The Slow Adjustment of Aggregate Consumption to Permanent Income

This paper investigates the relationship between aggregate consumption and permanent income using a new approach to the estimation of cointegrated systems that builds on Stock and Watson's common stochastic trends representation. The permanent and transitory movements in aggregate income and consumption are estimated directly using the Kalman filter and are allowed to be correlated. This approach avoids any implicit restriction that permanent income be as smooth as consumption. Instead, permanent income appears to be relatively volatile, with consumption adjusting toward it only slowly over time. These results provide a clear rejection of the standard version of the permanent income hypothesis and are suggestive of alternative theories of consumption behavior such as habit formation or precautionary savings.     

Where is the GE? Consumption Dynamics in DSGEs

We offer a partial equilibrium perspective on the behavior of consumption in dynamic stochastic general equilibrium (DSGE) models. We consider a benchmark dynamic general equilibrium model and show that a standard calibration implies that the real interest rate is essentially fixed. One manifestation of this feature is that, with separable preferences, the reaction of consumption to total factor productivity (TFP) shocks is flat: the random‐walk permanent income hypothesis holds almost exactly, pretty much as in a partial equilibrium consumption‐savings problem. These results help explain the prominent role of aggregate demand, and how it is achieved, in modern DSGE analysis.     

The independence axiom and asset returns

This paper integrates models of atemporal risk preference that relax the independence axiom into a recursive intertemporal asset-pricing framework. The resulting models are amenable to empirical analysis using market data and standard Euler equation methods. We are thereby able to provide the first nonlaboratory-based evidence regarding the usefulness of several new theories of risk preference for addressing standard problems in dynamic economics. Using both stock and bond returns data, we find that a model incorporating risk preferences that exhibit first-order risk aversion accounts for significantly more of the mean and autocorrelation properties of the data than models that exhibit only second-order risk aversion. Unlike the latter class of models which require parameter estimates that are outside of the admissible parameter space, e.g., negative rates of time preference, the model with first-order risk aversion generates point estimates that are economically meaningful. We also examine the relationship between first-order risk aversion and models that employ exogenous stochastic switching processes for consumption growth.     

The volatility of consumption-based stochastic discount factors and economic cycles

This paper aims to assess the macroeconomic and financial impact of economic uncertainty using information contained in the second moments of financial risk factors employed in the asset pricing literature. Specifically, we propose the volatility of consumption-based stochastic discount factors (SDFs) as a predictor of future economic and stock market cycles. We employ both contemporaneous and ultimate consumption risk specifications with durable and non-durable consumption. Alternative empirical tests show that this volatility has significant forecasting ability from 1985 to 2006. The degree of predictability tends to dominate that shown by standard predictor variables. We argue that the significant predictability of the volatility of consumption-based SDFs reported in this paper relies mainly on the joint effect of their components.     

Business Cycle Implications of Internal Consumption Habit for New Keynesian Models

We study the implications of internal consumption habit for New Keynesian dynamic stochastic general equilibrium (NKDSGE) models. Bayesian Monte Carlo methods are employed to evaluate NKDSGE model fit. Simulation experiments show that internal consumption habit often improves the ability of NKDSGE models to match the spectra of output and consumption growth. Nonetheless, the fit of NKDSGE models with internal consumption habit is susceptible to the sources of nominal rigidity, to spectra identified by permanent productivity shocks, to the choice of monetary policy rule, and to the frequencies used for evaluation. These vulnerabilities indicate that the specification of NKDSGE models is fragile.     

The time-varying asymmetry of exchange rate returns: A stochastic volatility – stochastic skewness model

While the time-varying volatility of financial returns has been extensively modelled, most existing stochastic volatility models either assume a constant degree of return shock asymmetry or impose symmetric model innovations. However, accounting for time-varying asymmetry as a measure of crash risk is important for both investors and policy makers. This paper extends a standard stochastic volatility model to allow for time-varying skewness of the return innovations. We estimate the model by extensions of traditional Markov Chain Monte Carlo (MCMC) methods for stochastic volatility models. When applying this model to the returns of four major exchange rates, skewness is found to vary substantially over time. In addition, stochastic skewness can help to improve forecasts of risk measures. Finally, the results support a potential link between carry trading and crash risk.     

