Time to Plan and Aggregate Fluctuations

It is an explicit response to it, and a different paper: Christiano and Todd argue that the time-to-build feature Kydland and Prescott emphasised is not the quantitatively important one, and that a distinct feature of the same microeconomic evidence – the low-resource planning phase – does most of the work. They describe Kydland and Prescott’s 1982 article as a “classic” example of using microeconomic data to parameterise macroeconomic models, and note that the underlying studies report two noteworthy features of investment projects, of which Kydland and Prescott emphasised one. Their own verdict on the other: “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… 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.”

Two published studies of major industrial capital projects, plus a time-series study of investment lags, all cited for the specific claim that the planning phase is both long and cheap. The authors describe their analysis as “based on a review of the principal source cited by Kydland and Prescott 1982 – Mayer 1960 – as well as of Krainer 1968,” both of which “analyze the results of questionnaires about major capital projects undertaken by industrial firms.” In Mayer’s data “on average, projects took 22 months, with the first 7 months being the preconstruction planning phase.” Krainer “studies 25 projects, mostly 1-2 years in duration. In all these projects, in the first three months, less than 5 percent of the total project cost was incurred. In 18 of them, that portion was actually less than 2.5 percent.” The authors add that Krainer “understates the length of the planning period because he dates the conception of a project with its approval by a company’s board of directors,” whereas Mayer dates a project’s start from the first drawing up of plans. They also cite Jorgenson and Stephenson’s finding for 15 industries that “investment expenditure lags behind its determinants by six to 12 quarters … on the average.” Summarising: “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.”

Only in the investment technology: one-period completion; four-period gestation with weights 0.25, 0.25, 0.25, 0.25; and four-period gestation with weights 0.01, 0.33, 0.33, 0.33. All three use the same preferences, production and shock processes. In the four-period specifications, investment is the resource-weighted sum of projects at each stage, projects advance one stage per period, starts are the newest stage, and the capital stock is augmented by the projects completing that period. The even-weight case is “the standard formulation of this investment technology,” which “chooses investment weights which sum to unity and which imply that the resource costs of an investment project are distributed evenly throughout the four periods.” The time-to-plan case sets the first weight to 0.01 and the rest to 0.33. Each model also comes in two versions governed by a parameter in the aggregate-consumption definition: when it equals 1 private and government consumption are perfect substitutes and “government consumption shocks do not matter,” and when it equals 0 they are neither substitutes nor complements and the shocks do matter.

Quarterly, following Christiano and Eichenbaum (1992), with technology as a random walk in logs and government consumption as a persistent AR(1); U.S. statistics from Citibase for 1947:1-1995:1. The discount factor is 1.03 to the power -0.25, the period endowment of usable hours is 1,369, the consumption/leisure weight is 3.92, output is Cobb-Douglas with a capital exponent of 0.344, and depreciation is 0.021 per period. The technology shock is i.i.d. normal with mean 0.004 and standard deviation 0.018, entering the log level of technology so that “the shock has a permanent impact on the level of technology in all three models.” Log government consumption relative to technology follows an AR(1) with coefficient 0.96 and an innovation standard deviation of 0.021. Model statistics come from 2,000 artificial observations. U.S. variables are per capita, in 1987 dollars, logged and Hodrick-Prescott filtered except output growth; hours-worked data run only to 1993:4.

It removes the incentive to work harder on impact. In a standard model without a planning period, hours worked rise after a positive technology shock, and “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.” In the impulse responses, “in the time-to-plan model, there is relatively little to do in the period of the shock, since starting up investment projects requires first passing through a low resource use planning phase. Thus, much of the increased output generated by the technology shock is simply consumed, hours worked actually falls a little, and investment shows hardly any response.”

From essentially zero to 0.36, against a U.S. figure of 0.37. The first-order autocorrelation of postwar U.S. GDP growth is 0.37 with a standard error of 0.07; the lag-2 autocorrelation is also significantly above zero while lag 3 is not. In the baseline one-period model “there is essentially no persistence in aggregate output; output growth displays basically zero autocorrelation at lags 1, 2, and 3,” and the paper confirms the same for the even-weight four-period model: “when the growth rate of the exogenous technology shock has no first-order autocorrelation, neither does equilibrium output growth.” Reweighting to the planning specification changes this: “equilibrium output growth now displays positive autocorrelation. Indeed, the model’s first-order autocorrelation is 0.36, virtually the value observed in the data.” The authors note in passing that in the version where government consumption does not matter, persistence actually overshoots the data “somewhat, at least at lag 1,” and that adding government shocks brings it back into line.

