Real Business Cycle Model Research Articles

Asset Prices in Affine Real Business Cycle Models

We develop a tractable way to solve for equilibrium quantities and asset prices in a class of real business cycle models featuring Epstein-Zin preferences and affine dynamics for productivity growth and volatility. The method relies on log-linearization and exploits the log-normality of all the quantities. It is an easy substitute for more involved numerical techniques, such as higher order perturbation methods, and allows for easy implementation and analytical results. We show explicitly the link with perturbation techniques and find that the quantitative difference between the two is insignificant for several models of interest.

On-the-job search and cyclical unemployment: Crowding out vs. vacancy effects

Incorporating on-the-job search (OTJS) into a real business cycle model has been shown to increase the cyclical volatility of unemployment. Using a particularly simple model of OTJS, we show that the increased search of employed workers during expansions induces firms to open more vacancies, but also crowds out unemployed workers in the job search, resulting in an ambiguous overall effect on unemployment volatility. We show analytically and numerically that the difference between the employer׳s share of the match surplus with an employed versus an unemployed job seeker determines the degree to which OTJS increases unemployment volatility. We use this result to re-consider some related papers of OTJS and explain the amplification of volatility they obtain. Finally, we show that a plausible calibration of the OTJS model allows us to reproduce most significant features of the US labor data.

THE HOURS WORKED–PRODUCTIVITY PUZZLE: IDENTIFICATION IN A FRACTIONAL INTEGRATION SETTING

A recent finding of the SVAR literature is that the response of hours worked to a (positive) technology shock depends on the assumed order of integration of the hours. In this work we relax this assumption, allowing fractional integration in hours and productivity. We find that the sign and magnitude of the estimated responses depend crucially on the identification assumptions employed. Although the responses of hours recovered with short-run (SR) restrictions are positive in all data sets, long-run (LR) identification results in negative, although sometimes not significant responses. We check the validity of these assumptions with the Sims procedure, concluding that both LR and SR are appropriate to recover responses in a fractionally integrated VAR. However, the application of the LR scheme always results in an increase in sampling uncertainty. Results also show that even the negative responses found in the data could still be compatible with real business cycle models.

Information Aggregation in a DSGE Model

We introduce the information microstructure of a canonical noisy rational expectations model (Hellwig, 1980) into the framework of a conventional real business cycle model. Each household receives a private signal about future productivity. In equilibrium, the stock price serves to aggregate and transmit this information. We find that dispersed information about future productivity affects the quantitative properties of our real business cycle model in three dimensions. First, households' ability to learn about the future affects their consumption-savings decision. The equity premium falls and the risk-free interest rate rises when the stock price perfectly reveals innovations to future productivity. Second, when noise trader demand shocks limit the stock market's capacity to aggregate information, households hold heterogeneous expectations in equilibrium. However, for a reasonable size of noise trader demand shocks the model cannot generate the kind of disagreement observed in the data. Third, even moderate heterogeneity in the equilibrium expectations held by households has a sizable effect on the level of all economic aggregates and on the correlations and standard deviations produced by the model. For example, the correlation between consumption and investment growth is 0.29 when households have no information about the future, but 0.41 when information is dispersed.

Intangible capital in a real business cycle model

Recent empirical studies have shown that intangible capital plays an important role in explaining productivity gains that have occurred during the last two decades. By introducing intangible capital in an otherwise standard theoretical real business cycle model, this paper aims to provide a theoretical foundation of the empirical findings. Our results indicate that investment in intangible capital is pro-cyclical. Both transitory as well as permanent productivity shocks increase investment in intangible capital. However, in case of a permanent technology shock we learn that firms allocate more labor and physical capital to the creation of intangible capital which increases future profits at the cost of current profit. We also find that investment in intangible capital plays an important role in producing endogenous movements in productivity.

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Editors’ Introduction

Editors’ Introduction

Wars and capital destruction

In this paper, we propose a theoretical framework to investigate the impact of conflicts and wars on key macroeconomic aggregates and welfare. Using a panel data with 9 countries from 1870 onwards, we first show that the consumption-to-output ratio is minimal during WWII for participants. While this can be explained by an increase in public spending in the USA, this cannot be the case in other countries that participated in WWII, as they experience a large fall in output during wartime. To account for this, we build a variation of a Real Business Cycle model first proposed by Hercowitz and Sampson (1991). We extend the initial model to account for specific shocks that destroy private and public capital stocks – as conflicts do – by assuming an (exogenously) time-varying parameter in the law of capital accumulation. In addition, the model imbeds generalized TFP shocks capturing standard technological factors as well as the potential effects of war on the labor force. The model is estimated and used (i) to assess the importance of capital shocks during war episodes, and (ii) to quantify the welfare effects of conflicts. We show that capital shocks are crucial to account for the macroeconomic dynamics of countries that have experienced large war-related destruction, and that the welfare losses from fluctuations can be quite large when considering data samples that include major war episodes.

