Essays on Bayesian Inference for Social Networks

This thesis presents Bayesian solutions to inference problems for three types of social network data structures: a single observation of a social network, repeated observations on the same social network, and repeated observations on a social network developing through time. A social network is conceived as being a structure consisting of actors and their social interaction with each other. A common conceptualisation of social networks is to let the actors be represented by nodes in a graph with edges between pairs of nodes that are relationally tied to each other according to some definition. Statistical analysis of social networks is to a large extent concerned with modelling of these relational ties, which lends itself to empirical evaluation. The first paper deals with a family of statistical models for social networks called exponential random graphs that takes various structural features of the network into account. In general, the likelihood functions of exponential random graphs are only known up to a constant of proportionality. A procedure for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods is presented. The algorithm consists of two basic steps, one in which an ordinary Metropolis-Hastings up-dating step is used, and another in which an importance sampling scheme is used to calculate the acceptance probability of the Metropolis-Hastings step. In paper number two a method for modelling reports given by actors (or other informants) on their social interaction with others is investigated in a Bayesian framework. The model contains two basic ingredients: the unknown network structure and functions that link this unknown network structure to the reports given by the actors. These functions take the form of probit link functions. An intrinsic problem is that the model is not identified, meaning that there are combinations of values on the unknown structure and the parameters in the probit link functions that are observationally equivalent. Instead of using restrictions for achieving identification, it is proposed that the different observationally equivalent combinations of parameters and unknown structure be investigated a posteriori. Estimation of parameters is carried out using Gibbs sampling with a switching devise that enables transitions between posterior modal regions. The main goal of the procedures is to provide tools for comparisons of different model specifications. Papers 3 and 4, propose Bayesian methods for longitudinal social networks. The premise of the models investigated is that overall change in social networks occurs as a consequence of sequences of incremental changes. Models for the evolution of social networks using continuos-time Markov chains are meant to capture these dynamics. Paper 3 presents an MCMC algorithm for exploring the posteriors of parameters for such Markov chains. More specifically, the unobserved evolution of the network in-between observations is explicitly modelled thereby avoiding the need to deal with explicit formulas for the transition probabilities. This enables likelihood based parameter inference in a wider class of network evolution models than has been available before. Paper 4 builds on the proposed inference procedure of Paper 3 and demonstrates how to perform model selection for a class of network evolution models.

Essays on Personnel Economics and Gender Issues

This thesis consists of four self-contained essays in economics. Tournaments and unfair treatment. This paper introduces the negative feelings associated with the perception of being unfairly treated into a tournament model and examines the impact of these perceptions on workers’ efforts and their willingness to work overtime. The effect of unfair treatment on workers’ behavior is ambiguous in the model in that two countervailing effects arise: a negative impulsive effect and a positive strategic effect. The impulsive effect implies that workers react to the perception of being unfairly treated by reducing their level of effort. The strategic effect implies that workers raise this level in order to improve their career opportunities and thereby avoid feeling even more unfairly treated in the future. An empirical test of the model using survey data from a Swedish municipal utility shows that the overall effect is negative. This suggests that employers should consider the negative impulsive effect of unfair treatment on effort and overtime in designing contracts and determining on promotions. Late careers in Sweden between 1970 and 2000. In this essay Swedish workers’ late careers between 1970 and 2000 are studied. The aim is to examine older workers’ career patterns and whether they have changed during this period. For example, is there a difference in career mobility or labor market exiting between cohorts? What affects the late career, and does this differ between cohorts? The analysis shows that between 1970 and 2000 the late careers of Swedish workers comprised of few job changes and consisted more of “trying to keep the job you had in your mid-fifties” than of climbing up the promotion ladder. There are no cohort differences in this pattern. Also a large fraction of the older workers exited the labor market before the normal retirement age of 65. During the 1970s and first part of the 1980s, 56 percent of the older workers made an early exit and the average drop-out age was 63. During the late 1980s and the 1990s the share of old workers who made an early exit had risen to 76 percent and the average drop-out age had dropped to 61.5. Different factors have affected the probabilities of an early exit between 1970 and 2000. For example, skills did affect the risk of exiting the labor market during the 1970s and up to the mid-1980s, but not in the late 1980s or the 1990s. During the first period old workers in the lowest occupations or with the lowest level of education were more likely to exit the labor market than more highly skilled workers. In the second period old workers at all levels of skill had the same probability of leaving the labor market. The growth and survival of establishments: does gender segregation matter? We empirically examine the employment dynamics that arise in Becker’s (1957) model of labor market discrimination. According to the model, firms that employ a large fraction of women will be relatively more profitable due to lower wage costs, and thus enjoy a greater probability of surviving and growing by underselling other firms in the competitive product market. In order to test these implications, we use a unique Swedish matched employer-employee data set. We find that female-dominated establishments do not enjoy any greater probability of surviving and do not grow faster than other establishments. Additionally, we find that integrated establishments, in terms of gender, age and education levels, are more successful than other establishments. Thus, attempts by legislators to integrate firms along all dimensions of diversity may have positive effects on the growth and survival of firms. Risk and overconfidence – Gender differences in financial decision-making as revealed in the TV game-show Jeopardy. We have used unique data from the Swedish version of the TV-show Jeopardy to uncover gender differences in financial decision-making by looking at the contestants’ final wagering strategies. After ruling out empirical best-responses, which do appear in Jeopardy in the US, a simple model is derived to show that risk preferences, the subjective and objective probabilities of answering correctly (individual and group competence), determine wagering strategies. The empirical model shows that, on average, women adopt more conservative and diversified strategies, while men’s strategies aim for the greatest gains. Further, women’s strategies are more responsive to the competence measures, which suggests that they are less overconfident. Together these traits make women more successful players. These results are in line with earlier findings on gender and financial trading.

