hdfeppml function

PPML Estimation with HDFE

hdfeppml fits an (unpenalized) Poisson Pseudo Maximum Likelihood (PPML) model with high-dimensional fixed effects (HDFE).

hdfeppml(
  data,
  dep = 1,
  indep = NULL,
  fixed = NULL,
  cluster = NULL,
  selectobs = NULL,
  ...
)

Arguments

• data: A data frame containing all relevant variables.
• dep: A string with the name of the independent variable or a column number.
• indep: A vector with the names or column numbers of the regressors. If left unspecified, all remaining variables (excluding fixed effects) are included in the regressor matrix.
• fixed: A vector with the names or column numbers of factor variables identifying the fixed effects, or a list with the desired interactions between variables in data.
• cluster: Optional. A string with the name of the clustering variable or a column number. It's also possible to input a vector with several variables, in which case the interaction of all of them is taken as the clustering variable.
• selectobs: Optional. A vector indicating which observations to use (either a logical vector or a numeric vector with row numbers, as usual when subsetting in R).
• ...: Further options. For a full list, see hdfeppml_int .

Returns

A list with the following elements:

• coefficients: a 1 x ncol(x) matrix with coefficient (beta) estimates.
• residuals: a 1 x length(y) matrix with the residuals of the model.
• mu: a 1 x length(y) matrix with the final values of the conditional mean $\mu$.
• deviance:
• bic: Bayesian Information Criterion.
• x_resid: matrix of demeaned regressors.
• z_resid: vector of demeaned (transformed) dependent variable.
• se: standard errors of the coefficients.

Details

This function is a thin wrapper around hdfeppml_int , providing a more convenient interface for data frames. Whereas the internal function requires some preliminary handling of data sets (y

must be a vector, x must be a matrix and fixed effects fes must be provided in a list), the wrapper takes a full data frame in the data argument, and users can simply specify which variables correspond to y, x and the fixed effects, using either variable names or column numbers.

More formally, hdfeppml_int performs iteratively re-weighted least squares (IRLS) on a transformed model, as described in Correia, Guimarães and Zylkin (2020) and similar to the ppmlhdfe package in Stata. In each iteration, the function calculates the transformed dependent variable, partials out the fixed effects (calling collapse:fhdwithin) and then solves a weighted least squares problem (using fast C++ implementation).

References

Breinlich, H., Corradi, V., Rocha, N., Ruta, M., Santos Silva, J.M.C. and T. Zylkin (2021). "Machine Learning in International Trade Research: Evaluating the Impact of Trade Agreements", Policy Research Working Paper; No. 9629. World Bank, Washington, DC.

Correia, S., P. Guimaraes and T. Zylkin (2020). "Fast Poisson estimation with high dimensional fixed effects", STATA Journal, 20, 90-115.

Gaure, S (2013). "OLS with multiple high dimensional category variables", Computational Statistics & Data Analysis, 66, 8-18.

Friedman, J., T. Hastie, and R. Tibshirani (2010). "Regularization paths for generalized linear models via coordinate descent", Journal of Statistical Software, 33, 1-22.

Belloni, A., V. Chernozhukov, C. Hansen and D. Kozbur (2016). "Inference in high dimensional panel models with an application to gun control", Journal of Business & Economic Statistics, 34, 590-605.

Examples

## Not run:

# To reduce run time, we keep only countries in the Americas:
americas <- countries$iso[countries$region == "Americas"]
test <- hdfeppml(data = trade[, -(5:6)],
                   dep = "export",
                   fixed = list(c("exp", "time"),
                                c("imp", "time"),
                                c("exp", "imp")),
                   selectobs = (trade$imp %in% americas) & (trade$exp %in% americas))
## End(Not run)