Time to Plan and Aggregate Fluctuations

This article investigates the business cycle implications of the planning phase of business investment projects. Time to plan is built into a Kydland-Prescott time-to-build model, which assumes that investment projects take four periods to complete. In the Kydland-Prescott time-to-build model, resources for these projects flow uniformly across the four periods; in the time-to-plan model, few resources are used in the first period. The investigation determines that incorporating time to plan in this way improves the model’s ability to account for three key features of U.S. business cycles: their persistence, or the fact that when output growth is above (or below) average, it tends to remain high (or low) for a few quarters; the fact that productivity leads hours worked over the business cycle; and the fact that business investment in structures and business investment in equipment lag output over the cycle. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. A major goal of macroeconomic research for the past three decades has been the integration of macroeconomics and microeconomics. Work aiming to reach that goal has taken two related paths. One type of work has tried to give theoretical macroeconomic models firmer microeconomic foundations. The other has tried to use microeconomic data sets to construct and parameterize macroeconomic models. An example of this second type is Kydland and Prescott’s (1982) classic Econometrica article, “Time to Build and Aggregate Fluctuations.” In that article, Kydland and Prescott specify the investment gestation lags in a macroeconomic model based on published studies of major investment projects. According to these studies, investment projects have two noteworthy features. One is that they usually require more time to complete than the quarterly time period in a typical macroeconomic model. This time-to-build feature of investment projects is emphasized by Kydland and Prescott (1982). The other noteworthy feature of investment projects is that they typically begin with a lengthy planning phase, during which architectural plans are drawn up, financing is arranged, permits are obtained from various local authorities, and so on. While these are important activities that can involve some high-priced talent, the actual resource cost of this phase is small in relation to the overall cost of investment projects. The really resource-intensive phase, when physical construction actually occurs, begins later. The planning phase is typically quite long. Of the total time from a project’s conception to its completion, on average, about a third is spent in the low resource use planning phase. Our investigation of these features of investment projects reveals that they have substantial business cycle implications. But it is the planning phase that is particularly important. The fact that investment projects take time per se has relatively modest implications for business cycle dynamics. That is documented by Kydland and Prescott (1982). They compare a model that has a four-quarter time-to-build technology but no planning period (in which the investment costs are spread evenly across the four quarters) with a model that has a one-quarter time-to-build technology. They report that, for the most part, the business cycle implications of these two specifications are very similar. Overview We will show that the planning phase of business investment helps account for at least three key features of business cycles: their persistence, the fact that productivity leads hours worked over the business cycle, and the fact that business investment in structures and business investment in equipment lag output over the business cycle. Persistence The persistence of business cycles refers to the fact that when the growth of output is above average, it tends to remain high for a few quarters, and when it is below average, it tends to remain low. A statistic for measuring persistence of output is the first-order autocorrelation of the growth of gross domestic product (GDP), that is, the correlation of GDP growth in one quarter with its growth in the preceding quarter. That autocorrelation in postwar U.S. data is 0.37. The only way standard real business cycle models can account for this degree of persistence is by assuming persistence in the growth rate of the disturbances, or shocks, that drive the business cycle. For example, Christiano (1988) documents that the first-order autocorrelation of equilibrium GDP growth in a standard model (with oneperiod time to build) corresponds roughly to the autocorrelation of the growth rate of the exogenous shock to the level of technology. The fact that standard models require persistent shocks to account for persistence in output is said to reflect the fact that the models are missing some important internal propagation mechanisms (Rouwenhorst 1991, Watson 1993, Rotemberg and Woodford 1994, and Cogley and Nason 1995). Enhancing internal propagation in models requires incorporating real-world features that have the effect of delaying the response of factors of production to the primary underlying shocks. We argue that, depending on the exact source of the shocks, the investment planning period can be such a feature. The need for a time-intensive, but low resource-using, planning phase at the start of new investment projects implies that the flow of resources into investment cannot be quickly changed, regardless of the type of shock. For shocks that are transmitted to factors of production primarily by changes in investment, the delay in the response of investment translates into a delay in the response of factors of production. The technology shock in standard real business cycle models is such a disturbance. In this type of model, there is no planning period and hours worked responds positively to a positive technology shock. An