Solutions to the Painlev\'e V equation through supersymmetric quantum mechanics

In this paper we shall use the algebraic method known as supersymmetric quantum mechanics (SUSY QM) to obtain solutions to the Painlev\'e V (PV) equation, a second-order non-linear ordinary differential equation. For this purpose, we will apply first the SUSY QM treatment to the radial oscillator. In addition, we will revisit the polynomial Heisenberg algebras (PHAs) and we will study the general systems ruled by them: for first-order PHAs we obtain the radial oscillator, while for third-order PHAs the potential will be determined by solutions to the PV equation. This connection allows us to introduce a simple technique for generating solutions of the PV equation expressed in terms of confluent hypergeometric functions. Finally, we will classify them into several solution hierarchies.Comment: 39 pages, 18 figures, 4 tables, 70 reference

Understanding the effects of government spending on consumption

Recent evidence on the effect of government spending shocks on consumption cannot be easily reconciled with existing optimizing business cycle models. We extend the standard New Keynesian model to allow for the presence of rule-of-thumb (non-Ricardian) consumers. We show how the interaction of the latter with sticky prices and deficit financing can account for the existing evidence on the effects of government spending. JEL Klassifikation: E32, E62

Rule-of-Thumb Consumers and the Design of Interest Rate Rules

We introduce rule-of-thumb consumers in an otherwise standard dynamic sticky price model, and show how their presence can change dramatically the properties of widely used interest rate rules. In particular, the existence of a unique equilibrium is no longer guaranteed by an interest rate rule that satisfies the so called Taylor principle. Our findings call for caution when using estimates of interest rate rules in order to assess the merits of monetary policy in specific historical periods.

Sticky-price models and the natural rate hypothesis

A major criticism of standard specifications of price adjustment in models for monetary policy analysis is that they violate the natural rate hypothesis by allowing output to differ from potential in steady state. In this paper we estimate a dynamic optimizing business cycle model whose price-setting behavior satisfies the natural rate hypothesis. The price-adjustment specifications we consider are the sticky-information specification of Mankiw and Reis (2002) and the indexed contracts of Christiano, Eichenbaum, and Evans (2005). Our empirical estimates of the real side of the economy are similar whichever price adjustment specification is chosen. Consequently, the alternative model specifications deliver similar estimates of the U.S. output gap series, but the empirical behavior of the gap series differs substantially from standard gap estimates.Monetary policy ; Prices

Understanding the Effects of Government Spending on Consumption

Recent evidence suggests that consumption rises in response to an increase in government spending. That finding cannot be easily reconciled with existing optimizing business cycle models. We extend the standard new Keynesian model to allow for the presence of rule-of-thumb consumers. We show how the interaction of the latter with sticky prices and deficit financing can account for the existing evidence on the effects of government spending.

Tobin's imperfect asset substitution in optimizing general equilibrium

In this paper, we present a dynamic optimizing model that allows explicitly for imperfect substitutability between different financial assets. This is specified in a manner which captures Tobin's (1969) view that an expansion of one asset's supply affects both the yield on that asset and the spread or "risk premium" between returns on that asset and alternative assets. Our estimates of this model on U.S. data confirm that some of the observed deviations of long-term rates from the expectations theory of the term structure can be traced to movements in the relative stocks of financial assets. The richer aggregate demand and asset specifications imply that there exists an additional channel of monetary policy. Our results suggest that central bank operations exercise a modest influence on the relative prices of alternative financial securities, and so exert an extra effect on long-term yields and aggregate demand separate from their effect on the expected path of short-term rates.Monetary policy ; Macroeconomics

Money and the natural rate of interest: structural estimates for the United States and the Euro area

We examine the role of money, allowing for three competing environments: the New Keynesian model with separable utility and static money demand; a non-separable utility variant with habit formation; and a version with adjustment costs for holding real balances. The last two variants imply forward-looking behavior of real money balances, as it is optimal for agents to allow their forecast of future interest rates to affect current portfolio decisions. We distinguish between these specifications by conducting a structural econometric analysis for the U.S. and the euro area. FIML estimates confirm the forward-looking character of money demand. Using these estimates we find that, in response to preference and technology shocks, real money balances are valuable in anticipating future variations in the natural interest rate.Money ; Interest rates

Technology Shocks and Monetary Policy: Assessing the Fed's Performance

The purpose of the present paper is twofold. First, we characterize the Fed's systematic response to technology shocks and its implications for U.S. output, hours and inflation. Second, we evaluate the extent to which those responses can be accounted for by a simple monetary policy rule (including the optimal one) in the context of a standard business cycle model with sticky prices. Our main results can be described as follows: First, we detect significant differences across periods in the response of the economy (as well as the Fed's) to a technology shock. Second, the Fed's response to a technology shock in the Volcker-Greenspan period is consistent with an optimal monetary policy rule. Third, in the pre-Volcker period the Fed's policy tended to over stabilize output at the cost of generating excessive inflation volatility. Our evidence reinforces recent results in the literature suggesting an improvement in the Fed's performance.

Direct introduction of nitrogen and oxygen functionality with spatial control using copper catalysis.

Synthetic chemists have spent considerable effort optimizing the synthesis of nitrogen and oxygen containing compounds through a number of methods; however, direct introduction of N- and O-functionality remains challenging. Presented herein is a general method to allow for the simultaneous installation of N- and O-functionality to construct unexplored N-O heterocyclic and amino-alcohol scaffolds. This transformation uses earth abundant copper salts to facilitate the formation of a carbon-centered radical and subsequent carbon-nitrogen bond formation. The intermediate aminoxyl radical is terminated by an intramolecularly appended carbon-centered radical. We have exploited this methodology to also access amino-alcohols with a range of aliphatic and aromatic linkers

CFD modeling of a fixed-bed biofilm reactor coupling hydrodynamics and biokinetics

Peer ReviewedPostprint (author's final draft