Stability under Learning of Equilibria in Financial Markets with Supply Information

In a recent paper Ganguli and Yang [2009] demonstrate, that there can exist multiple equilibria in a financial market model á la Grossman and Stiglitz [1980] if traders possess private information regarding the supply of the risky asset. The additional equilibria differ in some important respects from the usual equilibrium of the Grossman–Stiglitz type which still exists in this model. This note shows that these additional equilibria are always unstable under learning. This is true for both eductive learning following Guesnerie [2002] and adaptive learning via least–squares estimation (cf. Marcet and Sargent [1988] or Evans and Honkapohja [2001]). Regarding the original Grossman–Stiglitz type equilibrium, the stability results are less clear cut, since this equilibrium might be unstable under eductive learning while it is always stable under adaptive learning.Recursive Least Squares Learning, Eductive Stability, Rational Expectations, Private Information

E–stability and stability of adaptive learning in models with asymmetric information

The paper demonstrates how the E–stability principle introduced by Evans and Honkapohja [2001] can be applied to models with heterogeneous and private information in order to assess the stability of rational expectations equilibria under learning. The paper extends already known stability results for the Grossman and Stiglitz [1980] model to a more general case with many differentially informed agents and to the case where information is endogenously acquired by optimizing agents. In both cases it turns out that the rational expectations equilibrium of the model is inherently E-stable and thus locally stable under recursive least squares learning.Adaptive Learning, Eductive Stability, Rational Expectations

Endogenous Redistributive Cycles An Overlapping Generations Approach to Social Conflict and Cyclical Growth

This paper discusses the emergence of endogenous redistributive cycles in a stochastic growth model with incomplete asset markets and heterogeneous agents, where agents vote on the degree of progressivity in the tax-transfer-scheme. The model draws from Bénabou (1996) and ties the bias in the distribution of political power to the degree of inequality in the society, thereby triggering redistributive cycles which then give rise to a nonlinear, cyclical pattern of savings rates, growth and inequality over time.Inequality, growth, political cycles, redistribution, Hopf bifurcation

Credit Constraints, Idiosyncratic Risks, and the Wealth Distribution in a Heterogeneous Agent Model

This paper examines the effects of credit market imperfections and idiosyncratic risks on occupational choice, capital accumulation, as well as on the income and wealth distribution in a two sectore heterogeneous agent general equilibrium model. Workers and firm owners are subject to idiosyncratic shocks. Entrepreneurship is the riskier occupation. Compared to an economy with perfect capital markets, we find for the case of serially correlated shocks that more individuals choose the entrepreneurial profession in the presence of credit consraints, and that the fluctuation between occupationa increase too. Workers and entrepreneurs with high individual productivity tend to remain in their present occupantion, whereas low productivity individuals are more likely to switch between professions. Interestingly, these results reverse if we assume iid shocks, thus indicating that the nature of the underlying shocks plays an important role for the general equilibrium effects. In general, the likelihood of entrepreneurship increases with individual wealth.DSGE model, wealth distribution, occupational choice, credit constraints

On the Effects of Redistribution on Growth and Entrepreneurial Risk-Taking

This paper investigates the redistributive effects of taxation on occupational choice and growth. We discuss a twoñsector economy in the spirit of Romer (1990). Agents engage in one of two alternative occupations: either selfñemployment in an intermediate goods sector characterized by monopolistic competition, or employment as an ordinary worker in this sector. Entrepreneurial prots are stochastic. The occupational choice under risk endogenizes the number of rms in the intermediate goods industry. While the presence of entrepreneurial risk results in a suboptimally low number of rms and depresses growth, nonñlinear tax schemes are partly capable of compensating the negative by effects by ex post providing a social insurance.OLG, endogenous growth, entrepreneurship, occupational choice, redistributive taxation

On Entrepreneurial Risk–Taking and the Macroeconomic Effects of Financial Constraints

