The Optimal Inflation Tax

We determine the second best rule for the inflation tax in monetary general equilibrium models where money is dominated in rate of return. The results in the literature are ambiguous and inconsistent across different monetary environments. We derive and compare the optimal inflation tax solutions across the different environments and find that Friedman's policy recommendation of a zero nominal interest rate is the right one.Journal of Economic LiteratureClassification Numbers: E31, E41, E58, E62.     

Firms’ money demand and monetary policy

Standard New Keynesian models for monetary policy analysis are ‘cashless’. When the nominal interest rate is the central bank's operating instrument, the LM equation is endogenous and, it is argued, can be ignored. The modern theoretical and quantitative debate on the importance of money for monetary policy conduct, however, overlooks firms’ money demand. Working in an otherwise canonical New Keynesian setup, we show that macroeconomic dynamics are critically affected by the firms’ money demand choice. Under the conventional Taylor‐rule framework, we prove that equilibrium determinacy may require either an active interest rate policy, overreacting to inflation, or a passive interest rate policy, underreacting to inflation, depending on the elasticity of production with respect to cash balances. We then develop a numerical analysis to evaluate our theoretical results. We find that macroeconomic stability is more likely to occur under an active, but not overly aggressive, monetary policy stance. We also examine the dynamic effects of forward‐looking feedback rules. We show that, in this policy regime, indeterminacy is likely to be induced by both active and passive rules, even for relatively low productivity effects of money.     

Price Level Determinacy under a Pure Interest Rate Peg

In this article we reexamine a famous result by T. J. Sargent and N. Wallace (1975, Journal of Political Economy83, 241–254) according to which a “pure interest rate peg” leads to nominal price indeterminacy. We use P. Weil's (1991, International Economic Review32, 37–53) generalization of the Sidrauski–Brock model, where arrival of new “generations” of infinitely lived agents is allowed, and we obtain the following results: (i) Nominal indeterminacy holds in the traditional Sidrauski–Brock framework; (ii) This nominal indeterminacy disappears as soon as new generations arrive in time, via some rigorous version of Patinkin's “real balance effect”; (iii) A multiplicity of solutions may still remain, but full determinacy occurs in some cases, depending notably on fiscal policy or the distribution of endowments in time. Journal of Economic Literature Classification Numbers: E4, E5     

Markov rational expectations equilibria in an overlapping generations model

In this paper, we analyze rational expectations equilibrium paths in a stochastic overlapping generations model. The work presented here builds on results of S. E. Spear (J. Econ. Theory 35 (1985), 251–275), where is is shown that in a model with multiple goods and time non-separable preferences, a stochastic steady state equilibrium will generically fail to exist. A stochastic steady state is defined as an equilibrium in which the stochastic process of endogenously determined variables is measure isomorphic to the exogenous process driving the model. In this paper, we establish the existence of non-steady state equilibria and provide a characterization of their stochastic properties.     

Inflationary expectations and monetary policy: evidence from Bangladesh

This article first estimates inflationary expectations using a Blanchard–Quah VAR model by decomposing the nominal interest rate into expected inflation and the ex ante real interest rate. Then I utilize this expected inflation along with other macroeconomic variables as inputs to the monetary policy function in a recursive VAR model to identify exogenous policy shocks. To calculate inflationary expectations, I assume that ex ante real interest rate shocks do not have a long-run effect on the nominal interest rate. This article finds that the public expects lower inflation for the future during periods of high inflation. Estimated results from the recursive VAR suggest that a contractionary policy shock increases the real interest rate, appreciates domestic currency, and lowers inflationary expectations and industrial output. However, I find a lagged policy response from Bangladesh Bank to higher inflationary expectations.     

