Solving and Estimating Indeterminate DSGE Models

Abstract

1 We thank seminar participants at UCLA and at the Dynare workshop in Paris in July of 2010, where Farmer presented a preliminary draft of the solution technique discussed in this paper. That technique was further developed in Chapter 1 of Khramov's Ph.D. thesis (Khramov, 2013). We would like to thank Thomas Lubik and three referees of this journal who provided comments that have considerably improved the final version. AbstractWe propose a method for solving and estimating linear rational expectations models that exhibit indeterminacy and we provide step-by-step guidelines for implementing this method in the Matlab-based packages Dynare and Gensys. Our method redefines a subset of expectational errors as new fundamentals. This redefinition allows us to treat indeterminate models as determinate and to apply standard solution algorithms. We prove that our method is equivalent to the solution method proposed by Schorfheide (2003, 2004), and using the New-Keynesian model described in Lubik and Schorfheide (2004), we demonstrate how to apply our theoretical results with a practical exercise.

Monetary and Fiscal Policy When People Have Finite Lives

“…An updated solution method for rational expectations models that allows either J1 or J2 or both to be singular can be found in Sims (2001). Solution methods for models with indeterminacy are provided in Farmer et al (2015).…”

Monetary Policy Rules and Macroeconomic Stability

“…Consequently, the model specified by equations (7)-(10) is modified to accommodate for 'sunspot' shocks. Farmer and Khramov (2013) specify two alternative ways to redefine non-fundamental shocks as new fundamentals in a simple three equation New Keynesian model. One approach is to define the forecast error on output gap η 1,t = y t − E t−1 [y t ] as a fundamental shock, whereas the other approach is to define the forecast error on inflation η 2,t = π t − E t−1 [π t ] as a fundamental shock.…”

The Inverted Leading Indicator Property and Redistribution Effect of the Interest Rate

“…By this we mean that the borrower's budget and credit constraints are now: (19) while the lender's budget constraint is: (20) so that the interest repayment due in period t is now predetermined while the interest rate that enters the credit constraint is variable but now known in period t. It is then easy, using again the lender's first-order condition (10), to show that the interest rate is constant over time, that is, R t =β −1 , so that X t = 1 at all dates and the economy is forever in steady state absent fundamental shocks.…”