New methods are developed for identifying, estimating, and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit-root (UR), local unit-root (LUR), mildly integrated (MI), and mildly explosive (ME) specifications in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME specifications and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the differing forms of house price behavior in Australian state capital cities over the past decade.
Functional coefficient (FC) regressions allow for systematic flexibility in the responsiveness of a dependent variable to movements in the regressors, making them attractive in applications where marginal effects may depend on covariates. Such models are commonly estimated by local kernel regression methods. This paper explores situations where responsiveness to covariates is locally flat or fixed. The paper develops new asymptotics that take account of shape characteristics of the function in the locality of the point of estimation. Both stationary and integrated regressor cases are examined. The limit theory of FC kernel regression is shown to depend intimately on functional shape in ways that affect rates of convergence, optimal bandwidth selection, estimation, and inference. In FC cointegrating regression, flat behavior materially changes the limit distribution by introducing the shape characteristics of the function into the limiting distribution through variance as well as centering. In the boundary case where the number of zero derivatives tends to infinity, near parametric rates of convergence apply in stationary and nonstationary cases. Implications for inference are discussed and a feasible pre-test inference procedure is proposed that takes unknown potential flatness into consideration and provides a practical approach to inference.
A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived. Each buyer has private information about his arrival time and valuation where the latter evolves according to a geometric Brownian motion. Any incentive-compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We establish that the optimal stationary allocation policy can be implemented by a simple posted price. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem which determines the first time at which the buyer participates in the mechanism. The optimal mechanism thus induces progressive participation by each buyer: he either participates immediately or at a future random time.
This article considers a class of experimentation games with Lévy bandits encompassing those of Bolton and Harris (1999, Econometrica, 67, 349–374) and Keller, Rady, and Cripps (2005, Econometrica, 73, 39–68). Its main result is that efficient (perfect Bayesian) equilibria exist whenever players’ payoffs have a diffusion component. Hence, the trade-offs emphasized in the literature do not rely on the intrinsic nature of bandit models but on the commonly adopted solution concept (Markov perfect equilibrium). This is not an artefact of continuous time: we prove that efficient equilibria arise as limits of equilibria in the discrete-time game. Furthermore, it suffices to relax the solution concept to strongly symmetric equilibrium.
Decision theory can be used to test the logic of decision making---one may ask whether a given set of decisions can be justified by a decision-theoretic model. Indeed, in principal-agent settings, such justifications may be required---a manager of an investment fund may be asked what beliefs she used when valuing assets and a government may be asked whether a portfolio of rules and regulations is coherent. In this paper we ask which collections of uncertain-act evaluations can be simultaneously justified under the maxmin expected utility criterion by a single set of probabilities. We draw connections to the the Fundamental Theorem of Finance (for the special case of a Bayesian agent) and revealed-preference results.
We construct an endogenous growth model with random interactions where firms are subject to distortions. The TFP distribution evolves endogenously as firms seek to upgrade their technology over time either by innovating or by imitating other firms. We use the model to quantify the effects of misallocation on TFP growth in emerging economies. We structurally estimate the stationary state of the dynamic model targeting moments of the empirical distribution of R&D and TFP growth in China during the period 2007–2012. The estimated model fits the Chinese data well. We compare the estimates with those obtained using data for Taiwan and perform counterfactuals to study the effect of alternative policies. R&D misallocation has a large effect on TFP growth.
This paper uses an estimated interest rate rule of the Fed to argue that the low recent interest rates may be due to a change in Fed behavior. Prior to the Great Recession the Fed’s behavior is consistent with the rule. During the recession the zero lower bound was hit in 2008.4. The rule unconstrained called for negative nominal interest rates during this period, and so it became inoperative. The Fed kept the interest rate at roughly zero through 2015. This was a period of low inflation and still fairly high unemployment rates, and the rule called for essentially zero interest rates through about 2010. Beginning in 2011, however, the rule called for rising interest rates, and between 2011 and 2019 the predicted interest rates from the rule are always higher than the actual rates. Between 2011 and 2019 the Fed was more expansive than its historical behavior as estimated by the rule. The COVID experience through 2022.1 also shows the Fed setting historically low interest rates beginning in 2021 in the face of rising inflation and falling unemployment. In short, the low recent interest rates may be because of a change in Fed behavior.
Climate policies vary widely across countries, with some countries imposing stringent emissions policies and others doing very little. When climate policies vary across countries, energy-intensive industries have an incentive to relocate to places with few or no emissions restrictions, an effect known as leakage. Relocated industries would continue to pollute but would be operating in a less desirable location. We consider solutions to the leakage problem in a simple setting where one region of the world imposes a climate policy and the rest of the world is passive. We solve the model analytically and also calibrate and simulate the model. Our model and analysis imply: (1) optimal climate policies tax both the supply of fossil fuels and the demand for fossil fuels; (2) on the demand side, absent administrative costs, optimal policies would tax both the use of fossil fuels in domestic production and the domestic consumption of goods created with fossil fuels, but with the tax rate on production lower due to leakage; (3) taxing only production (on the demand side), however, would be substantially simpler, and almost as effective as taxing both production and consumption, because it would avoid the need for border adjustments on imports of goods; (4) the effectiveness of the latter strategy depends on a low foreign elasticity of energy supply, which means that forming a taxing coalition to ensure a low foreign elasticity of energy supply can act as a substitute for border adjustments on goods.
We consider a general nonlinear pricing environment with private information. We characterize the information structure that maximizes the sellerís profits. The seller who cannot observe the buyerís willingness to pay can control both the signal that a buyer receives about his value and the selling mechanism. The optimal screening mechanism has finitely many items even with a continuum of types. We identify sufficient conditions under which the optimal mechanism has a single item. Thus, the socially efficient variety of items is decreased drastically at the expense of higher revenue and lower information rents.