The inflationary bias of real uncertainty and the harmonic Fisher equation

Summary. We argue that real uncertainty itself causes long-run nominal inflation. Consider an infinite horizon cash-in-advance economy with a representative agent and real uncertainty, modeled by independent, identically distributed endowments. Suppose the central bank fixes the nominal rate of interest. We show that the equilibrium long-run rate of inflation is strictly higher, on almost every path of endowment realizations, than it would be if the endowments were constant.Indeed, we present an explicit formula for the long-run rate of inflation, based on the famous Fisher equation. The Fisher equation says the short-run rate of inflation should equal the nominal rate of interest less the real rate of interest. The long-run Fisher equation for our stochastic economy is similar, but with the rate of inflation replaced by the harmonic mean of the growth rate of money.Received: 25 February 2005, Revised: 26 May 2005, JEL Classification Numbers: C7, C73, D81, E41, E58.An earlier version of this paper “Inflationary Bias in a Simple Stochastic Economy,” as a 2001 Cowles Foundation Discussion Paper No. 1333.     

INTEREST RATE RULES AND WELFARE IN OPEN ECONOMIES

This paper analyses the welfare performance of a set of five alternative interest rate rules in an open economy stochastic dynamic general equilibrium model with nominal rigidities. A rule with a lagged interest rate term, high feedback on inflation and low feedback on output is found to yield the highest welfare for a small open economy. This result is robust across different degrees of openness, different sources of home and foreign shocks, alternative foreign monetary rules and different specifications for price-setting behaviour. The same rule emerges as both the Nash and cooperative equilibria in a two-country version of the model.     

Debt, liquidity and dynamics

Summary. Money, which provides liquidity, is distinct from debt. The introduction of a bank that issues money in exchange for debt and pays out its profit as dividend to shareholders modifies the model of overlapping generations. The set of equilibrium paths, their dynamic properties, as well as the scope and effectiveness of monetary policy are significantly altered: though low rates of interest are associated with superior steady state allocations, stability of the steady state may require a nominal rate of interest above a certain minimum: without production, a decrease in the nominal rate of interest may result in explosive behavior or convergence to an endogenous cycle, while in an economy with production, an increase in the nominal rate of interest may lead to indeterminacy and fluctuations.Received: 5 October 2004, Revised: 5 November 2004 JEL Classification Numbers: E30, E32, E50, E52.C. Rochon, H.M. Polemarchakis: We thank Jean-Michel Grandmont for helpful comments. Correspondence to: C. RochonThis revised version was published online in May 2005 with a corrected abstract.     

A Note on the Stability of Full Employment

This note investigates the stability properties of the Keynesian macro-model under the assumption of slow adjustment of nominal wages and expectations of inflation. First, the stability conditions of the 'flexible-interest-rate regime' are related to those derived by Cagan (1956) and Tobin (1975), emphasising the potentially destabilising effect of wage flexibility. Then, taking the restriction of a zero floor to the nominal interest rate into account it is shown that the model exhibits 'corridor stability'. From this follows the conjecture that increasing the rate of steady-state inflation makes it 'more probable' that the system returns to full-employment after a shock of given size.     

Modifying Taylor reaction functions in the presence of the zero‐lower‐bound — Evidence for the ECB and the Fed

We propose an alternative way of estimating Taylor reaction functions if the zero‐lower bound on nominal interest rates is binding. This approach relies on tackling the real rather than the nominal interest rate. So if the nominal rate is (close to) zero central banks can influence the inflation expectations via quantitative easing. The unobservable inflation expectations are estimated with a state‐space model that additionally generates a time varying series for the equilibrium real interest rate and the potential output — both needed for estimations of Taylor reaction functions. We test our approach for the ECB and the Fed within the recent crisis. We add other explanatory variables to this modified Taylor reaction function and show that there are substantial differences between the estimated reaction coefficients in the pre‐ and crisis era for both central banks. While the central banks on both sides of the Atlantic act less inertially, put a smaller weight on the inflation gap, money growth and the risk spread, the response to asset price inflation becomes more pronounced during the crisis. However, the central banks diverge in their response to the output gap and credit growth.     

