Social Security in an Analytically Tractable Overlapping Generations Model with Aggregate and Idiosyncratic Risk

Abstract

Many countries operate large social security systems. Social security can increase economic efficiency and provide insurance against household risks for which no private markets exist. However, social security systems also impose costs by distorting prices and decisions. The question arises whether the benefits of social security outweigh the costs.To study the welfare consequences of introducing a social security system this paper develops an analytically tractable model with two overlapping generations where households face many different sources of risks over their life-cycle. Key risks for the analysis of social security are idiosyncratic risks -e.g., the risk of unemployment -and aggregate risks -i.e., the risk of aggregate productivity losses which leads to reductions of wages and asset returns. Our analysis on the welfare effects of social security in light of these risks differs from the previous literature in that, thus far, prior studies have only considered models with one type of risk in isolation. One strand of the literature has examined social security when only aggregate risk is present. The other strand has only considered idiosyncratic risk.In our model we find that the two risks interact in multiple ways and influence the welfare effects of introducing a social security system. As a result, we show that these effects are less strong on the welfare costs of crowding out than on the welfare gains from insurance. Hence, the interactions of risks increase the total welfare benefits of social security.The findings of this paper must be investigated in a more realistic quantitative model which is suitably calibrated. This is done in our companion paper, Harenberg and Ludwig (2014). There we document that indeed the interactions of risks overturn conventional findings on the welfare effects of social security and we conclude that the introduction of a minimum flat pension is welfare improving once all household risks are appropriately taken into account. Social Security in an Analytically AbstractWhen markets are incomplete, social security can partially insure against idiosyncratic and aggregate risks. We incorporate both risks into an analytically tractable model with two overlapping generations and demonstrate that they interact over the life-cycle. The interactions appear even though the two risks are orthogonal and they amplify the welfare consequences of introducing social security.On the one hand, the interactions increase the welfare benefits from insurance. On the other hand, they can in-or decrease the welfare costs from crowding out of capital formation. This ambiguous effect on crowding out means that the net effect of these two channels is positive, hence the interactions of risks increase the total welfare benefits of social security.

Social Security and the Interactions between Aggregate and Idiosyncratic Risk

“…Loosely speaking, this makes the agent behave as if he were more risk-averse. In Harenberg and Ludwig (2014), we present an extension to a multi-period model and show that, in such a more general framework, LCI appears as a multiplicative background risk (Franke, Schlesinger, and Stapleton 2006), which comes on top of the additive background risk. The intuition follows from the dynamic budget constraint in the working period, in which total income is given by sR + wη.…”

“…We also ignore any feedback in general equilibrium. In Harenberg and Ludwig (2014), we incorporate both channels in a standard Diamond (1965) model with risk. Thus, in contrast to the simple model presented here, consumption and savings decisions occur in the first period and wages and returns are determined in general equilibrium.…”

Optimal taxes on capital in the OLG model with uninsurable idiosyncratic income risk

“…Each household has one unit of time in both periods, supplied inelastically to the market. Labor productivity when young is equal to (1 − κ), and, as in Harenberg and Ludwig (2015), in the second period labor productivity is given by κη t+1 , where κ ∈ [0, 1) is a parameter that captures relative labor income of the old, and η t+1 is an idiosyncratic labor productivity shock. We assume that the cdf of η t+1 is given by Ψ(η t+1 ) in every period and denote the corresponding pdf by ψ η t+1 .…”