Knowledge that Transforms

We axiomatize preferences that can be represented by a monotonic aggregation of subjective expected utilities generated by a utility function and some set of i.i.d. probability measures over a product state space, S∞. For such preferences, we define relevant measures, show that they are treated as if they were the only marginals possibly governing the state space, and connect them with the measures appearing in the aforementioned representation. These results allow us to interpret relevant measures as reflecting part of perceived ambiguity, meaning subjective uncertainty about probabilities over states. Under mild conditions, we show that increases or decreases in ambiguity aversion cannot affect the relevant measures. This property, necessary for the conclusion that these measures reflect only perceived ambiguity, distinguishes the set of relevant measures from the leading alternative in the literature. We apply our findings to a number of well-known models of ambiguity-sensitive preferences. For each model, we identify the set of relevant measures and the implications of comparative ambiguity aversion.

We define the class of two‐player zero‐sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For such games, we establish sufficient conditions for existence of a value of the game, maximin and minimax strategies for the players, and a Nash equilibrium. If all discontinuities favor one player, then a value exists and that player has a maximin strategy. A property called payoff approachability implies existence of an equilibrium, and that the resulting value is invariant: games with the same payoffs at points of continuity have the same value and ɛ‐equilibria. For voting games in which two candidates propose policies and a candidate wins election if a weighted majority of voters prefer his proposed policy, we provide tie‐breaking rules and assumptions about voters' preferences sufficient to imply payoff approachability. These assumptions are satisfied by generic preferences if the dimension of the space of policies exceeds the number of voters; or with no dimensional restriction, if the electorate is sufficiently large. Each Colonel Blotto game is a special case in which each candidate allocates a resource among several constituencies and a candidate gets votes from those allocated more than his opponent offers; in this case, for simple‐majority rule we prove existence of an equilibrium with zero probability of ties.

We develop a model of experimentation and learning in policymaking when control of power is temporary. We demonstrate how an early office holder who would otherwise not experiment is nonetheless induced to experiment when his hold on power is temporary. This preemptive policy experiment is profitable for the early office holder as it reveals information about the policy mapping to his successor, information that shapes future policy choices. Thus policy choices today can cast a long shadow over future choices purely through information transmission and absent any formal institutional constraints or real state variables. The model we develop utilizes a recent innovation that represents the policy mapping as the realized path of a Brownian motion. We provide a precise characterization of when preemptive experimentation emerges in equilibrium and the form it takes. We apply the model to several well known episodes of policymaking, reinterpreting the policy choices as preemptive experiments.

We develop an extension of Luce's random choice model to study violations of the weak axiom of revealed preference. We introduce the notion of a stochastic preference and show that it implies the Luce model. Then, to address well-known difficulties of the Luce model, we define the attribute rule and establish that the existence of a well-defined stochastic preference over attributes characterizes it. We prove that the set of attribute rules and random utility maximizers are essentially the same. Finally, we show that both the Luce and attribute rules have a unique consistent extension to dynamic problems.

We develop and estimate a comprehensive dynamic programming (DP) model for the joint decisions of residential location, employment location, occupational choices, and labor market outcomes. We use data on immigrants from the former Soviet Union (FSU). We provide an extensive empirical evaluation of policies that have been designed to affect the residential and employment location decisions of the migrant population. The results shed new, and important, light on several issues regarding this group of immigrants. We find large regional differences in wages for the white-collar workers, but only little differences for the blue-collar workers. A careful examination of a number of policy measures indicate that a direct subsidy, in the form of a lump-sum transfer, is most effective in achieving the government stated goal of inducing people to reside in the northern region of the Galilee and southern region of the Negev. Other policies, such as rental and wage subsidies, can also be quite effective, but these are more difficult to administer.

Local to unity limit theory is used in applications to construct confidence intervals (CIs) for autoregressive roots through inversion of a unit root test (Stock (1991)). Such CIs are asymptotically valid when the true model has an autoregressive root that is local to unity (ρ = 1 + c/n), but are shown here to be invalid at the limits of the domain of definition of the localizing coefficient c because of a failure in tightness and the escape of probability mass. Failure at the boundary implies that these CIs have zero asymptotic coverage probability in the stationary case and vicinities of unity that are wider than O(n−1/3). The inversion methods of Hansen (1999) and Mikusheva (2007) are asymptotically valid in such cases. Implications of these results for predictive regression tests are explored. When the predictive regressor is stationary, the popular Campbell and Yogo (2006) CIs for the regression coefficient have zero coverage probability asymptotically, and their predictive test statistic Q erroneously indicates predictability with probability approaching unity when the null of no predictability holds. These results have obvious cautionary implications for the use of the procedures in empirical practice.

This paper proposes a class of optimal tests for the constancy of parameters in random coefficients models. Our testing procedure covers the class of Hamilton's models, where the parameters vary according to an unobservable Markov chain, but also applies to nonlinear models where the random coefficients need not be Markov. We show that the contiguous alternatives converge to the null hypothesis at a rate that is slower than the standard rate. Therefore, standard approaches do not apply. We use Bartlett-type identities for the construction of the test statistics. This has several desirable properties. First, it only requires estimating the model under the null hypothesis where the parameters are constant. Second, the proposed test is asymptotically optimal in the sense that it maximizes a weighted power function. We derive the asymptotic distribution of our test under the null and local alternatives. Asymptotically valid bootstrap critical values are also proposed.

We analyze a dynamic stochastic general-equilibrium (DSGE) model with an externality—through climate change—from using fossil energy. Our central result is a simple formula for the marginal externality damage of emissions (or, equivalently, for the optimal carbon tax). This formula, which holds under quite plausible assumptions, reveals that the damage is proportional to current GDP, with the proportion depending only on three factors: (i) discounting, (ii) the expected damage elasticity (how many percent of the output flow is lost from an extra unit of carbon in the atmosphere), and (iii) the structure of carbon depreciation in the atmosphere. Thus, the stochastic values of future output, consumption, and the atmospheric CO2 concentration, as well as the paths of technology (whether endogenous or exogenous) and population, and so on, all disappear from the formula. We find that the optimal tax should be a bit higher than the median, or most well-known, estimates in the literature. We also formulate a parsimonious yet comprehensive and easily solved model allowing us to compute the optimal and market paths for the use of different sources of energy and the corresponding climate change. We find coal—rather than oil—to be the main threat to economic welfare, largely due to its abundance. We also find that the costs of inaction are particularly sensitive to the assumptions regarding the substitutability of different energy sources and technological progress.

We introduce and analyze expected uncertain utility theory (EUU). A prior and an interval utility characterize an EUU decision maker. The decision maker transforms each uncertain prospect into an interval-valued prospect that assigns an interval of prizes to each state. She then ranks prospects according to their expected interval utilities. We define uncertainty aversion for EUU, use the EUU model to address the Ellsberg Paradox and other ambiguity evidence, and relate EUU theory to existing models.

This paper studies inference in models that are identified by moment restrictions. We show how instability of the moments can be used constructively to improve the identification of structural parameters that are stable over time. A leading example is macroeconomic models that are immune to the well-known (Lucas (1976)) critique in the face of policy regime shifts. This insight is used to develop novel econometric methods that extend the widely used generalized method of moments (GMM). The proposed methods yield improved inference on the parameters of the new Keynesian Phillips curve.