Is Public Expenditure Productive?

Tyler Cowen says he wants to see evidence about the effectiveness of fiscal policy. This is from Michael Murray's econometrics text (which comes at the subject from an interesting perspective), and it is one of his "Regression's Greatest Hits." It speaks to dynamic government spending multipliers, and the effect of government spending on economic growth:

Is Public Expenditure Productive?: From the 1930s to the late 1980s, macroeconomists viewed government spending as rather homogeneous. They asked whether government spending crowded out private investment, drove up interest rates, or spurred consumer spending. They argued whether funding government expenditures by taxation had different effects than funding by issuing new government debt. They gave relatively little attention, however, to the different ways the government spends its money-on defense, on roads, on food stamps, and so on. Economist David Aschauer of Bates College dramatically altered macroeconomists' view of government spending with a paper he wrote in 1989, however. Aschauer's analysis places a particular kind of government spending - nonmilitary public investments, such as roads - at center stage. Aschauer finds government investment is so important for private sector productivity that a decline in public sector investment might account for much of the productivity slowdown observed in the 1970s and 1980s.

Aschauer asks whether private sector productivity is improved by public sector investments, and whether public sector investments have a different effect on private sector productivity than does other government spending. He assumes a Cobb-Douglas style of production function and uses two dependent variables - output and a measure of productivity called "total factor productivity - to study the effects of government spending on productivity. Aschauer assumes that both output and productivity depend on labor, the private capital stock, the public nonmilitary capital stock (for example, roads), and, perhaps, on other government spending. He also allows output to depend on the intensity with which the capital stock is being used, as measured by the capacity utilization rate of the private sector.

When Aschauer estimates an output equation that accounts for labor, capacity utilization, and a time trend, his Durbin-Watson statistic is 0.63. Either there is serial correlation in the model's underlying disturbances, or an important variable has been omitted. When Aschauer adds the public stock of nonmilitary capital to the output equation, the Durbin-Watson statistic no longer evidences serial correlation, and public capital becomes statistically  significant. The public, nnonmilitary capital stock is also significant in Aschauer's productivity equation. Public investment expenditures translate into higher private sector productivity and higher private sector output.

Aschauer finds no evidence of public military capital raising output or productivity, nor does he find the flow of spending on on capital goods to have any effect on output or productivity. Public spending raises private sector productivity to the extent that public sector spending is on nonmilitary capital goods. How government spends its money matters! It is not government spending, as such, that spurs private productivity, but rather specific government investments in capital goods that makes the private sector more productive.

We could reasonably worry that that the direction of causation runs not from government spending to output, but the other way around, from output (which translates into income) to government spending. But if this were the reason for Aschauer's findings, we would expect both military and nonmilitary capital to reflect such an effect of output on expenditure. The fact that only public-sector spending on nonmilitary capital goods shows a link with output suggests that the effect we see reflects a causal effect running from nonmilitary capital to output, and not the other way around.