**Income Insurance And The Equilibrium Term-Structure Of Equity**

__Roberto Marfe__

Collegio Carlo Alberto

June 8, 2016

*Journal of Finance, Forthcoming*

**Abstract: **

Output, wages and dividends feature term-structures of variance-ratios respectively flat, increasing and decreasing. Income insurance from shareholders to workers empirically and theoretically explains these term-structures. Risk sharing smooths wages but only concerns transitory risk and, hence, enhances the short-run dividend risk. A simple general equilibrium model, where labor rigidity affects dividend dynamics and the price of short-run risk, reconciles standard asset pricing facts with the term-structures of equity premium and volatility and those of macroeconomic variables, at odds in leading models. Consistently, actual labor-share variation largely forecasts dividend strips risk, premium and slope.

### Income Insurance And The Equilibrium Term-Structure Of Equity – Introduction

Leading asset pricing models describe many characteristics of financial markets but fail to explain the timing of equity risk. These models have different rationale (e.g. habit formation, time-varying expected growth, disasters, prospect theory) but share an important feature: priced risk comes from variation in long-run discounted cashflows.1 Instead, van Binsbergen, Brandt, and Koijen (2012), van Binsbergen, Hueskes, Koijen, and Vrugt (2013) and van Binsbergen and Koijen (2016) document that the term-structures of equity volatility and premia are downward sloping {that is markets compensate short-run risk. Moreover, standard models usually base on assumptions concerning dividend dynamics which imply an upwardsloping term-structure of dividend risk (i.e. volatilities or variance-ratios of dividends’ growth rates which increase with the horizon). Instead, consistently with Belo, Collin-Dufresne, and Goldstein (2015), this paper documents that dividend risk is strongly downward-sloping, such that many models overestimate long-horizon dividend risk by an order of magnitude.

Why is dividend risk downward-sloping? Under which conditions, does downward-sloping dividend risk transmit to equity risk and premia? What macroeconomic channel explains short-term equity returns? This paper empirically and theoretically addresses these questions by providing a macroeconomic foundation of the timing of risk and by reconciling, in equilibrium, standard asset pricing facts with the new evidence about the term-structures. This is important because the term-structures of both fundamentals and equity provide information about how prices are determined in equilibrium. Hence, a term-structure perspective offers additional testable implications to asset pricing frameworks and can help us to understand the macroeconomic determinants of asset prices.

The paper argues that labor rigidity is at the heart of the timing of macroeconomic risk. Danthine and Donaldson (1992, 2002), among others, show that a mechanism of income insurance from shareholders to workers, which takes place within the firm, leads to volatile and pro-cyclical dividends. Hence, this mechanism explains why equity commands a high compensation. 2 Beyond such a cyclicality effect of income insurance, I show that also a term-structure effect takes place. Since output, wages and dividends are co-integrated (Lettau and Ludvigson, 2005), income insurance implies that the transitory component of aggregate risk is shared asymmetrically among workers and shareholders, whereas the permanent component is faced by both. Namely, wages are partially insured with respect to transitory risk, whereas dividends load more on transitory risk as a result of operating leverage. Thus, wage and dividend risks shift respectively toward the long and the short horizon and workers and shareholders bear respectively more long-run risk and more short-run risk. I embed this mechanism of income insurance in an otherwise standard closed-form general equilibrium model and show that, under standard preferences, the term-structure effect of income insurance is inherited by financial markets and leads to downward sloping term-structures of equity risk and premia. Consistently, actual labor-share variation largely predicts short-term equity risk, premium and slope.

An empirical investigation supports the main model mechanism. First, I document that the timing of risk of macroeconomic variables is heterogeneous. The term-structures of risk of output, wages and dividends are respectively at, increasing and decreasing. In accord with the model, these term-structures {and the co-integrating relationship among the levels of these variables{ support the idea that both workers and shareholders are subject to permanent shocks but they share transitory shocks asymmetrically, as a result of income insurance. Consistently, Gamber (1988) and Menzio (2005) show that implicit contracts and labor market search frictions lead to wage rigidity over transitory risk only; Guiso, Pistaferri, and Schivardi (2005) and Ellul, Pagano, and Schivardi (2014) provide evidence that insurance does not concern permanent shocks; and Ros-Rull and Santaeulalia-Llopis (2010) document that the wage-share is stationary and counter-cyclical.

Second, I further support the term-structure effect of income insurance by investigating the model prediction that the variance ratios of dividends and the gap between the variance ratios of wages and dividends should be respectively decreasing and increasing with the laborshare. The model predicts that, after a negative transitory shock, wages are partially insured whereas dividends are hit more. This implies that, on the one hand, wages are high relative to dividends (the cyclicality effect) and that wages load less than dividends on transitory risk (the term-structure effect). Therefore, the distance between the upward-sloping variance ratios of wages and the downward-sloping variance ratios of dividends should increase when the labor-share is high. The opposite holds after a positive transitory shock. I provide robust empirical evidence that such a dynamic relation obtains in the actual data.

Third, in accord with the model, I document an extremely strong connection between laborshare variation and short-term equity returns. The correlations between the labor-share and one-year ahead dividend strips volatility (risk), excess return over the risk-free rate (premium) and excess return over the market return (slope) are respectively 86%, 57% and 52%.

Moreover, I show that the remainder of output minus wages features a term-structure of risk which is markedly downward-sloping and essentially recovers the negative slope of dividend risk. This implies that the bulk of the gap between the approximatively at varianceratios of output and the decreasing variance-ratios of dividends should be imputed to labor. Consistently, I document that the transitory component of dividends that should not be imputed to income insurance does not help to explain either the negative slope of dividend risk or dividend strip returns. Finally, the term-structure effect of income insurance implies that the labor-share positively forecasts dividend and consumption growth, which I show to be a robust feature of actual data.

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