% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/est_csardl.R
\name{csardl_estimator}
\alias{csardl_estimator}
\title{CS-ARDL Estimator Internals}
\description{
Internal functions for the Cross-Sectionally augmented ARDL (CS-ARDL)
estimator of Chudik, Mohaddes, Pesaran & Raissi (2016). Estimates an
ARDL\eqn{(p_y, p_x)} model with cross-sectional averages and recovers
long-run coefficients and the speed of adjustment via the delta method.
}
\details{
The unit-level regression is
\deqn{y_{it} = \alpha_i + \sum_{p=1}^{P_y} \phi_{ip} y_{i,t-p}
               + \sum_{q=0}^{P_x} \beta'_{iq} x_{i,t-q}
               + \delta'_{i} \bar{z}_t + e_{it}.}

The long-run coefficient on \eqn{x_k} is
\deqn{\theta_{ik} = \frac{\sum_{q=0}^{P_x} \beta_{ikq}}{1 - \sum_{p=1}^{P_y} \phi_{ip}}}
and the implied speed of adjustment is
\deqn{\varphi_i = -\left(1 - \sum_{p=1}^{P_y} \phi_{ip}\right).}
}
\keyword{internal}
