## Wednesday, November 6, 2019

### Primer: The Fiscal Multiplier

The concept of the fiscal multiplier can be viewed as simple, but there are many potential complexities to analysis. In this text, I keep the discussion simple (with a nod towards the complexities). There are multiple potential definitions of the fiscal multiplier, but I will use a straightforward one: it is the coefficient relating the expected change of nominal GDP based on an assumed change in a fiscal variable. For example, if a policy change scenario is expected to raise the fiscal deficit by \$100 million (relative to baseline), and the modelled change to nominal GDP is \$150 million higher than the baseline, we could say that the multiplier is 1.5 from the deficit to GDP.

The definition deliberately uses the vague term “fiscal variable” for reasons to be discussed later.

Note: this is an unedited draft of a section from my upcoming book on recessions. It refers to section numbers in the manuscript, which I am leaving in place. It skips over most of the usual subjects of debate (and research) around fiscal multipliers, rather it looks at the big picture. For a variety of reasons, the big debate about the fiscal multiplier is the size of the multiplier. The complexities of the topic are discussed in this text, and essentially explain why I am not too concerned with much of the debate around the size of the fiscal multiplier.

## Model SIM

As an example of such a scenario, I will take the simplest possible “Keynesian” model: model SIM from Chapter 3 of the textbook Monetary Economics by Wynne Godley and Marc Lavoie.[i]  I discussed the workings of this model in detail my book An Introduction to SFC Models Using Python. The advantage of using this model is that it is easily understood even if one is averse to mathematics. Although it has obvious shortcomings, they are easy to see and explain what they are. More advanced models have corresponding greater opacity.

The figure above shows the results of a hypothetical fiscal expansion. The economy is in a no-growth steady state up until time point 5, when the jump in government spending occurs. Government consumption rises from 15 to 20, while GDP rises from 75 and is tending to 100. The construction of model SIM is such that the steady state GDP is a multiple of government spending – with the textbook’s parameter values, the multiplier is 5.

We can also see that model GDP does not immediately jump to the final steady state, and so we immediately see a problem with discussing “the” multiplier: the effect of the change in spending properly has an effect that varies over time. We need to distinguish long-term effects from short-term effects, and this affects empirical estimates of multipliers.

## What Fiscal Variable is Changing?

The fiscal multiplier is the coefficient relating the change in fiscal policy to the change in GDP, which might be viewed as a sensitivity parameter. The previous example of model SIM illustrates the conventional way of viewing it: the multiple of a spending change to the effect on GDP. For the model economy, there is a spending multiplier of 5, so we multiply the change in spending by 5 to see the effect on (steady-state) GDP.

We can view most governmental programme spending as being a dollar amount under the control of the government – e.g., the salary expenses for permanently employed bureaucrats at a government agency, or defense department acquisitions. However, the other modes of fiscal policy are not properly described in dollar amounts (although that is exactly what conventional analysis does).
• Taxes (other than poll taxes, which are nearly non-existent in modern developed economies) are specified as a tax rate structure. Changing tax rates will have a non-obvious effect on revenue. For example, an increase in income tax rates might be modelled as causing an increase in tax revenue – but that requires an assumption about what will happen to taxable income. If the tax hike causes growth to slow, incomes would be lower than projected, and so the actual amount of revenue will be lower than expected. I would argue that the correct way to look at the problem is to look at the sensitivity of projected GDP to changes in tax rates. Unfortunately, that multiplier will not be as easily interpreted as the spending multiplier in model SIM.
• Welfare state spending programme expenditures depend on the state of the economy. The number of recipients of spending is not directly under the control of the government (putting aside the ability to change eligibility requirements). The government can change programme parameters – e.g., increase the length of time unemployment insurance payments may be drawn – but the actual effect on dollar expenditures is dependent upon the number of people in the programme. We need to keep in mind the counter-cyclical nature of the spending. If everything else is equal, welfare state spending will rise if the economy shrinks. This does not mean that the multiplier on welfare state spending is negative.

The conventional way to budgetary analysis is to look at projected budgets, and work with the projected dollar amounts. One can then use a straight multiplicative multiplier to see the projected effect on growth. However, we see that this is misleading except in the case of straight changes to non-welfare state expenditures.

## Further Complications

The other set of complexities with respect to multiplier is that not all taxes and expenditures have the same effect on the economy. We can see the following effects in simple macroeconomic models that are adapted to allow for these dynamics.

• Not all private sector entities will adjust their spending in the same way for the same dollar amount of spending. For example, an increase in interest income going to a pension fund will not prompt any immediate spending in response, rather the income flow will be hoarded. Similarly, richer households appear less likely to spend out of tax cuts than poorer ones.
• Similarly, the economic effects of tax increases will depend on who and what is being taxed.
• If the government purchases goods produced externally, there will be almost no effect on gross domestic product. (The increase in the trade deficit will cancel out the increased government expenditure.)

