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Econometrics.md

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Econometrics
Econometrics
Achim Zeileis, Grant McDermott, Kevin Tappe
2022-12-29

Base R ships with a lot of functionality useful for (computational) econometrics, in particular in the stats package. This functionality is complemented by many packages on CRAN, a brief overview is given below. There is also a certain overlap between the tools for econometrics in this view and those in the task views on r view("Finance"), r view("TimeSeries"), and r view("CausalInference").

The packages in this view can be roughly structured into the following topics. If you think that some package is missing from the list, please file an issue in the GitHub repository or contact the maintainer.

Basic linear regression

  • Estimation and standard inference: Ordinary least squares (OLS) estimation for linear models is provided by lm() (from stats) and standard tests for model comparisons are available in various methods such as summary() and anova().
  • Further inference and nested model comparisons: Functions analogous to the basic summary() and anova() methods that also support asymptotic tests (z instead of t tests, and Chi-squared instead of F tests) and plug-in of other covariance matrices are coeftest() and waldtest() in r pkg("lmtest", priority = "core"). (Non)linear hypothesis testing for a wide range of R packages can implemented through the deltamethod() function of r pkg("marginaleffects", priority = "core"). This expands on older (non)linear hypothesis test functions like linearHypothesis() and deltaMethod() from r pkg("car", priority = "core").
  • Robust standard errors: HC, HAC, clustered, and bootstrap covariance matrices are available in r pkg("sandwich", priority = "core") and can be plugged into the inference functions mentioned above.
  • Nonnested model comparisons: Various tests for comparing non-nested linear models are available in r pkg("lmtest") (encompassing test, J test, Cox test). The Vuong test for comparing other non-nested models is provided by r pkg("nonnest2") (and specifically for count data regression in r pkg("pscl")).
  • Diagnostic checking: The packages r pkg("car") and r pkg("lmtest") provide a large collection of regression diagnostics and diagnostic tests.
  • Miscellaneous: Much of the above functionality is bundled together in r pkg("fixest", priority = "core"), which provides a number of in-built convenience features that users may find attractive. This includes robust standard error specification, multi-model estimation, custom hypothesis testing, etc.