Persistence and cycles in US hours worked

This paper analyses monthly hours worked in the US over the sample period 1939m1–2011m10 using a cyclical long memory model. This model, which is based on Gegenbauer processes, is characterised by autocorrelations decaying to zero cyclically and hyperbolically, with a spectral density that is unbounded at a non-zero frequency. One reason for choosing this specification is that the periodogram of the hours worked series has a peak at a frequency away from zero. The empirical results confirm that this model works extremely well for hours worked, and it is then employed to analyse their relationship with productivity. It is found that hours worked increase on impact in response to a technology shock (though the effect dies away rapidly), consistently with Real Business Cycle (RBC) models.

Can Intangible Capital Explain Cyclical Movements in the Labor Wedge?

Intangible capital is an important factor of production in modern economies that is generally neglected in business cycle analyses. We demonstrate that intangible capital can have a substantial impact on business cycle dynamics, especially if the intangible is complementary with production capacity. We focus on customer capital: the capital embodied in the relationships a firm has with its customers. Introducing customer capital into a standard real business cycle model generates a volatile and countercyclical labor wedge, due to a mismeasured marginal product of labor. We also provide new evidence on cyclical variation in selling effort to discipline the exercise.

Wars as Large Depreciation Shocks

In this paper, we propose a theoretical framework to investigate the impact of conflicts and wars on key macroeconomic aggregates and welfare. Using a panel data with 9 countries from 1870 onwards, we first show that the consumption-to-output ratio is minimal during WWII for participants. While this can be explained by an increase in public spending in the USA, this can not be the case in other countries that participated in WWII, as they experience a large fall in output during wartime. To account for this, we build a variation of a Real Business Cycle model first proposed by Hercowitz and Sampson (1991). We extend the initial model to account for specific shocks that destroy private and public capital stocks -- as conflicts do -- by assuming an (exogenously) time-varying depreciation rate of the stock of capital. In addition, the model imbeds generalized TFP shocks capturing standard technological factors as well as the potential effects of war on the labor force. The model is estimated and used (i) to assess the importance of depreciation shocks during war episodes, and (ii) to quantify the welfare effects of conflicts. We show that depreciation shocks are crucial to account for the macroeconomic dynamics of countries that have experienced large war-related destruction, and that the welfare losses from fluctuations can be quite large when considering data samples that include major war episodes.

Divisia Monetary Aggregates, the Great Ratios, and Classical Money Demand Functions

King et al. () evaluate the empirical relevance of a class of real business cycle models with permanent productivity shocks by analyzing the stochastic trend properties of postwar U.S. macroeconomic data. They find a common stochastic trend in a three‐variable system that includes output, consumption, and investment, but the explanatory power of the common trend drops significantly when they add money balances and the nominal interest rate. In this paper, we revisit the cointegration tests in the spirit of King et al., using improved monetary aggregates whose construction has been stimulated by the Barnett critique. We show that previous rejections of the balanced growth hypothesis and classical money demand functions can be attributed to mismeasurement of the monetary aggregates.

News shocks and learning-by-doing

The idea that expectations about future economic fundamentals can drive business cycles dates back to the early 20th century. However, the standard real business cycle (RBC) model fails to generate positive comovement in output, consumption, labor-hours and investment in response to news shocks. This paper proposes a simple and intuitive solution to this puzzling feature of the RBC model, based on a mechanism that has strong empirical support: learning-by-doing (LBD). First, we show that the one-sector RBC model augmented by LBD can generate aggregate comovement in response to news shock about technology. Second, we show that in the two-sector RBC model, LBD along with an intratemporal adjustment cost can generate sectoral comovement in response to news about three types of shocks: i) neutral technology shock, ii) consumption technology shock, and iii) investment technology shock. We show that these results hold for contemporaneous technology shocks and for different specifications of LBD.

Aggregate Stability and Balanced-Budget Rules

It has been shown that under perfect competition and a Cobb-Douglas production function, a basic real business cycle model may exhibit indeterminacy and sunspots fluctuations when income tax rates are determined by a balanced-budget rule. This paper introduces in an otherwise standard real business cycle model a more general and data coherent class of production functions, namely a constant elasticity of substitution production function. We show that the degree of substitutability between production factors is a key ingredient to understand the (de)stabilising properties of a balanced-budget rule. Furthermore, when we calibrate the model consistently with the empirical evidence, i.e. the elasticity of substitutions between labour and capital below unity, balanced-budget rules deliver determinacy for a broad range of OECD countries.

Aggregate Stability and Balanced-Budget Rules

It has been shown that under perfect competition and a Cobb-Douglas production function, a basic real business cycle model may exhibit indeterminacy and sunspot fluctuations when income tax rates are determined by a balanced-budget rule. This paper introduces in an otherwise standard real business cycle model a more general and data coherent class of production functions, namely a constant elasticity of substitution production function. We show that the degree of substitutability between production factors is a key ingredient to understand the (de)stabilising properties of a balanced-budget rule. Then we calibrate the model consistently with the empirical evidence, i.e. we set the elasticity of substitution between labour and capital below unity. We show that compared to the Cobb-Douglas case, the likelihood of indeterminacy under a balanced-budget rule is greatly reduced in the United States, the European Union and the United Kingdom.

