A New Empirical Test of Relative Risk Aversion Hypothesis By Bayes Model: Bernoulli Core Approach

The RRA (relative risk aversion) hypothesis proposed by Breen and Goldthorpe (1997) is one of the most influential rational choice theory that attempts to explain educational differentials among social origins of students. They formalized a probabilistic model and assumed that decision-making about advancement of higher education is motivated by the individual’s preference to avoid downward social class mobility. Many empirical studies have tried to test the validity of the RRA hypothesis by statistical estimation of the effect of class origin on educational attainment (Davies et al 2002, Breen and Yaish 2006, Fujihara 2011;2012, Stocké 2007). However, many estimation models in previous studies contain serious misspecification error because of the over simplification of statistical models. Mathematically correct formula of advancement rate for higher education derived from B&G model cannot be represented by discrete choice model such as, binomial or multinomial logistic regression with maximum likelihood estimation. Therefore, all result of estimation by generalized linear models cannot be evidence for empirical test of RRA hypothesis.

Meanwhile, this paper implements a hierarchical Bayes MCMC estimation to test the RRA hypothesis correctly. We show that mathematical structure of the RRA hypothesis can be precisely expressed by hierarchical Bayes model. Using nationwide data, SSP 2015 and SSM 2015 in Japan, we show that 95% highest density intervals of posterior distribution of advancement rate for individuals from higher origin is greater than that of lower origin when assuming RRA hypothesis. Moreover, posterior distributions of theoretical parameters such as alpha, beta, and gamma that define the probability of reaching various social class, are all estimated by MCMC. It reveals that staying higher education may increase risk of downward mobility for individuals from middle class origin.