This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to embody a mixture of stochastic and deterministic trends, complications which result in asymptotic degeneracy of the kernel-weighted signal matrix. To address these complications new \textsl{local} and \textsl{global rotation} techniques are introduced to transform the covariate space to accommodate multiple scenarios of induced degeneracy. Under certain regularity conditions we derive asymptotic results that differ substantially from existing kernel regression asymptotics, leading to new limit theory under multiple convergence rates. For the practically important case of endogenous nonstationary regressors we propose a fully-modified kernel estimator whose limit distribution theory corresponds to the prototypical pure (i.e., exogenous covariate) cointegration case, thereby facilitating inference using a generalized Wald-type test statistic. These results substantially generalize econometric estimation and testing techniques in the cointegration literature to accommodate time variation and complications of co-moving regressors. Finally an empirical illustration to aggregate US data on consumption, income, and interest rates is provided.
This paper examines the link between legislative politics, hospital behavior, and health care spending. When trying to pass sweeping legislation, congressional leaders can attract votes by adding targeted provisions that steer money toward the districts of reluctant legislators. This targeted spending provides tangible local benefits that legislators can highlight when fundraising or running for reelection. We study a provision - Section 508 – that was added to the 2003 Medicare Modernization Act (MMA). Section 508 created a pathway for hospitals to apply to get their Medicare payment rates increased. We find that hospitals represented by members of the House of Representatives who voted ‘Yea’ on the MMA were significantly more likely to receive a 508 waiver than hospitals represented by members who voted ‘Nay.’ Following the payment increase generated by the 508 program, recipient hospitals treated more patients, increased payroll, hired nurses, added new technology, raised CEO pay, and ultimately increased their spending by over $100 million annually. Section 508 recipient hospitals formed the Section 508 Hospital Coalition, which spent millions of dollars lobbying Congress to extend the program. After the vote on the MMA and before the vote to reauthorize the 508 program, members of Congress with a 508 hospital in their district received a 22% increase in total campaign contributions and a 65% increase in contributions from individuals working in the health care industry in the members’ home states. Our work demonstrates a pathway through which the link between politics and Medicare policy can dramatically affect US health spending.
Limit theory for regressions involving local to unit roots (LURs) is now used extensively in time series econometric work, establishing power properties for unit root and cointegration tests, assisting the construction of uniform confidence intervals for autoregressive coefficients, and enabling the development of methods robust to departures from unit roots. The present paper shows how to generalize LUR asymptotics to cases where the localized departure from unity is a time varying function rather than a constant. Such a functional local unit root (FLUR) model has much greater generality and encompasses many cases of additional interest, including structural break formulations that admit subperiods of unit root, local stationary and local explosive behavior within a given sample. Point optimal FLUR tests are constructed in the paper to accommodate such cases. It is shown that against FLUR\ alternatives, conventional constant point optimal tests can have extremely low power, particularly when the departure from unity occurs early in the sample period. Simulation results are reported and some implications for empirical practice are examined.
This paper studies functional local unit root models (FLURs) in which the autoregressive coefficient may vary with time in the vicinity of unity. We extend conventional local to unity (LUR) models by allowing the localizing coefficient to be a function which characterizes departures from unity that may occur within the sample in both stationary and explosive directions. Such models enhance the flexibility of the LUR framework by including break point, trending, and multi-directional departures from unit autoregressive coefficients. We study the behavior of this model as the localizing function diverges, thereby determining the impact on the time series and on inference from the time series as the limits of the domain of definition of the autoregressive coefficient are approached. This boundary limit theory enables us to characterize the asymptotic form of power functions for associated unit root tests against functional alternatives. Both sequential and simultaneous limits (as the sample size and localizing coefficient diverge) are developed. We find that asymptotics for the process, the autoregressive estimate, and its $t$ statistic have boundary limit behavior that differs from standard limit theory in both explosive and stationary cases. Some novel features of the boundary limit theory are the presence of a segmented limit process for the time series in the stationary direction and a degenerate process in the explosive direction. These features have material implications for autoregressive estimation and inference which are examined in the paper.
This paper introduces identification-robust subvector tests and confidence sets (CS’s) that have asymptotic size equal to their nominal size and are asymptotically efficient under strong identification. Hence, inference is as good asymptotically as standard methods under standard regularity conditions, but also is identification robust. The results do not require special structure on the models under consideration, or strong identification of the nuisance parameters, as many existing methods do. We provide general results under high-level conditions that can be applied to moment condition, likelihood, and minimum distance models, among others. We verify these conditions under primitive conditions for moment condition models. In another paper, we do so for likelihood models. The results build on the approach of Chaudhuri and Zivot (2011), who introduce a C(α)-type Lagrange multiplier test and employ it in a Bonferroni subvector test. Here we consider two-step tests and CS’s that employ a C(α)-type test in the second step. The two-step tests are closely related to Bonferroni tests, but are not asymptotically conservative and achieve asymptotic efficiency under strong identification.
We provide an introduction to the recent developments in dynamic mechanism design, with a primary focus on the quasilinear case. First, we describe socially optimal (or efficient) dynamic mechanisms. These mechanisms extend the well-known Vickrey-Clark-Groves and D’Aspremont-Gérard-Varet mechanisms to a dynamic environment. Second, we discuss revenue optimal mechanisms. We cover models of sequential screening and revenue maximizing auctions with dynamically changing bidder types. We also discuss models of information management where the mechanism designer can control (at least partially) the stochastic process governing the agents’ types. Third, we consider models with changing populations of agents over time. After discussing related models with risk-averse agents and limited liability, we conclude with a number of open questions and challenges that remain for the theory of dynamic mechanism design.
Injury rates in twelve U.S. men’s collegiate sports are examined in this paper. The twelve sports ranked by overall injury rate are wrestling, football, ice hockey, soccer, basketball, lacrosse, tennis, baseball, indoor track, cross country, outdoor track, and swimming. The first six sports will be called “contact” sports, and the next five will be called “non-contact.” Swimming is treated separately because it has many fewer injuries. Injury rates in the contact sports are considerably higher than they are in the non-contact sports and they are on average more severe. Estimates are presented of the injury savings that would result if the contact sports were changed to have injury rates similar to the rates in the non-contact sports. The estimated savings are 49,600 fewer injuries per year and 5,990 fewer injury years per year. The estimated dollar value of these savings is between about 0.5 and 1.5 billion per year. About half of this is from football. Section 7 speculates on how the contact sports might be changed to have their injury rates be similar to those in the non-contact sports.
We study the division of trade surplus in a natural field experiment on German eBay. Acting as a seller, we offer Amazon gift cards with face values of up to 500 Euro. A random selection of buyers, the subjects of our experiment, make price offers according to the rules of eBay. Using a novel decomposition method, we infer the offered shares of trade surplus from the data and find that the average share proposed to the seller amounts to about $30 \%$. Additionally, we document: (i) insignificant effects of stake size; (ii) poor use of strategically relevant public information; and (iii) differences between East and West German subjects.
We study how cultural distance affects the rejection of imposed institutions. To do so, we exploit the transplantation of Piedmontese institutions on Southern Italy that occurred during the Italian unification. We assemble a novel and unique dataset containing municipal-level information on episodes of brigandage, a form of violent uprising against the unitary government. We use the geographic distance from local settlements of Piedmontese descent as a proxy for the cultural distance between each municipality and the new rulers. We find robust evidence that cultural distance from the origins of the transplanted institutions is significantly associated with more intense resistance to these institutions. Our results further suggest that the rejection of the transplanted institutions may have a long-lasting effect on political participation.