We show that the introduction of a constant tariff or subsidy levied on foreign energy can lead to a rich set of endogenous fluctuations around the unique steady state, including stable 2-, 4-, 8-, and 15-cycles, quasiperiodic orbits, and chaos. This is demonstrated in a standard neoclassical growth model with social increasing returns to scale. Numerical exercises could be viewed from a methodological perspective as illustrating that capital income taxes and tariffs are equivalent in generating endogenous fluctuations because Guo and Lansing [Guo, J.T. and K.J. Lansing (2002) Fiscal policy, increasing returns and endogenous fluctuations. Macroeconomic Dynamics 6, 633–664] show that a constant capital tax or subsidy has the same effect on the model dynamics in a one-sector closed economy.

The purpose of this note is to analyze the capability of bandpass filters to extract a known periodicity. The specific bandpass filters considered are a conventional discrete Fourier transform (DFT) filter and the filter recently proposed by Iacobucci and Noullez. We employ simulation methods to investigate cycle extraction properties. We also examine the implications arising from the Gibbs effect in practical settings that typically confront applied macroeconomists

The US Social Security program was created in part as an explicit response to the Great Depression. We evaluate the performance of Social Security as a protective safety net against a rare episode of sudden and significant loss of private wealth such as the Great Depression. We construct a model in which a rare event causes a shock to wealth at an unknown time. How well does Social Security function as a safety net against such risk? The answer depends critically on whether households optimize in the face of this risk. If the household has full information on the distribution of rare event risk and solves a dynamic stochastic problem to hedge this risk, then Social Security is unnecessary along this dimension. Alternatively, if the household does not account for rare event risk in its financial planning, then Social Security can provide very large welfare gains as a safety net.

We are motivated by central bank responses to the rise in inflation in the aftermath of the coronavirus pandemic and investigate monetary policy behavior in advanced and emerging economies. We speak to the debate on whether the conduct of monetary policy in emerging economies is fundamentally different from that in advanced economies. We also address the issue of whether the common practice of using market rates (instead of policy rates) to proxy for the stance of monetary policy leads to different conclusions regarding the cyclicality of monetary policy in emerging economies. Using time series data for the G7 and EM7 countries, we show that the conventional wisdom that monetary policy in emerging economies is different from monetary policy in advanced economies still holds.

Expectations are among the main driving forces for economic dynamics. Therefore, managing expectations has become a primary objective for monetary policy seeking to stabilize the business cycle. In this paper, we study whether central banks can manage private-sector expectations by means of publishing one-period ahead inflation projections in a New Keynesian learning-to-forecast experiment. Subjects in the experiment observe these projections along with the historic development of the economy and subsequently submit their own one-period ahead inflation forecasts. In this context, we find that the central bank can significantly manage private-sector expectations and that this management strongly supports monetary policy in stabilizing the economy. Moreover, published central bank inflation projections drastically reduce the probability of a deflationary spiral after strong negative shocks to the economy.

This paper estimates an enriched version of the mainstream medium-scale dynamic stochastic general equilibrium model, which features nonseparability between consumption and real money balances in utility and a systematic response of the policy rate to money growth. Estimation results show that money is a significant factor in the monetary policy rule. As a consequence, econometric analysis that omits money from Taylor rules may lead to biased estimates of the model parameters. In contrast to earlier studies that rely on small-scale models, the paper stresses the merits of using a sufficiently rich model. First, it delivers different results, such as the role of nonseparability between consumption and money in utility. Second, the rich dynamics embedded in the model allow us to explore the responses of a larger set of macroeconomic variables, making the model more informative on the effects of shocks and more useful for understanding the sources of business cycles. Third and most importantly, it reveals the possible pitfalls of relying on small-scale models when studying money’s role in business cycles.

This paper introduces a new measure to capture dynamic losses for exporting firms on markets that exhibit hysteresis on the supply side. Our indicator aims to quantify dynamic losses caused by sunk adjustment costs in case of exchange rate fluctuations. While the standard procedure in welfare analysis is to compare two equilibria, we focus on welfare effects that take place during dynamics. We analyze negative dynamic effects on producers' income that are generated due to writing off sunk adjustment costs. As an example, we investigate Italian wine exports to the United States over the period 1995–2013. After testing for hysteresis on the market, we present the indicator of hysteresis losses. It captures a continuous increase of dynamic losses during the period 2003–2008. Moreover, over-proportionately large hysteresis losses are generated in comparison to the exchange rate changes if the pain threshold of the exchange rate (ca. 1.25$/€) is passed.

