Quantifying the uncertainty about the fit of a new Keynesian pricing model

Recent studies by Gali and Gertler [1999. Inflation dynamics: a structural econometric analysis, Journal of Monetary Economics 44, 195-222] and Sbordone [2002. Prices and unit labor costs: testing models of pricing, Journal of Monetary Economics 49, 265-292] conclude that a theoretical inflation series implied by a forward-looking New Keynesian pricing equation fits post-1960 U.S. inflation closely. Their theoretical inflation series is conditional on (i) a reduced-form forecasting process for real marginal cost; and (ii) the calibration of the pricing equation. The present paper shows that both of these determinants are surrounded by considerable uncertainty. When quantifying the impact of this uncertainty on theoretical inflation, we can no longer say whether the forward-looking pricing equation explains observed inflation dynamics very well or very poorly.     

Measuring Financial Integration via Idiosyncratic Risk: What Effects Are We Really Picking Up?

We study the method proposed by Flood and Rose (FR, 2004, 2005) for checking for financial integration by estimating the risk-free rate using the idiosyncratic component of individual stock returns. Performing simulations with data with a known return generation process, we find that the FR methodology produces poor estimates of the risk-free rate, and hence the FR method fails to accept integration when true. We then show analytically that the FR method actually provides an estimate of the market return, and conclude the FR methodology would also falsely accept integration as long as the market returns in the two markets do not differ widely.     

Incomplete markets, labor supply and capital accumulation

Endogenous labor supply decisions are introduced in an equilibrium model of limited insurance against idiosyncratic shocks. Unlike in the standard case with exogenous labor (e.g. [Aiyagari, S.R., 1994. Uninsured idiosyncratic risk and aggregate saving. Quarterly Journal of Economics 109, 659-684; Huggett, M., 1997. The one-sector growth model with idiosyncratic shocks: steady states and dynamics. Journal of Monetary Economics 39, 385-403]), labor supply is likely to be lower than under complete markets. This is due to an ex post wealth effect on labor supply (rich productive agents work fewer hours) that runs counter the precautionary savings motive. As a result, equilibrium savings and output may be lower under incomplete markets. It is also found that long-run savings remain finite even when the interest rate equals the inverse of the discount factor.     

Equity market integration in the Asia Pacific region: Evidence from discount factors

The paper investigates stock market integration among 10 economies in the Asia Pacific region over the period April to May 2006 based on a recently developed technique that relies on estimating expected discount rates; see [Flood and Rose, 2005a] and [Flood and Rose, 2005b]. The results show a limited but varying degree of stock market integration among the 10 economies. Membership in a formal economic organization does not seem to affect the degree of integration.     

An open-economy new Keynesian Phillips curve for the U.K.

We estimate a pricing equation or “new Keynesian Phillips curve” (NKPC) obtained from a structural dynamic model of price setting based on Rotemberg [1982. Sticky prices in the United States. Journal of Political Economy 90(6), 1187-1211] and extended to capture employment adjustment costs and the openness of the United Kingdom. This model nests the baseline Galí and Gertler [1999. Inflation dynamics: a structural econometric analysis. Quarterly Journal of Economics 110, 127-159) and Sbordone [2002. Prices and unit labor costs: a new test of price stickiness. Journal of Monetary Economics 49, 265-292] relationship between inflation and marginal cost in the limiting case of no employment adjustment costs, no impact of relative prices of imported inputs on real marginal cost and a constant equilibrium markup. Our findings indicate that each of our modifications to the baseline NKPC model is important for U.K. data, so that inflation in the U.K. is explained both by changes in employment and by changes in real import prices, in general, and real oil prices, in particular. External competitive pressures also seem to affect U.K. inflation via their impact on the equilibrium price markup of domestic firms.     

