Welfare implications of net social security wealth

Real net social wealth (NSSW), the real present value of social security benefits received minus social security taxes paid, is frequently used as a direct proxy measure for the impact of a social security system on generation welfare. The present paper establishes to the contrary, for a class of overlapping generation economies, that NSSW can be simultaneously negatively correlated with welfare for every agent in every generation. More generally, the paper determines the extent to which social security is needed in these economies to ensure social optimality, and investigates the proper subset of economies for which NSSW and generation welfare exhibit positive correlation.     

Welfare variations and the comparative statics of demand

By employing order-theoretic comparative statics, we provide necessary and sufficient conditions on the direct utility function (alternatively, on the indirect utility function) to guarantee that the compensating and equivalent variations are monotonically increasing in income. We also show that these conditions are sufficient to guarantee normal demand. Our results do not depend on the smoothness or strict quasiconcavity of the utility function, and can be extended to a setting with non-linear prices.     

Nash equilibrium vs. maximin : A comparative game statics analysis

This paper derives comparative game statics results for both maximin and Nash strategies, thereby allowing a more systematic comparison between these two approaches.     

A program for algebraic and qualitative comparative statics and stability analysis

This paper presents a computer program designed by the author which determines algebraically and qualitatively both short- and long-run comparative statics multipliers for standard linear or linearized economic models. When the model is dynamic, i.e., when it involves linear of linearized differential equations, the program also provides the algebraic expressions and the qualitative signs for the coefficients of the characteristic polynomial.     

A framework for social security analysis

The public provision of pensions in the U.S. by means of the Social Security systems is examined relative to conventional arguments for public intervention. The system is analysed in terms of income redistribution, the provision of insurance where private markets are not efficient, and the compelling of saving by individuals.     

A life cycle analysis of social security

Summary We develop an applied general equilibrium model to examine the optimal social security replacement rate and the welfare benefits associated with it. Our setup consists of overlapping generations of 65-period lived individuals facing mortality risk and individual income risk. Private credit markets, including markets for private annuities, are closed by assumption. Unlike previous analyses, we find that an unfunded social security system may well enhance economic welfare. In our benchmark economy, the optimal social security replacement rate is 30%, and an empirically more plausible replacement rate of 60% raises welfare compared with an economy with no social security system.We would like to thank Andy Atkeson, V. V. Chari, Steve Davis, Paul Evans, Lars Hansen, Tim Kehoe, Nobu Kiyotaki, Ed Prescott, José-Victor Ríos-Rull, Richard Rogerson, Tom Sargent, Nancy Stokey, Dick Sweeney, Robert Townsend, and the participants of the NBER Economic Fluctuations Small Group Workshop on Micro and Macro Perspectives on the Aggregate Labor Market in Palo Alto, the NBER General Equilibrium Theory Conference in Minneapolis, the Money and Banking Workshop at the University of Chicago, and the NBER Summer Institute. An earlier version of this paper was titled A Dynamic Stochastic General Equilibrium Analysis of Social Security. This material is based upon work supported by the National Science Foundation under Grant No. SES-9210291. We also thank the Minnesota and San Diego Supercomputer Centers for their support.     

Market equilibrium in the presence of green consumers and responsible firms: A comparative statics analysis

This paper analyzes how the interaction between green consumers and responsible firms affects the market equilibrium. The main result is that a higher degree of responsibility of consumers and/or firms may both increase and decrease the total abatement and the social welfare. In general an increment in the degree of CSR of a firm entails an increase of its total clean-up and a reduction of the aggregate abatement of its rival. When the rival firm has a high degree of CSR this second effect is stronger than the first and total abatement falls down. At the same time, when the degree of consciousness of consumers and/or firms is very high, responsible firms overprovide environmental quality: in such case a further increment in the level of social responsibility of a market actor may trigger an increase of firms’ total clean-up but a reduction in social welfare.     

Strong comparative statics of equilibria

Some results in the monotone comparative statics literature tell us that if a parameter increases, some old equilibria are smaller than some new equilibria. We give a sufficient condition such that at a new parameter value every old equilibrium is smaller than every new equilibrium. We also adapt a standard algorithm to compute a minimal such newer parameter value and apply this algorithm to a game of network externalities. Our results are independent of a theory of equilibrium selection and are valid for games of strategic complementarities.     