This paper deals with credit market imperfections and idiosyncratic risks in a two–sector heterogeneous agent dynamic general equilibrium model of occupational choice. We focus especially on the effects of tightening financial constraints on macroeconomic performance, entrepreneurial risk–taking, and social mobility. Contrary to many models in the literature, our comparative static results cover a broad range for borrowing constraints, from an unrestrained to a perfectly constrained economy. In our baseline model, we find substantial gains in output, welfare, and wealth equality associated with credit market improvements. The marginal gains from relaxing constraints are largest for empirically relevant debt–equity ratios. Interestingly, the entrepreneurship rate and social mobility respond non–monotonically to a change in the tightness of financial constraints. The results crucially depend on the degree of income persistence and feedback effects in general equilibrium, where optimal firm sizes and the demand for credit are determined endogenously.CGE, occupational choice, financial constraints, wealth distribution

Strongly rational expectations equilibria with endogenous acquisition of information

This paper analyzes conditions for existence of a strongly rational expectations equilibrium (SREE) in models with private information, where the amount of private information is endogenously determined. It is shown that the conditions for existence of a SREE known from models with exogenously given private information do not change as long as it is impossible to use the information transmitted through market prices. In contrast, these conditions are too weak, when there is such learning from prices. It turns out that the properties of the function which describes the costs that are associated with the individual acquisition of information are important in this respect. In case of constant marginal costs, prices must be half as informative than private signals in order for a SREE to exist. An interpretation of this result that falls back on the famous Grossman– Stiglitz–Paradox is also given.Eductive Learning, Private Information, Rational Expectations, Strongly Rational Expectations Equilibrium

Borrowing Constraints, Entrepreneurial Risks, and the Wealth Distribution in a Heterogeneous Agent Model

This paper deals with credit market imperfections and idiosyncratic risks in a two–sector heterogeneous agent dynamic general equilibrium model of occupational choice. We focus especially on the effects of tightening financial constraints on macroeconomic performance, entrepreneurial risk–taking, and social mobility. Contrary to many models in the literature, our comparative static results cover the entire range of borrowing constraints, from complete markets to a perfectly constrained economy. In our baseline model, we find substantial gains in output, welfare, and wealth equality associated with relaxing the constraints, but argue that it might also prove worthwhile to examine the marginal gains from credit market improvements. Interestingly, the amount of entrepreneurial activity and social mobility increases if borrowing constraints become more tight. These results can be attributed to the general equilibrium nature of our approach, where optimal firm sizes and the demand for credit are determined endogenously. The comparative static results on the entrepreneurship rate and social mobility respond sensitively to a change in income persistence.DSGE model, wealth distribution, occupational choice, borrowing constraints

Borrowing Constraints, Entrepreneurial Risks, and the Wealth Distribution in a Heterogeneous Agent Model

This paper deals with credit market imperfections and idiosyncratic risks in a two-sector heterogeneous agent dynamic general equilibrium model of occupational choice. We focus especially on the effects of tightening financial constraints on macroeconomic performance, entrepreneurial risk-taking, and social mobility. Contrary to many models in the literature, our comparative static results cover the entire range of borrowing constraints, from complete markets to a perfectly constrained economy. In our baseline model, we find substantial gains in output, welfare, and wealth equality associated with relaxing the constraints, but argue that it might also prove worthwhile to examine the marginal gains from credit market improvements. Interestingly, the amount of entrepreneurial activity and social mobility increases if borrowing constraints become more tight. These results can be attributed to the general equilibrium nature of our approach, where optimal firm sizes and the demand for credit are determined endogenously. The comparative static results on the entrepreneurship rate and social mobility respond sensitively to a change in income persistence

Convergence of adaptive learning and expectational stability: The case of multiple rational-expectations equilibria

This paper analyzes the relationship between the expectational stability of rational expectations solutions and the possible convergence of adaptive learning processes. Both concepts are used as selection criteria in the case of multiple rational expectations solutions. Results obtained using recursive least squares lead to the conjecture that there exists a general one-to-one correspondence between these two selection criteria. On the basis of a simple linear model and a stochastic gradient algorithm as an alternative learning procedure, it is demonstrated that such a conjecture would be incorrect: There are cases in which stochastic gradient learning converges to rational expectations solutions that are not expectationally stable