<p>The fiscal multiplier is <a href="https://en.wikipedia.org/wiki/Fiscal_multiplier#Examples" rel="nofollow noreferrer">the ratio of a change in national income to the change in government spending that causes it</a>.</p>
<p>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 (<span class="math-container">$\alpha\in(0,1)$</span>) to consume (MPC) and Robinson Crusoe has a high (<span class="math-container">$\beta\in(0,1)$</span>) MPC, and a massive number of other people with an MPC of <span class="math-container">$\gamma\in(0,1)$</span> such that the economy wide MPC can be thought of <span class="math-container">$\gamma$</span>. Assume Crusoe's labor supply does not respond to taxes.</p>
<p>If you tax Crusoe \$1 and spend that \$1 on Friday then Crusoe cuts his consumption by <span class="math-container">$\beta$</span> dollars and Friday increases his by alpha dollars. Therefore, the the change in consumption, is:<span class="math-container">$$\alpha - \beta$$</span> which is negative by construction. In representative agent models the relationship between the multiplier and the MPC is:
<span class="math-container">$$Multiplier = 1 / (1 - MPC) $$</span></p>
<p>Here is a summary from the Investopedia how this works:</p>
<blockquote>
<p>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.</p>
<p>If the marginal propensity to consume is equal to 0.8 (4 / 5), then
the multiplier can be calculated as:</p>
<p>Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.8) = 1 / 0.2 = 5</p>
</blockquote>
<p>But in our example, there really are two shocks, one negative to Crusoe and one positive to Friday. The total effect is:
<span class="math-container">$$\frac{\alpha}{1-\gamma} - \frac{\beta}{1-\gamma} =  \frac{\alpha - \beta}{1-\gamma} &lt;0$$</span>
because the consumption reduction of Crusoe and the consumption increase of Friday both propagate into the same population with MPC of <span class="math-container">$\gamma$</span>. So the multiplier if this policy would be negative.</p>
<p>It is also possible to get a negative multiplier from a deadweight loss of taxation.</p>

CC BY-SA 3.0
2015-06-23T18:23:41.737Z
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
CC BY-SA 3.0
2015-06-23T15:49:33.137Z
2015-06-24T14:50:35.463Z
2020-06-17T09:40:54.643Z
BKay
<p>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.</p>

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

<p>There is no negative Multiplier.</p>

<p>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.</p>

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

CC BY-SA 3.0
2017-07-11T22:53:01.387Z
2017-07-11T22:53:01.387Z
Paul Ibram
<p>The paper <a href="http://www.nber.org/papers/w16479" rel="noreferrer">How Big (Small?) are Fiscal Multipliers?</a> by Ethan Ilzetzki, Enrique G. Mendoza, Carlos A. Végh (2010)should give you useful information.</p>

<blockquote>
  <p>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.</p>
</blockquote>

CC BY-SA 3.0
2015-06-23T07:34:03.257Z
2015-06-23T18:23:39.803Z
2015-06-23T18:23:39.803Z
Giskard
<p>I am looking for a case study or data which shows a negative (fiscal/spending) multiplier effect.</p>

<p>Does anyone know a study where this is analyzed?</p>

CC BY-SA 3.0
2015-06-29T07:19:22.863Z
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
<macroeconomics><reference-request><economic-growth>
When can the fiscal multiplier be negative?
Übel Yildmar
# When can the fiscal multiplier be negative?

(Asked by: username_0 on 2015-06-23)

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?

**Tags:** macroeconomics, reference-request, economic-growth

> **Comments:**
> **username_1**: I added the information you gave as a comment to username_2's answer, I hope this is in your interest. Unfortunately, it makes username_2's answer obsolete, but maybe helps to reopen the question.  

---

## 3 answers

### Answer by username_4 on 2015-06-23. Score: 6 | Accepted answer

The paper [How Big (Small?) are Fiscal Multipliers?](http://www.nber.org/papers/w16479) 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.


---

### Answer by username_2 on 2015-06-23. Score: 5

The fiscal multiplier is [the ratio of a change in national income to the change in government spending that causes it](https://en.wikipedia.org/wiki/Fiscal_multiplier#Examples).

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.

> **Comments:**
> **username_0**: 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, username_2?  

---

### Answer by username_3 on 2017-07-11. Score: -3

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.


---

