Note on nominal rigidities and news-driven business cycles

A news-driven business cycle is a positive comovement of consumption, output, labor, and investment from the news about the future. We show that nominal rigidities, especially sticky prices, can cause it in an estimated medium-scale DSGE economy.


Introduction
A news-driven business cycle (hereafter, NDBC) is a positive comovement of consumption, labor, investment, and output from a news shock about future productivity. It is well known that the standard real business cycle model cannot generate it. Since the paper by Beaudry and Portier (2004), many models of NDBCs are proposed. 1 In this paper, we focus on nominal rigidities as sources of NDBCs. We employ the model of Fujiwara, Hirose, and Shintani (2008), which is an estimated medium-scale DSGE economyà la Smets and Wouters (2007) with news shocks. It is shown that NDBCs are generated because of nominal rigidities, especially sticky prices. The news shock causes a boom through the countercyclical movements of price markup. We also find that sticky wages are not sources of NDBCs in our model. This paper is also closely related to the one by Kobayashi and Nutahara (2008).
They show that sticky prices and wages can be sources of NDBCs using a simple model theoretically. However, it is not clear that nominal rigidities work in realistic models with estimated parameter values. Medium-scale DSGE models are widely used for policy analysis and parameter values of our model are estimated. Therefore, we show that sticky prices are important sources of NDBCs in an widely used model with estimated parameter values, but sticky wages are not.
The rest of this paper is organized as follows. Section 2 introduces our model. In Section 3, it is shown that nominal rigidities, especially sticky prices, are sources of NDBCs. Section 4 draws our conclusions.

Baseline model
Our model is the same employed by Fujiwara, Hirose, and Shintani (2008), which is based on a medium-scale DSGE model of Smets and Wouters (2007) with news shocks.
The resource constraint is where ε g t is the government expenditure shock. The consumption Euler equation is where λ denotes the parameter on the external habit; γ, the steady-state growth rate; and σ c , the inverse of the intertemporal elasticity of substitution.
The investment Euler equation is where ε i t denotes the investment-specific technology shock; β, the discount factor of household; and ϕ, the steady-state elasticity of the capital adjustment cost function.

The capital Euler equation is
where q t denotes Tobin's Q and δ denotes the depreciation rate of capital.
The production function is The utilization rate, u t , is determined by where ψ denotes a positive function of the elasticity of the capital utilization adjustment cost function and normalized to be between zero and one.
The evolution of capital stock, k t , is The price markup, µ p t , is The Phillips curve with partial indexation is where ι p denotes the degree of indexation to past inflation; ξ p , the degree of price stickiness; ε p , the curvature of the Kimball goods market aggregator; and ε p t , the price markup shock.
The rental rate of capital is The wage markup, µ w t , is where σ ℓ denotes the elasticity of labor supply with respect to the real wage.
The wage Phillips curve with partial indexation is where ι w denotes the degree of wage indexation; ξ w , the degree of the wage stickiness; ε w , the curvature of the Kimball labor market aggregator; and ε w t denotes the wage markup shock.
The monetary policy is where ε r t denotes monetary policy shock. The evolutions of shocks are AR(1): Technology shock η a t is consist of unanticipated and anticipated components: where ν i,t−i denotes a news shock observed at period t − i.

Flexible price-wage economy
We also consider the role of news shocks in the flexible price-wage economy. In this economy, price and wage markups are constant: µ p t = µ w t = 0 and two Phillips curves (10) and (13) are removed from the baseline model.

Main result 3.1 Responses to news shocks
Following Christiano, Ilut, Motto, and Rostagno (2008), we consider the following impulse. Up until period t = 0, the economy is at the steady state. At period t = 0, a news shock hits the economy: ν 4,0 = .01. However, at period t = 4, the expected rise in productivity does not occur: ν 0,4 + ν 4,0 = 0. This is interpreted as the news turning out to be false.
We employ parameter values estimated by Fujiwara, Hirose, and Shintani (2008) for the Japanese economy. They estimate parameters using the Bayesian technique.  [Insert Figure 1] Positive comovements of consumption, labor, investment, and output occur t = 0, 1, 2, and 3, but these variables drop t = 4 since the news turns out to be false. Therefore, NDBCs are generated in the baseline model. However, in the flexible price-wage economy, NDBCs are not generated since consumption moves countercyclically.
In order to understand the mechanism, consider our model without capital utilization.
By (9) and (12), we obtain This equation implies that the positive comovements of consumption and labor inputs is possible if the markups, µ p t + µ w t , decrease sufficiently. High labor implies increase of output, and the news increases investment since the adjustment costs encourage current investment to prepare for the future. In our model, capital utilization is variable, but its response to the news shock is small and NDBCs are generated through the movements of  [Insert Figure 2 ] In the sticky-wage economy, consumption moves countercyclically while NDBCs are generated in the sticky-price economy. Kobayashi and Nutahara (2008) show that the sticky wages can be a source of NDBCs theoretically since it affects labor wedge: the ratio of the marginal rate of substitution between consumption and leisure to the marginal product of labor. However, our results tell that sticky wages are not sources of NDBCs in an estimated medium-scale DSGE economy.

Conclusion
In this paper, we focused on nominal rigidities as sources of NDBCs. Our model is a medium-scale DSGE economyà la Smets and Wouters (2007) with news shocks on productivity. Using the estimated parameter values of Fujiwara, Hirose, and Shintani (2008), we showed that, in this economy, NDBCs are generated since there are nominal rigidities, especially the sticky prices. Our results implies that nominal price rigidity not only generate persistent responses to unexpected current shocks, but also drive booms and recessions in response to the news shock.