A generic formula for the values at the boundary points of monic classical orthogonal polynomials

In a previous paper we have determined a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type σ(x)y"n(x)+τ(x)y'n(x)-λnyn(x)=0. In this paper, we give another such formula which enables us to present a generic formula for the values of monic classical orthogonal polynomials at their boundary points of definition.

Individual Decision-Making and Inflation Persistence

The traditional task of a central bank is to preserve price stability and, in doing so, not to impair the real economy more than necessary. To meet this challenge, it is of great relevance whether inflation is only driven by inflation expectations and the current output gap or whether it is, in addition, influenced by past inflation. In the former case, as described by the New Keynesian Phillips curve, the central bank can immediately and simultaneously achieve price stability and equilibrium output, the so-called ‘divine coincidence’ (Blanchard and Galí 2007). In the latter case, the achievement of price stability is costly in terms of output and will be pursued over several periods. Similarly, it is important to distinguish this latter case, which describes ‘intrinsic’ inflation persistence, from that of ‘extrinsic’ inflation persistence, where the sluggishness of inflation is not a ‘structural’ feature of the economy but merely ‘inherited’ from the sluggishness of the other driving forces, inflation expectations and output. ‘Extrinsic’ inflation persistence is usually considered to be the less challenging case, as policy-makers are supposed to fight against the persistence in the driving forces, especially to reduce the stickiness of inflation expectations by a credible monetary policy, in order to reestablish the ‘divine coincidence’. The scope of this dissertation is to contribute to the vast literature and ongoing discussion on inflation persistence: Chapter 1 describes the policy consequences of inflation persistence and summarizes the empirical and theoretical literature. Chapter 2 compares two models of staggered price setting, one with a fixed two-period duration and the other with a stochastic duration of prices. I show that in an economy with a timeless optimizing central bank the model with the two-period alternating price-setting (for most parameter values) leads to more persistent inflation than the model with stochastic price duration. This result amends earlier work by Kiley (2002) who found that the model with stochastic price duration generates more persistent inflation in response to an exogenous monetary shock. Chapter 3 extends the two-period alternating price-setting model to the case of 3- and 4-period price durations. This results in a more complex Phillips curve with a negative impact of past inflation on current inflation. As simulations show, this multi-period Phillips curve generates a too low degree of autocorrelation and too early turnings points of inflation and is outperformed by a simple Hybrid Phillips curve. Chapter 4 starts from the critique of Driscoll and Holden (2003) on the relative real-wage model of Fuhrer and Moore (1995). While taking the critique seriously that Fuhrer and Moore’s model will collapse to a much simpler one without intrinsic inflation persistence if one takes their arguments literally, I extend the model by a term for inequality aversion. This model extension is not only in line with experimental evidence but results in a Hybrid Phillips curve with inflation persistence that is observably equivalent to that presented by Fuhrer and Moore (1995). In chapter 5, I present a model that especially allows to study the relationship between fairness attitudes and time preference (impatience). In the model, two individuals take decisions in two subsequent periods. In period 1, both individuals are endowed with resources and are able to donate a share of their resources to the other individual. In period 2, the two individuals might join in a common production after having bargained on the split of its output. The size of the production output depends on the relative share of resources at the end of period 1 as the human capital of the individuals, which is built by means of their resources, cannot fully be substituted one against each other. Therefore, it might be rational for a well-endowed individual in period 1 to act in a seemingly ‘fair’ manner and to donate own resources to its poorer counterpart. This decision also depends on the individuals’ impatience which is induced by the small but positive probability that production is not possible in period 2. As a general result, the individuals in the model economy are more likely to behave in a ‘fair’ manner, i.e., to donate resources to the other individual, the lower their own impatience and the higher the productivity of the other individual. As the (seemingly) ‘fair’ behavior is modelled as an endogenous outcome and as it is related to the aspect of time preference, the presented framework might help to further integrate behavioral economics and macroeconomics.

Institutions, Behavior and Evolution

The three articles constituting this thesis are for reasons of content or method related to the following three fields in economics: Behavioral Economics, Evolutionary Game Theory and Formal Institutional Economics. A core element of these fields is the concept of individual preferences. Preferences are of central importance for the conceptional framework to analyze human behavior. They form the foundation for the theory of rational choice which is defined by the determination of the choice set and the selection of the most preferred alternative according to some consistency requirements. The theory of rational choice is based on a very simplified description of the problem of choice (object function and constraints). However, that choices depend on many more factors is for instance propagated by psychological theories and is supported by many empirical and experimental studies. This thesis adds to a better understanding of individual behavior to the extent that the evolution of certain characteristics of preferences and their consequences on human behavior forms the overarching theme of the dissertation. The long-term effect of evolutionary forces on a particular characteristic of importance in the theoretical, empirical and experimental economic literature, the concept of inequality aversion, is subject of the article “The evolution of inequality aversion in a simplified game of life” (Chapter 4). The contribution of the article is the overcoming of a restriction of former approaches to analyze the evolution of preferences in very simple environments. By classifying human interaction into three central economic games, the article provides a first step towards a simplified and sufficiently complete description of the interaction environment. Within such an environment the article characterizes the evolutionary stable preference distribution. One result shows, that the interaction of the aforementioned three classes can stabilize a preference of inequality aversion in the subpopulation which is favored in the problem of redistribution. The two remaining articles are concerned with social norms, which dissemination is determined by medium-run forces of cultural evolution. The article “The impact of market innovations on the evolution of social norms: the sustainability case.“ (Chapter 2) studies the interrelation between product innovations which are relevant from a sustainability perspective and an according social norm in consumption. This relation is based on a conformity bias in consumption and the attempt to avoid cognitive dissonances resulting from non-compliant consumption. Among others, it is shown that a conformity bias on the consumption side can lead to multiple equilibria on the side of norm adoption. The article “Evolution of cooperation in social dilemmas: signaling internalized norms.” (Chapter 3) studies the emergence of cooperation in social dilemmas based on the signaling of social norms. The article provides a potential explanation of cooperative behavior, which does not rely on the assumption of structured populations or on the unmotivated ability of social norms to restrict individual actions or strategy spaces. A comprehensive result of the single articles is the explanation of the phenomenon of partial norm adaption or dissemination of preferences. The plurality of the applied approaches with respect to the proximity to the rational choice approach and regarding the underlying evolutionary mechanics is a particular strength of the thesis. It shows the equality of these approaches in their potential to explain the phenomenon of cooperation in environments that provide material incentives for defective behavior. This also points to the need of a unified framework considering the biological and cultural coevolution of preference patterns.