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We explore the long-run relationship between income risk, inequality, and the macroeconomy in an overlapping-generations model in which households face uncertain streams of labor income and returns on their savings. To manage those risks, households can apportion their savings to a bond, whose return is safe and identical across households, and a productive asset, whose return is uncertain and can differ persistently across households. We find that greater polarization in households’ labor income and returns on their savings generally accentuates households’ demand for risk-free assets and the compensation they require for bearing risk, leading to higher measured income and wealth inequality, a lower risk-free real interest rate, and higher risk premiums. These findings suggest that the factors behind the observed rise in inequality over the past few decades might have contributed to the observed fall in the risk-free real interest rate and widening gap between the risk-free real interest rate and the rate of return on capital. We also find that the magnitude of the decline in the risk-free real interest rate and offsetting rise in risk premiums depend importantly on the source of income polarization, with the effects being especially large when greater inequality is caused by increased dispersion in returns on risky assets. Thus, the macroeconomic implications not only depend on the amount of inequality, but also the source of this inequality.

Well known research based on capitalized income tax data shows robust growth in wealth concentration in the late 2000s. We show that these robust growth estimates rely on an assumption---homogeneous rates of return across the wealth distribution---that is not supported by data. When the capitalization model incorporates heterogeneous rates of return (on just interest-bearing assets), wealth concentration estimates in 2011 fall from 40.5% to 33.9%. These estimates are consistent in levels and trend with other micro wealth data and show that wealth concentration increases until the Great Recession, then declines before increasing again.

This paper presents predictability evidence from the difference between implied and expected variances or variance risk premium that: (1) the variance difference measure predicts a significant positive risk premium across equity, bond, and credit markets (2) the predictability is short-run, in that it peaks around one to four months and dies out as the horizon increases and (3) such a short-run predictability is complementary to that of the standard predictor variables--P/E ratio, forward spread, and short rate. These findings are potentially justifiable by a general equilibrium model with recursive preference that incorporates stochastic economic uncertainty. Calibration evidence suggests that such a framework is capable of reproducing the variance premium dynamics, especially its high skewness and kurtosis, without introducing jumps. The calibrated model can also qualitatively explain the equity premium puzzle and the bond risk premia in short horizons.

This paper proposes a method for predicting the probability density of a variable of interest in the presence of model ambiguity. In the first step, each candidate parametric model is estimated minimizing the Kullback-Leibler 'distance' (KLD) from a reference nonparametric density estimate. Given that the KLD represents a measure of uncertainty about the true structure, in the second step, its information content is used to rank and combine the estimated models. The paper shows that the KLD between the nonparametric and the parametric density estimates is asymptotically normally distributed. This result leads to determining the weights in the model combination, using the distribution function of a Normal centered on the average performance of all plausible models. Consequently, the final weight is determined by the ability of a given model to perform better than the average. As such, this combination technique does not require the true structure to belong to the set of competing models and is computationally simple. I apply the proposed method to estimate the density function of daily stock returns under different phases of the business cycle. The results indicate that the double Gamma distribution is superior to the Gaussian distribution in modeling stock returns, and that the combination outperforms each individual candidate model both in- and out-of-sample.