Microeconometrics

  • Generalized linear models (GLMs): Many standard microeconometric models belong to the family of generalized linear models and can be fitted by glm() from package stats. This includes in particular logit and probit models for modeling choice data and Poisson models for count data.
  • Effects and marginal effects: Effects for typical values of regressors in GLMs and various other probabilistic regression models can be obtained and visualized using r pkg("effects"). Marginal effect tables and corresponding visualizations for a wide range of models can be be produced with r pkg("marginaleffects", priority = "core"). Other implementations of marginal effects for certain models are in r pkg("margins") and r pkg("mfx"). Interactive visualizations of both effects and marginal effects are possible in r pkg("LinRegInteractive").
  • Binary responses: The standard logit and probit models (among many others) for binary responses are GLMs that can be estimated by glm() with family = binomial. Bias-reduced GLMs that are robust to complete and quasi-complete separation are provided by r pkg("brglm"). Discrete choice models estimated by simulated maximum likelihood are implemented in r pkg("Rchoice"). r pkg("bife") provides binary choice models with fixed effects. Heteroscedastic probit models (and other heteroscedastic GLMs) are implemented in r pkg("glmx") along with parametric link functions and goodness-of-link tests for GLMs.
  • Count responses: The basic Poisson regression is a GLM that can be estimated by glm() with family = poisson as explained above. Negative binomial GLMs are available via glm.nb() in package r pkg("MASS"). Another implementation of negative binomial models is provided by r pkg("aod"), which also contains other models for overdispersed data. Zero-inflated and hurdle count models are provided in package r pkg("pscl"). A reimplementation by the same authors is currently under development in r rforge("countreg") on R-Forge which also encompasses separate functions for zero-truncated regression, finite mixture models etc.
  • Multinomial responses: Multinomial models with individual-specific covariates only are available in multinom() from package r pkg("nnet"). An implementation with both individual- and choice-specific variables is r pkg("mlogit"). Generalized multinomial logit models (e.g., with random effects etc.) are in r pkg("gmnl"). A flexible framework of various customizable choice models (including multinomial logit and nested logit among many others) is implemented in the r pkg("apollo") package. The newer r pkg("logitr") package combines many of the features from these preceding packages and also offers some meaningful performance improvements for fast estimation of multinomial and mixed logit models. Generalized additive models (GAMs) for multinomial responses can be fitted with the r pkg("VGAM") package. A Bayesian approach to multinomial probit models is provided by r pkg("MNP"). Various Bayesian multinomial models (including logit and probit) are available in r pkg("bayesm"). Furthermore, the package r pkg("RSGHB") fits various hierarchical Bayesian specifications based on direct specification of the likelihood function.
  • Ordered responses: Proportional-odds regression for ordered responses is implemented in polr() from package r pkg("MASS"). The package r pkg("ordinal") provides cumulative link models for ordered data which encompasses proportional odds models but also includes more general specifications. Bayesian ordered probit models are provided by r pkg("bayesm").
  • Censored responses: Basic censored regression models (e.g., tobit models) can be fitted by survreg() in r pkg("survival"), a convenience interface tobit() is in package r pkg("AER", priority = "core"). Further censored regression models, including models for panel data, are provided in r pkg("censReg"). Censored regression models with conditional heteroscedasticity are in r pkg("crch"). Furthermore, hurdle models for left-censored data at zero can be estimated with r pkg("mhurdle"). Models for sample selection are available in r pkg("sampleSelection") and r pkg("ssmrob") using classical and robust inference, respectively. Package r pkg("matchingMarkets") corrects for selection bias when the sample is the result of a stable matching process (e.g., a group formation or college admissions problem).
  • Truncated responses: r pkg("crch") for truncated (and potentially heteroscedastic) Gaussian, logistic, and t responses. Homoscedastic Gaussian responses are also available in r pkg("truncreg").
  • Fraction and proportion responses: Beta regression for responses in (0, 1) is in r pkg("betareg") and r pkg("gamlss").
  • Duration responses: Many classical duration models can be fitted with r pkg("survival"), e.g., Cox proportional hazard models with coxph() or Weibull models with survreg(). Many more refined models can be found in the r view("Survival") task view.
  • High-dimensional fixed effects: Linear and generalized linear models with potentially high-dimensional fixed effects, also for multiple groups, can be fitted with r pkg("fixest", priority = "core"), using optimized parallel C++ code. Other implementations of high-dimensional fixed effects are in r pkg("lfe") and r pkg("alpaca") for linear and generalized linear models, respectively.
  • Miscellaneous: Further more refined tools for microeconometrics are provided in the r pkg("micEcon") family of packages: Analysis with Cobb-Douglas, translog, and quadratic functions is in r pkg("micEcon"); the constant elasticity of scale (CES) function is in r pkg("micEconCES"); the symmetric normalized quadratic profit (SNQP) function is in r pkg("micEconSNQP"). The almost ideal demand system (AIDS) is in r pkg("micEconAids"). Stochastic frontier analysis (SFA) is in r pkg("frontier"). Semiparametric SFA in is available in r pkg("semsfa") and spatial SFA in r pkg("ssfa"). The package r pkg("bayesm") implements a Bayesian approach to microeconometrics and marketing. Inference for relative distributions is contained in package r pkg("reldist").

Common research designs for causal inference

We review packages related to some common research designs for causal inference below. This section is necessarily brief and should be paired with the r view("CausalInference") task view, since is there a high degree of overlap.

Difference-in-differences and synthetic control

  • Basic difference-in-differences (DiD): The canonical 2x2 DiD model (two units, two periods) can be estimated as a simple interaction between two factor variables in lm() or glm(), etc. Similarly, the equivalent two-way fixed effects (TWFE) design can be obtained using factors to control for unit and time fixed effects. However, for high-dimensional datasets TWFE is more conveniently estimated using a dedicated panel data package like r pkg("fixest") or r pkg("plm"). The former even provides a convenience i() operator for constructing and interacting factors in TWFE settings.
  • Advanced DiD and TWFE corrections: Despite its long-standing popularity, recent research has uncovered various problems with (naive) TWFE; for example, severe bias in the presence of staggered treatment rollout. A cottage industry of workarounds and alternative estimators now exists to address these problems. R package implementations include: r pkg("bacondecomp"), r pkg("did"), r pkg("did2s"), r pkg("DRDID"), r pkg("etwfe"), r pkg("fixest") (via the sunab() function), and r pkg("gsynth").
  • Synthetic control: The original synthetic control (SC) implementation is available through r pkg("Synth"), while r pkg("tidysynth") offers a newer SC implementation with various enhancements (speed, inspection, etc.) Similarly, r pkg("gsynth") generalizes the original SC implementation to multiple treated units and variable treatment periods, and also supports additional estimation methods like the EM algorithm and matrix completion.

