Non-Additivity of Subjective Beliefs over Different Time Intervals; Uwe Sunde (LMU Munich) joint with Peter Haan, Chen Sun, and Georg Weizsäcker

Abstract

We examine the additivity of subjective beliefs over time. Respondents from the German Socio-Economic Panel report their beliefs about the stock market in different time horizons. When asked about a ten-year time interval, only very few respondents report that they expect a stock-price increase (decrease) that is equal to the sum of the same respondent's expected increases (decreases) over two shorter time intervals that jointly cover the same ten-year horizon. Such non-additivity is irrational in that it cannot be explained by subjective per-period beliefs; likewise, we find that it cannot be explained by unsystematic reporting error or by a possible failure to account for cumulative growth effects. We also find that a respondent's degree of additivity is correlated with making larger financial investments. Estimations of nonlinear models indicate that sub-additivity is more prevalent than super-additivity, and that the pattern is consistent with a time perception where short time intervals have a proportionally larger weight than long time intervals.