Knowledge that Transforms

We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test statistic is based on a modified leave‐one‐out sample analog of a quadratic distance between the restricted and unrestricted sieve two‐stage least squares estimators. We provide computationally simple, data‐driven choices of sieve tuning parameters and Bonferroni adjusted chi‐squared critical values. Our test adapts to the unknown smoothness of alternative functions in the presence of unknown degree of endogeneity and unknown strength of the instruments. It attains the adaptive minimax rate of testing in L 2 . That is, the sum of the supremum of type I error over the composite null and the supremum of type II error over nonparametric alternative models cannot be minimized by any other tests for NPIV models of unknown regularities. Confidence sets in L 2 are obtained by inverting the adaptive test. Simulations confirm that, across different strength of instruments and sample sizes, our adaptive test controls size and its finite‐sample power greatly exceeds existing non‐adaptive tests for monotonicity and parametric restrictions in NPIV models. Empirical applications to test for shape restrictions of differentiated products demand and of Engel curves are presented.

We study how long‐lived, rational agents learn in a social network. In every period, after observing the past actions of his neighbors, each agent receives a private signal, and chooses an action whose payoff depends only on the state. Since equilibrium actions depend on higher‐order beliefs, it is difficult to characterize behavior. Nevertheless, we show that regardless of the size and shape of the network, the utility function, and the patience of the agents, the speed of learning in any equilibrium is bounded from above by a constant that only depends on the private signal distribution.

When does society eventually learn the truth, or take the correct action, via observational learning? In a general model of sequential learning over social networks, we identify a simple condition for learning dubbed excludability . Excludability is a joint property of agents' preferences and their information. We develop two classes of preferences and information that jointly satisfy excludability: (i) for a one‐dimensional state, preferences with single‐crossing differences and a new informational condition, directionally unbounded beliefs; and (ii) for a multi‐dimensional state, intermediate preferences and subexponential location‐shift information. These applications exemplify that with multiple states, “unbounded beliefs” is not only unnecessary for learning, but incompatible with familiar informational structures like normal information. Unbounded beliefs demands that a single agent can identify the correct action. Excludability, on the other hand, only requires that a single agent must be able to displace any wrong action, even if she cannot take the correct action.

We ask how fiscal deficits are financed in environments with two key features: (i) nominal rigidity, and (ii) a violation of Ricardian equivalence due to finite lives or liquidity constraints. In such environments, deficits can contribute to their own financing through two channels: a boom in real economic activity, which expands the tax base; and a surge in inflation, which erodes the real value of nominal government debt. Our main theoretical result establishes that this mechanism becomes more potent as fiscal adjustment is delayed, leading to full self‐financing in the limit: if the monetary authority does not lean too heavily against the fiscal stimulus, then the government can run a deficit today, refrain from tax hikes or spending cuts in the future, and still see its debt converge back to its initial level. We further demonstrate that a significant degree of self‐financing is achievable when the theory is disciplined by empirical evidence on marginal propensities to consume, nominal rigidities, the monetary policy reaction, and the speed of fiscal adjustment.

This paper shows that matching frictions and a thick market externality in firm‐to‐firm trade shape the agglomeration of economic activity. Using panel data of firm‐to‐firm trade in Japan, I demonstrate that firms gradually match with alternative suppliers following an unanticipated supplier bankruptcy, and that the rate of rematching increases in the geographic density of alternative suppliers. Motivated by these empirical findings, I develop a general equilibrium model of firm‐to‐firm matching in input trade across space. The model reveals that the thick market externality gives rise to an agglomeration externality affecting regional production and welfare. Using the calibrated model to the reduced‐form patterns of firm‐to‐firm matching, I estimate that the elasticity of a region's real wage with respect to population density due to the thick market externality is approximately 0.02. This finding highlights the substantial impact of the thick market externality on the overall agglomeration benefit.

The government budget constraint ties the market value of government debt to the expected present discounted value of fiscal surpluses. We find evidence that U.S. Treasury investors fail to impose this no‐arbitrage restriction in the United States. Both cyclical and long‐run dynamics of tax revenues and government spending make the surplus claim risky. In a realistic asset pricing model, this risk in surpluses creates a large gap between the market value of debt and its fundamental value, the PDV of surpluses, suggesting that U.S. Treasuries may be overpriced.

This paper considers a moral hazard problem where the agent can choose any output distribution with a support in a given compact set. The agent's effort‐cost is smooth and increasing in first‐order stochastic dominance. To analyze this model, we develop a generalized notion of the first‐order approach applicable to optimization problems over measures. We demonstrate each output distribution can be implemented and identify those contracts that implement that distribution. These contracts are characterized by a simple first‐order condition for each output that equates the agent's marginal cost of changing the implemented distribution around that output with its marginal benefit. Furthermore, the agent's wage is shown to be increasing in output. Finally, we consider the problem of a profit‐maximizing principal and provide a first‐order characterization of principal‐optimal distributions.

The gains from agglomeration economies are believed to be highly localized. Using confidential Census plant‐level data, we show that large industrial plant openings raise the productivity not only of local plants but also of distant plants hundreds of miles away, which belong to large multi‐plant, multi‐region firms that are exposed to the local productivity spillover through one of their plants. This “global” productivity spillover does not decay with distance and is stronger if plants are in industries that share knowledge with each other. To quantify the significance of firms' plant‐level networks for the propagation and amplification of local productivity shocks, we estimate a quantitative spatial model in which plants of multi‐region firms are linked through shared knowledge. Counterfactual exercises show that while large industrial plant openings have a greater local impact in less developed regions, the aggregate gains are greatest when the plants locate in well‐developed regions, which are connected to other regions through firms' plant‐level (knowledge‐sharing) networks.

Freedman (2008a,b) showed that the linear regression estimator is biased for the analysis of randomized controlled trials under the randomization model. Under Freedman's assumptions, we derive exact closed‐form bias corrections for the linear regression estimator. We show that the limiting distribution of the bias corrected estimator is identical to the uncorrected estimator. Taken together with results from Lin (2013), our results show that Freedman's theoretical arguments against the use of regression adjustment can be resolved with minor modifications to practice.

This paper studies the effect of a restorative justice intervention targeted at 143 youth ages 13 to 17 facing felony charges of medium severity (e.g., burglary, assault). Eligible youths were randomly assigned to participate in the Make‐it‐Right (MIR) restorative justice program or a control group where they faced standard criminal prosecution. We estimate the effects of MIR on the likelihood that a youth will be rearrested in the four years following randomization. Assignment to MIR reduces the probability of a rearrest within six months by 19 percentage points, a 44 percent reduction relative to the control group. Moreover, the reduction in recidivism persists even four years after randomization. Thus, our estimates show that restorative justice conferencing can reduce recidivism among youth charged with relatively serious offenses and can be an effective alternative to traditional criminal justice practices.