Fiscal Multipliers Explained (and Proved)

The Panic of 1837, blaming the Treasury Policies of Andrew Jackson

The IMF spokesperson, Mr Jeffrey Rice, said the following in a Press Briefing in Washington about 10 days ago:

(...) there's been a lot of discussion of this fiscal multiplier, which is probably something very few people had heard of until some months ago.(...)

I have shown the inaccuracy of Mr Rice's statements in a previous post and have no intention of doing the same again. It appears that the publication of Oliver Blanchard and Daniel Leigh's IMF paper about the problems of forecasting multipliers has caused more stir than it should, because it essentially does not say much. Quoting from their conclusions (page 19): "Our results suggest that actual fiscal multipliers have been larger than forecasters assumed. But what did forecasters assume? Answering this question is not easy, since forecasters use models in which fiscal multipliers are implicit and depend on the composition of the fiscal adjustment and other economic conditions."

What has not been noted in the existing literature of comments about the paper is that it does not really estimate multipliers or anything similar. It just points that the estimations concerning these multipliers, when the IMF staff were making them in 2008, can be proven wrong, ex post. (For those interested the IMF staff assumed a multiplier value of merely 0.5. We will see later why this does not appear to be very valid)

Thus, what we may infer from their comments is that the previous models of estimating multipliers had been wrong, yet they are not proposing how these errata can be fixed. In fact, they are not actually even saying how a multiplier actually works or how it affects the economy. Since many economists and politicians do not appear to understand the rationale of fiscal multipliers, I have decided to play the game on their own terms.

Let us consider the following model:

In each country the yearly output is measured by GDP=G+C+I+NX where G stands for government spending, C for Private Consumption, I for Private Investment and NX for Net Exports (Exports - Imports). We assume then that G is increased by €X billion. The amount of G here is unimportant to the result we are about to reach.

First of all, we have to understand where the €X billion chunk of Government Spending goes to. Wikipedia states that Government spending is the sum of government expenditures on final goods and services. It includes salaries of public servants, purchase of weapons for the military, and any investment expenditure by a government. Thus, we may safely conclude that this amount goes right into the consumers' pockets in forms of salaries, or other payments towards companies or individuals. 

Then, what do these consumers do with that €X billion "given" to them by their government? As usual, they have two options: either spend it or save it. There is also the option of repaying their loans but this falls in "saving" part for reasons which are not the purpose of this article. We may assume that this €X billion amount is saved or consumed in any fraction we can think of. Here we will note it as s*€X billion where is s signifies the amount saved in banks or other institutions (hiding under the mattress is not an option here!) and (1-s)*€X billion the amount consumed.

As it may have become visible through this analysis, Private Consumption will be increased by (1-s)*$€ billion. Then, if we believe neoclassical economics, i.e. David Ricardo or Alfred Marshall, all savings are used in the form of loans to entrepreneurs by banks and thus Investment is increased by s*€X.

What can be seen here is that through the standard measures of GDP, Government Spending is calculated twice. Once as spending by the government in the G part of the equation and then partly as an increase in Private Consumption (in C) and an increase in Private Investment (I). The total increase of C and I equals €X.

Now imagine if Government Spending was to be decreased by €X. The total contraction of GDP would equal €2X in the above example. (In the real world this amount might be slightly exaggerated or underrated, since other issues may also arise. For example the economy's rate of growth would cause the effect to be less but a further decrease in consumption as a result of people's fear about the future would contract GDP even more.)

For the skeptics, let us assume that neoclassical economists are all wrong and that the fraction of G which ends up in banks does not find its way to the entrepreneurs. Then the an €X increase in G would mean a (1-s)*€X+€X increase in GDP, which is still greater than €X. The decrease would go the other way around.

Are we forgetting something here though? If the reader was careful during the above analysis the fact that in the definition of government spending transfer payments, such as social security or unemployment benefits are not included should have rang a bell. Now, think about it again: transfer payments are being employed the same way as government spending, i.e. given to people for them to consume or save. Now, have a look at the following data compiled in an older post:

Now I will not even suggest that all of this money goes unnoticed in measuring Government Spending for GDP (although probably most of it does). Yet, even if 40% of the above amounts goes unnoticed and as already mentioned, people consume or save that amount, then an €X cut in the benefits would mean a 0.4*X*(1-s) reduction in consumption and a 0.4*X*s reduction in investment. In total, even though these amounts are not measured in GDP their effect appears to be of great importance.

The above are in accordance to empirical findings by the IMF (have a look at this article, pages 41-43) which now estimate that fiscal multipliers are in the range of 0.9 to 1.7. (This admittance that the multipliers were actually higher than they had expected, did not actually gain much publicity, only in the form of articles like Is the IMF short for I Must Fail?) Although the 0.9 number does appear to be rather too little based on the previous analysis, it may occur if the change in spending is little and the country experiences strong growth (although it would be tremendously difficult to achieve such low values for rapid changes in the level of spending) the 1.7 one appears to be more in the line of the above simple model.

Conclusion: Government spending is affecting GDP more than we believe. This means that we either have to alter our understanding about it or change the way we measure GDP. The former is much easier. I think...

Note: The above calculations would only be important if the amount slashed off the budget is significant. A country's GDP will surely reflect a 1-2% reduction in spending, yet nobody is going to notice a 0.0001% reduction in G when the natural growth rate of an economy is about 1%. On aggregate that is...