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Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information

Econometrica 2015 83(5), 1963-1999
This paper makes the following original contributions to the literature. (i) We develop a simpler analytical characterization and numerical algorithm for Bayesian inference in structural vector autoregressions (VARs) that can be used for models that are overidentified, just-identified, or underidentified. (ii) We analyze the asymptotic properties of Bayesian inference and show that in the underidentified case, the asymptotic posterior distribution of contemporaneous coefficients in an n-variable VAR is confined to the set of values that orthogonalize the population variance–covariance matrix of ordinary least squares residuals, with the height of the posterior proportional to the height of the prior at any point within that set. For example, in a bivariate VAR for supply and demand identified solely by sign restrictions, if the population correlation between the VAR residuals is positive, then even if one has available an infinite sample of data, any inference about the demand elasticity is coming exclusively from the prior distribution. (iii) We provide analytical characterizations of the informative prior distributions for impulse-response functions that are implicit in the traditional sign-restriction approach to VARs, and we note, as a special case of result (ii), that the influence of these priors does not vanish asymptotically. (iv) We illustrate how Bayesian inference with informative priors can be both a strict generalization and an unambiguous improvement over frequentist inference in just-identified models. (v) We propose that researchers need to explicitly acknowledge and defend the role of prior beliefs in influencing structural conclusions and we illustrate how this could be done using a simple model of the U.S. labor market

Poverty and Self-Control

Econometrica 2015 83(5), 1877-1911
We argue that poverty can perpetuate itself by undermining the capacity for self-control. In line with a distinguished psychological literature, we consider modes of self-control that involve the self-imposed use of contingent punishments and rewards. We study settings in which consumers with quasi-hyperbolic preferences confront an otherwise standard intertemporal allocation problem with credit constraints. Our main result demonstrates that low initial assets can limit self-control, trapping people in poverty, while individuals with high initial assets can accumulate indefinitely. Thus, even temporary policies that initiate accumulation among the poor may be effective. We examine implications concerning the effect of access to credit on saving, the demand for commitment devices, the design of financial accounts to promote accumulation, and the variation of the marginal propensity to consume across income from different sources. We also explore the nature of optimal self-control, demonstrating that it has a simple and behaviorally plausible structure that is immune to self-renegotiation.

Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality

Econometrica 2015 83(4), 1619-1639 open access
Mechanism design enables a social planner to obtain a desired outcome by leveraging the players’ rationality and their beliefs. It is thus a fundamental, but yet unproven, intuition that the higher the level of rationality of the players, the better the set of obtainable outcomes. In this paper, we prove this fundamental intuition for players with possibilistic beliefs, a model long considered in epistemic game theory. Specifically, • We define a sequence of monotonically increasing revenue benchmarks for single- good auctions, G0 ≤ G1 ≤ G2 ≤ · · ·, where each Gi is defined over the players’ beliefs and G0 is the second-highest valuation (i.e., the revenue benchmark achieved by the second-price mechanism). • We (1) construct a single, interim individually rational, auction mechanism that, without any clue about the rationality level of the players, guarantees revenue Gk if all players have rationality levels ≥ k + 1, and (2) prove that no such mechanism can guarantee revenue even close to Gk when at least two players are at most level-k rational.

Democratization Under the Threat of Revolution: Evidence From the Great Reform Act of 1832

Econometrica 2015 83(2), 505-547 open access
We examine the link between the threat of violence and democratization in the context of the Great Reform Act passed by the British Parliament in 1832. We geo-reference the so-called Swing riots, which occurred between the 1830 and 1831 parliamentary elections, and compute the number of these riots that happened within a 10 km radius of the 244 English constituencies. Our empirical analysis relates this constituency-specific measure of the threat perceptions held by the 344,000 voters in the Unreformed Parliament to the share of seats won in each constituency by pro-reform politicians in 1831. We find that the Swing riots induced voters to vote for pro-reform politicians after experiencing first-hand the violence of the riots.

Consumer Heterogeneity and Paid Search Effectiveness: A Large-Scale Field Experiment

Econometrica 2015 83(1), 155-174 open access
Internet advertising has been the fastest growing advertising channel in recent years, with paid search ads comprising the bulk of this revenue. We present results from a series of large-scale field experiments done at eBay that were designed to measure the causal effectiveness of paid search ads. Because search clicks and purchase intent are correlated, we show that returns from paid search are a fraction of non-experimental estimates. As an extreme case, we show that brand keyword ads have no measurable short-term benefits. For non-brand keywords, we find that new and infrequent users are positively influenced by ads but that more frequent users whose purchasing behavior is not influenced by ads account for most of the advertising expenses, resulting in average returns that are negative.

Necessity Is the Mother of Invention: Input Supplies and Directed Technical Change

Econometrica 2015 83(1), 67-100 open access
This study provides causal evidence that a shock to the relative supply of inputs to production can (1) affect the direction of technological progress and (2) lead to a rebound in the relative price of the input that became relatively more abundant (the strong induced-bias hypothesis). I exploit the impact of the U.S. Civil War on the British cotton textile industry, which reduced supplies of cotton from the Southern United States, forcing British producers to shift to lower-quality Indian cotton. Using detailed new data, I show that this shift induced the development of new technologies that augmented Indian cotton. As these new technologies became available, I show that the relative price of Indian/U.S. cotton rebounded to its pre-war level, despite the increased relative supply of Indian cotton. This is the first paper to establish both of these patterns empirically, lending support to the two key predictions of leading directed technical change theories.

Cautious Expected Utility and the Certainty Effect

Econometrica 2015 83(2), 693-728
Many violations of the Independence axiom of Expected Utility can be traced to subjects' attraction to risk-free prospects.Negative Certainty Independence, the key axiom in this paper, formalizes this tendency.Our main result is a utility representation of all preferences over monetary lotteries that satisfy Negative Certainty Independence together with basic rationality postulates.Such preferences can be represented as if the agent were unsure of how risk averse to be when evaluating a lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one.The set of utilities is unique in a well-defined sense.We show that our representation can also be derived from a 'cautious' completion of an incomplete preference relation.

Sharing Rule Identification for General Collective Consumption Models

Econometrica 2015 83(5), 2001-2041 open access
We propose a method to set identify bounds on the sharing rule for a general collective household consumption model. Unlike the effects of distribution factors, the level of the sharing rule cannot be uniquely identified without strong assumptions on preferences across households. Our new results show that, though not point identified without these assumptions, strong bounds on the sharing rule can be obtained. We get these bounds by applying revealed preference restrictions implied by the collective model to the household's continuous aggregate demand functions. We obtain informative bounds even if nothing is known about whether each good is public, private, or assignable within the household, though having such information tightens the bounds. We apply our method to US PSID data, obtaining narrow bounds that yield useful conclusions regarding the effects of income and wages on intrahousehold resource sharing, and on the prevalence of individual (as opposed to household level) poverty.

A Test for Instrument Validity

Econometrica 2015 83(5), 2043-2063 open access
This paper develops a specification test for instrument validity in the heterogeneous treatment effect model with a binary treatment and a discrete instrument. The strongest testable implication for instrument validity is given by the condition for nonnegativity of point‐identifiable compliers' outcome densities. Our specification test infers this testable implication using a variance‐weighted Kolmogorov–Smirnov test statistic. The test can be applied to both discrete and continuous outcome cases, and an extension of the test to settings with conditioning covariates is provided.