Sunday, Jan. 7, 2018 10:15 AM - 12:15 PM
A Generalized Approach to Indeterminacy in Linear Rational Expectations Models
AbstractWe propose a novel approach to deal with the problem of indeterminacy in Linear Rational Expectations models. The method consists of augmenting the original model with a set of auxiliary exogenous equations that are used to provide the adequate number of explosive roots in presence of indeterminacy. The solution in this expanded state space, if it exists, is always determinate, and is identical to the indeterminate solution of the original model. The proposed approach accommodates determinacy and any degree of indeterminacy, and it can be implemented even when the boundaries of the determinacy region are unknown. As a result, the researcher can estimate the model by using standard packages without restricting the estimates to a certain area of the parameter space. We apply our method to simulated data from the New-Keynesian model for both regions of the parameter space. We show that our method successfully recovers the true parameter values independent of the initial values.
A Tractable Framework for Analyzing a Class of Nonstationary Markov Models
AbstractDynamic stochastic economic models generally built on the assumption of stationary environment. However, the real-world economies constantly evolve over time, experiencing population growth, technological progress, trends in tastes and habits, policy regime changes, evolution of social and political institutions, etc. In certain cases, time-dependent environments can be modeled in a way that is consistent with the assumption of stationary economic environment, for example, labor augmenting technological progress and Markov switching models. However, many interesting applications with time-dependencies do not admit stationary representations. Unbalanced stochastic growth models fit into that class, but so do many other models and applications such as the entry into a monetary union, a nonrecurrent policy regime switch or deterministic seasonals. Such models have time-dependent value and decision functions and cannot be generally solved with conventional numerical methods that construct stationary Markov equilibria.
We introduce a simple and tractable extended function path (EFP) framework that can be used for for calibrating, solving, simulating and estimating such nonstationary models. Our method is related to Fair and Taylor (1983) analysis but we replace certainty equivalence approach with accurate projection and integration methods. We establish the existence and convergence (turnpike) theorems. We apply EFP to solve a collection of challenging nonstationary applications, including stochastic growth models with parameters shifts and drifts, capital augmenting technological progress, anticipated regime switches, time-trends in volatility of shocks and seasonal fluctuations. Also, we show an example of estimation and calibration of parameters in an unbalanced growth model using the U.S. data.
The EFP framework also provides a novel tool for policy analysis: it allows us to model time-dependent policies, complementing thus the mainstream of the literature that focuses on state-dependent policies. We apply the EFP framework for analyzing the effects of forward guidance and monetary policy normalization. Examples of the MATLAB code are provided.
Some Unpleasant Central Bank Balance Sheet Arithmetic
AbstractI model maturity and currency mismatches in the central bank balance sheet. The central bank holds long-term domestic or short-term foreign currency assets and issues short-term domestic currency liabilities. As in Sargent and Wallace (1981), I constrain such a central bank's remittances to the Treasury. Balance sheet arithmetic shows that a central bank then loses freedom in its policy actions. The expected future change of the short-term nominal interest rate or the nominal exchange rate get determined by balance sheet considerations: if they increase today, they have to decrease in future. I embed the balance sheet constrained central bank in an otherwise standard dynamic general equilibrium model and study monetary policy transmission mechanisms. Following a positive short-term nominal interest rate shock, central bank balance sheet considerations lead, dynamically, to a drop in the short-term interest rate and a positive correlation between it and inflation, even with sticky prices. The negative effects of the shock on interest rate, inflation, and output are large and persistent. Central bank balance sheet considerations make forward guidance less effective. Following news of a negative short-term nominal interest rate shock, while inflation and output increase initially, they do so by a diminished amount, and are in fact followed by deflation and contraction in economic activity in future.
- A1 - General Economics