Abstract
AbstractExchanges of practical or financial help between people living in different households are a major component of intergenerational exchanges within families and an increasingly important source of support for individuals in need. Using longitudinal data, bivariate dynamic panel models can be applied to study the effects of changes in individual circumstances on help given to and received from non-coresident parents and the reciprocity of exchanges. However, the use of a rotating module for collection of data on exchanges leads to data where the response measurements are unequally spaced and taken less frequently than for the time-varying covariates. Existing approaches to this problem focus on fixed effects linear models for univariate continuous responses. We propose a random effects estimator for a family of dynamic panel models that can handle continuous, binary or ordinal multivariate responses. The performance of the estimator is assessed in a simulation study. A bivariate probit dynamic panel model is then applied to estimate the effects of partnership and employment transitions in the previous year and the presence and age of children in the current year on an individual’s propensity to give or receive help. Annual data on respondents’ partnership, employment status and dependent children, and data on exchanges of help collected at 2- and 5-year intervals are used in this study.
Highlights
Dynamic models, known as autoregressive or lagged response models, have been widely used for the analysis of longitudinal data in a broad range of application areas such as unemployment (Arulampalam et al, 2000), political preferences (Stegmueller, 2013), and health and well-being (Pudney, 2008; Steele et al, 2013)
A common motivation for using a dynamic model is to investigate the relative contributions of persistence and unobserved heterogeneity as explanations for serial correlation in a response y, where persistence is a causal effect of an individual’s past values of y on their current value and unobserved heterogeneity refers to individual differences in y due to unmeasured time-invariant characteristics
Performance was good for the three additional conditions described above (n = 500, Mi ≤ 4 and skewed random effects distribution; see Table S2)
Summary
Known as autoregressive or lagged response models, have been widely used for the analysis of longitudinal data in a broad range of application areas such as unemployment (Arulampalam et al, 2000), political preferences (Stegmueller, 2013), and health and well-being (Pudney, 2008; Steele et al, 2013). Standard discrete-time dynamic panel models assume that measurements of the response and time-varying covariates are taken at the same spaced occasions. As the correlation between an individual’s responses at two points in time t1 and t2 will typically decay with |t2 − t1|, the coefficients of the lagged response and time-varying covariates capturing changes between t1 and t2 cannot be assumed invariant to spacing. The naïve treatment of unequally spaced observations as if they are spaced will lead to biased coefficients of the lagged response and serially correlated predictors (Millimet & McDonough, 2017; Sasaki & Xin, 2017). Unequal spacing is a common feature of longitudinal studies, which may arise by design or because of wave non-response (see Millimet and McDonough (2017) for a number of examples from developed countries). A common design feature of household panel studies is the use of rotating modules to reduce survey costs and respondent burden, which leads to some variables being measured less frequently, and often at unequal intervals, than variables collected in the core questionnaire at each (usually annual) wave
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