al., 2010).<sup>7</sup> LASSO models were fitted separately to four dependent variables. These are the transformed versions of the four labor market outcomes, AGEB male or female labor force participation and unemployment rates, using the arcsine transformation. The candidate predictors included in the LASSO model include all of the AGEB and municipal level geospatial auxiliary data described in the last section, as well as dummy variables for states. The state dummies were included with no penalty, and were included to both improve the model and to prioritize the selection of variables that predict variation in the labor market outcomes within states.

# **d. Model estimation**

We begin by constructing two separate estimates of LFP and unemployment in Mexico:

1. Direct estimates using only the pseudo survey of sampled AGEBs, which can only be constructed for in-sample municipalities.

2. Small area estimates using the pseudo survey of sampled AGEBs and the auxiliary geospatial data, which can be constructed for all municipalities, both in and out of sample.

These estimates are compared with the full census results along several different dimensions to assess their accuracy, as discussed below.

To generate the small area estimates for municipalities, we utilize a standard nested error model at the AGEB level (Battese, Harter, and Fuller, 1988, Jiang and Lahiri, 2006, Molina and Rao, 2010). The transformed version of the labor market outcome at the AGEB level is modeled as a linear function of geospatial auxiliary variables. The dependent variable was transformed using an arcsine transformation, a common transformation for proportions bounded between zero and one. The model used to generate municipal estimates is specified as follows: (1) s s 1<sup>+XX</sup> s 2<sup>+ XX</sup> 3<sup>+ υυ</sup> s s ss<sup>) = XX</sup> ss<sup>ββββ</sup> ss<sup>ββ</sup> ss<sup>, s=1,...,S,m=1,...,Ms; a=1,...,Asm,</sup> where G(G(yys + uu female LFP, and male and female unemployment rate) of AGEB a within municipality m and state ss<sup>) denotes the arcsine of one of the four estimated labor market outcomes (male and</sup> s, derived from the sample. The model is assumed to hold for the full population of AGEBs yy although it is estimated using the sample. Xsma is a vector of geospatial auxiliary variables specified at the AGEB level, while Xsm is a vector of geospatial auxiliary variables aggregated to the municipal level. Xs is a vector of state dummy variables. β1 , β2 , and β3 are vectors of regression coefficients, s 2 , and is a set of municipality conditional random effects. s 2) is a residual error term. As noted above, the set of vv predictor variables was selected using the BIC-minimizing lasso procedure from the full set of υυ is distributed normally with variance σσ ss<sup>~NN(0, σσ</sup> uu candidate variables, with the full set of state dummies Xuu s included with no penalty.

For the model used to generate estimates for states, the specification is similar, except that the conditional random effect is omitted from the model:

> 7 The BIC was based on the unpenalized regression of selected variables rather than the penalized regression, and when estimating the lasso, standard errors were clustered at the municipality level.

8