csdm

csdm estimates heterogeneous panel models when units may share unobserved common factors. It provides mean-group (MG), common correlated effects (CCE), dynamic CCE (DCCE), and cross-sectionally augmented ARDL (CS-ARDL) estimators, along with residual cross-sectional dependence diagnostics.

The package follows the econometric structure used by Stata’s xtdcce2, while using standard R model methods and explicit specification objects. It does not yet implement every xtdcce2 option.

Installation

Install the CRAN release:

install.packages("csdm")

Install the development version:

install.packages("remotes")
remotes::install_github("Macosso/csdm")

Estimators

All four estimators fit unit-specific regressions and average the eligible unit-level coefficients. CCE-based models add cross-sectional averages as proxies for latent common factors. CS-ARDL derives adjustment and long-run parameters from the fitted unit-level ARDL coefficients.

Quick start

The bundled data contain 93 countries observed annually from 1960 through 2007. The example below uses 12 countries from 1970 onward so it runs quickly.

library(csdm)

data(PWT_60_07, package = "csdm")
keep_ids <- unique(PWT_60_07$id)[1:12]
dat <- subset(PWT_60_07, id %in% keep_ids & year >= 1970)

form <- log_rgdpo ~ log_hc + log_ck + log_ngd
csa_vars <- c("log_rgdpo", "log_hc", "log_ck", "log_ngd")

mg <- csdm(form, data = dat, id = "id", time = "year", model = "mg")

cce <- csdm(
  form, data = dat, id = "id", time = "year", model = "cce",
  csa = csdm_csa(vars = csa_vars)
)

dcce <- csdm(
  form, data = dat, id = "id", time = "year", model = "dcce",
  csa = csdm_csa(vars = csa_vars, lags = 3),
  lr = csdm_lr(type = "ardl", ylags = 1, xdlags = 0)
)

cs_ardl <- csdm(
  form, data = dat, id = "id", time = "year", model = "cs_ardl",
  csa = csdm_csa(vars = csa_vars, lags = 3),
  lr = csdm_lr(type = "ardl", ylags = 1, xdlags = 0)
)

summary(cce)
coef(cs_ardl, component = "long_run")
vcov(cs_ardl, component = "long_run")

csdm_csa() controls the variables and lags used for cross-sectional averages. csdm_lr() controls lags of the dependent variable and regressors. Numeric time indexes use time_step = 1 by default, and lag construction preserves gaps in calendar time.

Cross-sectional dependence diagnostics

cd_test() accepts a fitted csdm model or an N by T residual matrix:

cd_test(cce, type = "CD")
cd_test(cce, type = "all", seed = 42)

The available diagnostics are classical CD, randomized CDw, power-enhanced CDw+, and bias-corrected CD*. CD uses pairwise-complete observations by default. CDw, CDw+, and CD* require a balanced residual sample. Periods with no finite residuals for any retained unit are removed automatically; for partially observed periods, request a common sample explicitly:

cd_test(cce, type = "all", seed = 42,
        na.action = "drop.incomplete.times")

Use a fixed seed when reporting CDw or CDw+ because their Rademacher weights are random. The tests use different corrections and should be interpreted against their own assumptions; agreement among p-values is not a substitute for checking those assumptions.

R model interface

Fitted models support the model methods expected by downstream R tools:

coef(cce)
vcov(cce)
residuals(cce)                  # unit-by-time matrix
residuals(cce, format = "long")
fitted(cce, format = "vector")
nobs(cce)
model.frame(cce)

library(modelsummary)
modelsummary(list(MG = mg, CCE = cce, DCCE = dcce))

tidy(), glance(), and augment() methods are available through the generics/broom interface. update() refits a model using its stored call and sample metadata.

Current scope

• Mean-group inference uses the cross-unit sample covariance of unit estimates divided by the number of eligible units and large-N normal approximations.
• CCE identification depends on cross-sectional averages spanning the relevant common-factor space. DCCE and CS-ARDL additionally require sufficient time observations for the requested lags.
• CS-ARDL reports levels coefficients, an implied adjustment coefficient, and implied long-run ratios. It does not fit a separate ECM or establish cointegration.
• Pooled restrictions, estimation weights, alternative fit-level covariance estimators, CS-DL, CS-ECM, and prediction on new data are not implemented.
• csdm_pooled(), get_residuals(), prepare_cd_input(), and the low-level covariance helpers are deprecated. Use standard model methods on fitted objects.

Corrected estimation samples and covariance calculations in the development version can change results from earlier releases. Refit saved models after upgrading.

Documentation

• Introduction and worked examples
• Function reference
• Issue tracker

Methodological foundations include Pesaran and Smith (1995), Pesaran (2006), Chudik and Pesaran (2015), Juodis and Reese (2022), and Pesaran and Xie (2022).