András Simonovits

Expectations, (in)stability and (in)viability in realistic overlapping cohorts models

Abstract In this paper we shall consider the multi-cohort generalization of overlapping generations models, namely overlapping cohorts (OLC) models. Each time-period consumers of different ages form expectations on future interest rates and conditionally maximize utility arising from their remaining consumption paths under the condition of zero bequest. For every time period a coordinator determines the new interest rate to ensure that the total consumption is equal to the total endowment of the society. The message of the paper is the following: (1) In OLC, the dynamics generated by rational expectations is frequently not only unstable but unviable. (2) In OLC, the dynamics generated by naive expectations is practically asymptotically stable and viable around the lower steady state.

What has been Wrong with the Retirement Rules in Hungary

A basic problem with the ever-changing Hungarian retirement rules has been that they created excessive shares of gainers and of losers. Certain workers with long (and continuous) employment could retire well below the normal retirement age (NRA) with full benefit. Other workers, with fragmented and therefore short employment had to work until reaching the ever rising NRA. A peculiar consequence of these rules is the strong negative correlation between the retirement age and the length of contribution. Moving in the direction of a fair system, like the Nonfinancial Defined Contribution system, would improve sustainability and fairness.

Applications of Dynamic Programming

The previous Chapter outlined the mathematical theory and the control- theoretic application of the dynamic programming, now some economic applications follow. Sections 8.1 and 8.2 discuss optimal saving (exogenous factor prices) and accumulation (endogenous factor prices), respectively. Section 8.3 extends the analysis of Section 8.2 to the n-dimensional case. Section 8.4 presents a game-theoretic application of dynamic programming (due to Levhari and Mirman, 1980). Detailed description is to be found in Sargent (1987), Manuelli and Sargent (1987) and Stokey and Lucas (1989) which is used again extensively.

Cap on Contribution Base

To eliminate excessive benefits, this chapter puts a cap on contribution base to the proportional pension studied in Chapter 5. Though there are only few analytical results, it is shown that a properly chosen cap increases the socially optimal contribution rate as well as its efficiency.

Proportional (Earnings-Related) Pension System

This chapter studies a proportional (earnings-related) pension system when there is a continuum of workers with continuous distribution of earnings. To increase the realism of earlier models, the discount factor is assumed to be an increasing function of the wage. We determine the socially optimal contribution rate as a function of the interest rate ruling private savings and of the elasticity of the discount factor to wages. Depending on the annual interest rate and the elasticity of the discount factor to the wage, the socially optimal contribution rate can vary between 20 and 33%.

Introductory Tax Models

This chapter presents two introductory tax models. Section 2.2 discusses intragenerational redistribution with flexible labor supply. There are at least two types of workers, differing in productivities. Their labor supply is flexible and a flat basic income is financed from a proportional tax system which diminishes inequalities. Total redistribution is destructive but depending on the strength of labor disutility, a well-chosen tax rate can eliminate the worst inequalities. Section 2.3 analyzes redistribution with tax morale, where workers pay taxes to finance a basic income. Depending on their exogenously given tax morale, they underreport their true earnings more or less. In the socially optimal tax system, the stronger the tax morale, the higher (rather than the lower) the tax rate.

Four Pension Models with Two Types

This chapter presents four pension models with two types: type L earns much less than type H and discounts the future much stronger. Section 4.2 introduces proportional (earnings-related) pensions, where the benefits are proportional to wages. Here, the socially optimal contribution rate is a decreasing function of the annual interest rate but even for very high (10% annual) interest rates, the contribution rate stays above 20%. Section 4.3 discusses means-tested pensions, where the better-paid and farsighted worker does not receive any pension. Section 4.4 reduces the burden of type H by introducing a cap on the pension contribution base. Section 4.5 adds voluntary pensions with matching, and its tax expenditure reduces their utility.

Imperfect Knowledge of Transfer Rules: Irrational Inattention

This chapter introduces a much neglected topic: the imperfect knowledge of the transfer rules: irrational inattention. Section 13.2 discusses the widespread phenomenon that citizens underestimate the collected taxes. As a result, the median voter selects on a lower tax rate than she should do. Section 13.3 outlines a general pension framework where the influence of imperfect knowledge can be studied. Section 13.4 analyzes a phenomenon observed in the Hungarian pension reform of 1998, where much more workers entered the two-pillar system than would have been optimal. The reason was simple: there was hidden loss at entering which the workers overlooked. Section 13.5 models a situation where workers underestimate the delayed retirement credit and retire earlier than it would have been optimal.

Child Support, Pension and Fertility

This chapter extends the model of Chapter 10 by adding pension to child support and fertility. To preserve the simplicity of the model, we return to a single homogenous worker generation and to the assumption that the child benefit is only spent on raising children. Insisting on the nonnegativity of savings, again we have to separate the analysis into two cases: either slack (S) or tight (T) credit constraint. Correspondingly, there are two social local optima, and for the sake of simplicity, we concentrate on the T-optimum. (We conjecture that the S-optimum is a rather uninteresting case of no tax and no pension.) In our model, the socially optimal values of the contribution and the tax rates are the same.

Progressive Transfer Systems

This chapter explores progressive transfer systems. Section 6.2 compares progressive personal income tax versus progressive benefits without optimization: (i) proportional tax and benefit create excessive polarization, (ii) progressive taxation and proportional benefits dampen polarization; (iii) proportional taxation and progressive benefits replicate (ii). Introducing flexible labor supply and individual, Sect. 6.3 determines the characteristics of the socially optimal progressive pension systems: basic versus means-tested pension and pension credit, where basic pensions are the same for all, means-tested pensions are only paid for citizen for too low pensions and pension credit combines the two pure systems.