A variety of international macroeconomic models predict a relationship between the real exchange rate and consumption. The empirical evidence in favor of such a relationship is limited, the so-called Backus and Smith puzzle. In this paper, we extend the analysis to allow for nonlinear dynamics and volatility changes across exchange rate regimes. Our findings suggest that long-run relationships in line with standard international business cycle models do exist for many Organization for Economic Co-operation and Development (OECD) countries. Further, Monte Carlo experiments illustrate that the nonlinear models can generate the Backus and Smith and the exchange rate disconnect puzzles. In this paper, we also contribute to the nonlinear real exchange rate literature by establishing a theoretical relationship between volatility and persistence. In accordance with the theoretical results, our empirical findings suggest that the increase in volatility in the post-Bretton Woods era is associated with relatively fast mean reversion of the real rate toward its equilibrium value.

Foliations provide a general, convenient, geometric way to catalogue information from topics as varied as sufficient statistics, solutions of differential equations, indifference curves for utility functions, distributed computing, and so forth. An introduction to aspects of this area is provided.

This paper analyzes the dynamical properties of monetary models with regime switching. We start with the analysis of the evolution of inflation when policy is guided by a simple monetary rule where coefficients switch with the policy regime. We rule out the possibility of a Hopf bifurcation and demonstrate the possibility of a period-doubling bifurcation. As a result, a small change in the parameters (e.g., a more active policy response) can lead to a drastic change in the path of inflation. We show that the New Keynesian model with a current-looking Taylor rule is not prone to bifurcations. A New Keynesian model with a hybrid rule, however, exhibits the same pattern of period-doubling bifurcations as the analysis with a simple monetary rule.

I develop and calibrate an equilibrium search model with endogenous savings and search intensity. The wage is endogenized using Nash bargaining and the number of vacancies is tied down by a free entry condition. This allows me to conduct a counterfactual analysis of the optimal unemployment insurance (UI) level. The provision of UI is motivated by the worker's inability to perfectly insure against income shocks, but at the same time UI introduces distortions into workers' search intensity decisions and firm vacancy creation. I find that equilibrium effects are important. When the UI level is raised 25%, they constitute around one-third of the increase in total unemployment. However, even with limited savings by workers, optimal UI is close to zero. It is further shown that ignoring the possibility of self-insurance greatly affects the optimal UI level.

William A. Brock has taught in the Departments of Economics at the University of Rochester, Cornell University, and the University of Chicago, before moving to the University of Wisconsin, Madison, where he is now Vilas Research Professor of Economics. He has also been an External Professor at the Santa Fe Institute since 1989. His many awards include election as a Fellow of the Econometric Society in 1974, a Fellow of the American Academy of Arts and Sciences in 1992, and as a Member of the National Academy of Sciences in 1998. His over 100 invited lectures include presentations in Poland, Belgium, France, Mexico, Canada, Japan, Australia, England, Sweden, Norway, and Australia.

Brock has been a leading contributor to the development of methods of intertemporal equilibrium analysis in the areas of growth theory, monetary theory, and finance. More recently, he has played a crucial role in the development of new methods for the analysis of nonlinear dynamics in macroeconomics and finance, and models of expectations that relax the assumption of rational expectations.

I interviewed Buz in the faculty cafeteria near the Social Science Research Institute building, on the Madison campus of the University of Wisconsin, on October 22, 1998. Our interview was interrupted when he had to go to teach, and then was finished by phone on December 11, 1998. The transcript that follows does little justice to the liveliness of Buz's conversation, mainly because of my inability to transcribe the animated facial expressions and hand gestures that made the mathematical references more concrete. I have added several footnotes to the transcript, identifying some of the published sources that were mentioned during our conversation.

We implement optimal economic outcomes at the lowest social cost by combining reputation and contracting mechanisms to overcome the time-inconsistency problem of monetary policy associated with an inflation bias. We characterize the conditions under which the reputation force alone induces a central bank to behave in a socially optimal way. When these conditions fail, an incentive contract is invoked, whose cost is significantly reduced by the presence of the reputation force. The contract poses a penalty threat that is a concave function of wage growth, which in equilibrium is tied to expected rather than realized inflation, with a global maximum that provides the least upper bound on all threatened penalties. This bound can be used as a uniform penalty threat to achieve optimal economic outcomes and still, for moderate to large shocks, its magnitude can be much smaller than the size of the transfers required by the standard contracts that are linear functions of realized inflation rates. Further, under both the concave and the uniform penalty threats, the central bank will behave in the socially optimal way and no transfer is materialized in equilibrium. Thus our hybrid mechanism solves the time-inconsistency problem while leaving the central bank with complete discretion to respond to new circumstances, without any reputation cost or penalty threatened by the contract actually invoked along the equilibrium path.

