Knowledge that Transforms

Few want to do business with a partner who has a bad reputation. Consequently, once a bad reputation is established, it can be difficult to get rid of. This leads on the one hand to the intuitive idea that a good reputation is easy to lose and hard to gain. On the other hand, it can lead to a strong form of history dependence in which a single beneficial or adverse event can cast a shadow over a very long period of time. It gives rise to a reputational trap where an agent rationally chooses not to invest in a good reputation because the chances others will find out is too low. Nevertheless, the same agent with a good reputation will make every effort to maintain it. Here, a simple reputational model is constructed and the conditions for there to be a unique equilibrium that constitutes a reputation trap are characterized.

Heteroskedasticity‐ and autocorrelation‐robust (HAR) inference in time series regression typically involves kernel estimation of the long‐run variance. Conventional wisdom holds that, for a given kernel, the choice of truncation parameter trades off a test's null rejection rate and power, and that this tradeoff differs across kernels. We formalize this intuition: using higher‐order expansions, we provide a unified size‐power frontier for both kernel and weighted orthonormal series tests using nonstandard “fixed‐ b ” critical values. We also provide a frontier for the subset of these tests for which the fixed‐ b distribution is t or F . These frontiers are respectively achieved by the QS kernel and equal‐weighted periodogram. The frontiers have simple closed‐form expressions, which show that the price paid for restricting attention to tests with t and F critical values is small. The frontiers are derived for the Gaussian multivariate location model, but simulations suggest the qualitative findings extend to stochastic regressors.

This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure that has been barely harnessed in the literature. Based on a monotonicity property afforded by such a geometric structure, we construct a bootstrap procedure that, unlike many studies in nonstandard settings, dispenses with estimation of local parameter spaces, and the critical values are obtained in a way as simple as computing the test statistic. Moreover, by appealing to strong approximations, our framework accommodates nonparametric regression models as well as distributional/density‐related and structural settings. Since the test entails a tuning parameter (due to the nonstandard nature of the problem), we propose a data‐driven choice and prove its validity. Monte Carlo simulations confirm that our test works well.

Haavelmo (1944) proposed a probabilistic structure for econometric modeling, aiming to make econometrics useful for decision making. His fundamental contribution has become thoroughly embedded in econometric research, yet it could not answer all the deep issues that the author raised. Notably, Haavelmo struggled to formalize the implications for decision making of the fact that models can at most approximate actuality. In the same period, Wald (1939, 1945) initiated his own seminal development of statistical decision theory. Haavelmo favorably cited Wald, but econometrics did not embrace statistical decision theory. Instead, it focused on study of identification, estimation, and statistical inference. This paper proposes use of statistical decision theory to evaluate the performance of models in decision making. I consider the common practice of as‐if optimization : specification of a model, point estimation of its parameters, and use of the point estimate to make a decision that would be optimal if the estimate were accurate. A central theme is that one should evaluate as‐if optimization or any other model‐based decision rule by its performance across the state space, listing all states of nature that one believes feasible, not across the model space. I apply the theme to prediction and treatment choice. Statistical decision theory is conceptually simple, but application is often challenging. Advancing computation is the primary task to complete the foundations sketched by Haavelmo and Wald.

The prevailing neo‐Wicksellian view holds that the central bank's objective is to track the natural rate of interest ( r * ), which itself is largely exogenous to monetary policy. We challenge this view using a fixed‐cost model of durable consumption demand, in which expansionary monetary policy prompts households to accelerate purchases of durable goods. This yields an intertemporal trade‐off in aggregate demand as encouraging households to increase durable holdings today leaves fewer households acquiring durables going forward. Interest rates must be kept low to support demand going forward, so accommodative monetary policy today reduces r * in the future. We show that this mechanism is quantitatively important in explaining the persistently low level of real interest rates and r * after the Great Recession.