Financial market imperfections and monetary policy strategy

In a model with imperfect money, credit and reserve markets, we examine if an inflation-targeting central bank applying the funds rate operating procedure to indirectly control market interest rates also needs a monetary aggregate as policy instrument. We show that if private agents use information extracted from money and financial markets to form inflation expectations and if interest rate pass-through is incomplete, the central bank can use a narrow monetary aggregate and the discount interest rate as independent and complementary policy instruments to reinforce the credibility of its announcements and the role of inflation target as a nominal anchor for inflation expectations. This study shows how a monetary policy strategy combining inflation targeting and monetary targeting can be conceived to guarantee macroeconomic stability and the credibility of monetary policy. Friedman's k-percent money growth rule, which can generate dynamic instability, and two alternative stabilizing feedback monetary targeting rules are examined.     

Endogenous monetary policy and the liquidity effect

We compare the transmission mechanism of exogenous and endogenous monetary policies in a calibrated small open economy model with nominal and real rigidities. Under an exogenous monetary policy rule it takes implausible values of the intertemporal elasticity of substitution and the price adjustment costs to generate the liquidity and overshooting effects. Endogenous rules with strong feedback to inflation and output help to reproduce the response of the nominal interest and exchange rates to unanticipated monetary policy shocks that characterize the transmission mechanism of standard sticky price models. The liquidty and overshooting effects are always obtained when the model is augmented with a Taylor interest rate rule.JEL Classification: E32, E43Javier Andrés acknowledges support of CICYT grant SEC2002-0026. We thank the comments of two anonymous referees and the editor, Jordi Caballé, to an earlier version of the paper. The views expressed here are those of the authors and do not represent the view of the Banco de España.     

Interest rate rules, inflation and the Taylor principle: an analytical exploration

Summary. The purpose of this article is to characterize optimal interest rate rules in the framework of a dynamic stochastic general equilibrium model, and notably to scrutinize the “Taylor principle”, according to which the nominal interest rate should respond more than one for one to inflation. This model yields explicit solutions for the optimal rule. We find that the elasticity of response depends on numerous factors, such as the degree of price rigidity, the autocorrelation of the underlying shocks, or which measure of inflation is used. In general the optimal elasticity of the interest rate with respect to inflation needs not be greater than one.Received: 6 November 2003, Revised: 17 August 2004 JEL Classification Numbers: E5, E52, E58.J.-P. Bénassy: I wish to thank Daniel Laskar and an anonymous referee for their perceptive comments on earlier drafts of this paper. Of course all remaining deficiencies are mine.     

Endogenous Money Supply and the Business Cycle

This paper documents changes in the cyclical behavior of nominal data series that appear after 1979:Q3 when the Federal Reserve implemented a policy to lower the inflation rate. Such changes were not apparent in real variables. A business cycle model with impulses to technology and a role for money is used to show how alternative money supply rules are expected to affect observed business cycle facts. In this model, changes in the money supply rules have almost no effect on the cyclical behavior of real variables, yet have a significant impact on the cyclical nature of nominal variables.Journal of Economic LiteratureClassification Numbers: E32, E42, E50.     

Budgetary policies in a DSGE model with finite horizons

This paper presents a dynamic stochastic general equilibrium model with nominal rigidities, capital accumulation and finite horizons. Our New Keynesian framework exhibits intergenerational wealth effects and is intended to investigate the macroeconomic implications of fiscal policy, which is specified by either a debt-based tax rule or a balanced-budget rule allowing for temporary deficits. The model predicts that fiscal expansions generate a trade-off in output dynamics between short-term gains and medium-term losses. It is shown that the effects of fiscal shocks crucially depend upon the conduct of monetary policy. Simulation analysis suggests that balanced-budget requirements enhance the determinacy properties of feedback interest rate rules by guaranteeing inflation stabilization.     

Does trend inflation make a difference?

