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Combining cross-sectional and time-series data is a long and well-established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two datasets. We focus on common factors as the mechanism behind this dependence. Using our central limit theorem (CLT), we establish the asymptotic properties of parameter estimates of a general class of models based on a combination of cross-sectional and time-series data, recognizing the interdependence between the two data sources in the presence of aggregate shocks. Despite the complicated nature of the analysis required to formulate the joint CLT, it is straightforward to implement the resulting parameter limiting distributions due to a formal similarity of our approximations with Murphy and Topel’s (1985, Journal of Business and Economic Statistics 3, 370–379) formula.
In this paper, we complement joint time-series and cross-section convergence results derived in a companion paper Hahn, Kuersteiner, and Mazzocco (2016, Central Limit Theory for Combined Cross-Section and Time Series) by allowing for serial correlation in the time-series sample. The implications of our analysis are limiting distributions that have a well-known form of long-run variances for the time-series limit. We obtain these results at the cost of imposing strict stationarity for the time-series model and conditional independence between the time-series and cross-section samples. Our results can be applied to estimators that combine time-series and cross-section data in the presence of aggregate uncertainty in models with rationally forward-looking agents.
Marriage patterns can be well understood only if researchers employ measures of marriage rates that are appropriate for the question asked. In this paper, we provide evidence that the two classes of measures typically used in the literature, the number of new marriages per population and the share of individuals currently or ever married within an age range, generally lead to misleading inference when used to study the probability someone marries during his or her life or fertile life, how it evolves, and how it differs across populations. An alternative measure, the share of individuals ever married in a given cohort by a given age, is better suited for such studies. When researchers are interested in year-on-year changes in marriage probabilities of singles, age-specific marriage hazards are more reliable than population-based measures. We conclude by discussing implications of our findings for studies of the drivers and consequences of marriage formation.
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