Estimating the expected marginal rate of substitution: A systematic exploitation of idiosyncratic risk

We develop a methodology to estimate the shadow risk free rate or expected intertemporal marginal rate of substitution, “EMRS”. Our technique relies upon exploiting idiosyncratic risk, since theory dictates that idiosyncratic shocks earn the EMRS. We apply our methodology to recent monthly and daily data sets for the New York and Toronto Stock Exchanges. We estimate EMRS with precision and considerable time-series volatility, subject to an identification assumption. Both markets seem to be internally integrated; different assets traded on a given market share the same EMRS. We reject integration between the stock markets, and between stock and money markets.     

Idiosyncratic risk and expected returns in frontier markets: Evidence from GCC

We investigate the pricing of idiosyncratic volatility of seven frontier markets in six GCC countries. We find a significant (marginal) negative relationship between expected returns and lagged idiosyncratic volatility for individual stocks in Saudi Arabia (Qatar) but none in Kuwait and Abu Dhabi. However, when we estimate conditional idiosyncratic volatility either by EGARCH or AR Models, the relationship turns positive. Introducing unexpected idiosyncratic volatility as an explanatory variable to control for any unexpected returns uncovers the true relationship between expected idiosyncratic volatility and expected returns. The evidence turns out to be robust for return reversals and other control variables. Moreover, the pricing of idiosyncratic risk is less evident in higher country governance and seems to be unrelated to the degree of financial development.     

Evaluation of linear asset pricing models by implied portfolio performance

We present a theoretical perspective that motivates the use of the Generalized Least Squares R-Square, prominently advocated by Lewellen et al. [Lewellen, J., Nagel, S., Shanken, J., forthcoming. A skeptical appraisal of asset-pricing tests. Journal of Financial Economics], as an evaluation measure for multivariate linear asset pricing models. Adapting results from Shanken [Shanken, J., 1985. Multivariate tests of the zero-beta CAPM. Journal of Financial Economics 14, 327–348] and Kandel and Stambaugh [Kandel, S., Stambaugh, R.F., 1995. Portfolio inefficiency and the cross-section of expected returns. Journal of Finance 50, 157–184], we provide various interpretations and a graphical account in mean-variance space of this measure, facilitating a better understanding of its properties. We furthermore relate it to another leading evaluation metric, the HJ-distance of Hansen and Jagannathan [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 557–590]. Additionally, we present a comparison between these evaluation measures using mean-variance mathematics in risk-return space, and we provide a simple formula for calculating both model evaluation measures that involves only the parameters of the mean-variance asset and factor frontiers.     

Comparing New Keynesian models of the business cycle: A Bayesian approach

The baseline New Keynesian model cannot replicate the observed persistence in inflation, output, and real wages for sensible parameter values. As a result, several extensions have been suggested to improve its fit to the data. We use a Bayesian approach to estimate and compare the baseline sticky price model of Calvo's [1983. Staggered prices in a utility maximizing framework. Journal of Monetary Economics 12, 383-398.] and three extensions. Our empirical results are as follows. First, we find that adding price indexation improves the fit of Calvo's [1983. Staggered prices in a utility maximizing framework. Journal of Monetary Economics 12, 383-398.] model. Second, models with both staggered price and wage setting dominate models with only price rigidities. Third, introducing wage indexation does not significantly improve the fit. Fourth, all model estimates suggest a high degree of price stickiness. Fifth, the estimates of labor supply elasticity are higher in models with both staggered price and wage contracts. Finally, the estimated inflation parameters of the Taylor rule are stable across models.     

Rejoinder to Paul Krugman

We provide a brief rejoinder to Krugman [2008, Response to Nelson and Schwartz. Journal of Monetary Economics 55, this issue] on three issues that are central to his original New York Review of Books article and his reply to our setting the record straight: (i) criticisms of Friedman; (ii) criticisms of monetarism; and (iii) interpretations of history.     