We propose a robust method of discrete choice analysis when agents' choice sets are unobserved. Our core model assumes nothing about agents' choice sets apart from their minimum size. Importantly, it leaves unrestricted the dependence, conditional on observables, between choice sets and preferences. We first characterize the sharp identification region of the model's parameters by a finite set of conditional moment inequalities. We then apply our theoretical findings to learn about households' risk preferences and choice sets from data on their deductible choices in auto collision insurance. We find that the data can be explained by expected utility theory with low levels of risk aversion and heterogeneous non‐singleton choice sets, and that more than three in four households require limited choice sets to explain their deductible choices. We also provide simulation evidence on the computational tractability of our method in applications with larger feasible sets or higher‐dimensional unobserved heterogeneity.

In many markets, transaction prices are determined in auctions. In the most common form, prospective buyers compete by submitting bids to a seller. Each bid is an offer to buy that states a quantity and a maximum price. The seller then allocates the available supply among those offering the highest prices exceeding the seller's asking price. The actual price paid by a successful bidder depends on a pricing rule, usually selected by the seller: two common pricing rules are that each successful bidder pays the price bid; or they all pay the same price, usually the highest rejected bid or the lowest accepted bid. Auctions have been used for millennia, and remain the simplest and most famil-iar means of price determination for multilateral trading without intermediary `market makers ' such as brokers and specialists. Their trading procedures, which simply process bids and offers, are direct extensions of the usual forms of bilateral bargaining. Auctions also implement directly the demand submission procedures used in Walrasian models of markets. They therefore have prominent roles in the theory of exchange and in studies of the effects of economic institutions on the volume and terms of trade. Their allocative ef-®ciency in many contexts ensures their continued prominence in economic theory. They are also favored in experimental designs investigating the predictive power of economic theories. Auctions are apt subjects for applications of game theory because they present ex-plicit trading rules that largely ®x the `rules of the game'. Moreover, they present sub-stantive problems of strategic behavior of practical importance. They are particularly valuable as illustrations of games of incomplete information because bidders ' private information is the main factor affecting strategic behavior. The simpler forms of auctions induce normal-form games that are essentially `solved ' by applying directly the basic

We study how endogenous innovation and technology diffusion interact to determine the shape of the productivity distribution and generate aggregate growth. We model firms that choose to innovate, adopt technology, or produce with their existing technology. Costly adoption creates a spread between the best and worst technologies concurrently used to produce similar goods. The balance of adoption and innovation determines the shape of the distribution; innovation stretches the distribution, while adoption compresses it. On the balanced growth path, the aggregate growth rate equals the maximum growth rate of innovators. While innovation drives long‐run growth, changes in the adoption environment can influence growth by affecting innovation incentives, either directly, through licensing of excludable technologies, or indirectly, via the option value of adoption.

At an initial time, an individual forms a belief about a future random outcome. As time passes, the individual may obtain, privately or subjectively, further information, until the outcome is eventually revealed. How can a protocol be devised that induces the individual, as a strict best response, to reveal at the outset his prior assessment of both the final outcome and the information flows he anticipates and, subsequently, what information he privately receives? The protocol can provide the individual with payoffs that depend only on the outcome realization and his reports. We develop a framework to design such protocols, and apply it to construct simple elicitation mechanisms for common dynamic environments. The framework is general: we show that strategyproof protocols exist for any number of periods and large outcome sets. For these more general settings, we build a family of strategyproof protocols based on a hierarchy of choice menus, and show that any strategyproof protocol can be approximated by a protocol of this family.

How much capital should financial intermediaries hold? We propose a general equilibrium model with a financial sector that makes risky long‐term loans to firms, funded by deposits from savers. Government guarantees create a role for bank capital regulation. The model captures the sharp and persistent drop in macro‐economic aggregates and credit provision as well as the sharp change in credit spreads observed during financial crises. Policies requiring intermediaries to hold more capital reduce financial fragility, reduce the size of the financial and non‐financial sectors, and lower intermediary profits. They redistribute wealth from savers to the owners of banks and non‐financial firms. Pre‐crisis capital requirements are close to optimal. Counter‐cyclical capital requirements increase welfare.