|dc.description.abstract||Abstract My dissertation consists of three papers on bifurcation and market game models. My research focuses on understanding bifurcation phenomena of macroeconometric models, exploring price stickiness and markup variations in market game models with production through strategic interaction, and analyzing the possibility of endogenous business cycles in the overlapping generation market game models with production. Specifically, the three chapters are: Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences is a survey paper I coauthored with Prof. Barnett (Barnett and Chen (2015)). In systems theory, it is well known that the parameter spaces of dynamical systems are stratified into bifurcation regions, with each supporting a different dynamical solution regime. Some can be stable, with different characteristics, such as monotonic stability, periodic damped stability, or multiperiodic damped stability, and some can be unstable, with different characteristics, such as periodic, multiperiodic, or chaotic unstable dynamics. But in general the existence of bifurcation boundaries is normal and should be expected from most dynamical systems, whether linear or nonlinear. Bifurcation boundaries in parameter space are not evidence of model defect. While existence of such bifurcation boundaries is well known in economic theory, econometricians using macroeconometric models rarely take bifurcation into consideration, when producing policy simulations from macroeconometric models. Such models are routinely simulated only at the point estimates of the models’ parameters. Barnett and He (1999) explored bifurcation stratification of Bergstrom and Wymer’s (1976) continuous time UK macroeconometric model. Bifurcation boundaries intersected the confidence region of the model’s parameter estimates. Since then, Barnett and his coauthors have been conducting similar studies of many other newer macroeconometric models spanning all basic categories of those models. So far, they have not found a single case in which the model’s parameter space was not subject to bifurcation stratification. In most cases, the confidence region of the parameter estimates were intersected by some of those bifurcation boundaries. The most fundamental implication of this research is that policy simulations with macroeconometric models should be conducted at multiple settings of the parameters within the confidence region. While this result would be as expected by systems theorists, the result contradicts the normal procedure in macroeconometrics of conducting policy simulations solely at the point estimates of the parameters. This survey provides an overview of the classes of macroeconometric models for which these experiments have so far been run and emphasizes the implications for lack of robustness of conventional dynamical inferences from macroeconometric policy simulations. By making this detailed survey of past bifurcation experiments available, we hope to encourage and facilitate further research on this problem with other models and to emphasize the need for simulations at various points within the confidence regions of macroeconometric models, rather than at only point estimates. Price Stickiness and Markup Variations in Market Games is a paper I coauthored with Prof. Stephen Spear and Dr. C. Gizem Korpeoglu (Chen et al. (2017)). Shapley-Shubik market game model received quite a bit of attention in the general equilibrium literature of the 1980’s and 1990’s, but never caught on as a possible alternative to models of monopolistic competition in macroeconomics. In this paper, we suggest that the market game model can provide a better micro-foundation for new Keynesian general equilibrium analysis than existing models based on monopolistic competition. We show that the market game generates equilibria that have two important features. First, we show that when firms have market power, their market-shares in both input and output markets affect the first-order conditions of their best responses, in ways that resemble the effects of price changes. From this observation, we are able to establish that firm quantity adjustments (holding input prices fixed) can maintain the Nash equilibrium of the model in versions of the model that exhibit indeterminacy of the Nash equilibrium. Hence, these versions of the model naturally admit sticky prices, regardless of the mechanism(s) that might lead firms to want to keep input prices unchanging. Second, we show that there is a close relationship between any individual firm’s markup of price over marginal cost and its market share. What the market game brings to the discussion of markups that is new, is the fact that markets populated by finite numbers of firms operating under possibly different technologies will generate data on markup movements over different equilibria that can vary positively, negatively, variably, or not at all over business-cycle-like expansions and contractions. Endogenous Business Cycles in the Overlapping Generations Market Game Model is my job market paper (Chen (2018)).
We then extend the analysis on market game models with production in chapter two to an overlapping generations (OLG) market game model, and study whether strategic interactions contribute to instabilities of the economic dynamics. Grandmont (1985) was one of the first papers to raise the possibility that endogenous complex dynamics might provide an alternative explanation for business cycle fluctuations, by showing that such dynamics could arise in conventional OLG models, although only for the case of sufficiently large risk aversion on the part of old agents in the model. Goenka et al. (1998) showed in the context of a pure exchange OLG market game model that the nonlinearities introduced by imperfect competition were such that one could obtain chaotic dynamics even for log utility, as long as markets were thin in terms of amount of endowment agents offered. Goenka et al.(1998) note that extensions of their work with this kind of model suggests that production smooths the model in the sense that complex dynamics are not as easily generated as in the pure exchange model. In this paper, analysis shows that production combined with price-taking behavior by households locks down the ratio of output and input prices, which then reduces the nonlinearity that arises in the pure exchange model. Specifically, we show in the paper that when incorporating production in the market game OLG model, the price dynamics depend on market thickness, general equilibrium price ratios, individual offers and particular choices of utility function. We find that for complex dynamics to occur, the preferences in our model must be a mix of preferences, for example, a combination of preferences with constant relative risk aversions and increasing relative risk aversions. We also show the impossibility of such price dynamics to occur for log-linear preferences. In other words, the case for complex dynamics to occur with particular production functions and utility functions is much more limited. As a result, complex dynamics are not as easily observable as in models without production. Finally, we are able to confirm the results from Goenka, et al. (1998) on the Pareto rankability of Nash equilibria in terms of market thickness, which has important welfare implications for business cycle-like activity based on the coordination equilibria that can arise in market game models.||