Long-Run Implications of Investment-Specific Technological Change

The paper opens with two documented patterns in the price and quantity of postwar U.S. equipment investment: a “low frequency” pattern in which the relative price of equipment fell substantially while the equipment-to-GNP ratio rose, and a “high frequency” pattern of negative comovement between the detrended relative price of new equipment and new equipment investment. Specifically, “the relative price of equipment has declined at an average annual rate of more than 3 percent” while the equipment-to-GNP ratio “increased substantially” (Figure 1), and there is “a negative correlation (-0.46) between the detrended relative price of new equipment and new equipment investment” (Figure 2). The authors read this comovement as evidence of technological change specific to the production of new equipment.

The model embeds a vintage-capital mechanism in a representative-agent neoclassical growth framework with two capital goods, equipment (ke) and structures (ks), in which the accumulation equation for equipment includes a technology term q that “represents the current state of the technology for producing equipment” and determines how much new equipment can be purchased per unit of forgone consumption. Structures, by contrast, accumulate on a one-to-one basis with investment (ks’ = (1-δs)ks + is), with no analogous technology term. Movements in q can equivalently be read either as a falling cost of producing a unit of equipment, or as each successive vintage of equipment being more productive at a fixed cost – the two representations are shown to be equivalent in Appendix B.

The paper gives two empirical reasons for confining this channel to equipment: the relative price of structures “appears to be stationary over time in the U.S. data,” as does the structures-to-GNP ratio, and “casual observation suggests that there is less productivity change in structures than in equipment.” This asymmetry is what gives the model its two distinct capital accumulation equations rather than a single aggregate capital stock.

Following the calibration approach of Kydland and Prescott (1982), the authors fix some parameters from outside information and choose the rest so that the model’s balanced growth path matches six long-run averages in U.S. data over 1954-1990. The externally fixed parameters include γq = 1.032, “the average annual rate of decline in the relative price of equipment” taken from Gordon’s (1990) price index (extended to 1990), physical depreciation rates δs = 0.056 and δe = 0.124 backed out from BEA capital-stock data, and a 40-percent marginal tax rate on labor income following Lucas (1990). The remaining six parameters (β, θ, αe, αs, g, τk) are set so the model matches: 1.24-percent average annual growth in GNP per hour, a 24-percent ratio of hours worked to available time, a 30-percent capital income share, equipment and structures investment-to-GNP ratios of 7.3 and 4.1 percent, and a 7-percent average after-tax return on capital – yielding θ = 0.40, αe = 0.17, αs = 0.13, τk = 0.42, and β = 0.95.

Constructing a residual neutral-productivity series z from the model’s production function and data on equipment, structures, output, and hours, the authors find that investment-specific technological change “contributes about 58 percent of all output growth, with neutral change providing the rest.” The underlying growth rates are 3.21 percent per year for q (investment-specific) versus 0.39 percent per year for z (neutral) over 1954-1990; applying the model’s balanced-growth formula to each in isolation implies output per hour would have grown 0.77 percent per year from investment-specific change alone and 0.56 percent per year from neutral change alone, against an actual average of 1.24 percent per year (the two components sum to slightly more than the actual figure because the formula is a balanced-growth approximation applied to sample averages).

The computed neutral-productivity series z shows “a dramatic downturn in total factor productivity which began in the seventies and continued without interruption until the end of the sample,” a sharper slowdown than conventional residual measures show. The authors attribute this to two features of their accounting: investment-specific technological change (q) was accelerating at exactly the point when neutral productivity growth (z) was decelerating, and treating equipment and structures as distinct capital goods – rather than aggregating them, as conventional measures implicitly do – changes the measured decomposition. Comparing four successively more disaggregated productivity measures (Figure 4), average labor productivity grew 1.24 percent per year, a standard one-sector Solow residual grew 0.71 percent, a residual using BEA’s own equipment and structures measures grew 0.68 percent, and the residual constructed with Gordon’s quality-adjusted equipment series – the paper’s own z – grew only 0.39 percent, which the authors describe as making the “productivity slowdown… all the more dramatic.”

The paper adopts a framework following Solow (1960), with a resource constraint that does not adjust output for equipment-quality improvement, and contrasts it with the Domar-Jorgenson framework (Domar 1963; Jorgenson 1966) that “has dominated the practice of growth accounting” and does adjust output for quality; the authors show algebraically that embedding the Domar-Jorgenson resource constraint in general equilibrium collapses the model to “the conventional neoclassical growth model,” in which an optimal allocation is independent of the behavior of q, so that framework “does not allow investment-specific technological change to affect growth” at all. This is a theoretical, not merely empirical, point: whichever convention is used has to be applied consistently, because the two conventions are shown to give mechanically different answers to how much growth investment-specific change can explain, independent of the data.

Hulten (1992), applying Domar-Jorgenson-style accounting to manufacturing gross-output data, attributes only about 20 percent of residual manufacturing growth to investment-specific technological change; the authors show this gap narrows sharply once two methodological choices are adjusted, with the quality-adjustment choice alone raising Hulten’s figure “from 43 percent to 66 percent,” which is “close to the current finding.” The first adjustment, raising the income-share weight on equipment in Hulten’s analysis from 0.11 to 0.17, raises his estimate from 20 to 43 percent; the second, dropping the quality adjustment from the computation entirely, raises it further to 66 percent. The authors also note that Hulten studies gross output in manufacturing while they study value added for the whole economy, which affects the measured income share of equipment.

The paper argues that conventional growth accounting performed on NIPA data will mistakenly attribute part of the growth driven by investment-specific technological change to neutral productivity growth, stating that “the use of NIPA data in conventional growth accounting will cause investment-specific technological change to appear as neutral.” The mechanism is that NIPA income measures value investment goods using a base-year price, so growth in the investment component of income is inflated by growth in q without the offsetting decline in equipment’s relative price being netted out; the authors state this problem “does not arise when output is measured in consumption units,” which is the procedure used throughout their own analysis.

The authors test this alternative directly with a two-sector extension (one sector producing consumption and structures, the other producing equipment) and conclude that explaining the observed decline in equipment’s relative price this way “looks bleak,” because it would require the equipment-producing sector to be far more capital-intensive, and to have an implausibly low labor income share, than the data support. Matching the observed magnitude of relative-price decline given actual output growth (Table 1) requires combinations of cross-sector share differences that conflict with external estimates of labor’s share in capital-goods production – around 0.70, per Hornstein and Praschnik (1994) and Huffman and Wynne (1995) – so the paper treats exogenous investment-specific technological change, rather than sectoral technology differences alone, as the more plausible source of the facts.

Without formally estimating any of them, the paper sketches three ways the exogenous q process might instead be derived from firm or household behavior: human-capital accumulation by skilled workers employed in the equipment-producing sector, a learning-by-doing externality in which “productivity in the investment sector is a weighted average of past production in the sector,” and an R&D-based model of monopolistic competition among equipment producers (building on Krusell 1992) that the authors state “would find the same rate of investment-specific technological change as found in this paper” once calibrated to match a balanced growth path. Each of these extensions is offered as a candidate explanation for why q rises over time, not as an estimated alternative to the paper’s own exogenous-process calibration.

The authors frame their 58-60 percent estimate as resting on an exogenous-technology growth-accounting exercise, stating explicitly that “the analysis was undertaken within the context of a simple framework where investment-specific technological change arose exogenously,” and that taking the sketched human-capital, externality, and R&D extensions to the data “should constitute an important robustness test on the findings obtained here.” That is, the paper’s own language treats its number as provisional pending that future robustness testing, rather than as a result independently confirmed by an endogenous-growth version of the model.