Reexamination of real business cycles in a small open economy.

• Author: Guo, Jang-Ting

1. Introduction

   Since the influential work of Mendoza (1991), it is now well known that dynamic stochastic general equilibrium models, specifically the real business cycle approach, can successfully explain some important stylized facts of a small open economy with incomplete asset markets in which domestic households only have access to a one-period risk-free foreign bond. In particular, Mendoza's model correctly predicts that the correlation between savings and investment rates is positive and that the balance of trade moves counter-cyclically with output over the business cycle. As pointed out by Correia, Neves, and Rebelo (1995), the ability of this class of models to mimic key international indicators of a small open economy depends crucially on adopting the period utility function, postulated by Greenwood, Hercowitz, and Huffman (GHH) (1988), whereby there is no income effect associated with the household's labor supply decision and the representative household's intertemporal elasticity of substitution in hours worked (or leisure) is zero.

   On the other hand, studies in this line of business cycle research have produced a set of clearly identified anomalies. One of the most robust puzzles, caused by the GHH preferences combined with a Cobb-Douglas production technology, is the perfectly positive correlation between detrended gross domestic product (GDP) and labor hours. Motivated by this counterfactual inconsistency, Schmitt-Grohe and Uribe's (2003, section 8.1) sensitivity analysis shows that a dynamic small open economy model that allows for a wealth effect in labor supply does not perform as well as that under the GHH utility formulation; the model-generated time series of consumption is too smooth compared to the observed variability, and the trade balance becomes procyclical.

   Moreover, this type of small open real business cycle model, similar to the corresponding closed-economy version, exhibits a weak internal propagation mechanism. Using the productivity-disturbance process that Letendre (2004) estimates from the Canadian post 1981 quarterly data, we find that in Mendoza's model with capital adjustment costs, output is less volatile than that observed in the actual economy, and the coefficients of serial correlation in GDP, investment, and work effort are all statistically lower than their empirical counterparts. (1) In addition, this benchmark specification exaggerates the negative correlations between GDP and the ratios of trade balance and current account to output.

   To address the above-mentioned anomalies, this paper incorporates intertemporally non-separable labor supply (or leisure) and variable capital utilization into Mendoza's one-sector, dynamic small open economy model with adjustment costs of net investment. Furthermore, in order to highlight the cyclical effects of these two additional features, technology shocks are postulated to be the only driving process for generating macroeconomic fluctuations. Most studies in the existing literature employ the GHH preferences that are separable over time, which in turn contributes to the perfectly positive correlation between output and employment. To overcome this counterfactual result, as in Kydland and Prescott (1982) and Lettau and Uhlig (2000) for closed-economy real business cycle models, we consider a time non-separable utility function that exhibits non-zero elasticities of substitution in hours worked across different periods. In addition, based on the empirical findings of Eichenbaum, Hansen, and Singleton (1988); Hotz, Kydland, and Sedlacek (1988); and Wen (1998), the formulation with either intertemporal substitutability (i.e., the fatigue effects) or complementarity (i.e., internal habit formation) of work effort is examined in our analyses. (2)

   We also follow Letendre (2004) and strengthen the model's endogenous propagation mechanism by allowing for variable capital utilization. Specifically, a more intensive utilization of capital is assumed to accelerate its rate of depreciation. In a symmetric equilibrium, the social technology displays a larger elasticity of output with respect to both the technology shock and labor inputs than the original Mendoza economy. As a result, varying capital utilization amplifies the business-cycle effects of productivity disturbances since it provides an additional margin to change output. It follows that, as in dosed-economy real business cycle models (see Burnside, Eichenbaum, and Rebelo [1993] and Burnside and Eichenbaum [1996], among others), smoother technology shocks are needed to match the observed volatility of GDP.

