Constant relative risk aversion utility and consumption CAPM: discount factors and risk aversions for Norway, Sweden, and the UK

This paper applies the newly suggested Markov chained Monte Carlo Surface Sampling Algorithm of Zappa estimating European discount factors and relative risk aversions for the CRRA utility functions based on the consumption capital asset pricing model (CCAPM). The relatively challenging estimation focuses on parameter equalities and their interpretations for three European countries, Norway, Sweden, and the UK. Moreover, European consumer behavior regarding risk and inter-temporal consumption substitution (including asset markets risk pricing) are of general interest applying robust estimation techniques. The empirical results from sssthe non-parametric Bayesian estimation technique with reported parameter paths, densities and diagnostics are compared. The UK (Swedish) investors show the highest (lowest) risk aversion (and lowest (highest) inter-temporal substitution in consumption). However, the risk aversion coefficient distributions are relatively wide, with an insignificant parameter for Sweden and Norway, and a significant parameter for the UK. The stochastic discount factor is approximately equal for all three countries reporting a yearly discount factor of 0.99. The quarterly discount factor is lowest for Sweden (0.997) followed by Norway and the UK (0.998), indicating that Sweden has the most impatient consumers. Bivariate conditional densities and simulation paths are extracted for interpretative purposes, specifically excessive shocks.The paper uses the national account data for inflation adjusted household consumption (non-durables and services) together with inflation adjusted stock (index) with dividends on all stock series for Norway, Sweden, and the UK. The most interesting aspect of Asset Pricing considers how securities markets price risk (the time dimension alone is largely mechanical). For this question to be interesting, it must be that there is a positive price for risk – i.e. investors require some compensation for exposing their portfolios to risk. This in turn requires that investors dislike risk or that they are risk averse. This paper’s main interest is therefore the stochastic discount factor for the constant relative risk aversion utility as described in the marginal rate of substitution.