انعطاف ناپذیری اسمی، بر گرداندن دارایی ها، و سیاست های پولی

Asset-return implications of nominal price and wage rigidities are analyzed in general equilibrium. Nominal rigidities, combined with permanent productivity shocks, increase expected excess returns on production claims. This is mainly explained by consumption dynamics driven by rigidity-induced changes in employment and markups. An interest-rate monetary policy rule affects asset returns. Stronger (weaker) rule responses to inflation (output) increase expected excess returns. Policy shocks substantially increase asset-return volatility. Price rigidity heterogeneity produces cross-sectoral differences in expected returns. The model matches important macroeconomic moments and the Sharpe ratio of stock returns, but only captures a small fraction of the observed equity premium

Explaining both asset return and aggregate business cycle fluctuations in a unified framework remains an important challenge in financial economics. Standard real business cycle models imply a counterfactually low compensation for risk in asset returns, partly because production factors can be freely adjusted to reduce consumption risk.2 This has motivated the introduction of real frictions to these models, such as investment adjustment costs and imperfect factor mobility,3 to attenuate the households׳ ability to smooth consumption. In the spirit of the New Keynesian literature, we study a different friction in an equilibrium model, i.e., rigidities in nominal product prices and wages, to address (i) how these rigidities and monetary policy affect the valuation of production claims such as stocks, and (ii) how productivity and monetary policy shocks affect the return dynamics of these claims. Exploring nominal rigidities for the analysis of asset returns is motivated first by ample evidence of their existence in United States data. For instance, Nakamura and Steinsson (2008) report a median duration of prices between 8 and 11 months, and Barattieri et al. (2014) suggest an average wage duration between 3 and 4 quarters.4 Second, models with nominal rigidities, such as Christiano et al. (2005) and Smets and Wouters (2007), have become the workhorse model for macroeconomic and policy analysis in central banks. These models capture important business cycle dynamics and are widely used to understand how monetary policy affects the real economy. It is then of significant importance to examine the link between monetary policy and asset returns implied by these models.5 The main findings in the paper are as follows. First, nominal rigidities, in combination with persistent shocks to productivity growth, improve the model׳s ability to generate positive and sizable expected excess returns in production claims. Second, the quantitative impact of wage rigidities on the equity premium is significantly larger than the impact of price rigidities. Third, monetary policy shocks have a large contribution to asset return volatility, but a minor effect on expected excess returns. Fourth, monetary policy rules with a greater weight on interest rate smoothing, a greater responsiveness to inflation, or a lower responsiveness to output lead to larger expected excess returns. Fifth, differences in price rigidities translate into differences in expected returns across production sectors. These differences are determined by product elasticities of substitution within and across sectors. Finally, the model calibration implies an annualized equity premium of only one percent, and a minor effect of monetary policy rules on asset returns. As in many other equilibrium models, it reflects the significant difficulty to amplify macroeconomic risk and generate enough asset return volatility. Our production economy model has four main ingredients. First, a representative household with Epstein and Zin (1989) recursive preferences over consumption and labor. Recursive preferences disentangle the elasticity of intertemporal substitution of consumption (EIS) from risk aversion. As illustrated by Tallarini (2000), this separation is useful to keep reasonable values for the elasticity of substitution to match macroeconomic dynamics, while having values for risk aversion that match empirical Sharpe ratios of financial assets. Second, nominal rigidities are modeled in a staggered wage and price setting following Calvo (1983). The representative household provides differentiated labor types to the production sector and has monopolistic power to set wages. However, at each point of time the household can only adjust wages optimally for a fraction of labor types. Similarly, firms provide differentiated products and have monopolistic power to set their prices. At each point of time, a firm can only adjust the price optimally with some positive probability. Third, monetary policy is modeled as a Taylor (1993) policy rule to set the level of a nominal interest rate. The rule responds to current economic conditions and is affected by policy shocks. Fourth, the model incorporates permanent and transitory shocks to productivity. This shock specification is motivated by Campbell (1994), who shows that permanent and transitory shocks have different effects on optimal consumption and asset returns, and by the Alvarez and Jermann (2005) empirical evidence of a significant permanent component in the pricing kernel. The model is calibrated to match relevant properties of quarterly U.S. data for the 1982–2008 period. Price and wage rigidity parameters are chosen to match the average duration of prices and wages in the data. Parameters describing shocks, preferences, and the monetary policy rule are calibrated to match consumption, inflation, and interest rate volatility. Risk aversion is set to match the Sharpe ratio implied by equity returns. The calibration implies an EIS of around 0.15, and a coefficient of relative risk aversion of around 1616. In the calibration, permanent productivity shocks contribute more than 96% to the risk premia in output and profit