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An Application of the Propensity Score Matching
The Analytical Services Branch recently investigated the usefulness of propensity score matching (PSM) in the context of the ABS Business Characteristics Survey (BCS). The research, which is based on the 2009-10 wave of the BCS data, aimed to produce an adequate matched sample for statistical analyses. Overall, the results show that the PSM can be a useful technique for creating matched samples from the BCS.
The methodology follows the propensity score matching approach suggested by Rosenbaum and Rubin (1983). By matching, the aim was to control for the impact of the variables that could contribute to the selection process, which are assumed to be captured by the selected observed variables, and to create a matched sample with balanced observed covariates. In the context of this study, the PSM was used to match the firms that received government assistance to similar firms that did not receive any government support.
As part of the methodology, the study considered three matching algorithms, namely, the nearest neighbour, the caliper, and the 5 to 1 digit matching. After making sure that the PSM assumptions were met, the algorithms were subjected to various robustness tests and micro assessments. Some of these tests include the chi-square, the standardised bias, and the pseudo R-squared.
As an application on the matched sample, the study tested for the impact of the correlation within matched pairs by considering a random effects model– i.e., a probit generalised linear mixed model. The results were then compared to those of an ordinary probit model (ignoring the within-group correlation), so as to observe the impact of the correlation within matched pairs, and to those of a probit model on a non-matched sample, so as to examine the impact of the PSM on the regression results.
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