*Guest blog – The Integral Reviews: Paper 3 – Hall (2009)*

*by “Integral”*

Reviewed: Robert Hall (2009), *“By How Much Does GDP Rise If the Government Buys More Output?”* NBER WP 15496

**Executive summary**

The average government purchases multiplier is about 0.5, taking into account empirical and structural evidence. The only way to get “large” multipliers of 1.6 is to assume a large degree of non-optimizing behavior, an inflexible wage rate, at the zero lower bound on nominal interest rates, and assuming monetary policy is completely ineffective at influencing aggregate demand but the fiscal authority retains that influence.

The key ingredients to generating a large output multiplier are sticky wages/prices, a highly countercyclical markup ratio, and “passive” monetary policy which does not counteract the fiscal expansion.

The assumptions that underlie “the effectiveness of monetary policy” (sticky prices and a countercyclical markup) also drive “the effectiveness of fiscal policy.” The two are similar in that respect.

**Summary**

Hall provides a convenient overview of the state of economic knowledge about the government purchases multiplier. He does this in four steps: simple regression evidence, VAR evidence, structural evidence from RBC models, and structural evidence from various sticky-price/sticky-wage models.

Empirical evidence begins with the simple OLS regression framework. Hall obtains the output multiplier by regressing the change in military expenditures (a proxy for the exogenous portion of government spending) on the change in output. He finds multipliers significantly larger than zero but less than unity, mostly in the neighborhood of one-half. This estimate of the “average multiplier” is confounded by two problems: (1) the implied multiplier be taken as a lower bound rather than an unbiased estimate due to omitted variable bias, and (2) the estimates are driven entirely by observations during WWII and the Korean War.

The VAR approach produces a range of estimates. Hall surveys five prior studies and finds that the government purchases multiplier is non-negative upon impact across all studies and consistently less than unity, but there is much variation in the exact point estimate. The VAR approach typically suffers the same omitted variable bias as OLS.

Hall then turns to a review of the structural evidence. He first shows the standard RBC result that if wages and prices are flexible, the output multiplier is essentially zero or even negative. While a useful benchmark this is not particularly useful for applied work.

Adding wage frictions forces laborers to operate off of the labor supply curve, so output could plausibly expand from an increase in government demand. Hall indeed finds that the multiplier is higher in small-scale NK models and depends on consumer behavior. With consumers pinned down by the permanent-income/life-cycle model, multipliers tend to range around 0.7. If consumers are rule-of-thumb or iiquidity constrained, one finally finds multipliers above unity, in the neighborhood of 1.7, in the presence of the zero lower bound on nominal interest rates.

*Review*

The empirical evidence is plagued by persistent endogeniety and omitted-variable bias, which Hall frankly acknowledges. Identification is extraordinarily difficult in macroeconomics; as a practical matter it is impossible to untangle all of the interrelated shocks the economy experiences each year.

On the theory side, Scott Sumner would consider this entire exercise a waste of time: the Fed steers the nominal economy and acts to offset nominal shocks; government shocks are a nominal shock, so the Fed will act so as to ensure that the government expenditures multiplier is zero, plus or minus some errors in the timing of fiscal and monetary policy.

Is this a good description of the world? On average over the postwar period, a $1 exogenous change in government spending has led to a $0.50 increase in output; excluding the WWII and Korean War data drive this number down significantly. As a first-order approximation the fiscal multiplier is likely zero on average. But we don’t care about the average, we care about the marginal multiplier, at the zero bound. In that scenario, multipliers are on average higher but still below unity. A crucial open question is to what degree the monetary authority “loses control” of nominal aggregates at the zero lower bound, and to what degree fiscal policy is impacted if the monetary authority is “helpless”. (If we are in a situation where the Fed cannot move nominal aggregates, why wouldn’t Congress be similarly constrained?)

Hall’s paper does not explicitly discuss monetary policy. However, adding a monetary authority to his models would only reduce the already-low multipliers that Hall uncovers. His point, that one cannot plausibly obtain multipliers in excess of unity in a modern macro model, is already well-established even without explicitly accounting for the central bank.