claims. This occurs despite the fact that the volatilities of the three model shocks are of comparable order of magnitude. To understand why, the pricing kernel is decomposed into short- and long-run components. Permanent productivity shocks have persistent effects that drive both components in the same direction, generating a large price for this risk. On the contrary, transitory productivity and monetary policy shocks have mean-reverting effects that drive the short- and long-run components in opposite directions, reducing their prices of risk. In the absence of nominal rigidities, permanent productivity shocks imply a negative equity premium if the EIS is lower than one, echoing the results in Bansal and Yaron (2004) and Kaltenbrunner and Lochstoer (2010). After a negative permanent shock, output decreases. A substitution effect reduces the demand for future output claims and, hence, lowers the price of these claims. A wealth effect raises the relative price of future consumption and, hence, the price of output claims. The wealth effect dominates if the EIS is less than one, and output claims have a negative expected excess return over the risk-free rate. In the presence of nominal rigidities, permanent productivity shocks generate a positive equity premium if the EIS is lower than one. Output dynamics are affected by the rigidities through their effects on employment and production markups. After a negative permanent shock, wages remain higher than optimal due to wage rigidities, and prices do not adjust enough to compensate for higher labor costs due to price rigidities. Employment decreases, amplifying the negative effect of the shock on output. Over time, real wages adjust towards their optimal levels, translating into higher expected future output growth. A substitution effect leads to a higher demand for claims on future output and, hence, a higher price for these claims. A wealth effect reduces the relative price of future output and lowers the price of output claims. The wealth effect dominates if the EIS is lower than one, and returns on output claims become procyclical and embed a positive risk premium. Procyclical product markups induced by the rigidities further amplify the volatility of dividend claims relative to output claims, increasing the equity premium. Monetary policy is not neutral under nominal rigidities. The model calibration implies that a 50-basis-point increase in the annualized nominal interest rate leads to a 62-basis-point decrease in equity returns, implying a positive equity premium. This premium is affected by the monetary policy rule. Rules with a higher responsiveness to inflation, lower responsiveness to output, or greater weight on interest-rate smoothing amplify the effects of permanent productivity shocks and increase expected excess returns. These results are explained by the effects of the rule on the real interest rate. However, monetary policy shocks have a small price of risk, only contribute with 1.5% of the total equity premium, and changes in risk premia from variations in the monetary policy rule parameters are quantitatively small. A model extension to incorporate two production sectors allows us to explore the asset return implications of different price rigidities across sectors. Differences in the returns of claims on sectoral profits are driven by the difference in product prices (relative price) induced by the heterogeneous price rigidities. A high relative price for one sector leads to two opposite effects: lower profits due to lower output demand, and higher profits due to a higher production markup. The elasticity of substitution of products across sectors determines the difference in sectoral output demands. The elasticity of substitution of products within each sector determines the difference in sectoral markups. Depending on the difference between the two elasticities, the sector with higher price rigidities could earn higher or lower expected returns than the sector with lower price rigidities. The contribution of the paper can be evaluated in three different dimensions. First, it shows that employment dynamics can play an important role in shaping risk premia. This channel can complement the investment channel already explored in the literature. Second, it links nominal rigidities to asset returns. This link can be important to understand the transmission channels of monetary policy. Third, it studies the effects of multiple shocks on asset prices in a calibrated framework. Asset returns can reflect compensations for shocks different than productivity shocks, that are important for macroeconomic dynamics. Quantitatively, nominal rigidities and permanent productivity shocks increase the equity premium relative to comparable real business cycle models. However, the model only generates one seventh of the observed equity premium, and the effects of monetary policy on asset returns are small. Despite this limitation, the model provides a reference point for asset-pricing New Keynesian models. Other elements such as additional frictions or shocks can be added to improve its quantitative performance. This paper joins the literature that links the real economy to asset prices in a unified framework,6 such as Kaltenbrunner and Lochstoer (2010), Croce (2014), and Gourio (2012). It is mostly related to Boldrin et al. (2001) and Christiano et al. (2005). Boldrin et al. (2001) show that adding frictions in intersectoral factor mobility and habit formation in preferences to the standard business cycle model of Kydland and Prescott (1982) reproduces important business cycle and equity return properties, simultaneously. However, habit formation also leads to a counterfactually high volatility in the risk-free rate. Our model instead relies on Epstein and Zin (1989) recursive preferences and permanent productivity shocks to achieve both a high price of risk and low volatility in the risk-free rate. As in the standard New Keynesian framework, described in Woodford (2003) and explored by Christiano