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

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