dusing the package FixedEffects.jl
- Estimates for
β, along with their standard errors, are obtained by regressing the projected
yon the projected
X(an application of the Frisch Waugh-Lovell Theorem)
- With the option
save = true, estimates for the high dimensional fixed effects are obtained after regressing the residuals of the full model minus the residuals of the partialed out models on
Dusing the package FixedEffects.jl
Baum, C. and Schaffer, M. (2013) AVAR: Stata module to perform asymptotic covariance estimation for iid and non-iid data robust to heteroskedasticity, autocorrelation, 1- and 2-way clustering, and common cross-panel autocorrelated disturbances. Statistical Software Components, Boston College Department of Economics.
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.
Fong, DC. and Saunders, M. (2011) LSMR: An Iterative Algorithm for Sparse Least-Squares Problems. SIAM Journal on Scientific Computing
Gaure, S. (2013) OLS with Multiple High Dimensional Category Variables. Computational Statistics and Data Analysis
Kleibergen, F, and Paap, R. (2006) Generalized reduced rank tests using the singular value decomposition. Journal of econometrics
Kleibergen, F. and Schaffer, M. (2007) RANKTEST: Stata module to test the rank of a matrix using the Kleibergen-Paap rk statistic. Statistical Software Components, Boston College Department of Economics.