Knowledge that Transforms

We propose a new methodology for structural estimation of dynamic discrete choice models. We combine the Dynamic Programming (DP) solution algorithm with the Bayesian Markov Chain Monte Carlo algorithm into a single algorithm that solves the DP problem and estimates the parameters simultaneously. As a result, the computational burden of estimating a dynamic model becomes comparable to that of a static model. Another feature of our algorithm is that even though per solution-estimation iteration, the number of grid points on the state variable is small, the number of effective grid points increases with the number of estimation iterations. This is how we help ease the "Curse of Dimensionality". We simulate and estimate several versions of a simple model of entry and exit to illustrate our methodology. We also prove that under standard conditions, the parameters converge in probability to the true posterior distribution, regardless of the starting values.

We propose a new Walrasian tâtonnement process called a double-track procedure for efficiently allocating multiple heterogeneous indivisible items in two distinct sets to many buyers who view items in the same set as substitutes but items across the two sets as complements. In each round of the process, a Walrasian auctioneer first announces the current prices for all items, buyers respond by reporting their demands at these prices, and then the auctioneer adjusts simultaneously the prices of items in one set upward but those of items in the other set downward. It is shown that this procedure converges globally to a Walrasian equilibrium in finitely many rounds.

In this paper, we build a model where the presence of liquidity constraints tends to magnify the economy's response to aggregate shocks. We consider a decentralized model of trade, where agents may use money or credit to buy goods. When agents do not have access to credit and the real value of money balances is low, agents are more likely to be liquidity constrained. This makes them more concerned about their short-term earning prospects when making their consumption decisions and about their short-term spending opportunities when making their production decisions. This generates a coordination element in spending and production which leads to greater aggregate volatility and greater comovement across producers.

We develop a model of friendship formation that sheds light on segregation patterns observed in social and economic networks. Individuals have types and see type-dependent benefits from friendships. We examine the properties of a steady-state equilibrium of a matching process of friendship formation. We use the model to understand three empirical patterns of friendship formation: (i) larger groups tend to form more same-type ties and fewer other-type ties than small groups, (ii) larger groups form more ties per capita, and (iii) all groups are biased towards same-type relative to demographics, with the most extreme bias coming from middle-sized groups. We show how these empirical observations can be generated by biases in preferences and biases in meetings. We also illustrate some welfare implications of the model.

In Bayesian environments with private information, as described by the types of Harsanyi, how can types of agents be (statistically) disassociated from each other and how are such disassociations reflected in the agents' knowledge structure? Conditions studied are (i) subjective independence (the opponents' types are independent conditional on one's own) and (ii) type disassociation under common knowledge (the agents' types are independent, conditional on some common-knowledge variable). Subjective independence is motivated by its implications in Bayesian games and in studies of equilibrium concepts. We find that a variable that disassociates types is more informative than any common-knowledge variable. With three or more agents, conditions (i) and (ii) are equivalent. They also imply that any variable which is common knowledge to two agents is common knowledge to all, and imply the existence of a unique common-knowledge variable that disassociates types, which is the one defined by Aumann.

We use a controlled experiment to explore whether there are gender differences in selecting into competitive environments across two distinct societies: the Maasai in Tanzania and the Khasi in India. One unique aspect of these societies is that the Maasai represent a textbook example of a patriarchal society, whereas the Khasi are matrilineal. Similar to the extant evidence drawn from experiments executed in Western cultures, Maasai men opt to compete at roughly twice the rate as Maasai women. Interestingly, this result is reversed among the Khasi, where women choose the competitive environment more often than Khasi men, and even choose to compete weakly more often than Maasai men. These results provide insights into the underpinnings of the factors hypothesized to be determinants of the observed gender differences in selecting into competitive environments. Copyright 2009 The Econometric Society.

Information asymmetries are important in theory but difficult to identify in practice. We estimate the presence and importance of hidden information and hidden action problems in a consumer credit market using a new field experiment methodology. We randomized 58,000 direct mail offers to former clients of a major South African lender along three dimensions: (i) an initial “offer interest rate” featured on a direct mail solicitation; (ii) a “contract interest rate” that was revealed only after a borrower agreed to the initial offer rate; and (ii) a dynamic repayment incentive that was also a surprise and extended preferential pricing on future loans to borrowers who remained in good standing. These three randomizations, combined with complete knowledge of the lender's information set, permit identification of specific types of private information problems. Our setup distinguishes hidden information effects from selection on the offer rate (via unobservable risk and anticipated effort), from hidden action effects (via moral hazard in effort) induced by actual contract terms. We find strong evidence of moral hazard and weaker evidence of hidden information problems. A rough estimate suggests that perhaps 13% to 21% of default is due to moral hazard. Asymmetric information thus may help explain the prevalence of credit constraints even in a market that specializes in financing high-risk borrowers.

Two key issues in the literature on female labor supply are (i) whether persistence in employment status is due to unobserved heterogeneity or state dependence, and (ii) whether fertility is exogenous to labor supply. Until recently, the consensus was that unobserved heterogeneity is very important and fertility is endogenous. Hyslop (1999) challenged this. Using a dynamic panel probit model of female labor supply including heterogeneity and state dependence, he found that adding autoregressive errors led to a substantial diminution in the importance of heterogeneity. This, in turn, meant he could not reject that fertility is exogenous. Here, we extend Hyslop (1999) to allow classification error in employment status, using an estimation procedure developed by Keane and Wolpin (2001) and Keane and Sauer (2005). We find that a fairly small amount of classification error is enough to overturn Hyslop's conclusions, leading to overwhelming rejection of the hypothesis of exogenous fertility. © 2009 The Econometric Society.

We identify a new way to order functions, called the interval dominance order, that generalizes both the single crossing property and a standard condition used in statistical decision theory. This allows us to provide a unified treatment of the major theorems on monotone comparative statics with and without uncertainty, the comparison of signal informativeness, and a non-Bayesian theorem on the completeness of increasing decision rules. We illustrate the concept and results with various applications, including an application to optimal stopping time problems where the single crossing property is typically violated.

This paper develops a method for inference in dynamic discrete choice models with serially correlated unobserved state variables. Estimation of these models involves computing high-dimensional integrals that are present in the solution to the dynamic program and in the likelihood function. First, the paper proposes a Bayesian Markov chain Monte Carlo estimation procedure that can handle the problem of multidimensional integration in the likelihood function. Second, the paper presents an efficient algorithm for solving the dynamic program suitable for use in conjunction with the proposed estimation procedure.