et al. (2005), frictions in the model result from nominal price and wage rigidities. While Christiano et al. (2005) focus on their business cycle implications, this paper analyzes the effects of these frictions on asset prices. The paper also is related to empirical studies on the response of the stock market to monetary policy shocks, such as Thorbecke (1997), Rigobon and Sack (2004), and Bernanke and Kuttner (2005), among others. Consistent with these studies, our model reproduces the positive (negative) response in the stock market value to expansionary (contractionary) policy shocks. However, this response in the model calibration is only one quarter of the one found empirically. Recent efforts to understand the effects of labor and its frictions on asset returns are related to this paper. Lettau and Uhlig (2000) find that labor negatively affects the performance of habit models to capture the equity premium. This performance can be improved by adding real wage rigidities as shown by Uhlig (2007). In the same spirit, Favilukis and Lin (2013) analyze different asset return quantitative implications of infrequent renegotiation of real wages. This paper explores nominal instead of real wage rigidities, and time-varying instead of fixed employment, to understand their effects on asset returns. A particular channel linking monetary policy to asset returns, i.e., monetary policy interest rate rules through nominal rigidities, is studied in this paper. Other channels have been explored theoretically or found empirically. For instance, Bhamra et al. (2011) provide an alternative channel for monetary policy to affect the real economy based on nominal rigidities in debt obligations. Lucca and Moench (2013) find robust evidence of a significant stock return during the 24-hour period before the FOMC meeting. This evidence suggests a puzzling strong link between asset returns and monetary policy difficult to study in equilibrium models. The paper is organized as follows. 2 and 3 present the model, its calibration and main implications. 4 and 5 explain the mechanisms linking asset returns to nominal rigidities and monetary policy rules, respectively. Section 6 summarizes some cross-sectional implications and Section 7 concludes.

The nominal rigidities explored in this paper have interesting qualitative and quantitative implications for asset returns. Qualitatively, nominal price and wage rigidities, in combination with permanent productivity shocks, generate procyclical mean-reverting variation in labor demand that increases the riskiness of output and profit claims. In addition, price rigidities, when combined with wage rigidities, generate procyclical production markups that increase the riskiness of profit claims relative to output claims. In the presence of rigidities, real asset returns become sensitive to the response to economic conditions in an interest rate policy rule, and policy shocks become a priced risk factor that affect asset return volatility. Differences in price rigidities translate into differences in expected returns across production sectors. Quantitatively, wage rigidities have larger effects on expected asset returns than price rigidities, mainly as a compensation for permanent productivity shocks. However, the equity premium is only a small fraction of its empirical counterpart and has a minor sensitivity to the specification of the interest rate policy rule. How should we interpret the limited quantitative performance of the model? On one hand, it highlights a significant shortcoming of the traditional New Keynesian framework to capture asset pricing dynamics. It raises doubts on whether nominal rigidities can be an important driver of asset returns and an important channel of transmission of monetary policy through asset prices. On the other hand, the model results can be taken as a reference point for future model developments and empirical analysis. The model can be extended in at least four dimensions. First, the model abstracts from capital accumulation and, therefore, ignores any potential effects of nominal rigidities on investment behavior. The joint study of investment dynamics, nominal rigidities, and asset prices merits further exploration. Second, the model does not incorporate shocks that are becoming standard in New Keynesian models such as price and wage markup shocks or investment specific technological shocks. These shocks are important in these models to reproduce some observed macroeconomic dynamics, and can become significant risk factors in asset returns. Third, we assume homogeneous wage rigidities within and across sectors. Heterogeneity in wage rigidities and imperfect labor mobility can be an additional source of differences in the cross section of asset returns. Fourth, we assume that financial markets are complete and frictionless. The effects of monetary policy and nominal rigidities on asset returns can be amplified by financial frictions such as the financial accelerator in Bernanke et al. (1999), or under limited financial market participation as in Galí et al. (2004). The model delivers predictions for the link between nominal rigidities and expected asset returns that can be tested empirically. All else equal, economies with higher wage or price rigidities should have higher expected excess returns on production claims than economies with lower wage or price rigidities. Different labor laws or different market power regulations around the world translate into differences in wage and price frictions, that can be a source of variation across international equity returns. Different pricing policies across firms and production sectors can be reflected in heterogeneity in their expected stock returns. This study is already being undertaken by Gorodnichenko and Weber (2013) with positive results. Finally, the model prediction that interest rate monetary policy rules with more weight on inflation relative to output stabilization imply higher expected stock returns can be tested in the data.