Evaluating time-varying treatment effects in latent Markov models: An application to the effect of remittances on poverty dynamics

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 interest is in an individual characteristic that is not directly observable and the analysis is focused on: (i) clustering individuals in a finite number of classes according to this latent characteristic and (ii) modelling its evolution across time depending on the received treatment. Parameter estimation is based on a two-step procedure in which individual weights are computed for each time period based on predetermined covariates and a weighted version of the standard LM model likelihood based on such weights is maximised by means of an expectation-maximisation algorithm. Finite-sample properties of the estimator 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 response variables are indicators of deprivation.