Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity

We develop tests of the proportional hazards assumption, with respect to a continuous covariate, in the presence of unobserved heterogeneity with unknown distribution at the individual observation level. The proposed tests are specially powerful against ordered alternatives useful for modeling non-proportional hazards situations. By contrast to the case when the heterogeneity distribution is known up to …nite dimensional parameters, the null hypothesis for the current problem is similar to a test for absence of covariate dependence. However, the two testing problems di¤er in the nature of relevant alternative hypotheses. We develop tests for both the problems against ordered alternatives. Small sample performance and an application to real data highlight the usefulness of the framework and methodology.

Testing the Tunnel Effect: Comparison, Age and Happiness in UK and German Panels

In contrast to previous results combining all ages we find positive effects of comparison income on happiness for the under 45s, and negative effects for those over 45. In the BHPS these coefficients are several times the magnitude of own income effects. In GSOEP they cancel to give no effect of effect of comparison income on life satisfaction in the whole sample, when controlling for fixed effects, and time-in-panel, and with flexible, age-group dummies. The residual age-happiness relationship is hump-shaped in all three countries. Results are consistent with a simple life cycle model of relative income under uncertainty.

Empirical testing of genuine savings as an indicator of weak sustainability: a three-country analysis of long run trends

Genuine Savings has emerged as a widely-used indicator of sustainable development. In this paper, we use long-term data stretching back to 1870 to undertake empirical tests of the relationship between Genuine Savings (GS) and future well-being for three countries: Britain, the USA and Germany. Our tests are based on an underlying theoretical relationship between GS and changes in the present value of future consumption. Based on both single country and panel results, we find evidence supporting the existence of a cointegrating (long run equilibrium) relationship between GS and future well-being, and fail to reject the basic theoretical result on the relationship between these two macroeconomic variables. This provides some support for the GS measure of weak sustainability. We also show the effects of modelling shocks, such as World War Two and the Great Depression.