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This paper studies how the rates of deduction for early retirement have to be determined in pay-as-you-go (PAYG) systems in order to keep their budget stable. The derivation of these deductions requires the use of a multiperiod intertemporal budget constraint that involves assumptions about the retirement behavior of past, present, and future cohorts. In general, it is not possible to calculate budget-neutral deductions from the budget constraint of a single individual who retires before the target retirement age—an approach that dominates the related literature. Only for specific cases one can use this second approach but then one has to adjust the discount rate to the assumption about collective retirement. If there is only one deviating individual, then the right choice is the market interest rate while for a stationary retirement distribution it is the internal rate of return of the PAYG system. In this case, the necessary deductions are lower than under the standard approach. This is also true for retirement ages that fluctuate randomly around a stationary distribution. Various long-run developments (e.g., increases in life expectancy or permanent changes in the average retirement age) might cause challenges for the sustainability of the pension system. These developments, however, can only be dealt with by adequate adjustments to the basic pension formulas and not by the use of deduction rates.

In this paper, I study how pay-as-you-go pension systems of the notional defined contribution type can be designed such that they remain financially stable in the presence of increasing life expectancy. For this to happen three crucial parameters must be set in an appropriate way: the notional interest rate, the adjustment rate and the annuity conversion factor. I show that there exist two main approaches to implement a stable system. The first uses period-specific annuitization and indexation rates that correct for labor force increases, which are only due to rises in the retirement age which are necessary to ‘neutralize’ the increase in life expectancy. The second approach uses cohort-specific annuitization and indexation rates that are larger than in a stationary situation. This is due to the fact that a continuously increasing life expectancy leads to higher internal rates of return that can be passed on via the indexation.

Subjective views of the extent of inequality and preferences for redistribution depend on how people perceive the true income (wealth) distribution. We present a novel formal framework in which individuals look at reference groups when guessing the extent of inequality and derive its implications for four dimensions of inequality perceptions. First, we show that the presence of reference groups that put more weight on the own income class leads low (high) income individuals to overestimate (underestimate) their own position. Second, the framework implies that subjective estimates of the average income increases with the own income position. Third, it predicts that people in different income deciles will assess the "distributional shape" of society (e.g. pyramid or diamond) differently. Fourth, the subjective extent of inequality is lower for high-income individuals. While the previous literature has treated these aspects of inequality separately, our model demonstrates that they are connected and follow from a unified framework of reference group formation. This allows us to study these and to reconcile conflicting findings from the literature. We confront these predictions with survey data from 40 countries and find strong support for the model.

In this paper I study the impact of increasing longevity on pay-as-you-go pension systems. First, I show that increasing longevity increases the internal rate of return. The size of the effect differs for different policy regimes. It is higher for the case where the retirement age is increased to keep the system in balance than for the case where the necessary adjustment is achieved by reducing pension benefits. Second, I study optimally chosen retirement decisions and I show that the socially optimal policy involves a shorter working life than the private optimum. The social optimum can be implemented by the use of a PAYG system that combines an actuarial and a flat pension.

This article studies the role of staggered efficiency wages in a small-scale DSGE model. The simple structure of the model allows for closed-form solutions. The set-up differs from the related literature in that I assume wages are sticky and unions are responsible for wage-setting. The model has the potential to explain why wages depend strongly on past wage levels as it is suggested by empirical data. The presence of efficiency wages increases persistence, however, only for certain parameter constellations. In particular, the elasticity of effort with respect to the wage has to be large. In an extension of the model I show that this is more likely to be the case if wages are the outcome of a bargaining process between unions and firms.

