Research Database

This paper proposes a new way of modeling age, period, and cohort effects that improves substantively and methodologically on the conventional linear model. The linear model suffers from a well-known identification problem: If we assume an outcome of interest depends on the sum of an age effect, a period effect, and a cohort effect, then it is impossible to distinguish these three separate effects because, for any individual, birth year = current year – age. Less well appreciated is that the model also suffers from a conceptual problem: It assumes that the influence of age is the same in all time periods, the influence of present conditions is the same for people of all ages, and cohorts do not change over time. We argue that in many applications, these assumptions fail. We propose a more general model in which age profiles can change over time and period effects can have different influences on people of different ages. Our model defines cohort effects as an accumulation of age-by-period interactions. Although a long-standing literature on theories of social change conceptualizes cohort effects in exactly this way, we are the first to show how to statistically model this more complex form of cohort effects. We show that the additive model is a special case of our model and that, except in special cases, the parameters of the more general model are identified. We apply our model to analyze changes in age-specific mortality rates in Sweden over the past 150 years. Our model fits the data dramatically better than the additive model. The estimates show that the rate of increase of mortality with age among adults became more steep from 1881 to 1941, but since then the rate of increase has been roughly constant. The estimates also allow us to test whether early-life conditions have lasting impacts on mortality, as under the cohort morbidity phenotype hypothesis. The results give limited support to this hypothesis: The impact of early-life conditions lasts for several years but is unlikely to reach all the way to old age.

How well do people share risk? Standard risk-sharing regressions assume that any variation in households’ risk preferences is uncorrelated with variation in the cyclicality of income. I combine administrative and survey data to show that this assumption is questionable: Risk-tolerant workers hold jobs where earnings carry more aggregate risk. The correlation makes risk-sharing regressions in the previous literature too pessimistic. I derive techniques that eliminate the bias, apply them to U.S. data, and find that the effect of idiosyncratic income shocks on consumption is practically small and statistically difficult to distinguish from zero.

We construct a random matching model of a monetary economy with commodity money in the form of potentially different types of silver coins that are distinguishable by the quantity of metal they contain. The quantity of silver in the economy is assumed to be fixed, but agents can mint and melt coins. Coins yield no utility, but can be traded. Uncoined silver yields direct utility to the holder. We find that optimal coin size increases with the probability of trade and with the stock of silver. We use these predictions of our model to analyze the coinage decisions of the monetary authorities in medieval Venice and England. Our model provides theoretical support for the view that decisions about coin sizes and types during the medieval period reflected a desire to improve the economic welfare of the general population, not just the desire for seigniorage revenue.

The 2007–2009 crisis was characterized by an unprecedented degree of international synchronization as all major industrialized countries experienced large macroeconomic contractions around the date of Lehman bankruptcy. At the same time countries also experienced large and synchronized tightening of credit conditions. We present a two-country model with financial market frictions where a credit tightening can emerge as a self-fulfilling equilibrium caused by pessimistic but fully rational expectations. As a result of the credit tightening, countries experience large and endogenously synchronized declines in asset prices and economic activity (international recessions). The model suggests that these recessions are more severe if they happen after a prolonged period of credit expansion.

We show that much of the recent reported decrease in interstate migration is a statistical artifact. Before 2006, the Census Bureau’s imputation procedure for dealing with missing data in the Current Population Survey inflated the estimated interstate migration rate. An undocumented change in the procedure corrected the problem starting in 2006, thus reducing the estimated migration rate. The change in imputation procedures explains 90 percent of the reported decrease in interstate migration between 2005 and 2006, and 42 percent of the decrease between 2000 (the recent high-water mark) and 2010. After we remove the effect of the change in procedures, we find that the annual interstate migration rate follows a smooth downward trend from 1996 to 2010. Contrary to popular belief, the 2007–2009 recession is not associated with any additional decrease in interstate migration relative to trend.