Long term risk return tradeoffs across countries

There are large amount of solid evidences in the U.S. stock market to confirm the risk return tradeoffs in the long term by finding an increasingly positive estimated coefficient and an increased ?2 value. However, after extending the sample to a global dataset including twelve developed countries, the predictive pattern of the past market variances diminished. The estimated coefficients in seven out of those countries become fluctuant near zero and the highest ?2 values in one-third of those countries are less than 25%. By introducing a set of macro-economic state variables, the newly-built bivariate model improves the estimated coefficients to an increasingly positive pattern in seven out of the twelve countries and the highest ?2 values up to more than 60% in ten out of the twelve countries. The out-of-sample forecast MSE-F test shows that the bivariate model is superior to the benchmark model by reject the null hypothesis that the mean-squared errors of the two models are equal. However, the bivariate model cannot explain the whole difference across countries because there still exist at least two countries holding a fluctuant and sometimes negative coefficients. More complicated models need to be constructed in the further study.