Why is the life cycle of happiness unusual in Japan

This paper attempts to explain an unusual finding in previous studies about the life cycle of happiness in Japan. While it has become common to find happiness U-shaped over the life cycle, with the lowest point reached in the early 40s and a recovery up to the old age (Blanchflower and Oswald, 2004, 2008; Clark, 2007), a different pattern was reported for Japan (Cabinet Office, 2009; Tsutsui et al., 2010; Commission on Measuring Well-being, 2011). Specifically, Japan does not seem much different in the first half of the life cycle, with a declining happiness from young age to the early 40s. But a notable divergence appears in the second half of life cycle, when happiness in Japan does not increase after the 40s, but largely stays flat (Tsutsui et al., 2010). Evidently, the age-happiness profile in Japan is not U-shaped like in many other countries, but L-shaped, with a conspicuous lack of increased happiness in the old age. Overall, it is the elderly in Japan that appear to be the least happy across different age groups (Commission on Measuring Well-being, 2011, p. 16). As a possible explanation for this peculiar pattern of the age-happiness profile in Japan, Tsutsui et al. (2010) suggested a possible bias in estimated age effects due to omitted cohort effects (p. 51-53). This potential bias in age effects was previously emphasized by Clark (2007), who examined whether cohort effects may account for the U-shape in happiness in the United Kingdom, but found that U-shape remained largely unchanged even with included cohort effects. So far, no similar study has been done with Japanese data. Our goal in this paper is to verify whether cohort effects may explain the L-shape in age-happiness profile in Japan. In practice, when cohort effects are added to regression specifications, they are commonly used together with the effects of age and calendar year. This creates an identification problem among age, cohort and period effects, because these three effects are linearly dependent, with the individual’s age equal exactly to the current year minus the year of birth. The identification problem in age-period-cohort (A-P-C) models has long been known in economics (Deaton and Paxson, 1994), and it can be solved by imposing restrictions on parameter estimates of the A-P-C effects. In this paper, we consider two approaches that solve the identification problem. First, we deal with the exact linearity among A-P-C effects by specifying one of these effects with a non-linear function, as a part of a semiparametric regression model (Wunder et al., in press; Movshuk, 2011). We also consider an alternative restriction from Deaton and Paxson (1994), who solved the identification problem by restricting period effects to be orthogonal to a linear time trend1. The key assumption of the Deaton-Paxson (D-P) restriction is that period effects do not contain linear time trends. If linear trends are actually present in period effects, the D-P approach would attribute them to age and cohort effects, leading to biased estimates of these effects (Deaton and Paxson, 1997, p. 103). Fortunately, we could verify the validity of the D-P assumption with our semiparametric approach to solve the identification problem and we found no significant linear time trend in estimated period effects. This made either of our two approaches applicable to estimating A-P-C models of happiness in Japan.