Although the average inflation rate of developed countries in the postwar period has been greater than zero, much of the extensive literature on monetary policy has employed models that assume zero steady-state inflation. In comparing four estimated medium–scale NK DSGE models with real and nominal frictions, we seek to shed light on the quantitative implications of omitting trend inflation, that is, positive steady–state inflation. We compare certain population characteristics and the IRFs for the four models by applying two loss functions based on a point distance criterion and on a distribution distance criterion, respectively. Finally, we compare the RMSE forecasts and we consider also an indirect inference test. We repeat the analysis for three sub-periods: the Great Inflation, the Great Moderation and the union of the two periods. We do not find strong evidence that a model with trend inflation should always be preferred. During periods of high inflation or when a backward-looking component, indexed to past inflation, is not incorporated in the model, using a model that employs trend inflation can improve the analysis. Nevertheless, where there is uncertainty concerning the change of an inflation regime, such as the recent drop, we suggest adopting a traditional approach that does not use trend inflation.     

The NAIRU reconsidered: why labour market deregulation may raise unemployment

According to the mainstream theory of equilibrium unemployment, persistent unemployment is caused mainly by ‘excessive’ labour market regulation, whereas aggregate demand, capital accumulation and technological progress have no lasting effect on unemployment. We show that the mainstream non‐accelerating inflation rate of unemployment (NAIRU) model is a special case of a general model of equilibrium unemployment, in which aggregate demand, investment and endogenous technological progress do have long‐term effects. It follows that labour market deregulation does not necessarily reduce steady‐inflation unemployment. Theoretically, if the decline in real wage growth claims owing to deregulation is smaller than the ensuing decline in labour productivity growth and in the warranted real wage growth, then in that case steady‐inflation unemployment may increase. Empirical evidence for 20 Organisation for Economic Cooperation and Development (OECD) countries (1984–1997) indicates that the impact of labour market deregulation on OECD unemployment is zero, and possibly negative (causing a higher rate of unemployment).     

Correct cointegration tests of the long-run relationship between nominal interest and inflation

The Fisher (1930) hypothesis suggests that a long-run equilibrium relationship exists between the non-stationary series: nominal interest and expected inflation. Testing such a cointegrating relationship is complicated by the presence of the unobserved ex antereal rate of interest in residuals from the cointegrating regression. Assumptions concerning the stochastic properties of the expected real rate of interest are examined, and two proxies for the ex antereal rate are employed in multivariate cointegration tests of the Fisher hypothesis.     

Partial inflation indexation and long-run inflation targeting in a growing economy: A comparison of Calvo and Rotemberg pricing models

The observed 2% long run inflation target in most developed industrial nations is in variance with the zero or negative optimal inflation rates predicted by prominent monetary theories. Using a calibrated simple New-Keynesian model with endogenous growth and nominal rigidity, we compare two price setting environments of Calvo (1983) and Rotemberg (1982). In our growth model, the steady state welfare maximizing inflation takes into account the growth effect as well as the price distortionary effects of inflation. The long-run welfare maximizing trend inflation could be positive in economies with nominal rigidity in the form of partial inflation indexation and price stickiness. A higher degree of inflation indexation lowers the steady state price distortion in the Calvo model and steady state price adjustment cost in Rotemberg model and raises the long run optimal inflation. Since the productive inefficiency caused by partial inflation indexation is higher in Calvo economy compared to Rotemberg, the long run optimal trend inflation is higher in Rotemberg than in Calvo. In both models, a two percent long run inflation target is attainable for a reasonable degree of inflation indexation.     

Keynes‐Marx and Keynes‐Wicksell Models of Monetary Growth: A framework for future analysis

This paper reconsiders and generalizes a dichotomizing two-sector real growth model of Marglin which claims that the steady state of capitalist economies is plagued by secular inflation. We show that this implication need not be true from the perspective of a more general steady state analysis and that the Marglin model can be embedded into a general Keynes‐Marx‐Friedman or Keynes‐Wicksell framework where money is superneutral, where therefore inflation is due solely to excessive monetary growth, where the private sector is basically asymptotically stable and where there is a steady state rate of employment that differs from the 'natural' rate of employment of monetarist models of inflation. We consider this model a benchmark model that requires equally general alternatives if the above implications are to be rejected.