A note on comparative statics and dynamics of stationary states

Certain results are communicated regarding effects of parameter changes, when the stationary state is stable, on the stationary state and an optimal paths in its neighbourhood in discrete time multi-sectoral optimal growth models where period utilities are discounted.     

A life-cycle analysis of social security with housing

This paper incorporates two features of housing in a life-cycle analysis of social security: housing as a durable good and housing market frictions. We find that both housing quantities and homeownership rates respond strongly to eliminating social security. Accordingly, the aggregate impacts of this policy reform are significantly larger in an economy with explicit housing choices than in a standard life-cycle economy. Our analysis shows that the key mechanism behind these results is the substitution effects of a change in interest rates and, thus, the price of housing services on the choice of nondurable consumption versus housing services.     

Weak and strong monotone comparative statics

Summary This paper develops necessary and sufficient conditions for the set of solutions to an optimization problem to be nondecreasing in a weak sense still strong enough to guarantee the existence of an increasing selection, and thus strong enough to guarantee monotonicity when the solution is unique, as well as necessary and sufficient conditions for the set of optimizers to be nondecreasing in a strong sense which is strong enough to rule out the possibility of a decreasing selection. These necessary and sufficient conditions are variations of quasisupermodularity and the single crossing property introduced in Milgrom-Shannon [13]. Moreover, to determine when an objective function satisfies these conditions, this paper develops several characterizations of quasisupermodularity and the single crossing property and their variants, both in terms of differential conditions and in terms of restrictions on the structure of the level sets of these functions. Several examples are given to choice theory under loss aversion and to an auction problem.I am grateful to Don Brown and Paul Milgrom for numerous helpful conversations concerning earlier versions of this paper. This paper is a revised and expanded version of the paper An Ordinal Theory of Games with Strategic Complementarities (Shannon [15]). I am pleased to acknowledge the financial support of the National Science Foundation, and an Alfred P. Sloan Foundation Doctoral Dissertation Fellowship.     

Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach

We analyze comparative risk aversion in a new way, through a comparative statics problem in which, for a cost, agents can shift from an initial probability distribution toward a preferred distribution. The Ross characterization arises when the original distribution is riskier than the preferred distribution and the cost is monetary, and the Arrow-Pratt characterization arises when the original distribution differs from the preferred distribution by a simple mean-preserving spread and the cost is a utility cost. Higher-order increases in risk lead to higher-order generalizations, and the comparative statics method yields a unified approach to the problem of comparative risk attitudes.     

A unified approach to comparative statics puzzles in experiments

The paper shows that several game-theoretic solution concepts provide similar comparative statics predictions over a wide class of games. I start from the observation that, in many experiments, behavior is affected by parameter shifts that leave the Nash equilibrium unchanged. I explain the direction of change with a heuristic structural approach, using properties such as strategic complementarities and increasing differences. I show that the approach is consistent with general comparative statics results for (i) the Nash equilibrium of a game with perturbed payoff functions, (ii) the quantal response equilibrium, (iii) level-k reasoning. I also relate the structural approach to equilibrium selection concepts.     

Topics in nonparametric comparative statics and stability

This paper presents the analysis of the Jacobian matrix of a small, macroeconomic model to determine the robustness of the model's comparative statics. The values of the model's coefficients are assessed with respect to seven alternative estimation strategies such as ordinary least squares or two-stage least squares. For each alternative version, the invertibility and stability of the Jacobian matrix is studied. The model is robust to the degree that these characteristics are shared by any matrix with the same sign pattern or other similar nonparametric conditions on its entries. One way to address the relative success of the different estimation strategies is through the robustness of the comparative statics of the resulting model.     

Welfare analysis of the coordinating role of a redundant security

The purpose of this paper is to provide a sufficient condition under which a security with the coordinating role does not lead to a Pareto superior equilibrium allocation.     

A welfare analysis of social security in a dynastic framework*

In this article, we study the welfare effects of unfunded social security in a general equilibrium model populated with overlapping generations of altruistic individuals that differ in lifetime expectancy and earnings ability. Contrary to previous research, our results indicate that steady‐state welfare increases with social security for most households, although by very different amounts. This result is mainly due to two factors. First, the presence of two‐sided altruism significantly mitigates the crowding out effect of unfunded social security. Second, ability shocks and uncertain lifetimes generate significant heterogeneity among households to yield different induced preferences for social security.