In this paper, we study the relationship between changes in the world interest rate and within-country inequality during the 1985–2005 period in which the world interest rate sharply declined. In line with the predictions of the seminal model of Galor and Zeira [Income distribution and macroeconomics. Review of Economic Studies 60, 35–52], the analysis suggests that the decrease in the world interest rate is associated with a decrease in inequality in poor countries and an increase in inequality in rich ones.

In the context of I(1) time series, we provide some asymptotic results for the Davidson-MacKinnon J-type test. We examine both the case where our regressor sets x1t and x2t are not cointegrated, and the case where they are. In the former case, the OLS estimator of the weighting coefficient from the artificial compound model converges at rate T to a mixed normal distribution, and the associated t-statistic has an asymptotic standard normal distribution. In the latter case, we find that the J-test also has power against violation of weak exogeneity (with respect to the short-run coefficients of the null model), which is caused by correlation between the disturbance of the null model and that of the cointegrating equation linking x1t and x2t. Moreover, unlike the previous case, the OLS estimator of the weighting coefficient from the artificial compound model converges at \sqrt{T} to an asymptotic normal distribution when the null model is specified correctly. In an empirical illustration, we use the tests to examine an industrial production data set for six countries.

The Divisia monetary index weights each monetary asset by its expenditure share, evaluated at its user cost.See Barnett et al. [1997, equations (5) and (6)]. In a world of perfect certainty, the user costs can be computed directly from asset return data, and so, the index is model-free. In the presence of uncertainty, however, the true user cost of a monetary asset depends on the covariance of the asset's return with the marginal utility of wealth. Intuitively, an asset's value depends both on its expected payoff and on the asset's ability to hedge wealth fluctuations. As a result, the true user cost cannot be computed without an explicit model of preferences. It follows that the exact Divisia monetary index in a stochastic economy is not model-free, but depends on the underlying preference assumptions.

By developing a class of dynamic stochastic general equilibrium models with nominal rigidities and assuming a two-country currency union with sovereign risk, we show that there is not necessarily a trade-off between the prevention of default risk and stabilizing inflation. Under optimal monetary and fiscal policy, comprising a de facto inflation stabilization policy, the tax rate as an optimal fiscal policy tool plays an important role in stabilizing inflation, although not completely because of the distorted steady state. Changes in the tax rate to minimize welfare costs via stabilizing inflation then improve the fiscal surplus, and because of this and the incompletely stabilized inflation, the default rate does not increase as much.

We study whether monetary authorities in the G7 countries were changing their responses to inflation in a similar manner during and following the Great Inflation era. We find that the common to the G7 countries inflation pattern during the Great Inflation period could be associated with a common pattern in the monetary policy response to inflation: we find that until the early 1980s monetary authorities in the G7 countries responded mildly to inflation, systematically fought it throughout the 1980s and lessened again their response during the 2000s. The estimated Taylor rule coefficients on inflation are co-integrated, implying the existence of a long-run relationship in the responses to inflation during and after the Great Inflation period. At the same time, principal component analysis of the residuals of the estimated Taylor rules indicates that the shocks' structure cannot account enough for the monetary policies' co-movements. We interpret these findings as suggestive of common monetary policy patterns.

We reassess the evidence for (or against) a key implication of the basic real business cycle model: that aggregate hours worked increase in response to a positive technology shock. Two novel aspects are the scope (14 OECD countries) and the inclusion of data on both labor supply margins to analyze the key margin of adjustment in aggregate hours. The short-run response of aggregate hours to a positive technology shock is remarkably similar across countries, with an impact fall in 13 out of 14 countries. In contrast, its decomposition into intensive and extensive labor supply margins reveals substantial heterogeneity in labor market dynamics across OECD countries. For instance, movements in the intensive margin are the dominant channel of adjustment in aggregate hours in 6 out of 14 countries of our sample, including France and Japan.