This paper studies how the elasticity of intertemporal substitution (EIS) influences labor market fluctuations in the labor search and matching model with both extensive and intensive margins of labor supply. With the curvature of utility, the countercyclical marginal utility of consumption induces the flow value of unemployment to be procyclical, and the stock returns to be countercyclical. The former effect reduces unemployment volatility by weakening wage rigidity. In contrast, the latter effect magnifies unemployment volatility by discounting higher future payoffs at a lower discount rates, if wages do not absorb all of productivity shocks. The higher EIS reduces the procyclicality of the flow value of unemployment, and reinforces the countercyclicality of the stock returns. We quantitatively show that high values of the EIS are required to resolve the unemployment volatility puzzle.