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21
The Solution of Singular Linear Difference Systems Under Rational Expectations
, 1997
"... Many linear macroeconomic models can be cast in the firstorder form, AE t y t+1 = By t +CE t x t ; if the matrix A is permitted to be singular. For this singular linear dierence system under rational expectations, we show there is a unique stable solution under two requirements: (i) the determinent ..."
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Cited by 40 (2 self)
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Many linear macroeconomic models can be cast in the firstorder form, AE t y t+1 = By t +CE t x t ; if the matrix A is permitted to be singular. For this singular linear dierence system under rational expectations, we show there is a unique stable solution under two requirements: (i) the determinental polynomial jAz Bj is not zero for some value of z, and (ii) a rank condition is satisfied which is a direct generalization of Blanchard and Kahn's (1980) requirement for the nonsingular system. The unique solution is characterized using a familiar approach: a canonical variables transformation which separates the dynamics associated with stable and unstable eigenvalues. In singular models, however, there are also canonical variables associated with infinite eigenvalues. These new canonical variables arise from nonexpectational behavioral relations or dynamic identities present in the singular linear dierence system.
Money, Prices, Interest Rates and the Business Cycle
, 1996
"... The mechanisms governing the relationship of money, prices and interest rates to the business cycle are one of the most studied and most disputed topics in macroeconomics. In this paper, we first document key empirical aspects of this relationship. We then ask how well three benchmark rational expec ..."
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Cited by 32 (1 self)
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The mechanisms governing the relationship of money, prices and interest rates to the business cycle are one of the most studied and most disputed topics in macroeconomics. In this paper, we first document key empirical aspects of this relationship. We then ask how well three benchmark rational expectations macroeconomic models  a real business cycle model, a sticky price model and a liquidity effect model  account for these central facts. While the models have diverse successes and failures, none can account for the fact that both real and nominal interest rates are "inverted leading indicators" of real economic activity. That is, none of the models captures the post...
Sticky prices, marginal cost, and the behavior of inflation’, Federal Reserve Bank of Richmond Economic Quarterly 85
, 1999
"... Aprincipal goal of economic modeling is to improve the formulation of economic policy. Macroeconomic models with imperfect competition and sticky prices set in a dynamic optimizing framework have gained wide popularity in recent years for examining issues involving monetary policy. For example, Rote ..."
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Cited by 27 (2 self)
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Aprincipal goal of economic modeling is to improve the formulation of economic policy. Macroeconomic models with imperfect competition and sticky prices set in a dynamic optimizing framework have gained wide popularity in recent years for examining issues involving monetary policy. For example, Rotemberg and Woodford (1999b) and McCallum and Nelson (1999) examine the behavior of model economies under a variety of monetary policy rules; Ireland (1995) examines the optimal way to disinflate; and Benhabib, SchmittGrohe, and Uribe (forthcoming) and Wolman (1998) study the monetary policy implications of the zero bound on nominal interest rates. 1 Nevertheless, serious questions remain as to whether these models accurately describe the U.S. economy, and therefore as to how one should interpret the results of this research. One criticism of optimizing stickyprice models is that the relationship between output and inflation they generate is inconsistent with the behavior of these variables in the United States. 2 However, recent research by Sbordone (1998) and Galí and Gertler (1999) has breathed new life into these models by shifting attention away from the relationship between output and inflation and toward one between marginal cost and inflation—the latter being a more fundamental relationship in the models. If firms have some market power, as under imperfect competition, the behavior of their marginal cost of production is an important determinant of how they set prices. In turn, the overall price The author thanks Mike Dotsey, Andreas Hornstein, Tom Humphrey, Bob King, Wenli Li, and Pierre Sarte for helpful comments and discussions. This article does not necessarily represent the views of the Federal Reserve Bank of Richmond or any branch of the Federal
Secondorder approximation of dynamic models without the use of tensors
, 2009
"... Several approaches to finding the secondorder approximation to a dynamic model have been proposed recently. This paper differs from the existing literature in that it makes use of the Magnus and Neudecker (1999) definition of the Hessian matrix. The key result is a linear system of equations that c ..."
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Cited by 17 (2 self)
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Several approaches to finding the secondorder approximation to a dynamic model have been proposed recently. This paper differs from the existing literature in that it makes use of the Magnus and Neudecker (1999) definition of the Hessian matrix. The key result is a linear system of equations that characterizes the secondorder coefficients. No use is made of multidimensional arrays or tensors, a practical implication of which is that it is much easier to transcribe the mathematical representation of the solution into usable computer code. Matlab code is available from
Monetary Policy in Emerging Markets: Can liability Dollarization Explain contractionary Devaluation?” mimeo, Hong Kong Unviersity of Science and Technology
, 2000
"... In emerging markets, external debt is denominated almost entirely in large, developed country currencies such as the U.S. dollar. This liability dollarization offers a channel through which exchange rate variation can lead to business cycle instability. When firms ’ assets are denominated in domesti ..."