Capacity utilization and the effects of energy price increases in Japan

It is well known that the standard real business cycle (RBC) model with energy cannot generate the large drops in value added following the energy price increases in the 1970s, although previous empirical studies have confirmed the important role of energy prices. In this paper, endogenous capacity utilization is incorporated into an otherwise standard RBC model as an amplification mechanism. The simulated results show that the endogenous capacity utilization successfully generates the large contraction in value added observed in the Japanese data. It is also shown that the introduction of capacity utilization produces more realistic dynamics of total factor productivity.

Optimal Control Indicators for the Assessment of the Influence of Approximate Optimal Feedback in the Baseline RBC Model

This paper utilizes the baseline Real Business Cycle (RBC) model in order to construct a time recursive approximate optimal decision rule as a linear function of the model's state variables and an exogenous surprise shock that hits the economy. The constructed rule is subsequently used in order to examine and compare the dynamics of the capital stock and random total factor productivity (TFP). For this purpose, an open-loop control system is analyzed and compared with the closed-loop control system which results from the application of the time recursive approximate optimal decision rule. A set of optimal control indicators is proposed in order to evaluate the effects resulting from the application of this rule on the behavior of the open-loop control system. The results obtained show a significant reduction in the volatility of the capital stock when the constructed approximate optimal decision rule is applied to the open-loop control system.

OccBin: A Toolkit for Solving Dynamic Models with Occasionally Binding Constraints Easily

We describe how to adapt a first-order perturbation approach and apply it in a piecewise fashion to handle occasionally binding constraints in dynamic models. Our examples include a real business cycle model with a constraint on the level of investment and a New Keynesian model subject to the zero lower bound on nominal interest rates. We compare the piecewise linear perturbation solution with a high-quality numerical solution that can be taken to be virtually exact. The piecewise linear perturbation method can adequately capture key properties of the models we consider. A key advantage of this method is its applicability to models with a large number of state variables.

Idiosyncratic Investment Risk and Business Cycles

I show that, due to imperfect risk sharing, aggregate shocks to uncertainty about idiosyncratic return on investment generate economic contractions with elevated risk premia and a decrease in the risk-free rate. I present a tractable real business cycle model in which firms experience idiosyncratic shocks, to which managers are at least partially exposed; the distribution of these shocks is time-varying and stochastic. I show that the path for aggregate quantities, the price of physical capital, and the equity premium are the same as in a model without idiosyncratic risk, but with time-preference shocks. That is, in response to an increase in idiosyncratic uncertainty, the response of these variables is the same as if there were no idiosyncratic uncertainty but managers were suddenly reluctant to invest. However, time-preference and idiosyncratic uncertainty shocks are not isomorphic: an increase in idiosyncratic uncertainty leads to greater demand for precautionary saving and hence a decrease in the risk-free rate; in contrast, an increase in impatience has the opposite effect. In addition, with an idiosyncratic uncertainty shock, investment in physical capital can remain low even after the stock market and firm profitability recover, because managers cannot fully transfer idiosyncratic risk to diversified investors. Thus, shocks to idiosyncratic investment risk can explain, qualitatively, the aftermath of financial panics--elevated risk premia, a sharp and persistent decrease in investment, and a decrease in the risk-free rate. In a calibration, an increase in idiosyncratic investment risk similar to that experienced during the Great Recession leads firms to invest as if their cost of capital were 10 percentage points higher than the cost of capital implied by financial markets, and to a large decrease in the real risk-free rate.

Idiosyncratic investment risk and business cycles

I show that, due to imperfect risk sharing, aggregate shocks to uncertainty about idiosyncratic return on investment generate economic contractions with elevated risk premia and a decrease in the risk-free rate. I present a tractable real business cycle model in which firms experience idiosyncratic shocks, to which managers are at least partially exposed the distribution of these shocks is time-varying and stochastic. I show that the path for aggregate quantities, the price of physical capital, and the equity premium are the same as in a model without idiosyncratic risk, but with time-preference shocks. That is, in response to an increase in idiosyncratic uncertainty, the response of these variables is the same as if there were no idiosyncratic uncertainty but managers were suddenly reluctant to invest. However, time-preference and idiosyncratic uncertainty shocks are not isomorphic: an increase in idiosyncratic uncertainty leads to greater demand for precautionary saving and hence a decrease in the risk-free rate in contrast, an increase in impatience has the opposite effect. In addition, with an idiosyncratic uncertainty shock, investment in physical capital can remain low even after the stock market and firm profitability recover, because managers cannot fully transfer idiosyncratic risk to diversified investors. Thus, shocks to idiosyncratic investment risk can explain, qualitatively, the aftermath of financial panics--elevated risk premia, a sharp and persistent decrease in investment, and a decrease in the risk-free rate. In a calibration, an increase in idiosyncratic investment risk similar to that experienced during the Great Recession leads firms to invest as if their cost of capital were 10 percentage points higher than the cost of capital implied by financial markets, and to a large decrease in the real risk-free rate.