We would need a detailed macroeconomic model to capture low-level dynamics to properly model the effects of changing fiscal policy in the real world. Since such models are not particularly successful, we are stuck with approximations. This creates a great deal of fuzziness around “multiplier” estimation in practice.

My argument is that any relatively simple macro model that disaggregates the private sector will result in different fiscal policy changes having different sensitivities with respect to their effect on growth. It is only possible to generate a single multiplier in a model where we avoid any attempt at disaggregation (such as simple post-Keynesian SFC models, or neoclassical unitary representative household models without business sectors). Therefore, one should expect empirical multiplier estimation to be an extremely difficult task. As a result, I do not see much value pursuing the literature on multipliers within this text, since that will just tell us what we already can guess from first principles.

## Concluding Remarks

The difficulty of estimating the fiscal multiplier means that it is normally difficult to gauge the effects of fiscal policy on growth. Although I believe that fiscal policy is more important than monetary policy, much of the effect is via automatic stabiliser effects. In practice, fiscal policymakers have generally shied away from aggressive fiscal policy adjustments since the early 1990s (the euro area periphery being a key exception, as will be discussed in Section 3.4). Correspondingly, the effects of fiscal policy have often been much less visible than was expected by somewhat sensationalistic market analysis.

Nonetheless, the basic multiplier story remains pertinent for the discussion of recessions. Sufficiently tight fiscal policy will always be enough to generate a recession, and one might hope that a well-timed fiscal boost could prevent recessions (as will be returned to Section 3.5).

Footnote:

[i] Monetary Economics: An Integrated Approach to Credit, Money Income, Production and Wealth (Second Edition), Wynne Godley and Marc Lavoie. Palgrave Macmillan, 2012. ISBN: 978-0-230-30184-9.

(c) Brian Romanchuk 2019

1. Very important to note is the fact that money comes in existance as credit and then gets destroyed as the credit is payed back. This has a significant effect on money multiplyer but it isbiddenbehind so called "propensity to save". Calling it as it is in the real world would have a significant impact on economic thought at large.
The fact that money is destroyed as paying off credits is the answer to why fiscal multiplyer has lower effect if deppression already started. Many would keep paying off loans instead of defaulting if they kept a job due to extra fiscal spending. Also the production capacity is way lower then prerecession times if it is prolonged. Many firms default and shut down if the fiscal spending is not timely.
Not mentioning the fact that money is destroyed is a big hole in talks about the fiscal multiplyer because its the biggest factor in it. Calling it propensity to save is protecting mainstream narative.

1. I would have to think about it, but I am unsure whether the fiscal multiplier would necessarily be much lower when a recession is already started. When in recessionary conditions, there is a self-fulfilling loop of cutting back spending within the private sector. The injection of income via governmental deficit spending will short-circuit that loop, and so it may also have a relatively high impact relative to not having the deficit spending.

I am not a huge fan of a focus on money (as the title of my book "Abolish Money (From Economics)!" suggests). Private sector entities want to shrink their balance sheets in a crisis, and whether they are eliminating instruments that are classified as "money" is not entirely material.

2. "I am not a huge fan of a focus on money "
If you are not such fan,the fiscal multiplayer is a fan of a focus on money. All people and firms/ private sector entities have a huge focus on money when deciding how much to spend or to go bankrupt. A balance sheet is focused on money.
As my experience tells me that I can linger for a while in a recession before I closed my firm and bancrupted personally I can take new orders immediately if they arrive but if I close down then it would be not that easy. So again. After some time in a recession the fiscal multiplayer become lower then before recession.
Again, I mention "after some time" not " when recession starts" as you took it. It says that you did not give much thought about it as you have already mention.
If you stay in mainstream explanation about fiscal multiplayer in your book, why do you write again what was already told million times already? I thought that you will write something new

1. Post-Keynesian economics is not “mainstream,” and has a notion of a fiscal multiplier. The money multiplier was a key part of Monetarism, which was mainstream.

Firms are focussed on profits, not the amount of money on the balance sheet. Courtesy of being able to borrow, it is entirely possible to function with no almost no “money” on your balance sheet. That’s why the “money multiplier” breaks down.

I wrote about this at length in my book. Otherwise, a lot of the content is available as articles here.

3. Exploring Godley & Lavoie's ModelSIM was a game-changer for me in understanding the very basics of how government finance might work. I built an agent-based interpretation of their model and applied an accompanying story that seemed to grow and grow. The result, along no doubt with my errors and misinterpretations, can be found here: www.linguafinancier.com

Of course, G&L's Monetary Economics was not my only source of knowledge. Understanding Government Finance and Interest Rate Cycles: An Introduction also feature among my book purchases. :)

1. Thanks. Yes, Monetary Economics is one of the clearest introductions to economics - at least from the perspective of being familiar with mathematics.

Note: Posts are manually moderated, with a varying delay. Some disappear.

The comment section here is largely dead. My Substack or Twitter are better places to have a conversation.

Given that this is largely a backup way to reach me, I am going to reject posts that annoy me. Please post lengthy essays elsewhere.