# When can the fiscal multiplier be negative?

I am looking for a case study or data which shows a negative (fiscal/spending) multiplier effect.

Does anyone know a study where this is analyzed?

• I added the information you gave as a comment to BKay's answer, I hope this is in your interest. Unfortunately, it makes BKay's answer obsolete, but maybe helps to reopen the question. – The Almighty Bob Jun 29 '15 at 7:19

The paper How Big (Small?) are Fiscal Multipliers? by Ethan Ilzetzki, Enrique G. Mendoza, Carlos A. Végh (2010)should give you useful information.

We contribute to the debate on the macroeconomic effects of fiscal stimuli by showing that the impact of government expenditure shocks depends crucially on key country characteristics, such as the level of development, exchange rate regime, openness to trade, and public indebtedness. Based on a novel quarterly dataset of government expenditure in 44 countries, we find that (i) the output effect of an increase in government consumption is larger in industrial than in developing countries, (ii) the fiscal multiplier is relatively large in economies operating under predetermined exchange rates but is zero in economies operating under flexible exchange rates; (iii) fiscal multipliers in open economies are smaller than in closed economies; (iv) fiscal multipliers in high-debt countries are negative.

The fiscal multiplier is the ratio of a change in national income to the change in government spending that causes it.

Assume that the government runs a balanced budget and so any raise in spending comes with a raise in taxes. Imagine there are three types of people in this economy, Friday has a low marginal propensity ($$\alpha\in(0,1)$$) to consume (MPC) and Robinson Crusoe has a high ($$\beta\in(0,1)$$) MPC, and a massive number of other people with an MPC of $$\gamma\in(0,1)$$ such that the economy wide MPC can be thought of $$\gamma$$. Assume Crusoe's labor supply does not respond to taxes.

If you tax Crusoe \$1 and spend that \$1 on Friday then Crusoe cuts his consumption by $$\beta$$ dollars and Friday increases his by alpha dollars. Therefore, the the change in consumption, is:$$\alpha - \beta$$ which is negative by construction. In representative agent models the relationship between the multiplier and the MPC is: $$Multiplier = 1 / (1 - MPC)$$

Here is a summary from the Investopedia how this works:

Suppose a large corporation decides to build a factory in a small town and that spending on the factory for the first year is \$5 million. That \$5 million will go to electricians, engineers and other various people building the factory. If MPC is equal to 0.8, those people will spend \$4 million on various goods and services. The various business and individual receiving that \$4 million will in turn spend \\$3.2 million and so on.

If the marginal propensity to consume is equal to 0.8 (4 / 5), then the multiplier can be calculated as:

Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.8) = 1 / 0.2 = 5

But in our example, there really are two shocks, one negative to Crusoe and one positive to Friday. The total effect is: $$\frac{\alpha}{1-\gamma} - \frac{\beta}{1-\gamma} = \frac{\alpha - \beta}{1-\gamma} <0$$ because the consumption reduction of Crusoe and the consumption increase of Friday both propagate into the same population with MPC of $$\gamma$$. So the multiplier if this policy would be negative.

It is also possible to get a negative multiplier from a deadweight loss of taxation.

• Thank you for the deep explanation! I understand the theory more clearly, but I am looking for a real-world example, such as a case study on the negative (fiscal/spending) multiplier effect. Do you know any material like this, BKay? – Übel Yildmar Jun 23 '15 at 18:23

Only the injection is multiplied not the withdrawal - once money leaves the economy that is the end of it's journey in the circular flow of income - full stop.

The injection continues being spent around the economy which is why it is subject to the Multiplier.

There is no negative Multiplier.

The Multiplier is not a micro concept - the withdrawal is on the money supply not on an individual or even groups income even if he is called Clouseau.

Therefore there is no real world example - only in the surreal world of micro economists.