Statistical properties of demand fluctuation in the financial market

Numerical integration methods for stochastic volatility models in financial markets are discussed. We concentrate on two classes of stochastic volatility models where the volatility is either directly given by a mean-reverting CEV process or as a transformed Ornstein–Uhlenbeck process. For the latter, we introduce a new model based on a simple hyperbolic transformation. Various numerical methods for integrating mean-reverting CEV processes are analysed and compared with respect to positivity preservation and efficiency. Moreover, we develop a simple and robust integration scheme for the two-dimensional system using the strong convergence behaviour as an indicator for the approximation quality. This method, which we refer to as the IJK (137) scheme, is applicable to all types of stochastic volatility models and can be employed as a drop-in replacement for the standard log-Euler procedure.     

Notes on Multiperiod Valuation and the Pricing of Options

A mean-variance risk-return tradeoff relationship is derived for the diffusion process limiting case of a state-preference model, with aggregate consumption serving as a pivotal variable. The model is compared to other recent models along the dimensions of generality and tractable implementation. The incorporation of stochastic interest rates in general equilibrium and arbitrage-based valuation models is examined, and an extension to earlier methods is discussed, in connection with the implementation of “robust” general valuation procedures.     

Is sustainable growth optimal?

This paper analyzes sustainable growth in a stochastic environment, with human extinction as a possible outcome. The basic constraint of sustainability is that consumption never decreases over an infinite horizon, which requires that the probability of extinction be maintained at zero. We show that this problem can be examined in a standard optimal-growth model. Under certain conditions, the solution of this problem is a corner solution with probability of survival equal to one, at the cost of economic growth. These conditions depend on the initial development level and on the elasticity of utility with respect to consumption. In some circumstances, which depend on the social discount rate, optimal-growth paths do not exist. In these situations, the sustainable-growth concept has a clear autonomy with respect to the usual optimality criterion.     

Lifetime asset allocation with idiosyncratic and systematic mortality risks

This paper considers a lifetime asset allocation problem with both idiosyncratic and systematic mortality risks. The novelty of the paper is to integrate stochastic mortality, stochastic interest rate and stochastic income into a unified framework. An investor, who is a wage earner receiving a stochastic income, can invest in a financial market, consume part of his wealth and purchase life insurance or annuity so as to maximize the expected utility from consumption, terminal wealth and bequest. The problem is solved via the dynamic programming principle and the Hamilton–Jacobi–Bellman equation. Analytical solutions to the problem are derived, and numerical examples are provided to illustrate our results. It is shown that idiosyncratic mortality risk has significant impacts on the investor’s investment, consumption, life insurance/annuity purchase and bequest decisions regardless of the length of the decision-making horizon. The systematic mortality risk is largely alleviated by trading the longevity bond. However, its impacts on consumption, purchase of life insurance/annuity and bequest as well as the value function are still pronounced, when the decision-making horizon is sufficiently long.     

Gold rush fever in business cycles

A flexible price model of the business cycle is proposed, in which fluctuations are driven primarily by inefficient movements in investment around a stochastic trend. A boom in the model arises when investors rush to exploit new market opportunities even though the resulting investments simply crowd out the value of previous investments. A metaphor for such profit driven fluctuations are gold rushes, as they are periods of economic boom associated with expenditures aimed at securing claims near new found veins of gold. An attractive feature of the model is its capacity to provide a simple structural interpretation to the properties of a standard consumption and output Vector Autoregression.     

Examining the bond premium puzzle with a DSGE model

The basic inability of standard theoretical models to generate a sufficiently large and variable nominal bond risk premium has been termed the “bond premium puzzle.” We show that the term premium on long-term bonds in the canonical dynamic stochastic general equilibrium (DSGE) model used in macroeconomics is far too small and stable relative to the data. We find that introducing long-memory habits in consumption as well as labor market frictions can help fit the term premium, but only by seriously distorting the DSGE model's ability to fit other macroeconomic variables, such as the real wage; therefore, the bond premium puzzle remains.     

