The bull and bear market model of Huang and Day: Some extensions and new results

We develop a financial market model with interacting chartists and fundamentalists that embeds the famous bull and bear market model of Huang and Day as a special case. Their model is given by a one-dimensional continuous piecewise-linear map. Our model, on the other hand, is more flexible and is represented by a one-dimensional discontinuous piecewise-linear map. Nevertheless, we are able to provide a more or less complete analytical treatment of the model dynamics by characterizing its possible outcomes in parameter space. In addition, we show that quite different scenarios can trigger real-world phenomena such as bull and bear market dynamics and excess volatility.     

Instability in the cobweb model under the BNN dynamic

The cobweb model where firms choose between rational and naive forecasting strategies has a 2-cycle when the slope of supply is greater than the slope of demand for a number of different dynamics describing the evolution of strategy choices. This paper proves that the 2-cycle is exponentially unstable under the learning dynamic of Brown et al. (1950). Issues arising in the analysis of piecewise smooth discrete time maps are discussed.     

Jumps in equilibrium prices and market microstructure noise

Asset prices observed in financial markets combine equilibrium prices and market microstructure noise. In this paper, we study how to tell apart large shifts in equilibrium prices from noise using high frequency data. We propose a new nonparametric test which allows us to asymptotically remove the noise from observable price data and to discover jumps in fundamental asset values. We provide its asymptotic distribution to decide when such jumps occur. In finite samples, our test offers reasonable power for distinguishing between noise and jumps. Empirical evidence indicates that it is necessary to incorporate the presence of jumps in equilibrium prices.     

Estimating willingness to pay for medicare using a dynamic life-cycle model of demand for health insurance

Medicare is the largest health insurance program in the US. This paper uses a dynamic random utility model of demand for health insurance in a life-cycle human capital framework with endogenous production of health to calculate the individual willingness to pay (WTP) for Medicare. The model accounts for the feature that the demand for health insurance is derived through the demand for health, which is jointly determined with the production of health over the life-cycle. The WTP measure incorporates the effects of Medicare insurance on aggregate consumption through effects on medical expenditures and mortality, and consumption utility of health. The model is estimated using panel data from the Health and Retirement Study. The average WTP or change in lifetime expected utility resulting from delaying the age of eligibility to 67 is found to be $ 24,947 in 1991 dollars ($ 39,435 in 2008 dollars). However, there is considerable variation in the WTP, e.g., in 1991 dollars the WTP of individuals who have less than a high school education and are white is $ 28,347 ($ 44,810 in 2008 dollars), while the WTP of those with at least a college degree and who are neither white nor black is $ 15,584 ($ 24,635 in 2008 dollars). More generally, the less educated have a higher WTP to avoid a policy change that delays availability of Medicare benefits. Additional model simulations imply that the primary benefits of Medicare are insurance against medical expenditures with relatively smaller benefits in terms of improved health status and longevity. Medicare also leads to large increases in medical utilization due to deferring of medical care prior to eligibility.     

Policy change and learning in the RBC model

What is the impact of surprise and anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations? We examine this issue using the standard stochastic real business cycle model with lump-sum taxes. Agents combine knowledge about future policy with econometric forecasts of future wages and interest rates. Dynamics under learning can have large impact effects and a gradual hump-shaped response, and tend to be prominently characterized by oscillations not present under rational expectations. These fluctuations reflect periods of excessive optimism or pessimism, followed by subsequent corrections.     

Semiparametric inference in a GARCH-in-mean model

A new semiparametric estimator for an empirical asset pricing model with general nonparametric risk-return tradeoff and GARCH-type underlying volatility is introduced. Based on the profile likelihood approach, it does not rely on any initial parametric estimator of the conditional mean function, and it is under stated conditions consistent, asymptotically normal, and efficient, i.e., it achieves the semiparametric lower bound. A sampling experiment provides finite sample comparisons with the parametric approach and the iterative semiparametric approach with parametric initial estimate of Conrad and Mammen (2008). An application to daily stock market returns suggests that the risk-return relation is indeed nonlinear.     

Dispersed initial ownership and the efficiency of the stock market under moral hazard

We generalize a standard general equilibrium framework extended for moral hazard to allow for a dispersed initial ownership distribution of firms. We show that the market allocation is constrained-efficient only when in each firm the entrepreneur who generates payoffs through unobservable effort has full initial ownership in his firm.     

On the Ramsey equilibrium with heterogeneous consumers and endogenous labor supply

In this paper, we address the stability issue, stressing the role of labor supply, in a Ramsey model with heterogeneous households subject to borrowing constraints. Making labor supply endogenous leads us to prove the existence of two kinds of steady state: the one where everybody supplies labor, the other where only the most patient agent refrains from working. Going beyond models with inelastic labor supply, we show how preferences of impatient agents affect the saddle-path stability of each type of steady state and the occurrence of endogenous cycles. When their elasticity of intertemporal substitution in consumption exceeds one, instability and cycles are less likely, requiring lower degrees of capital-labor substitution. Conversely, elasticity values below one promote the emergence of fluctuations. We end the paper by showing the existence of the intertemporal equilibrium under market incompleteness, using a local approach based on the first-order conditions.     