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Cited by 10 (0 self)
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In emerging markets, external debt is denominated almost entirely in large, developed country currencies such as the U.S. dollar. This liability dollarization offers a channel through which exchange rate variation can lead to business cycle instability. When firms ’ assets are denominated in domestic currency and liabilities are denominated in foreign currency, an exchange rate depreciation worsens firms ’ balance sheets, which leads to higher capital costs and contractions in capital spending. To illustrate this, I construct a quantitative, sticky price, small open economy model in which a monetary policy induced devaluation leads to a persistent contraction in output. In this model, fixed exchange rates offer greater stability than an interest rule that targets inflation.
A limited participation model of the monetary transmission mechanism in the United Kingdom’, Bank of England Working Paper, forthcoming
, 2000
"... The views expressed are those of the authors and do not necessarily reflect those of the Bank of England. We gratefully acknowledge comments on this paper received from ..."
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Cited by 5 (4 self)
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The views expressed are those of the authors and do not necessarily reflect those of the Bank of England. We gratefully acknowledge comments on this paper received from
The monetary instrument matters
 Federal Reserve Bank of St. Louis Review (September/October
, 2005
"... This paper revisits the debate over the money supply versus the interest rate as the instrument of monetary policy. Using a dynamic stochastic general equilibrium framework, the authors examine the effects of alternative monetary policy rules on inflation persistence, the information content of mone ..."
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Cited by 2 (1 self)
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This paper revisits the debate over the money supply versus the interest rate as the instrument of monetary policy. Using a dynamic stochastic general equilibrium framework, the authors examine the effects of alternative monetary policy rules on inflation persistence, the information content of monetary data, and real variables. They show that inflation persistence and the variability of inflation relative to money growth depend on whether the central bank follows a money growth rule or an interest rate rule. With a money growth rule, inflation is not persistent and the price level is much more volatile than the money supply. Those counterfactual implications are eliminated by the use of interest rate rules whether prices are sticky or not. A central bank’s use of interest rate rules, however, obscures the information content of monetary aggregates and also leads to subtle problems for econometricians trying to estimate money demand functions or to identify shocks to the trend and cycle components of the money stock. Federal Reserve Bank of St. Louis Review, September/October 2005, 87(5), pp. 63358. Central banks around the world have long settled on the use of interest rates as instruments to implement monetary
Computationally Efficient Solution and Maximum Likelihood Estimation of Nonlinear Rational Expectations Models
, 1996
"... This paper presents new, computationally efficient algorithms for solution and estimation of nonlinear dynamic rational expectations models. The innovations in the algorithms are as follows: (1) The entire solution path is obtained simultaneously by taking a small number of Newton steps, using analy ..."
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Cited by 2 (0 self)
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This paper presents new, computationally efficient algorithms for solution and estimation of nonlinear dynamic rational expectations models. The innovations in the algorithms are as follows: (1) The entire solution path is obtained simultaneously by taking a small number of Newton steps, using analytic derivatives, over the entire path; (2) The terminal conditions for the solution path are derived from the uniqueness and stability conditions from the linearization of the model around the terminus of the solution path; (3) Unit roots are allowed in the model; (4) Very general models with expectational identities and singularities of the type handled by the KingWatson (1995a,b) linear algorithms are also allowed; and (5) Rankdeficient covariance matrices that arise owing to the presence of expectational identities are admissible. Reasonably complex models are solved in less than a second on a Sun Sparc20. This speed improvement makes derivativebased estimation methods feasible. Algorithms for maximum likelihood estimation and sample estimation problems are presented.
ASSET PRICING AND HOUSING SUPPLY IN A PRODUCTION ECONOMY
, 1454
"... publications feature a motif taken from the €50 banknote. NOTE: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily refl ect those of the ECB. Acknowledgements This article has ben ..."
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Cited by 1 (0 self)
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publications feature a motif taken from the €50 banknote. NOTE: This Working Paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily refl ect those of the ECB. Acknowledgements This article has benefited from comments and suggestions from J. Heathcote, two anonymous referees, M. Piazzesi, G. Fagan, P. Weil,
Monetary Policy and Natural Disasters in a DSGE Model: How Should the Fed Have Responded to Hurricane Katrina?
, 2007
"... The views expressed are those of the individual authors and do not necessarily reflect official positions of the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors. Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulat ..."
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The views expressed are those of the individual authors and do not necessarily reflect official positions of the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors. Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to Federal Reserve Bank of St. Louis Working Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.