Essays on Wage and Price Formation in Sweden

Study IReal Wage Determination in the Swedish Engineering Industry This study uses the monopoly union model to examine the determination of real wages and in particular the effects of active labour market programmes (ALMPs) on real wages in the engineering industry. Quarterly data for the period 1970:1 to 1996:4 are used in a cointegration framework, utilising the Johansen's maximum likelihood procedure. On a basis of the Johansen (trace) test results, vector error correction (VEC) models are created in order to model the determination of real wages in the engineering industry. The estimation results support the presence of a long-run wage-raising effect to rises in the labour productivity, in the tax wedge, in the alternative real consumer wage and in real UI benefits. The estimation results also support the presence of a long-run wage-raising effect due to positive changes in the participation rates regarding ALMPs, relief jobs and labour market training. This could be interpreted as meaning that the possibility of being a participant in an ALMP increases the utility for workers of not being employed in the industry, which in turn could increase real wages in the industry in the long run. Finally, the estimation results show evidence of a long-run wage-reducing effect due to positive changes in the unemployment rate. Study IIIntersectoral Wage Linkages in Sweden The purpose of this study is to investigate whether the wage-setting in certain sectors of the Swedish economy affects the wage-setting in other sectors. The theoretical background is the Scandinavian model of inflation, which states that the wage-setting in the sectors exposed to international competition affects the wage-setting in the sheltered sectors of the economy. The Johansen maximum likelihood cointegration approach is applied to quarterly data on Swedish sector wages for the period 1980:1–2002:2. Different vector error correction (VEC) models are created, based on assumptions as to which sectors are exposed to international competition and which are not. The adaptability of wages between sectors is then tested by imposing restrictions on the estimated VEC models. Finally, Granger causality tests are performed in the different restricted/unrestricted VEC models to test for sector wage leadership. The empirical results indicate considerable adaptability in wages as between manufacturing, construction, the wholesale and retail trade, the central government sector and the municipalities and county councils sector. This is consistent with the assumptions of the Scandinavian model. Further, the empirical results indicate a low level of adaptability in wages as between the financial sector and manufacturing, and between the financial sector and the two public sectors. The Granger causality tests provide strong evidence for the presence of intersectoral wage causality, but no evidence of a wage-leading role in line with the assumptions of the Scandinavian model for any of the sectors. Study IIIWage and Price Determination in the Private Sector in Sweden The purpose of this study is to analyse wage and price determination in the private sector in Sweden during the period 1980–2003. The theoretical background is a variant of the “Imperfect competition model of inflation”, which assumes imperfect competition in the labour and product markets. According to the model wages and prices are determined as a result of a “battle of mark-ups” between trade unions and firms. The Johansen maximum likelihood cointegration approach is applied to quarterly Swedish data on consumer prices, import prices, private-sector nominal wages, private-sector labour productivity and the total unemployment rate for the period 1980:1–2003:3. The chosen cointegration rank of the estimated vector error correction (VEC) model is two. Thus, two cointegration relations are assumed: one for private-sector nominal wage determination and one for consumer price determination. The estimation results indicate that an increase of consumer prices by one per cent lifts private-sector nominal wages by 0.8 per cent. Furthermore, an increase of private-sector nominal wages by one per cent increases consumer prices by one per cent. An increase of one percentage point in the total unemployment rate reduces private-sector nominal wages by about 4.5 per cent. The long-run effects of private-sector labour productivity and import prices on consumer prices are about –1.2 and 0.3 per cent, respectively. The Rehnberg agreement during 1991–92 and the monetary policy shift in 1993 affected the determination of private-sector nominal wages, private-sector labour productivity, import prices and the total unemployment rate. The “offensive” devaluation of the Swedish krona by 16 per cent in 1982:4, and the start of a floating Swedish krona and the substantial depreciation of the krona at this time affected the determination of import prices.