Do siblings freeride in “ being there ” for parents ?

ing from the dynamic aspects of siblings’ location decisions with the exception of birth order. For our estimates to be meaningful and credible, our empirical framework must be approximately consistent with the underlying data generating process. In particular, the explanatory variables used in estimation are taken from information recorded many years after children have made their location decisions. The results can be interpreted consistently with our behavioral model if all our explanatory variables were either observed or accurately predicted at the time children made those decisions. For this reason, we have carefully selected our independent variables such that they can be argued as being time-invariant or reasonably stable and predictable in the long run. Nevertheless, a number of factors may undermine the validity of our cross-sectional approach. A child’s location decision might have a long-term effect on our explanatory variables, such as parental health (reverse causality). Location and spouse might be determined at the same time (simultaneity). A child might have responded to recent parental health decline many years after that child first left the parent (misspecification of the time frame), and current variables might have accumulated stochastic errors since the child makes the decision; thus they may lead to downward bias even if the child’s prediction is not biased (measurement error). To address these concerns, we estimate a model that excludes parental health and marital variables, which may be endogenous events in later life. We find that the results of the simplified model are consistent with the full model overall, despite its poorer model fit. Counterfactual simulation results also remain similar. This finding provides 20We find slightly larger estimates of externality as well as a smaller proportion of families experiencing inefficient family location. These two findings arise at the same time because although the sample of siblings with a larger age gap leads to a larger estimate of strategic effect, such siblings tend to have more diverse characteristics than siblings of similar age. When players differ to a greater extent, they are more likely to have a dominant strategy and game outcomes depend less on strategic interaction. 308 Maruyama and Johar Quantitative Economics 8 (2017) some assurance that our main findings are not driven by the time inconsistency due to the time-variant variables.21 8.2 Alternative behavioral assumptions We have so far centered our analysis on perfect-information sequential games. To investigate the appropriateness of this behavioral assumption, we discuss three alternative models. Cooperative maximization First, we examine the assumption of noncooperative decision making. This assumption is to some extent justified by the discrete and long-term nature of location choice, but siblings may be able to arrange enforceable side-payment transfers to achieve the highest joint utility possible, as discussed by Engers and Stern (2002). We examine this possibility by estimating a model of joint-utility maximization. This model uses the same functional-form specification as our preferred model, namely, (3), (4), and (6), and assumes the joint-utility maximization