Testing for non-nested conditional moment restrictions using unconditional empirical likelihood

We propose non-nested hypothesis tests for conditional moment restriction models based on the method of generalized empirical likelihood (GEL). By utilizing the implied GEL probabilities from a sequence of unconditional moment restrictions that contains equivalent information of the conditional moment restrictions, we construct Kolmogorov–Smirnov and Cramér–von Mises type moment encompassing tests. Advantages of our tests over Otsu and Whang’s (2011) tests are: (i) they are free from smoothing parameters, (ii) they can be applied to weakly dependent data, and (iii) they allow non-smooth moment functions. We derive the null distributions, validity of a bootstrap procedure, and local and global power properties of our tests. The simulation results show that our tests have reasonable size and power performance in finite samples.     

Menu theorems for bilateral contracting

This paper studies bilateral contracting where multiple principals negotiate contracts with multiple agents independently. It is shown that pure-strategy equilibrium allocations relative to any ad hoc set of feasible mechanisms are supported by pure-strategy perfect Bayesian equilibria relative to the set of menus. This paper also shows that all equilibrium allocations to any ad hoc set of feasible mechanisms are supported by correlated equilibria relative to the set of menus, where a state is a probability distribution function over payoff-relevant variables. Furthermore, all equilibrium allocations relative to the set of menus persist even if principals use more complex mechanisms.     

Doubly robust uniform confidence band for the conditional average treatment effect function

In this paper, we propose a doubly robust method to estimate the heterogeneity of the average treatment effect with respect to observed covariates of interest. We consider a situation where a large number of covariates are needed for identifying the average treatment effect but the covariates of interest for analyzing heterogeneity are of much lower dimension. Our proposed estimator is doubly robust and avoids the curse of dimensionality. We propose a uniform confidence band that is easy to compute, and we illustrate its usefulness via Monte Carlo experiments and an application to the effects of smoking on birth weights.     

A bargaining model of tax competition

This paper develops a model in which competing governments offer financial incentives to induce individual firms to locate within their jurisdictions. Equilibrium is described under three specifications of the supplementary taxes. There is no misallocation of capital under two of these specifications, and there might or might not be capital misallocation under the third. This result contrasts strongly with that of the standard tax competition model, which does not allow governments to treat firms individually. That model finds that competition among governments almost always leads to capital misallocation.     

Consistent Testing for Stochastic Dominance under General Sampling Schemes

We propose a procedure for estimating the critical values of the extended Kolmogorov–Smirnov tests of Stochastic Dominance of arbitrary order in the general  K  -prospect case. We allow for the observations to be serially dependent and, for the first time, we can accommodate general dependence amongst the prospects which are to be ranked. Also, the prospects may be the residuals from certain conditional models, opening the way for conditional ranking. We also propose a test of Prospect Stochastic Dominance. Our method is based on subsampling and we show that the resulting tests are consistent and powerful against some  N^−1/2  local alternatives. We also propose some heuristic methods for selecting subsample size and demonstrate in simulations that they perform reasonably. We describe an alternative method for obtaining critical values based on recentring the test statistic and using full-sample bootstrap methods. We compare the two methods in theory and in practice.     

Are there Monday effects in stock returns: A stochastic dominance approach

We provide a test of the Monday effect in daily stock index returns. Unlike previous studies we define the Monday effect based on the stochastic dominance criterion. This is a stronger criterion than those based on comparing means used in previous work and has a well defined economic meaning. We apply our test to a number of stock indexes including US large caps and small caps as well as UK and Japanese indexes. We find strong evidence of a Monday effect in many cases under this stronger criterion. The effect has reversed or weakened in the Dow Jones and S&P 500 indexes post 1987, but is still strong in more broadly based indexes like the NASDAQ, the Russell 2000 and the CRSP.     

Random walk or chaos: A formal test on the Lyapunov exponent

A formal test on the Lyapunov exponent is developed to distinguish a random walk model from a chaotic system, which is based on the Nadaraya–Watson kernel estimator of the Lyapunov exponent. The asymptotic null distribution of our test statistic is free of nuisance parameter, and simply given by the range of standard Brownian motion on the unit interval. The test is consistent against the chaotic alternatives. A simulation study shows that the test performs reasonably well in finite samples. We apply our test to some of the standard macro and financial time series, finding no significant empirical evidence of chaos.     

Testing functional inequalities

This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of _Lp$L_p$-type functionals of kernel estimators (1≤p<∞)$(1\le p<\infty )$. Drawing on the approach of Poissonization, this paper establishes that the tests are asymptotically distribution free, admitting asymptotic normal approximation. In particular, the tests using the standard normal critical values have asymptotically correct size and are consistent against general fixed alternatives. Furthermore, we establish conditions under which the tests have nontrivial local power against Pitman local alternatives. Some results from Monte Carlo simulations are presented.     

The quantilogram: With an application to evaluating directional predictability

We propose a new diagnostic tool for time series called the quantilogram. The tool can be used formally and we provide the inference tools to do this under general conditions, and it can also be used as a simple graphical device. We apply our method to measure directional predictability and to test the hypothesis that a given time series has no directional predictability. The test is based on comparing the correlogram of quantile hits to a pointwise confidence interval or on comparing the cumulated squared autocorrelations with the corresponding critical value. We provide the distribution theory needed to conduct inference, propose some model free upper bound critical values, and apply our methods to S&P500 stock index return data. The empirical results suggest some directional predictability in returns. The evidence is strongest in mid range quantiles like 5–10% and for daily data. The evidence for predictability at the median is of comparable strength to the evidence around the mean, and is strongest at the daily frequency.