Knowledge that Transforms

We study optimal control problems in the multivariate linear‐quadratic‐Gaussian framework under rational inattention. We propose a three‐step procedure to solve this problem using semidefinite programming and derive the optimal signal structure without strong prior restrictions. We analyze both the transition dynamics of the optimal posterior covariance matrix and its steady state. We characterize the optimal information structure for some special cases and develop numerical algorithms for general cases. Applying our methods to solve three multivariate economic models, we obtain some results qualitatively different from the literature.

Airfares fluctuate due to demand shocks and intertemporal variation in willingness to pay. I estimate a model of dynamic airline pricing accounting for both sources of price adjustments using flight‐level data. I use the model estimates to evaluate the welfare effects of dynamic airline pricing. Relative to uniform pricing, dynamic pricing benefits early‐arriving, leisure consumers at the expense of late‐arriving, business travelers. Although dynamic pricing ensures seat availability for business travelers, these consumers are then charged higher prices. When aggregated over markets, welfare is higher under dynamic pricing than under uniform pricing. The direction of the welfare effect at the market level depends on whether dynamic price adjustments are mainly driven by demand shocks or by changes in the overall demand elasticity.

This paper studies the role of private sector companies in the development of local amenities. We use evidence from one of the largest multinationals of the 20th century: the United Fruit Company (UFCo). The firm was given a large land concession in Costa Rica—one of the so‐called “Banana Republics”—from 1899 to 1984. Using administrative census data with census‐block geo‐references from 1973 to 2011, we implement a geographic regression discontinuity design that exploits a land assignment that is orthogonal to our outcomes of interest. We find that the firm had a positive and persistent effect on living standards. Company documents explain that a key concern at the time was to attract and maintain a sizable workforce, which induced the firm to invest heavily in local amenities—like the development of education and health infrastructure—that can account for our result. Consistent with this mechanism, we show, empirically and through a proposed model, that the firm's investment efforts increase with worker mobility.

In this paper, we argue that a large class of recursive contracts can be studied by means of the conventional Negishi method. A planner is responsible for prescribing current actions along with a distribution of future utility values to all agents, so as to maximize their weighted sum of utilities. Under convexity, the method yields the exact efficient frontier. Otherwise, the implementation requires contracts be contingent on publicly observable random signals uncorrelated to fundamentals. We also provide operational first‐order conditions for the characterization of efficient contracts. Finally, we compare extensively our approach with the dual method established in the literature.

Many schools in large urban districts have more applicants than seats. Centralized school assignment algorithms ration seats at over‐subscribed schools using randomly assigned lottery numbers, non‐lottery tie‐breakers like test scores, or both. The New York City public high school match illustrates the latter, using test scores and other criteria to rank applicants at the city's screened schools, combined with lottery tie‐breaking at the rest. We show how to identify causal effects of school attendance in such settings. Our approach generalizes regression discontinuity methods to allow for multiple treatments and multiple running variables, some of which are randomly assigned. The key to this generalization is a local propensity score that quantifies the school assignment probabilities induced by lottery and non‐lottery tie‐breakers. The utility of the local propensity score is demonstrated in an assessment of the predictive value of New York City's school report cards. Schools that earn the highest report card grade indeed improve SAT math scores and increase graduation rates, though by much less than OLS estimates suggest. Selection bias in OLS estimates of grade effects is egregious for screened schools.

I study a dynamic model in which a decision‐maker (DM) acquires information about the payoffs of different alternatives prior to making a decision. The model's key feature is the flexibility of information: the DM can choose any dynamic signal process as an information source, subject to a flow cost that depends on the informativeness of the signal. Under the optimal policy, the DM acquires a signal that arrives according to a Poisson process . The optimal Poisson signal confirms the DM's prior belief and is sufficiently precise to warrant immediate action. Over time, given the absence of the arrival of a Poisson signal, the DM continues seeking an increasingly precise but less frequent Poisson signal.

We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise process based on high‐frequency data, where the noise process could be serially dependent, endogenous, and nonstationary. We characterize the limit distributions of the proposed estimators and construct confidence intervals under infill asymptotics. Our simulation and empirical studies show that the ReMeDI approach is very effective to measure the scale and the serial dependence of microstructure noise. Moreover, the estimators are quite robust to model specifications, sample sizes, and data frequencies.

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross‐fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps. We characterize double robustness and give a variety of new doubly robust moment functions. We give general and simple regularity conditions for asymptotic theory.

We study the optimal design of corporate taxation and R&D policies as a dynamic mechanism design problem with spillovers. Firms have heterogeneous research productivity, and that research productivity is private information. There are non‐internalized technological spillovers across firms, but the asymmetric information prevents the government from correcting them in the first best way. We highlight that key parameters for the optimal policies are (i) the relative complementarities between observable R&D investments, unobservable R&D inputs, and firm research productivity, (ii) the dispersion and persistence of firms' research productivities, and (iii) the magnitude of technological spillovers across firms. We estimate our model using firm‐level data matched to patent data and quantify the optimal policies. In the data, high research productivity firms get disproportionately higher returns to R&D investments than lower productivity firms. Very simple innovation policies, such as linear corporate taxes combined with a nonlinear R&D subsidy—which provides lower marginal subsidies at higher R&D levels—can do almost as well as the unrestricted optimal policies. Our formulas and theoretical and numerical methods are more broadly applicable to the provision of firm incentives in dynamic settings with asymmetric information and spillovers, and to firm taxation more generally.

We study the competitive provision and endogenous acquisition of political information. Our main result identifies a natural equilibrium channel through which a more competitive market decreases the efficiency of policy outcomes. A critical insight we put forward is that competition among information providers leads to informational specialization: firms provide relatively less information on issues that are of common interest and relatively more information on issues on which agents' preferences are heterogeneous. This enables agents to acquire information about different aspects of the policy, specifically, those that are particularly important to them. This leads to an increase in social disagreement, which has negative welfare implications. We establish that, in large enough societies, competition makes every agent worse off by decreasing the utility that she derives from the policy outcome. Furthermore, we show that this decline cannot be compensated by the decrease in prices resulting from competition.