Knowledge that Transforms

Johansen’s (1988, 1991) likelihood ratio test for cointegration rank of a Gaussian VAR depends only on the squared sample canonical correlations between current changes and past levels of a simple transformation of the data. We study the asymptotic behavior of the empirical distribution of those squared canonical correlations when the number of observations and the dimensionality of the VAR diverge to infinity simultaneously and proportionally. We find that the distribution almost surely weakly converges to the so-called Wachter distribution. This finding provides a theoretical explanation for the observed tendency of Johansen’s test to find “spurious cointegration”. It also sheds light on the workings and limitations of the Bartlett correction approach to the over-rejection problem. We propose a simple graphical device, similar to the scree plot, for a preliminary assessment of cointegration in high-dimensional VARs.

implies and is implied by additive separability of choice of treatment equations in terms of observed and unobserved variables. These results follow from properties of binary matrices developed in this paper. We investigate conditions under which unordered monotonicity arises as a consequence of choice behavior. We characterize IV estimators of counterfactuals as solutions to discrete mixture problems.

This paper provides a framework for identifying preferences in a large network where links are pairwise stable. Network formation models present difficulties for identification, especially when links can be interdependent, for example, when indirect connections matter. We show how one can use the observed proportions of various local network structures to learn about the underlying preference parameters. The key assumption for our approach restricts individuals to have bounded degree in equilibrium, implying a finite number of payoff‐relevant local structures. Our main result provides necessary conditions for parameters to belong to the identified set. We then develop a quadratic programming algorithm that can be used to construct this set. With further restrictions on preferences, we show that our conditions are also sufficient for pairwise stability and therefore characterize the identified set precisely. Overall, the use of both the economic model along with pairwise stability allows us to obtain effective dimension reduction.

Conjugate duality relationships are pervasive in matching and implementation problems and provide much of the structure essential for characterizing stable matches and implementable allocations in models with quasilinear (or transferable) utility. In the absence of quasilinearity, a more abstract duality relationship, known as a Galois connection, takes the role of (generalized) conjugate duality. While weaker, this duality relationship still induces substantial structure. We show that this structure can be used to extend existing results for, and gain new insights into, adverse-selection principal-agent problems and two-sided matching problems without quasilinearity.

We investigate the role of uncertainty in business cycles. First, we demonstrate that microeconomic uncertainty rises sharply during recessions, including during the Great Recession of 2007–2009. Second, we show that uncertainty shocks can generate drops in gross domestic product of around 2.5% in a dynamic stochastic general equilibrium model with heterogeneous firms. However, we also find that uncertainty shocks need to be supplemented by first†moment shocks to fit consumption over the cycle. So our data and simulations suggest recessions are best modelled as being driven by shocks with a negative first moment and a positive second moment. Finally, we show that increased uncertainty can make first†moment policies, like wage subsidies, temporarily less effective because firms become more cautious in responding to price changes.

This paper studies the behavioral foundations of non-Bayesian models of learning over social networks and develops a taxonomy of conditions for information aggregation in a general framework. As our main behavioral assumption, we postulate that agents follow social learning rules that satisfy “imperfect recall,” according to which they treat the current beliefs of their neighbors as sufficient statistics for the entire history of their observations. We augment this assumption with various restrictions on how agents process the information provided by their neighbors and obtain representation theorems for the corresponding learning rules (including the canonical model of DeGroot). We then obtain general long-run learning results that are not tied to the learning rules' specific functional forms, thus identifying the fundamental forces that lead to learning, non-learning, and mislearning in social networks. Our results illustrate that, in the presence of imperfect recall, long-run aggregation of information is closely linked to (i) the rate at which agents discount their neighbors' information over time, (ii) the curvature of agents' social learning rules, and (iii) whether their initial tendencies are amplified or moderated as a result of social interactions.

We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite‐sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is not known. When the function class is centrosymmetric, these efficiency bounds imply that minimax CIs are close to efficient at smooth regression functions. This implies, in particular, that it is impossible to form CIs that are substantively tighter using data‐dependent tuning parameters, and maintain coverage over the whole function class. We specialize our results to inference on the regression discontinuity parameter, and illustrate them in simulations and an empirical application.

Which equilibria will arise in signaling games depends on how the receiver interprets deviations from the path of play. We develop a micro-foundation for these off-path beliefs, and an associated equilibrium refinement, in a model where equilibrium arises through non-equilibrium learning by populations of patient and long-lived senders and receivers. In our model, young senders are uncertain about the prevailing distribution of play, so they rationally send out-of-equilibrium signals as experiments to learn about the behavior of the population of receivers. Differences in the payoff functions of the types of senders generate different incentives for these experiments. Using the Gittins index (Gittins (1979)), we characterize which sender types use each signal more often, leading to a constraint on the receiver's off-path beliefs based on “type compatibility” and hence a learning-based equilibrium selection.

Conditional independence of treatment assignment from potential outcomes is a commonly used but nonrefutable assumption. We derive identified sets for various treatment effect parameters under nonparametric deviations from this conditional independence assumption. These deviations are defined via a conditional treatment assignment probability, which makes it straightforward to interpret. Our results can be used to assess the robustness of empirical conclusions obtained under the baseline conditional independence assumption.

I construct an informationally robust auction to sell a common‐value good. I examine the revenue guarantee of an auction over all information structures of bidders and all equilibria. As the number of bidders gets large, the revenue guarantee of my auction converges to the full surplus, regardless of how information changes as more bidders are added. My auction also maximizes the revenue guarantee when there is a single bidder.