Flows of constant mean curvature tori in the 3-sphere: The equivariant case

We present a deformation for constant mean curvature tori in the 3-sphere. We show that the moduli space of equivariant constant mean curvature tori in the 3-sphere is connected, and we classify the minimal, the embedded, and the Alexandrov embedded tori therein. We conclude with an instability result.Comment: v2: 33 pages, 9 figures. Instability result adde

Only in the Heat of the Moment? A Study of the Relationship between Weather and Mortality in Germany

In this study we analyze the relationship between heat events and mortality in Germany. The main research questions are: Does heat lead to rising mortality and if yes, are the effects persistent or compensated for in the near future? Furthermore, we consider differences between heat effects in urban and rural environments. Cause specific daily mortality and meteorological data is connected on the county level. We allow for static as well as dynamic relations between extreme temperatures and mortality and implement several panel data estimation approaches. We find that heat has a significant positive impact on mortality. The strongest effects can be measured on the day when heat occurs and the first week afterwards. The mortality increase ranges between 0.003 and 3.5 per 100,000 inhabitants depending on the particular death cause. We do not find a significant negative, and thus compensating impact in a medium term, which is in the contrary to the Harvesting Hypothesis. Using a value of statistical life approach we estimate that one additional hot day in Germany induces for the overall population a loss of m € 1,861. Moreover, the environment plays an important role. The heat induced increase in mortality is significantly higher in urban areas.Climate Change, Harvesting Hypothesis, Heat Waves, Mortality, Urban Heat Island effect

Anticipated Ramsey Reforms and the Uniform Taxation Principle: the Role of International Financial Markets

This paper studies the role of asset-market completeness for the properties of optimal policy. A suitable framework for this purpose is the small open economy with complete international asset markets. For in this environment changes in policy represent country-specific risk diversifiable in world markets. Our main finding is that the fundamental public finance principle whereby when taxes on all final goods are available, it is optimal to tax final goods uniformly fails to obtain. In general, uniform taxation is optimal because it amounts to a nondistorting tax on fixed factors of production. In the open economy this principle fails because when households can insure against the risk of a policy reform, initial private asset holdings are contingent on actual policy and thus no longer represent an inelastically supplied source of income. Two further differences between optimal policy in the closed and open economies with complete markets are: (a) In the open economy, optimal consumption and income tax rates are unchanged in response to government purchases shocks. By contrast, in the closed economy tax rates do respond to innovations in public spending. (b) In the open economy, the Friedman rule is optimal only if the Ramsey planner has access to consumption taxes. In the absence of consumption taxes, deviations from the Friedman rule are large. On the other hand, in the closed economy, the availability of either consumption or income taxes suffices to render the Friedman rule optimal.

Optimal Inflation Stabilization in a Medium-Scale Macroeconomic Model

This paper characterizes Ramsey-optimal monetary policy in a medium-scale macroeconomic model that has been estimated to fit well postwar U.S.\ business cycles. We find that mild deflation is Ramsey optimal in the long run. However, the optimal inflation rate appears to be highly sensitive to the assumed degree of price stickiness. Within the window of available estimates of price stickiness (between 2 and 5 quarters) the optimal rate of inflation ranges from -4.2 percent per year (close to the Friedman rule) to -0.4 percent per year (close to price stability). This sensitivity disappears when one assumes that lump-sum taxes are unavailable and fiscal instruments take the form of distortionary income taxes. In this case, mild deflation emerges as a robust Ramsey prediction. In light of the finding that the Ramsey-optimal inflation rate is negative, it is puzzling that most inflation-targeting countries pursue positive inflation goals. We show that the zero bound on the nominal interest rate, which is often cited as a rationale for setting positive inflation targets, is of no quantitative relevance in the present model. Finally, the paper characterizes operational interest-rate feedback rules that best implement Ramsey-optimal stabilization policy. We find that the optimal interest-rate rule is active in price and wage inflation, mute in output growth, and moderately inertial. This rule achieves virtually the same level of welfare as the Ramsey optimal policy.