Instrumental variables

  • Basic instrumental variables (IV) regression: Two-stage least squares (2SLS) is provided by r pkg("ivreg", priority = "core"), which separates out the dedicated 2SLS routines previously found in r pkg("AER")). Another implementation is available as tsls() in package r pkg("sem").
  • Binary responses: An IV probit model via GLS estimation is available in r pkg("ivprobit"). The r pkg("LARF") package estimates local average response functions for binary treatments and binary instruments.
  • Panel data: Several panel data model packages (see below) provide their own dedicated IV routines for efficient estimation in the presence of high-dimensional data. These include r pkg("fixest") and r pkg("lfe") for fixed effects, and r pkg("plm") for first-difference, between, and multiple random effects methods.
  • Miscellaneous: r pkg("REndo") fits linear models with endogenous regressor using various latent instrumental variable approaches. r pkg("SteinIV") provides semi-parametric IV estimators, including JIVE and SPS.

Regression discontinuity design

  • Regression discontinuity design (RDD) methods are implemented in r pkg("rdrobust") (offering robust confidence interval construction and bandwidth selection), r pkg("rddensity") (density discontinuity testing (also known as manipulation testing)), r pkg("rdlocrand") (inference under local randomization), and r pkg("rdmulti") (analysis with multiple cutoffs or scores).
  • Tools to perform power, sample size and minimum detectable effects (MDE) calculations are available in r pkg("rdpower"), while r pkg("RATest") provides a collection of randomization tests, including a permutation test for the continuity assumption of the baseline covariates in the sharp RDD.

Panel data models

  • Panel standard errors: A simple approach for panel data is to fit the pooling (or independence) model (e.g., via lm() or glm()) and only correct the standard errors. Different types of clustered, panel, and panel-corrected standard errors are available in r pkg("sandwich") (incorporating prior work from r pkg("multiwayvcov")), r pkg("clusterSEs"), r pkg("pcse"), r pkg("clubSandwich"), r pkg("plm", priority = "core"), and r pkg("geepack"), respectively. The latter two require estimation of the pooling/independence models via plm() and geeglm() from the respective packages (which also provide other types of models, see below).
  • Linear panel models: r pkg("fixest", priority = "core") provides very efficient fixed-effect routines that scale to high-dimensional data and multiple fixed-effects. r pkg("plm"), providing a wide range of within, between, and random-effect methods (among others) along with corrected standard errors, tests, etc. Various dynamic panel models are available in r pkg("plm"), with estimation based on moment conditions in r pkg("pdynmc"), and dynamic panel models with fixed effects in r pkg("OrthoPanels"). r pkg("feisr") provides fixed effects individual slope (FEIS) models. Panel vector autoregressions are implemented in r pkg("panelvar").
  • GLMs and generalized estimation equations. The aformentioned r pkg("fixest") supports a variety of GLM-like models in addition to linear panel models. This includes efficient fixed-effect estimation of logit, probit, Poisson, and negative binomial models. Similar functionality is provided by r pkg("alpaca") (which also accounts for incidental parameter problems) and r pkg("pglm"). GEE models for panel data (or longitudinal data in statistical jargon) are available in in r pkg("geepack").
  • Mixed effects models: Linear and nonlinear models for panel data (and more general multi-level data) are available in r pkg("lme4") and r pkg("nlme").
  • Instrumental variables: r pkg("fixest"). See also above.
  • Miscellaneous: Threshold regression and unit root tests are in r pkg("pdR"). The panel data approach method for program evaluation is available in r pkg("pampe"). Dedicated fast data preprocessing for panel data econometrics is provided by r pkg("collapse").

