Three essays on dynamic economics

In the first chapter (with Mukul Majumdar) we examine the problem of economic survival under uncertainty in static and dynamic general equilibrium models. The event of the ruin of an agent is defined as the set of all states of environment in which the wealth of this agent falls below his minimum expenditure function at equilibrium price system. An agent can be ruined in a particular state because of a meager endowment (“direct effect”) and/or unfavorable equilibrium price system (“indirect”, or “terms of trade effect”) in this state. We compute asymptotic probability of survival in a static economy with intrinsic uncertainty in the endowments. To focus on the indirect effect we construct an example of a dynamic economy with extrinsic uncertainty (“sunspots”) in which an agent can be ruined by self-fulfilling beliefs. To explore the role of insurance in the problem of survival with uncertainty in endowments we consider an economy with complete markets for Arrow-type securities. We show that trade in securities can worsen survival prospects of the agents.; In the second chapter (with Salvador Ortigueira) we develop an endogenous business cycle model with search in the labor market. Unlike in the previous literature, in our model patterns of the business cycles are generated by purely extrinsic uncertainty, without serially correlated shocks to fundamentals. Because of the thin market externalities the equilibrium path is indeterminate, and there is a room for sunspot equilibria (self-fulfilling beliefs). The properties of the simulated macroeconomic time series are compared to the U.S. data and some business cycle models.; In the third chapter (with Timothy Vogelsang) we propose a new asymptotic approximation for sampling distribution of non-parametric spectral density estimators. The autocovariance truncation lag is modeled as a fixed proportion of the sample size, whereas in the traditional approach (normal and Tukey's chi-squared approximation) it is assumed to grow slower than the sample size. Under this new assumption the distribution of spectral density estimators can be approximated by a function of independent Wiener processes. Finite sample simulations indicate the situations in which the new asymptotics can provide better approximations than the standard asymptotics.