In this paper I study the relation between real wage rigidity (RWR) and nominal price and wage rigidity. I show that in a standard DSGE model RWR is mainly affected by the interaction of the two nominal rigidities and not by other structural parameters. The degree of RWR is, however, considerably influenced by the modelling assumption about the structure of wage contracts (Calvo vs. Taylor) and about other institutional characteristics of wage-setting (clustering of contracts, heterogeneous contract length, indexation). I use survey evidence on price- and wage-setting for 15 European countries to calculate the degrees of RWR implied by the theoretical model. The average levels of RWR are broadly in line with empirical estimates based on macroeconomic data. In order to be able to also match the observed cross-country variation in RWR it is, however, essential to move beyond the country-specific durations of price and wages and to take more institutional details into account. JEL Classification: E31, E32, E24, J51

This article presents an extension of the Taylor model with staggered wages in which wage setting is also influenced by reference norms. We show that reference norms can considerably increase the persistence of inflation but that the size of this effect depends on the exact definition (e.g., external vs. internal, symmetric vs. asymmetric norms). Using data on collectively bargained wages in Austria from 1980 to 2006 we show that wage setting is strongly influenced by reference norms, that external norms seem to matter more than internal norms, and that there is a clear indication for the existence of wage leadership (asymmetric norms).

The paper studies the optimal portfolio mix between funded and unfunded pension systems when people care about relative consumption. In pay-as-you-go systems with fixed contribution rates, pensions are tied to wages. This lowers the uncertainty of individuals' future relative position thereby increasing the attractiveness of unfunded systems. The paper shows analytically that the optimal share of funding decreases with the importance of relative standing. A calibrated version of the model suggests that the concern for relative standing has also a quantitatively important impact on the optimal share of funding. For reasonable assumptions it is typically around 20%.

By analysing almost 1000 money demand estimations this paper attempts to summarize the diverse findings of the literature on this topic. Using both descriptive statistics and meta-regressions, several stylized facts are derived about the two most prominent determinants of money demand income and interest rate elasticities. In particular, it is shown we show that the size and signs of average elasticities are systematically related to the choice of included variables (e.g. M1 or M3, short-run or long-run interest rates), the country grouping (e.g. USA versus Germany) and the empirical specification (e.g. the inclusion of one or two interest rates).

In this paper, we use meta-analytic methods to investigate possible sources for the large variation in empirical findings about the income elasticity of money demand. Our results suggest that the broadness of the monetary aggregate, the inclusion of wealth and the consideration of financial innovation exert a significant influence on estimated income elasticities. Furthermore, we find substantial cross-country differences, in particular between the US and other countries. These differences can, to some extent, be explained by the macrofeconomic environment and the dissemination of payment cards.

A growing economic literature stresses the importance of relative comparisons, e.g., for savings and consumption or happiness. In this literature it is usually assumed that reference standards against which people compare themselves are exogenously given. In contrast, findings from social psychology suggest that people play an active role in determining their reference standards. We introduce a social comparison model where people choose their reference standards to serve motives of self-improvement and self-enhancement. The model predicts that reference standards increase in individuals’ abilities and that people thus tend to compare themselves to similar others. The results of a questionnaire study confirm the prediction of the model.

Over the recent years one could repeatedly hear the claim that a rising concern for relative standing (in terms of consumption) was partly responsible for the decline in household savings and in growth that could be observed in some developed countries (particularly in the US) and that the rise in income inequality had further aggravated this process.In this paper we want to analyze under which conditions (concerning the importance of social comparisons for peoples' behavior and their choice of reference groups) this claim is valid. We show that an increase in a societies' concern for relative standing aggravates a negative impact of inequality on growth if two conditions are fulfilled: individuals have a higher concern for their present than for their future relative standing and individuals have a tendency to find their reference groups among people that are wealthier then they are themselves. Empirical data suggest that the negative impact of inequality on growth is stronger in highly developed economies. This is compatible with the explanation that is presented in this paper if individuals living in highly developed countries are more likely to have a high concern for relative standing. We will argue (using research on the cultural consequences of economic development) that this is a reasonable assumption to make.

As a side event to the conference “Game Theory, Experience, Rationality”, the Institute for System Simulation of Socio-economic Processes (SYSIS) organized a computer tournament. It was based on the well-known game-theoretical model “Tragedy of the Commons”. This model — in many respects similar to the even more famous “Prisoners’ Dilemma” — illustrates the instability of “good” equilibria in games, where each player can gain by deviating from the cooperative strategy.