Equity Returns and Business Cycles in Small Open Economies

This is the first paper in the dynamic stochastic general equilibrium literature to match key business cycle moments and long‐run equity returns in a small open economy with production. These results are achieved by introducing four modifications to a standard real business cycle model: (i) borrowing and lending costs are imposed to increase the volatility of the marginal rate of substitution over time, (ii) capital adjustment costs are assumed to make equity returns more volatile, (iii) GHH preferences are employed to smooth consumption, and (iv) a working capital constraint to generate countercyclical trade balances. Our results are based on data from Argentina, Brazil, and Chile.     

An Induced Theory of Financial Ratios

In recent years, a considerable volume of research has emerged on the analytical, empirical and statistical properties of financial ratios. In the present paper the methods of continuous time stochastic calculus are applied to the modelling of financial ratios. Two standard stochastic processes are examined and applied, namely the geometric Brownian motion and the elastic random walk. The properties of aggregate or ‘industry ratios’ and the reasonableness or otherwise of the ‘proportionality assumption’ are also examined. Typically, the approach of this paper implies that accounting ratios will be non-linear functions of time and normality will be the exception rather than the rule.     

Alleviating Transitory Food Crises in Sub-Saharan Africa: International Altruism and Trade

The donor community has responded to unexpected or transitorydrops in domestic food production in many countries in Sub-SaharanAfrica. An empirical framework estimates and analyzes the correlationbetween this food aid and domestic production. Both emergencyfood aid and commercial imports are used to offset the effectsof negative output shocks in Sub-Saharan African countries—themajor recipients of global emergency food aid. On average everyone-ton drop in cereal production is offset by the deliveryof 0.8 tons of cereal and dairy products from abroad (over fouryears). Most food aid arrives within a year of a shock, andcorrelation of shocks over time along with the differences betweencrop years and calendar years may explain the link between aidand production. The economic and political considerations alsodetermine the global response to the emergency food needs ofcountries in Africa. The international response is not contingenton the form of government or the level of political and humanrights violations. Poorer countries and those with well-establishednon-emergency food aid programs receive larger amounts of emergencyaid when needed.     

The Meta Taylor Rule

We characterize U.S. monetary policy within a generalized Taylor rule framework that accommodates uncertainties about the duration of policy regimes and the specification of the rule, in addition to the standard parameter and stochastic uncertainties inherent in traditional Taylor rule analysis. Our approach involves estimation and inference based on Taylor rules obtained through standard linear regression methods, but combined using Bayesian model averaging techniques. Employing data that were available in real time, the estimated version of the “meta” Taylor rule provides a flexible but compelling characterization of monetary policy in the United States over the last 40 years.     

The Macroeconomic Effects of Nonzero Trend Inflation

We study the macroeconomic effects of nonzero trend inflation in a simple dynamic stochastic general equilibrium model under three common time-dependent pricing schemes: Calvo, truncated-Calvo, and Taylor. We show that, regardless of the pricing mechanism, trend inflation leads to a reduction in the stochastic means of output, consumption and employment, and an increase in the stochastic mean of inflation beyond its deterministic steady-state level. The variability of most aggregates also increases. These effects are quantitatively much stronger with Calvo pricing.     

Intertemporal Commodity Futures Hedging and the Production Decision

This paper deals with the producer's optimal use of commodity futures in hedging. The framework for analysis is an intertemporal consumption and investment model. The producer makes his production decisions at the beginning of the period and realizes his return at the end of the time interval. During the period, he faces both price and output uncertainties. In applying stochastic dynamic programming methods, this paper shows the effect of these risks on his consumption behavior. Further, the paper investigates his optimal hedging positions in the futures market over time and his optimal production decisions. Finally, implications of these results on the futures markets are discussed.     

Portfolio optimisation with jumps: Illustration with a pension accumulation scheme

In this paper, we address portfolio optimisation when stock prices follow general Lévy processes in the context of a pension accumulation scheme. The optimal portfolio weights are obtained in quasi-closed form and the optimal consumption in closed form. To solve the optimisation problem, we show how to switch back and forth between the stochastic differential and standard exponentials of the Lévy processes. We apply this procedure to both the Variance Gamma process and a Lévy process whose arrival rate of jumps exponentially decreases with size. We show through a numerical example that when jumps, and therefore asymmetry and leptokurtosis, are suitably taken into account, then the optimal portfolio share of the risky asset is around half that obtained in the Gaussian framework.