Research Database

This paper develops new recursive methods for studying stationary sequential equilibria in games with private monitoring. We first consider games where play has occurred forever into the past and develop methods for analyzing a large class of stationary strategies, where the main restriction is that the strategy can be represented as a finite automaton. For a subset of this class, strategies which depend only on the players’ signals in the last k periods, these methods allow the construction of all pure strategy equilibria. We then show that each sequential equilibrium in a game with infinite histories defines a correlated equilibrium for a game with a start date and derive simple necessary and sufficient conditions for determining if an arbitrary correlation device yields a correlated equilibrium. This allows, for games with a start date, the construction of all pure strategy sequential equilibria in this subclass.

Prior to 1863, state-chartered banks in the United States issued notes–dollar-denominated promises to pay specie to the bearer on demand. Although these notes circulated at par locally, they usually were quoted at a discount outside the local area. These discounts varied by both the location of the bank and the location where the discount was being quoted. Further, these discounts were asymmetric across locations, meaning that the discounts quoted in location A on the notes of banks in location B generally differed from the discounts quoted in location B on the notes of banks in location A. Also, discounts generally increased when banks suspended payments on their notes. In this paper we construct a random matching model to qualitatively match these facts about banknote discounts. To attempt to account for locational differences, the model has agents that come from two distinct locations. Each location also has bankers that can issue notes. Banknotes are accepted in exchange because banks are required to produce when a banknote is presented for redemption and their past actions are public information. Overall, the model delivers predictions consistent with the behavior of discounts.

This paper presents a simple model of search and matching between consumers and firms. The firm size distribution has a Pareto-like right tail if the population of consumers grows at a positive rate and the mean rate at which incumbent firms gain customers is also positive. This happens in equilibrium when entry is sufficiently costly. As entry costs grow without bound, the size distribution approaches Zipf’s law. The slow rate at which the right tail of the size distribution decays and the 10% annual gross entry rate of new firms observed in the data suggest that more than a third of all consumers must switch from one firm to another during a given year. A substantially lower consumer switching rate can be inferred only if part of the observed firm entry rate is attributed to factors outside the model. The realized growth rates of large firms in the model are too smooth.

We make three comparisons relevant for the business cycle accounting approach. We show that in theory representing the investment wedge as a tax on investment is equivalent to representing this wedge as a tax on capital income as long as the probability distributions over this wedge in the two representations are the same. In practice, convenience dictates that the underlying probability distributions over the investment wedge are different in the two representations. Even so, the quantitative results under the two representations are essentially identical. We also compare our methodology, the CKM methodology, to an alternative one used in Christiano and Davis (2006) as well as by us in early incarnations of the business cycle accounting approach. We argue that the CKM methodology rests on more secure theoretical foundations. Finally, we show that the results from the VAR-style decomposition of Christiano and Davis reinforce the results of the business cycle decomposition of CKM.

This article describes a newly constructed data set of all U.S. state banks from 1782 to 1861. It contains the names and locations of all banks and branches that went into business and an estimate of when each operated. The compilation is based on reported balance sheets, listings in banknote reporters, and secondary sources. Based on these data, the article presents a count of the number of banks and branches in business by state. I argue that my series are superior to previously existing ones for reasons of consistency, accuracy, and timing. The article contains examples to support this argument.

Prior to the Civil War there were three major differences among states in how U.S. banks were regulated: (1) Whether they were established by charter or under free-banking laws. (2) Whether they were permitted to branch. (3) Whether the state established a state-owned bank. I use a census of the state banks that existed in the United States prior to the Civil War that I recently constructed to determine how these differences in state regulation affected the banking outcomes in these states. Specifically, I determine differences in banks per capita by state over time; bank longevities (survival rates) by state, size, and type of organization; and bank failure probabilities also by state, size, and type of organization. In addition, I estimate the losses experienced by note holders and determine whether there were systematic differences in these depending on whether or not a bank was organized under a free banking law.

A central debate in applied macroeconomics is whether statistical tools that use minimal identifying assumptions are useful for isolating promising models within a broad class. In this paper, I compare three statistical models—a vector autoregressive moving average (VARMA) model, an unrestricted state space model, and a restricted state space model—that are all consistent with the same prototype business cycle model. The business cycle model is a prototype in the sense that many models, with various frictions and shocks, are observationally equivalent to it. The statistical models I consider differ in the amount of a priori theory that is imposed, with VARMAs imposing minimal assumptions and restricted state space models imposing the maximal. The objective is to determine if it is possible to successfully uncover statistics of interest for business cycle theorists with sample sizes used in practice and only minimal identifying assumptions imposed. I find that the identifying assumptions of VARMAs and unrestricted state space models are too minimal: The range of estimates are so large as to be uninformative for most statistics that business cycle researchers need to distinguish alternative theories.

People are having longer retirement periods, and population growth is slowing and has even stopped in some countries. In this paper we determined the implications of these changes for the needed amount of government debt. The needed debt is near zero if there are high tax rates and the transfer share of gross national income (GNI) is high. But, with such a system there are huge dead-weight losses as the result of the high tax rate on labor income. With a savings system, a large government debt to annual GNI ratio is needed, as large as 5 times GNI, and welfare is as much as 24 percent higher in terms of lifetime consumption equivalents than the tax-and-transfer system.

Micro data over the life cycle shows two different patterns of consumption of housing and non-housing goods: the consumption profile of non-housing goods is hump-shaped while the consumption profile for housing first increases monotonically and then flattens out. These patterns hold true at each consumption quartile. This paper develops a quantitative, dynamic general equilibrium model of life cycle behavior, which generates consumption profiles consistent with the observed data. Borrowing constraints are essential in explaining the accumulation of housing assets early in life, while transaction costs are crucial in generating the slow downsizing of the housing assets later in life. The bequest motives play a role in determining total life time wealth, but not the housing profile.

In this paper we present an analytically tractable general equilibrium overlapping-generations model of human capital accumulation, and study its implications for the evolution of the U.S. wage distribution from 1970 to 2000. The key feature of the model, and the only source of heterogeneity, is that individuals differ in their ability to accumulate human capital. Therefore, wage inequality results only from differences in human capital accumulation. We examine the response of this model to skill-biased technical change (SBTC) theoretically. We show that in response to SBTC, the model generates behavior consistent with the U.S. data including (i) a rise in overall wage inequality in both the short run and long run, (ii) an initial fall in the education premium followed by a strong recovery, leading to a higher premium in the long run, (iii) the fact that most of this fall and rise takes place among younger workers, (iv) stagnation in median wage growth (and a slowdown in aggregate labor productivity), and (v) a rise in consumption inequality that is much smaller than the rise in wage inequality. These results suggest that the heterogeneity in the ability to accumulate human capital is an important feature for understanding the effects of SBTC, and interpreting the transformation that the U.S. economy has gone through since the 1970s.