Alexander Meyer-Gohde

Sticky Information and Determinacy

The infinite-dimensional sticky-information Phillips curve is cast as a finite-dimensional timevarying system of difference equations in order to directly assess determinacy in the model with demand given by the forward-looking IS equation and monetary policy by an interest rate rule. An equivalence to the model without lagged expectations holds (albeit tenuously) for the particular specification and a common truncation method produces spurious determinacy.

Existence and Uniqueness of Perturbation Solutions to DSGE Models

We prove the existence of unique solutions for all undetermined coefficients of nonlinear perturbations of arbitrary order in a wide class of discrete time DSGE models under standard regularity and saddle stability assumptions for linear approximations. Our result follows from the straightforward application of matrix analysis to our perturbation derived with Kronecker tensor calculus. Additionally, we relax the assumptions needed for the local existence theorem of perturbation solutions and prove that the local solution is independent of terms first order in the perturbation parameter.

Monetary Policy, Determinacy, and the Natural Rate Hypothesis

Imposing the natural rate hypothesis (NRH) can dramatically alter the determinacy bounds on mone- tary policy by closing the output gap in the long run. I show that the hypothesis eliminates any role for the output gap in determinacy and renders the conditions for determinacy identical for all conforming supply equations. Specializing further to IS demand, determinacy depends only on the parameters in the interest rate rule and a pure forward or backward-looking inflation target is inconsistent with deter- minacy. Monetary policy that embodies the Taylor principle with respect to contemporaneous inflation delivers a determinate equilibrium in all models that satis fy the NRH. JEL classification: C62; E31; E43; E52

Solving linear rational expectations models with lagged expectations quickly and easily

A solution method is derived in this paper for solving a system of linear rationalexpectations equation with lagged expectations (e.g., models incorporating sticky information) using the method of undetermined coefficients for the infinite MA representation. The method applies a combination of a Generalized Schur Decomposition familiar elsewhere in the literature and a simple system of linear equations when lagged expectations are present to the infinite MA representation. Execution is faster, applicability more general, and use more straightforward than with existing algorithms. Current methods of truncating lagged expectations are shown to not generally be innocuous and the use of such methods are rendered obsolete by the tremendous gains in computational efficiency of the method here which allows for a solution to floating-point accuracy in a fraction of the time required by standard methods. The associated computational application of the method provides impulse responses to anticipated and unanticipated innovations, simulations, and frequency-domain and simulated moments.

Decomposing Risk in Dynamic Stochastic General Equilibrium

We analyze the theoretical moments of a nonlinear approximation to a model of business cycles and asset pricing with stochastic volatility and recursive preferences. We find that heteroskedastic volatility operationalizes a time-varying risk adjustment channel that induces variability in conditional asset pricing measures and assigns a substantial portion of the variance of macroeconomic variables to variations in precautionary behavior, both while leaving its ability to match key macroeconomic and asset pricing facts untouched. Our method decomposes moments into contributions from realized shocks and differing orders of approximation and from shifts in the distribution of future shocks, enabling us to identify the common channel through which stochastic volatility in isolation operates and through which conditional asset pricing measures vary.

Strategic Complementarities and Nominal Rigidities

We reconsider the canonical model of price setting with menu costs by Ball and Romer (1990). Their original model exhibits multiple equilibria for nominal aggregate demand shocks of intermediate size. By abandoning Ball and Romer’s (1990) assumption that demand shocks are common knowledge among price setters, we derive a unique symmetric threshold equilibrium where agents adjust prices whenever the demand shock falls outside the thresholds. The comparative statics of this threshold may differ from the one that gives rise to maximal nominal rigidity examined by Ball and Romer (1990). In contrast to their analysis, we find that a decrease in real rigidities can be associated with an increase in nominal rigidities due to the endogenous adjustment of agents’ beliefs regarding the aggregate price level.

Un)expected Monetary Policy Shocks and Term Premia

The term structure of interest rates is crucial for the transmission of monetary policy to financial markets and the macroeconomy. Disentangling the impact of monetary policy on the components of interest rates, expected short rates and term premia, is essential to understanding this channel. To accomplish this, we provide a quantitative structural model with endogenous, time-varying term premia that are consistent with empirical findings. News about future policy, in contrast to unexpected policy shocks, has quantitatively significant effects on term premia along the entire term structure. This provides a plausible explanation for partly contradictory estimates in the empirical literature.