This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987. Copyright 1991 by The Econometric Society.

Conditional heteroskedasticity in asset returns: a new approach

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility. THE TRADEOFF BETWEEN RISK and return has long been an important topic in asset valuation research. Most of this research has examined the tradeoff between risk and return among different securities within a given time period. The intertemporal relation between risk and return has been examined by several authors-Fama and Schwert (1977), French, Schwert, and Stambaugh (1987), Harvey (1989), Campbell and Hentschel (1992), Nelson (1991), and Chan, Karolyi, and Stulz (1992), to name a few. This paper extends that research.

https://faculty.washington.edu/ezivot/econ589/GJRJOF1993.pdf

On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks

This paper discusses the discounted utility (DU) model: its historical development, underlying assumptions, and "anomalies" - the empirical regularities that are inconsistent with its theoretical predictions. We then summarize the alternate theoretical formulations that have been advanced to address these anomalies. We also review three decades of empirical research on intertemporal choice, and discuss reasons for the spectacular variation in implicit discount rates across studies. Throughout the paper, we stress the importance of distinguishing time preference, per se, from many other considerations that also influence intertemporal choices.

/pdf/time-discounting-and-time-preference-a-critical-review-47don96ek5.pdf

Time Discounting and Time Preference: A Critical Review

We develop a new index of economic policy uncertainty (EPU) based on newspaper coverage frequency Several types of evidence – including human readings of 12,000 newspaper articles – indicate that our index proxies for movements in policy-related economic uncertainty Our US index spikes near tight presidential elections, Gulf Wars I and II, the 9/11 attacks, the failure of Lehman Brothers, the 2011 debt-ceiling dispute and other major battles over fiscal policy Using firm-level data, we find that policy uncertainty raises stock price volatility and reduces investment and employment in policy-sensitive sectors like defense, healthcare, and infrastructure construction At the macro level, policy uncertainty innovations foreshadow declines in investment, output, and employment in the United States and, in a panel VAR setting, for 12 major economies Extending our US index back to 1900, EPU rose dramatically in the 1930s (from late 1931) and has drifted upwards since the 1960s

/pdf/measuring-economic-policy-uncertainty-4nrg3ei76f.pdf

Measuring Economic Policy Uncertainty

(This article originally appeared in Management Science, April 1997, Volume 43, Number 4, pp. 546-558, published by The Institute of Management Sciences.)

Consider a series of companies in a supply chain, each of whom orders from its immediate upstream member. In this setting, inbound orders from a downstream member serve as a valuable informational input to upstream production and inventory decisions. This paper claims that the information transferred in the form of "orders" tends to be distorted and can misguide upstream members in their inventory and production decisions. In particular, the variance of orders may be larger than that of sales, and distortion tends to increase as one moves upstream-a phenomenon termed "bullwhip effect." This paper analyzes four sources of the bullwhip effect: demand signal processing, rationing game, order batching, and price variations. Actions that can be taken to mitigate the detrimental impact of this distortion are also discussed.

Information distortion in a supply chain: the bullwhip effect

This paper introduces a utility function that nests three classes of utility functions: (1) time-separable utility functions; (2) "catching up with the Joneses" utility functions that depend on the consumer's level of consumption relative to the lagged cross-sectional average level of consumption; and (3) utility functions that display habit formation. Closed-form solutions for equilibrium asset prices are derived under the assumption that consumption growth is i.i.d. The equity premia under catching up with the Joneses and under habit formation are, for some parameter values, as large as the historically observed equity premium in the United States.

Asset Prices Under Habit Formation and Catching Up with the Joneses

This paper introduces a utility function that nests three classes of utility functions: (1) time-separable utility functions; (2) "catching up with the Joneses" utility functions that depend on the consumer's level of consumption relative to the lagged cross-sectional average level of consumption; and (3) utility functions that display habit formation. Closed-form solutions for equilibrium asset prices are derived under the assumption that consumption growth is i.i.d. The equity premia under catching up with the Joneses and under habit formation are, for some parameter values, as large as the historically observed equity premium in the United States

/pdf/asset-prices-under-habit-formation-and-catching-up-with-the-252x802iwg.pdf

Asset Prices under Habit Formation and Catching Up with the Joneses

This paper examines the effect of output price uncertainty on the investment decision of a risk-neutral competitive firm which faces convex costs of adjustment.' This issue has been analyzed by Richard Hartman (1972) and by Robert Pindyck (1982), but they reached dramatically different results. Hartman showed that with a linearly homogeneous production function, increased output price uncertainty leads the competitive firm to increase its investment. However, Pindyck found increased output price uncertainty leads to increased investment only if the marginal adjustment cost function is convex; but, if the marginal adjustment cost function is concave, then increased uncertainty will reduce the rate of investment. Pindyck argues that his results differ from Hartman's results because of a different stochastic specification of the price of output. In Hartman's discrete-time model, price is random in each period including the current period, whereas in Pindyck's continuous-time model, the current price is known but the future evolution of prices is stochastic. In this paper, I demonstrate that Hartman's results continue to hold using Pindyck's stochastic specification and that Pindyck's analysis applies to a socalled "target" rate of investment, which in general is not optimal. The model developed herein, which is a special case of Pindyck's model, is used because it can be solved explicitly, unlike Pindyck's more general model. Since Pindyck did not derive an expression for the optimal rate of investment, he used a phase diagram to determine the target capital stock. This target capital stock is determined by the intersection of a locus for which the rate of change of the capital stock is zero, and a locus for which the expected change in the rate of investment is zero. A problem with this stochastic phase diagram approach is that in general there is no reason for the firm to be on the locus with zero expected change in investment, even in the long run. Indeed, in the particular model in this paper, optimal behavior is such that the expected proportional rate of change of investment is (in general, a nonzero) constant over time.

/pdf/optimal-investment-under-uncertainty-8ffqt20x3l.pdf

Optimal Investment under Uncertainty.

This paper extends the theory of investment under uncertainty to incorporate fixed costs of investment, a wedge between the purchase price and sale price of capital, and potential irreversibility of investment. In this extended framework, investment is a non-decreasing function of q, the shadow price of installed capital. There are potentially three investment regimes, which depend on the value of q relative to two critical values. For values of q above the upper critical value, investment is positive and is an increasing function of q, as is standard in the theory branch of the adjustment cost literature. For intermediate values of q, between two critical values, investment is zero. Although this regime features prominently in the irreversibility literature, it is largely ignored in the adjustment cost literature. Finally, if q is below the lower critical value, gross investment is negative, a possibility that is ruled out by assumption in the irreversibility of literature. In general, however, the shadow price q is not directly observable, so we present two examples relating q to observable varieties.

A Unified Model of Investment Under Uncertainty

/pdf/a-unified-model-of-investment-under-uncertainty-vp8dobcv7e.pdf

Andrew B. Abel

Papers

Asset Prices Under Habit Formation and Catching Up with the Joneses

Asset Prices under Habit Formation and Catching Up with the Joneses

Optimal Investment under Uncertainty.

A Unified Model of Investment Under Uncertainty

A Unified Model of Investment Under Uncertainty