The `penppml`

package is a set of tools that enables
efficient estimation of penalized Poisson Pseudo Maximum Likelihood
(PPML) regressions, using lasso or ridge penalties, for models that
feature one or more sets of high-dimensional fixed effects (HDFE). The
methodology is based on Breinlich, Corradi, Rocha, Ruta, Santos Silva,
and Zylkin (2021) and takes advantage of the method of alternating
projections of Gaure (2013) for dealing with HDFE, as well as the
coordinate descent algorithm of Friedman, Hastie and Tibshirani (2010)
for fitting lasso regressions. The package is also able to carry out
cross-validation and to implement the plugin lasso of Belloni,
Chernozhukov, Hansen and Kozbur (2016).

You can install the released version of penppml from CRAN with:

`install.packages("penppml")`

And the development version from GitHub with:

```
# install.packages("devtools")
::install_github("diegoferrerasg/penppml") devtools
```

This is a basic example which demonstrate how to estimate a gravity model of international trade with three sets of HDFE using the package:

```
# Setup:
library(penppml)
<- countries$iso[countries$region %in% c("Americas")]
selected <- trade[(trade$exp %in% selected) & (trade$imp %in% selected), -(5:6)]
trade2 <- c(0.05, 0.025, 0.01, 0.0075, 0.005, 0.0025, 0.001, 0.00075, 0.0005, 0.00025, 0.0001, 0) lambdas
```

```
# Main command:
<- mlfitppml(data = trade2,
reg dep = "export",
fixed = list(c("exp", "time"),
c("imp", "time"),
c("exp", "imp")),
penalty = "lasso",
lambdas = lambdas)
```

We can plot the resulting regularization path as follows:

For more examples and details on how to use the package, see the vignette.

Breinlich, H., Corradi, V., Rocha, N., Ruta, M., Santos Silva, J.M.C. and T. Zylkin, T. (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.