   We obtain simulated second moments and impulse response functions from six versions of our model economy and then compare them with the Hodrick-Prescott (H-P) filtered, post-1981 Canadian quarterly data documented by Letendre (2004). The first three models exhibit time-invariant capital utilization and depreciation rates. As discussed earlier, our benchmark specification (Model 1) corresponds to Mendoza's one-sector, dynamic small open economy model subject to the productivity-disturbance process estimated by Letendre (2004). When the household's current and previous choices of hours worked are included in its period utility function either as substitutes (Model 1a) or as complements (Model 1b), we show that both models perform no worse than the baseline configuration in terms of matching the contemporaneous correlations with GDP; whereas, the model's predictions of the serial correlations in key macroeconomic aggregates are significantly improved because of the presence of labor persistence. Moreover, allowing for intertemporal substitutability raises the elasticity of labor supply with respect to changes in its marginal productivity, which in turn leads to more variable hours worked as well as more volatile GDP compared to those in Model 1. However, output volatility in this case remains lower than that in the Canadian economy. By contrast, intertemporal complementarity of labor hours dampens the cyclical effects of technology shocks; thus, work effort and output become less variable in comparison with the benchmark Model 1.

   With a time non-separable preference formulation, the household's period-t labor supply decision takes into account its expected influence on future utilities; hence, GDP and hours worked are no longer perfectly correlated. Compared to Model 1, intertemporal substitutability generates higher initial increases of labor hours and output in response to a positive transient technology shock and then displays similar oscillatory dynamics before falling back gradually to the steady state. As a result, the correlation between output and employment remains statistically too high (0.99) vis-a-vis the Canadian data (0.91). On the contrary, intertemporal complementarity leads to weaker initial responses of hours worked and output than are associated with Model 1. The associated sluggish movement in the household's labor supply decision causes GDP and work effort to continue to rise after the impact period in spite of a decreasing marginal productivity of labor, thereby generating hump-shaped impulse response functions. Moreover, the subsequent adjustment paths of labor hours and output are not closely synchronized in that work effort now becomes a lagging variable of the business cycle. This will result in a lower correlation coefficient between GDP and employment (0.92) that is remarkably close to the Canadian economy.

   The remaining three models exhibit time-varying capital utilization and depreciation rates, and they are driven by the same technology-shock process as their fixed-utilization counterparts. This will allow us to better understand ceteris paribus the quantitative business cycle effects of endogenous capital utilization and labor persistence. As expected, variable capital utilization raises the variabilities of all macroeconomic variables; however, it does not significantly influence the model's predictions of autocorrelations, contemporaneous correlations with output, and the savings-investment co-movement. Moreover, as in the benchmark Model 1, the no-labor-persistence Model 2 continues to show a counterfactual perfectly positive correlation between output and hours worked. On the other hand, Model 2a (with intertemporal substitutability) statistically "overshoots" the volatilities of output, consumption, investment, and employment and underpredicts the autocorrelations in GDP and labor hours. By contrast, the formulation with intertemporal complementarity (Model 2b) produces a statistically close match with the observed variabilities of output, investment, hours worked, and the trade balance--to-output ratio. It also successfully matches the persistence of GDP, consumption, investment, work effort, and the ratios of trade balance and current account to output.

   In terms of impulse response functions for the three models with variable capital utilization, the impact responses of hours worked and GDP to a positive transitory productivity disturbance are stronger because of a larger equilibrium output elasticity. Higher work effort also leads to more intensive utilization of capital, which in turn contributes to a further immediate rise in output. Moreover, the ensuing dynamic paths of labor hours and GDP are qualitatively identical to those in the Model 1 counterparts. It follows that the correlation coefficient between output and employment will not be affected by the addition of variable capital utilization alone. In sum, our analysis shows that a dynamic, technology shock--driven small open economy model with internal labor habits and variable capital utilization is able to account for the main real business cycle regularities of Canada after 1981.

   The remainder of this paper is organized as follows: Section 2 describes the model economy and analyzes its equilibrium conditions; section 3 calibrates the model's parameters and...