important motivation underlying this work response is households’ incentive to accumulate the investable resources they need to exploit the high rate of return on investment associated with a positive technology shock. By eliminating this incentive, incorporating a planning period into a standard real business cycle model has the effect of delaying the hours-worked response to a technology shock. Incorporating the planning period does not have the effect of delaying the response of factors of production to every kind of shock. For example, if shocks to government consumption are temporary, the optimal response to such a shock in a standard real business cycle model is to let investment drop in order to absorb the rise in government consumption. This drop in effect allows households to insulate the response of hours worked and consumption from the shock. But when there is a planning period, investment cannot play this role, so hours worked must rise substantially in the period of the shock to avoid a substantial crowding out of consumption. Thus, for this kind of shock, incorporating the planning period into the model actually enhances the response of hours worked. In our analysis, we use variants of the Christiano and Eichenbaum (1992) model, which includes both technology and government consumption shocks. In that model, the technology shock is the primary disturbance driving the business cycle. Therefore, incorporating the investment planning period into this model enhances persistence. We discover that the amount of persistence introduced by the planning period is actually quite substantial. To establish a benchmark, we first consider the conventional time-to-build specification of constant resource use over four periods. We find that, in this case, when the growth rate of the exogenous technology shock has no first-order autocorrelation, neither does equilibrium output growth. We then adapt this specification to accommodate a planning period by assuming that essentially no resources are used in the first period of a project, while a constant flow of resources is required in the remaining three periods. As before, we specify that the exogenous technology shock displays no autocorrelation in its growth rate. However, unlike before, equilibrium output growth now displays positive autocorrelation. Indeed, the model’s first-order autocorrelation is 0.36, virtually the value observed in the data. Productivity and Hours Worked We also show that the planning period helps account for the fact that output per hour worked (productivity) leads hours worked over the business cycle. The reason it does has to do with the impact of the planning period on the dynamic effects of the technology shock. As discussed above, initially hours worked does not rise after a positive technology shock because agents are awaiting the completion of the planning phase of investment projects conceived in the period of the shock. Because of the damped response of hours worked, productivity rises substantially in the period of the shock. Later, after the planning phase of new investment projects is complete, hours worked surges. This pattern of response to a technology shock—first productivity rises a lot; then hours worked rises—accounts for the model’s prediction that productivity leads hours worked over the cycle. Business Investment in Structures and Equipment As noted above, the planning period has the effect of delaying the response of investment to shocks. Thus, after a positive technology shock, output rises immediately, but investment rises only with a delay. This is why the model predicts that investment lags output over the business cycle. This implication is consistent with an important feature of the data, namely, that business investment in structures and business investment in equipment lag aggregate output (Kydland and Prescott 1990, Greenwood and Hercowitz 1991, Fisher 1994b). Presumably, business investment in structures is the category of investment for which the planning period is most directly relevant. The planning period may also have an indirect effect on investment in equipment via the complementarity of structures and equipment. The Models . . . In our analysis, we use three types of models. For comparison, we analyze a standard real business cycle model which abstracts altogether from gestation considerations in investment, by specifying that the completion of an investment project requires just one period. The specific model we use for comparison is the model with technology and government consumption shocks studied by Christiano and Eichenbaum (1992, their divisible labor model). We call this the one-period time-to-build model. We also consider a version of this model, modified to incorporate a standard four-period time-to-build investment technology like the one proposed by Kydland and Prescott (1982). This technology assumes that, to complete an investment project, a constant flow of resources is required over the life of the project. We call this simply the time-tobuild model. By comparing the implications of these two models, we can assess the business cycle consequences of time-to-buildconsiderationsperse,abstractingfrominvestment planning considerations. To quantify the business cycle impact of the planning phase of investment projects, we consider as well a specification in which essentially no resources are used in the period an investment project is initiated, while the remaining three periods require a uniform flow of resources. We refer to this as the time-to-plan model. In all models considered, competitive allocations coincide with the choices of a fictitious benevolent planner. At time period t, that agent selects contingent plans for aggregate consumption (Ct), the number of hours for households to work in the market (nt), and the beginning of period t + 1 capital stock (Kt+1) in order to maximize