Strategy switching in the Japanese stock market

This paper investigates the expectation formation process of Japanese stock market professionals. By utilizing a monthly forecast survey dataset on the TOPIX distributed by QUICK Corporation, we sort forecasters into buy-side and sell-side professionals. We empirically demonstrate that the buy-side and sell-side professionals use either fundamental or trend-following strategies throughout their expectation formation processes and that they switch between fundamental and trend-following strategies over time. We also discuss that strategy switching can be key in understanding the persistent deviation of the TOPIX from the fundamentals.     

The VIX,the variance premium and stock market volatility

We decompose the squared VIX index, derived from US S&P500 options prices, into the conditional variance of stock returns and the equity variance premium. We evaluate a plethora of state-of-the-art volatility forecasting models to produce an accurate measure of the conditional variance. We then examine the predictive power of the VIX and its two components for stock market returns, economic activity and financial instability. The variance premium predicts stock returns while the conditional stock market variance predicts economic activity and has a relatively higher predictive power for financial instability than does the variance premium.     

On bootstrapping the mode in the nonparametric regression model with random design

In the nonparametric regression model with random design and based on i.i.d. pairs of observations (X _i, Y _i), where the regression function m is given by m(x)=?(Y _i|X _i=x), estimation of the location θ (mode) of a unique maximum of m by the location of a maximum of the Nadaraya-Watson kernel estimator for the curve m is considered. In order to obtain asymptotic confidence intervals for θ, the suitably normalized distribution of is bootstrapped in two ways: we present a paired bootstrap (PB) where resampling is done from the empirical distribution of the pairs of observations and a smoothed paired bootstrap (SPB) where the bootstrap variables are generated from a smooth bivariate density based on the pairs of observations. While the PB requires only relatively small computational effort when carried out in practice, it is shown to work only in the case of vanishing asymptotic bias, i.e. of “undersmoothing” when compared to optimal smoothing for mode estimation. On the other hand, the SPB, although causing more intricate computations, is able to capture the correct amount of bias if the pilot estimator for m oversmoothes. Received: May 2000     

On the uniqueness of local equilibria

The purpose of this paper is to define a new notion of local equilibrium in an exchange economy, where the consumers face lower bounds on net trades. Then, we show that the local equilibrium is unique if the lower bounds are closed enough to 0. By the way, we also provide a convergence result of local equilibrium price toward Walras equilibrium price of a suitable tangent linear economy.     

Econometric analysis of jump-driven stochastic volatility models

This paper introduces and studies the econometric properties of a general new class of models, which I refer to as jump-driven stochastic volatility models, in which the volatility is a moving average of past jumps. I focus attention on two particular semiparametric classes of jump-driven stochastic volatility models. In the first, the price has a continuous component with time-varying volatility and time-homogeneous jumps. The second jump-driven stochastic volatility model analyzed here has only jumps in the price, which have time-varying size. In the empirical application I model the memory of the stochastic variance with a CARMA(2,1) kernel and set the jumps in the variance to be proportional to the squared price jumps. The estimation, which is based on matching moments of certain realized power variation statistics calculated from high-frequency foreign exchange data, shows that the jump-driven stochastic volatility model containing continuous component in the price performs best. It outperforms a standard two-factor affine jump–diffusion model, but also the pure-jump jump-driven stochastic volatility model for the particular jump specification.     

Quasi-experimental evidence on the effect of aircraft noise on apartment rents

Inferring the implicit price of an environmental good hinges on ceteris paribus conditions that are often hard to justify. This paper uses an unexpected change in flight regulations as source of exogenous variation and identifies aircraft noise effects from price adjustments in the market for rental apartments. Controlling for spatial and apartment heterogeneity, we find that aircraft noise reduces apartment rents by about 0.5% per decibel. Our results indicate (i) that noise discounts are overestimated in cross-sectional studies because aircraft noise tends to be negatively correlated with omitted neighborhood and housing amenities and (ii) that noise effects are unlikely to be constant over the entire noise range.     

Options and efficiency in spaces of bounded claims

In a seminal contribution, Ross (1976) showed that a static finite state-space market can be completed by supplementing the primitive securities with ordinary call and put options. Galvani (2009) extends this result to norm separable _Lp$L_p$-spaces, with 1≤p<∞$1\le p<\infty$. This study concludes that options maintain the same spanning power in the space of bounded payoffs topologized by the duality with the space of the state price densities. In particular, under mild assumptions on the probability space, options written on a claim that is a.s. equal to an injective function complete the market.