Idiosyncratic risk and the cross-section of stock returns: Merton (1987) meets Miller (1977)

Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predicts that idiosyncratic risk should be priced when investors hold sub-optimally diversified portfolios, and cross-sectional stock returns should be positively related to their idiosyncratic risk. However, the literature generally finds a negative relationship between returns and idiosyncratic risk, which is more consistent with Miller's [1977. Risk, uncertainty, and divergence of opinion. Journal of Finance 32, 1151–1168] analysis of asset pricing under short-sale constraints. We examine the cross-sectional effects of idiosyncratic risk while explicitly recognizing the confounding effects that dispersion of beliefs and short-sale constraints produce in the Merton framework. We find strong support for Merton's [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] model among stocks that have low levels of investor recognition and for which short selling is limited. For these stocks, the relation between idiosyncratic risk and expected returns is positive, as predicted by Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510].     

Do long swings in the business cycle lead to strong persistence in output?

This paper investigates how the occasional long swing in the business cycle can produce long-memory behavior in US output. To prove this theoretical relationship, we extend the Hamilton Markov chain regime switching model of real aggregate output to include the occasional long regime. We do this by modeling the duration length of the expansion and recession regimes as draws from a fat-tailed distribution with realized durations that are high in variability and occasionally extreme in value. Empirically, we find that the tail indices for the length of US economic booms and busts correspond with the long-memory parameter estimates of Diebold and Rudebusch [1989. Long memory and persistence in aggregate output. Journal of Monetary Economics 24, 189-209] and Sowell [1992a. Modeling long-run behavior with the fractional ARIMA model. Journal of Monetary Economics 29, 277-302] for real US output. Estimates of our extended regime switching model produce better short- and long-run forecasts of output in comparison to forecasts with a fractionally integrated model. Furthermore, our estimated regime-switching model finds US expansions to be fragile during their infancy, but become more and more likely to continue after surviving the first seven quarters.     

Asset-pricing Puzzles and Incomplete Markets

The representative agent theory of asset pricing is modified to incorporate heterogeneous agents and incomplete markets. The model features two types of agents who differ up to a nontradable, idiosyncratic component in their endowment processes. Numerical solutions indicate that individuals are able to diversify a substantial portion of their idiosyncratic income risk through riskless borrowing and lending alone. Restrictions on the variability of intertemporal marginal rates of substitution ( Hansen and Jagannathan (1991) ) are used to argue that incomplete markets, as modeled here, cannot account for the properties of asset returns that are anomalous from the perspective of representative agent theory.     

Earnings quality at initial public offerings

We show that, contrary to popular belief, initial public offering (IPO) firms report more conservatively. We attribute this to the higher quality reporting demanded of public firms by financial statement users and consequentially higher monitoring by auditors, boards, analysts, rating agencies, press, and litigants, and to greater regulatory scrutiny [Ball, R., Shivakumar, L., 2005. Earnings quality in UK private firms: comparative loss recognition timeliness. Journal of Accounting and Economics 39, 83–128]. We also question the evidence of Teoh et al. [1998b. Earnings management and the subsequent market performance of initial public offerings. Journal of Finance 53, 1935–1974] supporting the alternative hypothesis that managers opportunistically inflate earnings to influence IPO pricing. We conjecture that upward-biased estimates of “discretionary” accruals occur in a broad genre of studies on earnings management around similar large transactions and events.     

Measuring skewness premia

We provide a new methodology to empirically investigate the respective roles of systematic and idiosyncratic skewness in explaining expected stock returns. Using a large number of predictors, we forecast the cross-sectional ranks of systematic and idiosyncratic skewness, which are easier to predict than their actual values. Compared to other measures of ex ante systematic skewness, our forecasts create a significant spread in ex post systematic skewness. A predicted systematic skewness risk factor carries a significant and robust risk premium that ranges from 6% to 12% per year. In contrast, the role of idiosyncratic skewness in pricing stocks is less robust.     

