A new Stata command for spatial differencing estimation is now available. sreg fits the following model:

$y_{ic}= \theta_z + \mathbf{x}_{ic}'\mathbf{\beta} + \epsilon_{ic}$

where $y_{ic}$ is the outcome of unit $i$ located in area $c$ with $c=1,\ldots,C$, $\mathbf{x}_{ic}$ is a $k$-vector of exogenous covariates, $\epsilon_{ic}$ is the idiosyncratic error and $\theta_z$ is an unobserved local effect for the unobserved location $z$, $z=1,\ldots,Z$, possibly at a finer spatial scale than $c$. Estimating this model by ordinary least squares ignoring $\theta_z$ gives a consistent estimate of $\mathbf{\beta}$ only if $\mathbb{E}(\theta_z|\mathbf{x}_{ic})=0$. If we set aside this unrealistic assumption and allow for arbitrary correlation between the local unobservables and the explanatory variables, i.e. $\mathbb{E}(\theta_z|\mathbf{x}_{ic})\neq 0$, a non-experimental approach to estimating the model involves, in some way, transforming the data to rule out $\theta_z$. An increasingly common way to deal with this issue is the so-called spatial differencing approach.

sreg implements the spatial differencing estimator described in Belotti et al. (2017), as well as different variance-covariance estimators, among which the dyadic-robust (Cameron and Miller, 2014) and the Duranton et al. (2011)'s analytically-corrected estimators. Of special note is that sreg also allow to apply the spatial differencing transformation to units located in contiguous clusters ("boundary-discontinuity" design).

The command was written together with Edoardo Di Porto and Gianluca Santoni.

You may install it by typing

net install sreg, from(http://www.econometrics.it/stata)

in your Stata command bar. Stata version 14.2 is required.

HTH,
Federico