Further regression models

  • Nonlinear least squares modeling: nls() in package stats.
  • Quantile regression: r pkg("quantreg") (including linear, nonlinear, censored, locally polynomial and additive quantile regressions).
  • Generalized method of moments (GMM) and generalized empirical likelihood (GEL): r pkg("gmm").
  • Spatial econometric models: The r view("Spatial") view gives details about handling spatial data, along with information about (regression) modeling. In particular, spatial regression models can be fitted using r pkg("spatialreg") and r pkg("sphet") (the latter using a GMM approach). r pkg("splm") is a package for spatial panel models. Spatial probit models are available in r pkg("spatialprobit") and spatial seemingly unrelated regression (SUR) models in r pkg("spsur").
  • Bayesian model averaging (BMA): A comprehensive toolbox for BMA is provided by r pkg("BMS") including flexible prior selection, sampling, etc. A different implementation is in r pkg("BMA") for linear models, generalizable linear models and survival models (Cox regression).
  • Linear structural equation models: r pkg("lavaan") and r pkg("sem"). See also the r view("Psychometrics") task view for more details.
  • Machine learning: There are several packages that combine machine learning techniques with econometric inference (especially for identifying causal effects). These include r pkg("grf") for causal random forests and estimation of heterogeneous treatment effects, r pkg("DoubleML") for double machine learning of a wide range of models from the mlr3 family, and r pkg("hdm") for selected high-dimensional econometric models. For a more general overview see the r view("MachineLearning") task view.
  • Simultaneous equation estimation: r pkg("systemfit").
  • Nonparametric methods: r pkg("np") using kernel smoothing and r pkg("NNS") using partial moments.
  • Linear and nonlinear mixed-effect models: r pkg("nlme") and r pkg("lme4").
  • Generalized additive models (GAMs): r pkg("mgcv"), r pkg("gam"), r pkg("gamlss") and r pkg("VGAM").
  • Design-based inference: r pkg("estimatr") contains fast procedures for several design-appropriate estimators with robust standard errors and confidence intervals including linear regression, instrumental variables regression, difference-in-means, among others.
  • Extreme bounds analysis: r pkg("ExtremeBounds").
  • Miscellaneous: The packages r pkg("VGAM"), r pkg("rms") and r pkg("Hmisc") provide several tools for extended handling of (generalized) linear regression models.

Time series data and models

  • The r view("TimeSeries") task view provides much more detailed information about both basic time series infrastructure and time series models. Here, only the most important aspects relating to econometrics are briefly mentioned. Time series models for financial econometrics (e.g., GARCH, stochastic volatility models, or stochastic differential equations, etc.) are described in the r view("Finance") task view.
  • Infrastructure for regularly spaced time series: The class "ts" in package stats is R's standard class for regularly spaced time series (especially annual, quarterly, and monthly data). It can be coerced back and forth without loss of information to "zooreg" from package r pkg("zoo", priority = "core").
  • Infrastructure for irregularly spaced time series: r pkg("zoo") provides infrastructure for both regularly and irregularly spaced time series (the latter via the class "zoo") where the time information can be of arbitrary class. This includes daily series (typically with "Date" time index) or intra-day series (e.g., with "POSIXct" time index). An extension based on r pkg("zoo") geared towards time series with different kinds of time index is r pkg("xts"). Further packages aimed particularly at finance applications are discussed in the r view("Finance") task view.
  • Classical time series models: Simple autoregressive models can be estimated with ar() and ARIMA modeling and Box-Jenkins-type analysis can be carried out with arima() (both in the stats package). An enhanced version of arima() is in r pkg("forecast", priority = "core").
  • Linear regression models: A convenience interface to lm() for estimating OLS and 2SLS models based on time series data is r pkg("dynlm"). Linear regression models with AR error terms via GLS is possible using gls() from r pkg("nlme").
  • Structural time series models: Standard models can be fitted with StructTS() in stats. Further packages are discussed in the r view("TimeSeries") task view.
  • Filtering and decomposition: decompose() and HoltWinters() in stats. The basic function for computing filters (both rolling and autoregressive) is filter() in stats. Many extensions to these methods, in particular for forecasting and model selection, are provided in the r pkg("forecast") package.
  • Vector autoregression: Simple models can be fitted by ar() in stats, more elaborate models are provided in package r pkg("vars") along with suitable diagnostics, visualizations etc. Panel vector autoregressions are available in r pkg("panelvar").
  • Unit root and cointegration tests: r pkg("urca", priority = "core"), r pkg("tseries", priority = "core"), r pkg("CADFtest"). See also r pkg("pco") for panel cointegration tests and r pkg("plm", priority = "core") for panel unit root tests.
  • Miscellaneous:
    • r pkg("tsDyn") - Threshold and smooth transition models.
    • r pkg("midasr") - MIDAS regression and other econometric methods for mixed frequency time series data analysis.
    • r pkg("gets") - GEneral-To-Specific (GETS) model selection for either ARX models with log-ARCH-X errors, or a log-ARCH-X model of the log variance.
    • r pkg("bimets") - Econometric modeling of time series data using flexible specifications of simultaneous equation models.
    • r pkg("dlsem") - Distributed-lag linear structural equation models.
    • r pkg("lpirfs") - Local projections impulse response functions.
    • r pkg("apt") - Asymmetric price transmission models.

