Causal inference for time-varying treatments in latent Markov models: An application to the effects of remittances on poverty dynamics

Abstract

To assess the effectiveness of remittances on the poverty level of recipient households, we propose a causal inference approach that may be applied with longitudinal data and time-varying treatments. The method relies on the integration of a propensity score based technique, the inverse propensity weighting, with a general latent Markov (LM) framework. It is particularly useful when the outcome of interest is a characteristic that is not directly observable, and the analysis is focused on: (i) clustering units in a finite number of classes according to this latent characteristic and (ii) modelling the evolution of this characteristic across time depending on the received treatment. Parameter estimation is based on a two-step procedure. First, individual propensity score weights are computed accounting for predetermined covariates. Then, a weighted version of the standard LM model likelihood, based on such weights, is maximised by means of an expectation-maximisation algorithm or, alternatively, adopting a stepwise procedure. Finite-sample properties of the proposed estimators are studied by simulation. The application is focused on the effect of remittances on the poverty status of Ugandan households, based on a longitudinal survey spanning the period 2009–2014, and where manifest variables are indicators of deprivation. We find that remittances reduce the probability of falling into poverty, whereas they exert no impact on the probability of moving out of poverty.