This paper provides formulae for computing perturbation method approximations of unconditional variances of variables in nonlinear DSGE models. Spurious higher order terms that creep into multi-step ahead forecasts can produce explosive time paths frustrating traditional approaches to estimating...

This paper details some of the results of a student/teacher collaboration to develop computer algebra materials for use by students in an intermediate macroeconomics course. Many years ago the teacher required students solve macro models using a pencil and paper. For the most part these models...

We provide an overview of automatic differentiation (AD), a technique for the efficient computation of derivatives of functions defined in some programming language. We give a short explanation of how AD works, indicate the anticipated cost of derivatives computed using AD, and survey what AD...

When crossing the boundary of stability of a given dynamical system only indicates a bifurcation point and the type of the bifurcating solutions. But it doesn't tell us how and how many new solutions bifurcate or disappear in a bifurcation point. To answer this question one has to take into...

Generally, in the financial literature, the notion of quadratic VaR is implicitly confused with the Delta-Gamma VaR, because more authors dealt with portfolios that contained derivatives instruments. In this paper, we postpone to estimate both the expected shortfall and Value-at-Risk of a...

While under recursive least squares learning the dynamics of the economy converges to rational expectations equilibria (REE) which are E–stable, some recent examples propose that E–stability is not a sufficient condition for learnability. In this paper, we provide some further...

Emprical studies of hyperinflations reveal that the rational expectations hypothesis fails to hold. To address this issue, we study a model of hyperinflation and learning in an attempt to better understand the volatility in movements of expectations, money, and prices. The findings surprisingly...

We provide sufficient conditions and necessary conditions for stability of an economy under structural mixed recursive least squares/stochastic gradient heterogeneous learning of agents with possibly different degrees of inertia. We have found a unifying condition which is sufficient for...

The assumption of perfectly rational representative agents is now commonly questioned. This paper explores the equilibrium properties of boundedly rational heterogeneous agents. We combine an adaptive learning process in a modified cobweb model within a Stackleberg framework. We assume that...