Abstract
We model shifts in marriage probabilities in India’s National Family Health Survey-4 (NFHS-4) data by using the discrete time death process. We treat marriages as ‘deaths’, allowing us to incorporate a change point mechanism in the death process. For that, we introduce two new procedures for detecting a discrete change point in the death process. The first test is based on the theoretical distribution of the maximum likelihood estimator (MLE), while the second procedure uses confidence intervals constructed via the parametric bootstrap method. The MLE-based test is shown to have robust power across a wide range of parameter values and sample sizes, but it can have low power when the death rates are near zero. The bootstrap-based procedure is shown to have superior performance in these scenarios. The paper also proposes a new method for constructing confidence intervals for the discrete change point parameter. A method based on the Monte Carlo expectation-maximization algorithm is proposed. This method is more reliable and accurate than the estimation based on the Bayesian information criterion. These methods enable us to capture and analyze the evolution of marriage trends over discrete time intervals. The results show that age is more important in marriage dynamics for females than for males.
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