Data sets

  • Textbooks and journals: Packages r pkg("AER"), r pkg("Ecdat"), and r pkg("wooldridge") contain a comprehensive collections of data sets from various standard econometric textbooks (including Greene, Stock & Watson, Wooldridge, Baltagi, among others) as well as several data sets from the Journal of Applied Econometrics and the Journal of Business & Economic Statistics data archives. r pkg("AER") and r pkg("wooldridge") additionally provide extensive sets of examples reproducing analyses from the textbooks/papers, illustrating various econometric methods. In r pkg("pder") a wide collection of data sets for "Panel Data Econometrics with R" (Croissant & Millo 2018) is available. The r github("ccolonescu/PoEdata") package on GitHub provides the data sets from "Principles of Econometrics" (4th ed, by Hill, Griffiths, and Lim 2011).
  • Canadian monetary aggregates: r pkg("CDNmoney").
  • Penn World Table: r pkg("pwt") provides versions 5.6, 6.x, 7.x. Version 8.x and 9.x data are available in r pkg("pwt8") and r pkg("pwt9"), respectively.
  • Time series and forecasting data: The packages r pkg("expsmooth"), r pkg("fma"), and r pkg("Mcomp") are data packages with time series data from the books "Forecasting with Exponential Smoothing: The State Space Approach" (Hyndman, Koehler, Ord, Snyder, 2008, Springer) and "Forecasting: Methods and Applications" (Makridakis, Wheelwright, Hyndman, 3rd ed., 1998, Wiley) and the M-competitions, respectively.
  • Empirical Research in Economics: Package r pkg("erer") contains functions and datasets for the book of "Empirical Research in Economics: Growing up with R" (Sun 2015).
  • Panel Study of Income Dynamics (PSID): r pkg("psidR") can build panel data sets from the Panel Study of Income Dynamics (PSID).
  • World Bank data and statistics: The r pkg("wbstats") package provides programmatic access to the World Bank API.

Miscellaneous

  • Model tables: A flexible implementation of side-by-side summary tables for a wide range of statistical models along with corresponding visualizations and data summary tables is provided in r pkg("modelsummary"). Other implementations as well as further utilities for integrating econometric and statistical results in scientific papers etc. are discussed in the r view("ReproducibleResearch") task view.
  • Matrix manipulations: As a vector- and matrix-based language, base R ships with many powerful tools for doing matrix manipulations, which are complemented by the packages r pkg("Matrix") and r pkg("SparseM").
  • Optimization and mathematical programming: R and many of its contributed packages provide many specialized functions for solving particular optimization problems, e.g., in regression as discussed above. Further functionality for solving more general optimization problems, e.g., likelihood maximization, is discussed in the the r view("Optimization") task view.
  • Bootstrap: In addition to the recommended r pkg("boot") package, there are some other general bootstrapping techniques available in r pkg("bootstrap") or r pkg("simpleboot") as well some bootstrap techniques designed for time-series data, such as the maximum entropy bootstrap in r pkg("meboot") or the tsbootstrap() from r pkg("tseries"). The r pkg("fwildclusterboot") package provides a fast wild cluster bootstrap implementation for linear regression models, especially when the number of clusters is low.
  • Inequality: For measuring inequality, concentration and poverty the package r pkg("ineq") provides some basic tools such as Lorenz curves, Pen's parade, the Gini coefficient, Herfindahl-Hirschman index and many more.
  • Structural change: R is particularly strong when dealing with structural changes and changepoints in parametric models, see r pkg("strucchange") and r pkg("segmented").
  • Exchange rate regimes: Methods for inference about exchange rate regimes, in particular in a structural change setting, are provided by r pkg("fxregime").
  • Global value chains: Tools and decompositions for global value chains are in r pkg("gvc") and r pkg("decompr").
  • Regression discontinuity design: A variety of methods are provided in the r pkg("rdd"), r pkg("rdrobust"), and r pkg("rdlocrand") packages. The r pkg("rdpower") package offers power calculations for regression discontinuity designs. And r pkg("rdmulti") implements analysis with multiple cutoffs or scores.
  • Gravity models: Estimation of log-log and multiplicative gravity models is available in r pkg("gravity").
  • z-Tree: r pkg("zTree") can import data from the z-Tree software for developing and carrying out economic experiments.
  • Numerical standard errors: r pkg("nse") implements various numerical standard errors for time series data, especially in simulation experiments with correlated outcome sequences.

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