Testing for time stochastic dominance

Abstract

We propose nonparametric tests for the null hypothesis of time stochastic dominance. Time stochastic dominance makes a partial order of different prospects over time based on the net present value criteria for general utility and time discount function classes. For example, time stochastic dominance can be used for ranking investment strategies or environmental policies based on the expected net present value of the future benefits. We consider an Lp-type test statistic and derive its large sample distribution under standard panel data sampling scheme with fixed time dimension. We suggest a path-wise (or cluster) bootstrap procedure that allows individual time series dependence over the time horizon. We describe two approaches, the contact-set approach and the numerical delta method, that may lead to enhanced power compared to the conventional least-favorable-case based approach. We prove the asymptotic validity of our testing procedures. We investigate the finite sample performance of the tests in simulation studies. As an illustration, we apply the proposed tests to evaluate the Million Baht Village Fund Program in Thailand and carbon emission trading scheme in China.