Last month, I used this space to write about the multiplier effect associated with government spending. Theoretically, each dollar spent by the government — or anyone else, for that matter — is multiplied in its impact on the economy.

Last month, I provided two examples:

• SNAP benefits, commonly known as food stamps, have been estimated to have a multiplier effect of about 1.5. This means that $1 billion in government spending on SNAP benefits results in a $1.5 billion increase in GDP, as each dollar spent on groceries through SNAP is multiplied as wages for individuals working in food production, sales, and transportation.

• The CARES act, passed early in the pandemic to provide cash relief to each American household, is estimated to have a multiplier close to 1. Our GDP will regain almost exactly what was spent in stimulus.

Today, with all due respect to my fellow economists who spend countless hours analyzing data to arrive at these multiplier estimates, I am going to walk this back a little.

Among economists, there actually is a good deal of debate about multiplier effects. Economist Daniel Carroll of the Federal Reserve Bank of Cleveland describes the reasons for this debate in a 2014 article, which I summarize below.

Theoretically, there is some dispute about the existence of a multiplier effect.

This goes back to the definition of GDP. GDP is the sum of consumption, investment, government spending, and net exports. Although an increase in government spending is a direct increase to GDP, that spending must be financed somehow, either through increased taxes, increased government debt or monetary expansion. Any one of these three options has the effect of decreasing private consumption or investment or both.

An increase in government spending will only increase GDP if the increase in spending more than offsets the effects of financing that spending.

Generally, I think most folks agree that there probably is some positive multiplier effect on government spending. However, the details of how we assign a value to that multiplication are always in contest. As Carroll points out in his article, and I can attest from my own experience, measuring money multiplication empirically is no simple task and almost always involves making assumptions and doing a lot of guess work.

A major difficulty with estimating the size of any economic relationship is that economic studies change in the real world, and we can rarely observe these changes in a vacuum.

In the case of multipliers, it is really hard to tell whether a change in GDP is a result of a specific spending policy, whether the change in spending is a result of the change in GDP, or whether both the changes in GDP and spending are results of some third variable. In fact, it is very likely that all three of these relationships occur at once.

This difficulty establishing causality would tend to lead to overestimations of multipliers should we assume that GDP changes result from spending changes.

Another issue with empirically measuring the size of multipliers is that changes to government spending often are debated and publicized for long periods of time prior to their being enacted. This gives businesses and individuals time to anticipate future increases in their cash flow and change their behavior prior to the actual implementation of the new spending policy.

This anticipation problem would tend to lead to underestimates of multipliers if we cannot measure the extent to which prior GDP changes are related to future government spending.

And all of this is complicated by the fact that there is no single multiplier for government spending. The size of the multiplier depends on the strength of the economy at the time of the spending as well as where the money is spent.

In sum, I believe spending is multiplied, and I believe attempting to measure the size of multipliers is useful for informing policymaking. But, I do not envy those whose job it is to do the estimating. It’s a tough, if not impossible, job.

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