Knowledge that Transforms

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications in economics. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part, and so we have to extend existing results that only apply to either one or the other case. We also propose a refinement to the asymptotic approximation that we show works much better in finite samples. We apply our test to the study of intergenerational income mobility.

I study individuals who use frequentist models to draw uniform inferences from independent and identically distributed data. The main contribution of this paper is to show that distinct models may be consistent with empirical evidence, even in the limit when data increases without bound. Decision makers may then hold different beliefs and interpret their environment differently even though they know each other's model and base their inferences on the same evidence. The behavior modeled here is that of rational individuals confronting an environment in which learning is hard, rather than individuals beset by cognitive limitations or behavioral biases.

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill-posed inverse problems. In functional cointegrating regressions where the regressor is an integrated time series, it is shown here that inverse and ill-posed inverse problems do not arise. Remarkably, nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution theory is mixed normal, giving simple useable asymptotics in practical work. The results provide a convenient basis for inference in structural nonparametric regression with nonstationary time series. The methods may be applied to a wide range of empirical models where functional estimation of cointegrating relations is required.

We create an analytical structure that reveals the long-run risk-return relationship for nonlinear continuous-time Markov environments. We do so by studying an eigenvalue problem associated with a positive eigenfunction for a conveniently chosen family of valuation operators. The members of this family are indexed by the elapsed time between payoff and valuation dates, and they are necessarily related via a mathematical structure called a semigroup. We represent the semigroup using a positive process with three components: an exponential term constructed from the eigenvalue, a martingale, and a transient eigenfunction term. The eigenvalue encodes the risk adjustment, the martingale alters the probability measure to capture long-run approximation, and the eigenfunction gives the long-run dependence on the Markov state. We discuss sufficient conditions for the existence and uniqueness of the relevant eigenvalue and eigenfunction. By showing how changes in the stochastic growth components of cash flows induce changes in the corresponding eigenvalues and eigenfunctions, we reveal a long-run risk-return trade-off.

We examine the competition between a group of Internet retailers who operate in an environment where a price search engine plays a dominant role. We show that for some products in this environment, the easy price search makes demand tremendously price-sensitive. Retailers, though, engage in obfuscation—practices that frustrate consumer search or make it less damaging to firms—resulting in much less price sensitivity on some other products. We discuss several models of obfuscation and examine its effects on demand and markups empirically.

This paper uses control variables to identify and estimate models with nonseparable, multidimensional disturbances. Triangular simultaneous equations models are considered, with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance. Here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable. Also, for any control variable, identification results are given for quantile, average, and policy effects. Bounds are given when a common support assumption is not satisfied. Estimators of identified objects and bounds are provided, and a demand analysis empirical example is given.

We develop a search-theoretic model of financial intermediation in an over-the-counter market and study how trading frictions affect the distribution of asset holdings and standard measures of liquidity. A distinctive feature of our theory is that it allows for unrestricted asset holdings, so market participants can accommodate trading frictions by adjusting their asset positions. We show that these individual responses of asset demands constitute a fundamental feature of illiquid markets: they are a key determinant of trade volume, bid–ask spreads, and trading delays—the dimensions of market liquidity that search-based theories seek to explain.

The English auction is susceptible to tacit collusion when post-auction inter-bidder resale is allowed. We show this by constructing equilibria where, with positive probability, one bidder wins the auction without any competition and divides the spoils by optimally reselling the good to the other bidders. These equilibria interim Pareto dominate (among bidders) the standard value-bidding equilibrium, without requiring the bidders to make any commitment on bidding behavior or post-bidding spoil-division.

We show by counterexample that Proposition 2 in Fernández-Villaverde, Rubio-Ramírez, and Santos (Econometrica (2006), 74, 93–119) is false. We also show that even if their Proposition 2 were corrected, it would be irrelevant for parameter estimates. As a more constructive contribution, we consider the effects of approximation error on parameter estimation, and conclude that second order approximation errors in the policy function have at most second order effects on parameter estimates.

Comparative advantage, whether driven by technology or factor endowment, is at the core of neoclassical trade theory. Using tools from the mathematics of complementarity, this paper offers a simple yet unifying perspective on the fundamental forces that shape comparative advantage. The main results characterize sufficient conditions on factor productivity and factor supply to predict patterns of international specialization in a multifactor generalization of the Ricardian model which we refer to as an “elementary neoclassical economy.” These conditions, which hold for an arbitrarily large number of countries, goods, and factors, generalize and extend many results from the previous trade literature. They also offer new insights about the joint effects of technology and factor endowments on international specialization.