Knowledge that Transforms

We develop inference methods about long†run comovement of two time series. The parameters of interest are defined in terms of population second moments of low†frequency transformations (“low†pass†filtered versions) of the data. We numerically determine confidence sets that control coverage over a wide range of potential bivariate persistence patterns, which include arbitrary linear combinations of I(0), I(1), near unit roots, and fractionally integrated processes. In an application to U.S. economic data, we quantify the long†run covariability of a variety of series, such as those giving rise to balanced growth, nominal exchange rates and relative nominal prices, the unemployment rate and inflation, money growth and inflation, earnings and stock prices, etc.

Peer Reviewed

It is generally difficult to know whether the parameters in nonlinear econometric models are point‐identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of the full parameter vector and of subvectors in models defined through a likelihood or a vector of moment equalities or inequalities. The CSs are based on level sets of “optimal” criterion functions (such as likelihoods, optimally‐weighted or continuously‐updated GMM criterions). The level sets are constructed using cutoffs that are computed via Monte Carlo (MC) simulations from the quasi‐posterior distribution of the criterion. We establish new Bernstein–von Mises (or Bayesian Wilks) type theorems for the quasi‐posterior distributions of the quasi‐likelihood ratio (QLR) and profile QLR in partially‐identified models. These results imply that our MC CSs have exact asymptotic frequentist coverage for identified sets of full parameters and of subvectors in partially‐identified regular models, and have valid but potentially conservative coverage in models whose local tangent spaces are convex cones. Further, our MC CSs for identified sets of subvectors are shown to have exact asymptotic coverage in models with singularities. We provide local power properties and uniform validity of our CSs over classes of DGPs that include point‐ and partially‐identified models. Finally, we present two simulation experiments and two empirical examples: an airline entry game and a model of trade flows.

Measurements of ambiguity attitudes have so far focused on artificial events, where (subjective) beliefs can be derived from symmetry of events and can be then controlled for. For natural events as relevant in applications, such a symmetry and corresponding control are usually absent, precluding traditional measurement methods. This paper introduces two indexes of ambiguity attitudes, one for aversion and the other for insensitivity/perception, for which we can control for likelihood beliefs even if these are unknown. Hence, we can now measure ambiguity attitudes for natural events. Our indexes are valid under many ambiguity theories, do not require expected utility for risk, and are easy to elicit in practice. We use our indexes to investigate time pressure under ambiguity. People do not become more ambiguity averse under time pressure but become more insensitive (perceive more ambiguity). These findings are plausible and, hence, support the validity of our indexes.

Multivalued treatment models have typically been studied under restrictive assumptions: ordered choice, and more recently, unordered monotonicity. We show how treatment effects can be identified in a more general class of models that allows for multidimensional unobserved heterogeneity. Our results rely on two main assumptions: treatment assignment must be a measurable function of threshold‐crossing rules, and enough continuous instruments must be available. We illustrate our approach for several classes of models.

We introduce the test†set equilibrium refinement of Nash equilibrium to formalize the idea that players contemplate only deviations from equilibrium play in which a single competitor plays a non†equilibrium best response. We then apply this refinement to three well†known auction games, comparing our findings to similar ones previously obtained by specialized equilibrium selections. We also introduce a theory of high stakes versions of games, in which strategies are first proposed and then subjected to a potentially costly review†and†revise process. We demonstrate a sense in which the test†set equilibria emerge from such processes when the cost of revision is small.

Is the standard hyperbolic†discounting model capable of robust qualitative predictions for savings behavior? Despite results suggesting a negative answer, we provide a positive one. We give conditions under which all Markov equilibria display either saving at all wealth levels or dissaving at all wealth levels. Moreover, saving versus dissaving is determined by a simple condition comparing the interest rate to a threshold made up of impatience parameters only. Our robustness results illustrate a well†behaved side of the model and imply that qualitative behavior is determinate, dissipating indeterminacy concerns to the contrary (Krusell and Smith, 2003). We prove by construction that equilibria always exist and that multiplicity is present in some cases, highlighting that our robust predictions are not due to uniqueness. Similar results may be obtainable in related dynamic games, such as political economy models of public spending.

In French parliamentary and local elections, candidates ranked first and second in the first round automatically qualify for the second round, while a third candidate qualifies only when selected by more than 12.5 percent of registered citizens. Using a fuzzy RDD around this threshold, we find that the third candidate's presence substantially increases the share of registered citizens who vote for any candidate and reduces the vote share of the top two candidates. It disproportionately harms the candidate ideologically closest to the third and causes her defeat in one fifth of the races. Additional evidence suggests that these results are driven by voters who value voting expressively over voting strategically for the top‐two candidate they dislike the least to ensure her victory; and by third candidates who, absent party‐level agreements leading to their dropping out, value the benefits associated with competing in the second round more than influencing its outcome.

We analyze dynamic trading by an activist investor who can expend costly effort to affect firm value. We obtain the equilibrium in closed form for a general activism technology, including both binary and continuous outcomes. Variation in parameters can produce either positive or negative relations between market liquidity and economic efficiency, depending on the activism technology and model parameters. Two results that contrast with the previous literature are that (a) the relationship between market liquidity and economic efficiency is independent of the activist's initial stake for a broad set of activism technologies, and (b) an increase in noise trading can reduce market liquidity because it increases uncertainty about the activist's trades (the activist trades in the opposite direction of noise traders) and thereby increases information asymmetry about the activist's intentions.

International audience