Because the two responses to a technology shock are separated in time: productivity jumps immediately while hours are held back until planning is complete. The paper’s explanation is direct: “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.” The quantitative signature is the contemporaneous correlation, which “drops from roughly 0.90 in the other two models to 0.28 in the time-to-plan model,” against a U.S. contemporaneous correlation that is “nearly zero, while the correlation between productivity and future hours is positive and quite significant.”

Not for aggregate investment, but yes for the components where a planning period is most plausible. The paper is explicit that the implication “is not consistent with the evidence on aggregate investment,” which is contemporaneous with the cycle, but “it is qualitatively consistent with the evidence on business investment in structures and equipment,” which the U.S. statistics show lagging output. The authors suggest a reading and a caution in the same breath: business structures is “the category of investment for which the planning period is most directly relevant,” and the planning period “may also have an indirect effect on investment in equipment via the complementarity of structures and equipment.” They also warn that “the size of the standard errors for all these types of investment suggests that there is considerable sampling uncertainty in the data, so caution is warranted in making inferences about their cyclical properties.” Working the other way, residential investment in structures and household durables both lead the cycle, which “suggests that significant planning periods may not be required for these types of investment.”

It slightly worsens the model’s fit. Introducing the four-period even-weight gestation on its own changes the dynamics of consumption “substantially: the relative volatility of consumption is quite high, and the contemporaneous correlation of consumption with output is low,” and it raises the volatility of productivity relative to hours worked. Reading the impulse responses, “in the time-to-build model compared to in the one-period time-to-build model, consumption responds more to a shock, hours worked responds less, and, hence, productivity responds more. Thus, the small changes introduced by time to build actually hurt the model’s ability to account for business cycles.” This is consistent with what the authors report of Kydland and Prescott’s own comparison – that the business cycle implications of a four-quarter even-weight technology and a one-quarter technology “are very similar” – and with Rouwenhorst’s argument along the same lines.

Because the propagation of a temporary government shock runs through the opposite channel: in a standard model investment falls to absorb it, and the planning phase blocks that escape valve. “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.” With investment “almost completely determined at the time of a shock,” the consumption/leisure choice becomes a static problem in which investment acts as an exogenous tax and the government shock as an exogenous drop in income, so normality of leisure “guarantees that hours worked must rise sharply.” The authors flag the scope of this result themselves: for government shocks “even more persistent than in our model… we conjecture that the effect of the planning period with highly persistent government consumption shocks would be to delay the response of hours worked.”

Four things, on the authors’ own accounting: it lowers persistence into conformity with the data, leaves the productivity-leads-hours result intact while marginally improving it, fixes the excess volatility of consumption, and adds almost nothing to output volatility. The first follows from Q9 – time to plan amplifies rather than damps the hours response to a transient government shock – and brings “the model’s implied first-order autocorrelation… to 0.36,” in rough conformity with the empirical estimate. The second is that government shocks “do not alter the model’s implication that productivity leads hours worked” but produce “an overall reduction in the dynamic correlation between hours worked and productivity.” The third is that they reduce the relative volatility of consumption, “offsetting a counterfactual implication of the model without” them. The fourth matters for interpretation: “government consumption shocks contribute almost nothing to output volatility. It is because technology shocks dominate in the dynamic behavior of the model that time to plan results in so much persistence in output.”

Consumption leads the cycle and is too volatile, both counterfactual, and the authors trace both to the same feature that generates their main results. “Consumption surges in the period of the shock, while the impact on output is delayed. This implication of the model is counterfactual.” Model performance “deteriorates noticeably with respect to the relative volatility of consumption and its correlation with output. This also reflects the very strong response of consumption in the period of the shock.” Their diagnosis is aggregation, not mechanism: in their one-good model “there is nowhere else for the extra resources to go, since investment cannot be changed in the short run,” whereas in an economy where residential investment and household durables are available, households would use them. They conjecture that a model distinguishing business structures (with a planning period) from residential and durable investment, with structures and equipment complementary, would deliver both the lagging business investment and the leading residential investment seen in the data, while keeping a somewhat weaker delay in hours and output.

Deliberately weakly. The summary claim is that the planning period “may help account for” three features of business cycles, not that it does account for them. The closing position is that “we view our work primarily as preliminary and, we hope, suggestive. Further analysis of quantitative models is required to fully evaluate the idea that the planning period plays an important role in propagating business cycle” disturbances. They also flag a specific empirical question that could undercut the mechanism: it “would be interesting to know to what extent firms do project planning in advance, so that when the incentive arises, they” have projects ready to implement immediately – and “to the extent that this is true, the business cycle significance of the planning considerations analyzed here would be reduced.” A further acknowledged tension is that the projects in Mayer and Krainer last roughly two years, while the model uses a one-year specification “in order to preserve comparability with the existing literature and in order to capture the mix between major and minor investment projects.”