Costly capital reallocation and the effects of government spending

The paper’s central argument is that “it is costly to shift factors of production across sectors,” and that government spending changes “are often accompanied by dramatic shifts in government spending in a few industries” – for example, during the 1987-1995 defense builddown, government spending on aerospace equipment, ships, and military vehicles fell by 79 percent. The paper cites its own companion work (Ramey and Shapiro 1998) as evidence on the costs of reallocating capital across sectors, and notes that Phelan and Trejos (1996) similarly argue the defense builddown caused the 1990-91 recession through the sectoral shifts it produced.

The paper states that several authors, including Rotemberg and Woodford (1992) and Devereux, Head, and Lapham (1996), “have maintained that only a model with imperfect competition and increasing returns to scale can explain the aggregate effects of government spending,” based on empirical evidence that spending increases are accompanied by increases in consumption, real wages, and productivity that they argue the standard neoclassical model cannot reproduce. Against this, the paper argues that “the two-sector neoclassical model can produce a much richer set of implications for the data than the standard, one-sector neoclassical model,” including episodes where some measures of real wages rise and interest rates fall in response to a spending increase – outcomes “previously believed only obtainable in a model with imperfect competition and increasing returns.”

The model assumes capital physically loses a fraction γ of its value when it is shifted from one sector to the other, and must additionally sit out of production for one year to be reallocated; the baseline calibration sets γ = 0.5, with a lower-cost case of γ = 0.25 also reported. The paper justifies this parameter using evidence that “used aerospace equipment sold at prices that were less than half the price of similar new equipment, even after taking vintage into account,” while noting that the price discount from a given physical loss will generally be smaller than the physical loss itself as long as the shrinking sector still demands some capital.

The paper calibrates sector sizes using 1958 input-output tables, identifying eighteen industries that sent 15 percent or more of their shipments to the federal government; these industries accounted for 6.65 percent of value added in 1958, with 41.6 percent of their sales going to the federal government, and the model’s “second sector” – the one that absorbs the entire increase in government spending during the simulated buildup – is calibrated to match this size. The paper reports simulations under two alternative production technologies: a standard Cobb-Douglas technology, and a Leontief technology in which firms can vary capital utilization only through costly shift work and overtime, calibrated so that a shift premium of about 25 percent and roughly one-quarter of work time on night shifts match evidence in Shapiro (1995, 1996).

With γ = 0.5, the paper reports that “shifting capital is so costly that none shifts in equilibrium,” so the costly-mobility case is equivalent to one in which capital is completely irreversible, and under Cobb-Douglas technology this friction “has little impact on the results for aggregate output and private output” relative to the frictionless case. Other variables are more affected: the positive impact of the spending increase on hours “is magnified some 15 percent with capital mobility frictions,” which the paper attributes to an additional negative wealth effect from the misallocation of capital’s current market value across sectors, and the composition of investment differs sharply, with the sector receiving the spending increase raising its own investment while the other sector cuts its investment, rather than one sector’s output being used to produce the other’s capital goods as in the frictionless case.

Under Leontief technology, the paper reports that capital-mobility frictions “magnify the output response by about 20 percent” – in contrast to the negligible effect on output found under Cobb-Douglas – because labor productivity is fixed by the Leontief assumption, so the larger wealth-driven increase in hours translates one-for-one into additional output rather than being partly absorbed by diminishing marginal productivity. The paper also reports that “capital frictions produce a greater impact on consumption in the Leontief case than in the Cobb-Douglas case,” with consumption falling “only half as much when capital mobility is costly” under Leontief, so that the same friction simultaneously magnifies the wealth effect on hours and attenuates the wealth effect on consumption.

The paper reports a separate simulation in which government demand rises in one sector and falls by the same amount in the other, with no net change in total spending, and finds that this “pure sectoral shift in demand creates what looks like a typical recession” – aggregate output, hours, consumption, and real wages all fall while interest rates rise. The paper attributes this pattern to the fact that the capital needed to produce the incremental output in the expanding sector “is stuck in” the contracting sector, illustrating that the model’s mechanism operates through the sectoral reallocation of demand itself, not merely through the overall change in government purchases.

Following a narrative approach modeled on Hamilton’s (1985) dating of oil shocks and Romer and Romer’s (1989) dating of monetary policy shocks, the paper reads contemporaneous accounts (principally Business Week) to date the onset of three large, unanticipated post-World War II military buildups: the Korean War (1950:3), the Vietnam War (1965:1), and the Carter-Reagan buildup following the Soviet invasion of Afghanistan (1980:1). The paper reports that adding this buildup dummy (current and eight lags) to a regression of real GDP growth on eight lags of its own log level and time trends “raises the R-squared from 0.218 to 0.321,” with the joint significance of the buildup dates having a p-value of 0.003, and that the buildup dates add more explanatory power for GDP growth than the Romer monetary-policy dates, though somewhat less than the Hamilton oil-shock dates.

The paper reports that both total GDP and private GDP (GDP net of government purchases) rise in the first few quarters after a buildup, but that private GDP “becomes negative after two years” while total GDP stays positive for three years, a pattern the paper says is “not out of line with” its two-sector model’s prediction that private output rises temporarily before turning negative. Hours in private business and in manufacturing both rise (peaking at 1.1 percent and 3.9 percent respectively) but imprecisely; output per hour in manufacturing “falls significantly” following the buildup, which the paper describes as “countercyclical labor productivity” that “is what a neoclassical model would predict and matches the predictions of our Cobb-Douglas model,” whereas output per hour in total business moves with hours rather than against it, a pattern the paper notes “is not consistent with a neoclassical model,” though estimated imprecisely.

The paper reports that nondurable and service consumption “show a statistically significant fall after the shock,” down 1.2 percent in the first quarter before slowly returning to trend, while durable-goods consumption rises briefly (partly reflecting “panic buying after the start of the Korean War”) before turning significantly negative, and that residential investment “falls substantially and statistically significantly,” reaching a trough 26 percent below trend after nine quarters. In contrast, nonresidential fixed investment “rises significantly after the military shock” with little subsequent reversal, which the paper interprets as “a sustained increase in the stock of productive capital” and a shift in the composition of wealth toward productive capital and away from consumer durables and housing, matching the model’s predictions.

The paper reports that real compensation per hour, deflated by the CPI, “declines in response to a military buildup” in both total private business (peak decline about two percent) and manufacturing (somewhat more), and that the manufacturing product wage – compensation deflated by the manufacturing producer price index – likewise “falls with the military buildup,” which the paper says “accords with the neoclassical model.” By contrast, the manufacturing real wage deflated by the GDP deflator falls only slightly and insignificantly; the paper notes this contrasts with Rotemberg and Woodford (1992), who reported an increase in a similarly GDP-deflated wage measure and used it to argue against models with stable labor-demand curves, and argues its sectoral framework explains the discrepancy, since “when defense purchases are sector specific, and when capital is not perfectly mobile across sectors, prices and average wages behave differently across sectors.”

The paper is explicit that it does not: while its results “are consistent with the neoclassical framework, they are also potentially consistent with other models,” since “the empirical evidence showing the negative comovement of real product wages and hours is consistent with any model in which an increase in government spending moves the economy along a given labor-demand curve,” including Keynesian models in which workers are fooled into supplying more labor or are bound by fixed-nominal-wage contracts. The paper’s claim is narrower: that a two-sector neoclassical model with costly capital mobility can reproduce facts – rising hours and output together with falling product wages, consumption-wage movements, and shifts in the composition of investment – that had previously been thought to require imperfect competition and increasing returns to explain.