* Treasury inflation-indexed securities (TIIS) have yet to live up to one of their primary goals: reducing the U.S. Treasury's expected financing costs. * Since 1997, yields on TIIS have been surprisingly high relative to yields on comparable nominal Treasury securities, with the spread between yields falling, on average, well below survey measures of long-run inflation expectations. * This study attributes this "valuation puzzle" to several factors: investor difficulty adjusting to a new asset class, divergent supply trends between TIIS and nominal Treasuries, and the lower liquidity of TIIS. In addition, investors may have had a benign outlook for inflation and inflation risks. * More recently, the liquidity and breadth of investor participation in the TIIS market have increased notably, and the valuation of these securities appears to have improved. l. INTRODUCTION In January 1997, the U.S. Treasury began issuing Treasury inflation-indexed securities (TIIS)--debt securities with coupon and principal payments that adjust in line with a measure of consumer prices. Through 2003, the Treasury had issued $172 billion of these securities, with maturity dates ranging from 2002 to 2032. By the end of 2003, the amount of TIIS outstanding (including inflation accrual) totaled approximately $176 billion, or nearly 7 percent of all outstanding Treasury notes and bonds. Inflation-indexed debt held the promise of providing benefits to both investors and the Treasury. Investors could benefit, it was argued, from access to a new type of asset that reduces the risks associated with inflation. By purchasing inflation-indexed securities, they could lock in a real rate of return--measured in terms of the amounts of goods and services that can be purchased--over the maturity of the security, thereby protecting themselves against the possibility that an unexpected rise in inflation would erode the real return on a nominal debt security. (1) Moreover, the Treasury's willingness to issue TIIS could provide a benchmark that would spur private issuance of inflation-indexed securities. The Treasury would also benefit, some argued, because the issuance of inflation-indexed debt would likely reduce its financing costs. The rationale was that investors typically demand a higher return on nominal debt securities to compensate for the risks associated with future inflation. By issuing inflation-indexed debt, the Treasury would eliminate that risk for investors and therefore avoid having to pay this "inflation risk premium," which would also lower its financing costs. (2) In addition, some argued that issuing indexed debt would offer ancillary benefits by providing policymakers and market participants with a useful reading of real interest rates. In that case, comparing the yields on TIIS with those on nominal securities would provide a measure of the amount of compensation that investors demand to offset future inflation and the associated risks--a potentially useful gauge for monetary policymakers. This article describes the U.S. experience with inflation-indexed debt, including the evolution of activity in the TIIS market since its inception and the valuation of those securities relative to nominal Treasury issues. We show that despite the potential appeal of TIIS, their yields have been surprisingly high relative to those on comparable nominal Treasury securities. Indeed, the spread between ten-year yields on nominal securities and TIIS has, on average, fallen about 50 basis points below the long-run inflation expectations reported in the Survey of Professional Forecasters, conducted by the Federal Reserve Bank of Philadelphia. We analyze several explanations for this "valuation puzzle" as well as offer evidence that bears on those explanations. One possibility is that the low relative valuation of TIIS has reflected investor difficulty adjusting to a new asset class. …

To provide insight into the accuracy of U.S. data on international equity transactions, we compare estimates of U.S. holdings of equities in over 40 countries with actual holdings given by comprehensive U.S. benchmark surveys. If the rate of return used to revalue U.S. holdings in a given country is accurate, accurate holdings estimates imply accurate transactions data. For some countries, such as Canada and much of Latin America, the holdings estimates are quite accurate. For the majority of countries, however, there is a great disparity between our estimates and actual amounts, likely because U.S. data on international equity transactions record the country of the transactor, not the country of the issuer. Our estimates are far too high for financial centers--because many U.S. transactions that go through these countries involve securities issued in other countries--and far too low in most other countries, particularly in Europe and Asia. To illustrate the potential pitfalls of using estimated country-specific holdings data, we briefly present two cases in which the use of actual data leads to different conclusions. One case examines the determinants of U.S. equity holdings across countries; the other concerns the turnover rate of foreign equity portfolios.

Three surveys of exchange rate expectations allow us to measure directly the expected rates of return on the yen versus the dollar. Expectations of yen appreciation against the dollar have been (1) consistently large, (2) variable, and (3) greater than the forward premium, implying that investors were willing to accept a lower expected return on dollar assets. At short-term horizons expectations exhibit bandwagon effects, while at longer-term horizons they show the reverse. A l0% yen appreciation generates the expectation of a further appreciation of 2.4% over the following week, for example, but a depreciation of 3.4% over the following year. At any horizon, investors would do better to reduce the absolute magnitude of expected depreciation. The true spot rate process behaves more like a random walk. J. Japan. Int. Econ. , September 1987, 1 (3), pp. 249–274. Department of Economics, University of California, Berkeley, CA 94720; and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02139.