Optimal Fiscal and Monetary Policy Under Imperfect Competition

This paper studies optimal fiscal and monetary policy under imperfect competition in a stochastic, flexible-price, production economy without capital. It shows analytically that in this economy the nominal interest rate acts as an indirect tax on monopoly profits. Unless the social planner has access to a direct 100 percent tax on profits, he will always find it optimal to deviate from the Friedman rule by setting a positive and time-varying nominal interest rate. The dynamic properties of the Ramsey allocation are characterized numerically. As in the perfectly competitive case, the labor income tax is remarkably smooth, whereas inflation is highly volatile and serially uncorrelated. An exact numerical solution method to the Ramsey conditions is proposed.

Optimal Simple and Implementable Monetary and Fiscal Rules

The goal of this paper is to compute optimal monetary and fiscal policy rules in a real business cycle model augmented with sticky prices, a demand for money, taxation, and stochastic government consumption. We consider simple policy rules whereby the nominal interest rate is set as a function of output and inflation, and taxes are set as a function of total government liabilities. We require policy to be implementable in the sense that it guarantees uniqueness of equilibrium. We do away with a number of empirically unrealistic assumptions typically maintained in the related literature that are used to justify the computation of welfare using linear methods. Instead, we implement a second-order accurate solution to the model. Our main findings are: First, the size of the inflation coefficient in the interest-rate rule plays a minor role for welfare. It matters only insofar as it affects the determinacy of equilibrium. Second, optimal monetary policy features a muted response to output. More importantly, interest rate rules that feature a positive response of the nominal interest rate to output can lead to significant welfare losses. Third, the optimal fiscal policy is passive. However, the welfare losses associated with the adoption of an active fiscal stance are negligible.

Backward-Looking Interest-Rate Rules, Interest-Rate Smoothing, and Macroeconomic Instability

The existing literature on the stabilizing properties of interest-rate feedback rules has stressed the perils of linking interest rates to forecasts of future inflation. Such rules have been found to give rise to aggregate fluctuations due to self-fulfilling expectations. In response to this concern literature has focused on the stabilizing properties of interest-rate rules whereby the central bank responds to a measure of past inflation. The consensus view that has emerged is that backward-looking rules contribute to protecting the economy from embarking on expectations-driven fluctuations. A common characteristic of the existing studies that arrive at this conclusion is their focus on local analysis. The contribution of this paper is to conduct a more global analysis. We find that backward-looking interest-rate feedback rules do not guarantee uniqueness of equilibrium. We present examples in which for plausible parameterizations attracting equilibrium cycles exist. The paper also contributes to the quest for policy rules that guarantee macroeconomic stability globally. Our analysis indicates that policy rules whereby the interest rate is set as a function of the past interest rate and current inflation are likely to ensure global stability provided that the coefficient on lagged interest rates is greater than unity.

Incomplete Cost Pass-Through Under Deep Habits

A number of empirical studies document that marginal cost shocks are not fully passed through to prices at the firm level and that prices are substantially less volatile than costs. We show that in the relative-deep-habits model of Ravn, Schmitt-Grohe, and Uribe (2006), firm-specific marginal cost shocks are not fully passed through to product prices. That is, in response to a firm-specific increase in marginal costs, prices rise, but by less than marginal costs leading to a decline in the firm-specific markup of prices over marginal costs. Pass-through is predicted to be even lower when shocks to marginal costs are anticipated by firms. In our model, unanticipated firm-specific cost shocks lead to incomplete pass-through (or a decline in markups) of about 20 percent and anticipated cost shocks are associated with incomplete pass-through of about 50 percent. The model predicts that cost pass-through is increasing in the persistence of marginal cost shocks and U-shaped in the strength of habits. The relative-deep-habits model implies that conditional on marginal cost disturbances, prices are less volatile than marginal costs.

Chaotic Interest Rate Rules: Expanded Version

A growing empirical and theoretical literature argues in favor of specifying monetary policy in the form of Taylor-type interest rate feedback rules. That is, rules whereby the nominal interest rate is set as an increasing function of inflation with a slope greater than one around an intended inflation target. This paper shows that such rules can easily lead to chaotic dynamics. The result is obtained for feedback rules that depend on contemporaneous or expected future inflation. The existence of chaotic dynamics is established analytically and numerically in the context of calibrated economies. The battery of fiscal policies that has recently been advocated for avoiding global indeterminacy induced by Taylor-type interest-rate rules (such as liquidity traps) are shown to be unlikely to provide a remedy for the complex dynamics characterized in this paper.

The Perils of Taylor Rules

interest rate feedback rules; zero bound on nominal rates; liquidity traps; multiple equilibria