The cross section of cashflow volatility and expected stock returns

I show that historical cashflow volatility is negatively related to future returns cross-sectionally. The negative association is large; economically meaningful; long-lasting up to five years; robust to known return-informative effects of size, value, price and earnings momentums and illiquidity; and extends to both systematic and idiosyncratic cashflow volatilities. Using the standard deviations of cashflow to sales and of cashflow to book equity as proxies for cashflow volatility, the least volatile decile portfolio outperforms the most volatile decile portfolio by 13% a year relative to the Fama–French four factors. The cashflow volatility effect is closely related to the idiosyncratic return volatility effect documented in Ang et al. [Ang, A., Hodrick, R.J., Xing, Y. and Zhang, X. “The cross-section of volatility and expected returns.” Journal of Finance, 51 (2006), 259–299.]. However, in portfolios simultaneously sorted on both cashflow and return volatilities, and in cross sectional regressions of returns at the firm level, these two effects neither drive out nor dominate each other. While the pricing of idiosyncratic cashflow volatility represents an anomaly against the traditional asset pricing theories, the pricing of historical cashflow uncertainty sheds light on potential fundamental risks embodied in the Fama–French HML and SMB factors.     

Robustness of the estimates of the hybrid New Keynesian Phillips curve

Galí and Gertler [1999. Inflation dynamics: a structural econometric approach. Journal of Monetary Eonomics 44(2), 195-222] developed a hybrid variant of the New Keynesian Phillips curve that relates inflation to real marginal cost, expected future inflation and lagged inflation. GMM estimates of the model suggest that forward-looking behavior is dominant: the coefficient on expected future inflation substantially exceeds the coefficient on lagged inflation. While the latter differs significantly from zero, it is quantitatively modest. Several authors have suggested that our results are the product of specification bias or suspect estimation methods. Here we show that these claims are incorrect, and that our results are robust to a variety of estimation procedures, including GMM estimation of the closed form, and nonlinear instrumental variables. Also, as we discuss, many others have obtained very similar results to ours using a systems approach, including FIML techniques. Hence, the conclusions of GG and others regarding the importance of forward-looking behavior remain robust.     

Industry‐Specific Human Capital,Idiosyncratic Risk,and the Cross‐Section of Expected Stock Returns

Human capital is one of the largest assets in the economy and in theory may play an important role for asset pricing. Human capital is heterogeneous across investors. One source of heterogeneity is industry affiliation. I show that the cross‐section of expected stock returns is primarily affected by industry‐level rather than aggregate labor income risk. Furthermore, when human capital is excluded from the asset pricing model, the resulting idiosyncratic risk may appear to be priced. I find that the premium for idiosyncratic risk documented by several empirical studies depends on the covariance between stock and human capital returns.     

Idiosyncratic risk and the cross-section of expected stock returns

Theories such as Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predict a positive relation between idiosyncratic risk and expected return when investors do not diversify their portfolio. Ang, Hodrick, Xing, and Zhang [2006. The cross-section of volatility and expected returns. Journal of Finance 61, 259–299], however, find that monthly stock returns are negatively related to the one-month lagged idiosyncratic volatilities. I show that idiosyncratic volatilities are time-varying and thus, their findings should not be used to imply the relation between idiosyncratic risk and expected return. Using the exponential GARCH models to estimate expected idiosyncratic volatilities, I find a significantly positive relation between the estimated conditional idiosyncratic volatilities and expected returns. Further evidence suggests that Ang et al.'s findings are largely explained by the return reversal of a subset of small stocks with high idiosyncratic volatilities.     

Testing heterogeneous-agent models: an alternative aggregation approach

Starting from the cross-sectional aggregation of marginal utilities, rather than intertemporal marginal rates of substitution, this paper develops a new heterogeneous-agent pricing kernel. A closed-form version of the new kernel depends on changes in the cross-sectional variance of log consumption, rather than the variance of changes in log consumption, as in Constantinides and Duffie [1996. Asset pricing with heterogeneous consumers. Journal of Political Economy 104, 219-237]. We implement the new kernel on household consumption data from the Consumer Expenditure Survey (CEX). At monthly and quarterly horizons, the new kernel reconciles the premium on U.S. equities with the consumption of asset holders, for reasonable values of relative risk aversion. The new kernel also fares better than kernels based on the aggregation of intertemporal marginal rates of substitution in explaining the cross-sectional variation of risk premia on stocks and bonds. Portfolios mimicking changes in the cross-sectional variance of log consumption for asset holders command significant negative Sharpe ratios.