Fiscal Stimulus: Does the Multiplier Really Have to be 1?

The “stimulus” plan has now passed. So, this discussion is purely academic. We shall see what if any effect the legislation has. But, I heard over and over again during the debate that “of course, the multiplier on government spending must be at least one”. This statement is based on a false assumption.

A multiplier of one means that an increase in government spending increases output dollar for dollar. That is, the government can increase its spending without any change in consumption, investment, or net exports. Take a look through the lens of the national income identity:

Y = C + I + G + Ex - Im

Y is output, C is private consumption, I is private investment, G is government consumption and investment, Ex is exports, and Im is imports. A multiplier of one means an increase in G leads to an equal increase in Y. That is,

↑Y = C + I + ↑G + Ex – Im.

Taking the identity seriously, how exactly did G increase? G is real government consumption and investment; it does not include transfer payments. If the government increased G, it must have increased its purchases of inputs: labor, capital, and materials. Where did the government purchase these resources? The answer to this question determines the amount of stimulus embedded in government spending.

The idea behind stimulative Keynesian government spending is that there are idle resources during recessions and the government (following a different objective function than the private sector) is best positioned to use these resources. I actually have no problem with the underlying thought experiment: high unemployment and rising inventories certainly implies underutilized resources. And, the government certainly has the capability of quickly hiring workers and purchasing inventories.

However, while these resources may have been idle, they likely still had positive prices. If they had positive prices before the government spending program, then the increase in demand from the increase in government expenditures must have pushed the price up: the government had to outbid the current holder of the resource. This rise in price, no matter how small, reduces private-sector demand.

It is easiest to think of the government hiring labor from the pool of unemployed workers. The existence of unemployment (let’s leave aside temporary frictions) implies that at current wages firms are unwilling to hire all available workers. Equivalently, at current wages workers, in aggregate, are unwilling to supply more labor. If the government steps in with a jobs program, wages increase. [Take this as an axiom, where the wage is actually the shadow price of labor. I don’t want to get into a discussion on LaGrange multipliers.] With higher wages, some marginal firm in the economy will reduce its demand for labor. This reduction private-sector employment prevents the multiplier from being automatically one: the increase in government spending resulted in a decrease in private employment. We can do the same thought experiment for any other input.

Of course, the multiplier could still be one; I have only shown that it is not automatic or obvious. The bar for large multipliers is quite high. For the multiplier to be one or higher, the government spending must increase output itself and somehow spur either private investment or private consumption. In the spirit of Keynes, the government spending must reignite otherwise dampened Animal Spirits.

The question is then an empirical question. Last month, Robert Barro examined the case of the United States during WWII. He found a multiplier on government spending of 0.8. Krugman inaptly points out that WWII does not count because of the consumption quotas. To me the existence of the quotas are the proof of Barro’s point.

Why did the government need quotas during the war? Apparently, the government believed that its acquisition of private resources would drive up prices. For either budgetary or social reasons, the government found these price increases unpalatable and instead imposed quotas. With the quotas in place, they effectively created a supply of goods with zero price (this is where we need the LaGrange multipliers). By my grandmother’s account, these quotas were binding. At existing prices, people wanted to consume more. In the absence of the quotas, the government would have had to consume less.

But, WWII is Barro’s example. For me, I like Japan’s experience in the 1990s.

The Case of Japan: In the early 1990s, asset prices in Japan collapsed. Most famously the collapse was in equity prices but bond prices also fell sharply as companies stopped making payments. In many ways, that crisis is similar to that faced today. In particular, the government was forward looking and wanted to implement the stimulus early, to get ahead of the curve.

The following picture shows private demand, government demand, and in light bars four-quarter GDP growth for Japan between 1989 and 2001.
In 1991, Japan enacted a substantial stimulus plan. By the time the plan ended in 1994, the stimulus amounted to about 3.5 percent of Japanese GDP. The first thing to notice is that neither in terms of private demand nor in terms of GDP growth was Japan’s economy faltering at the time the stimulus was put in place. In the first quarter of the stimulus, marked by the first vertical line, four-quarter GDP growth remained above four percent. Private demand growth was robust.

Therefore, while the government may have simply been forecasting the drop in GDP two full years later, it does not seem we can make the case that the economy was contemporaneously weak. What is striking is that in the same quarter in which government spending began to increase, private demand stagnated.

The government could not have been reacting to fall in private demand for two reasons: First, government spending takes a long time to implement. No government in the world is that fast. Second, and much more importantly, the government did not know at the time. Demand data is released with a considerable lag. We do not learn current quarter GDP growth until about 6 weeks after the end of a quarter.

Further, private demand growth was positive both before and after the stimulus. (The second bump in 1996 is the government’s spending response to a surge in revenue and is not an announced stimulus.) Taking the data series as given, I find a multiplier on government spending of 0.38, positive but well below one. I will go one step farther. If I take as the counterfactual rising private demand, as opposed to flat in the first experiment. If for example, I use the slowest annual growth rate of private demand two years on either side of the stimulus, the multiplier becomes a large negative number.

Of course, many economists believe that government spending in this period is all that kept Japan going. They take private demand as given and calculate the path of GDP that would have occurred had the government spending not been in place. Some go farther, comfortable in their knowledge that the multiplier is greater than one, they compute quite abysmal paths for GDP in the absence of government spending.

We do not have the counterfactual. I cannot directly falsify their statements. The picture above is just a picture. In the end, the debate comes down to one of philosophy. And, as with every adherent to his chosen philosophy, I believe my views are the correct.

Government spending crowds out private demand.