Unit 5 Macroeconomic policy: Inflation and unemployment

5.7 The size of the multiplier and the impact of fiscal policy

In the multiplier model of Unit 3, we used simplified ways of modelling aggregate consumption, investment, trade, and government discretionary fiscal policy. This means there are a small number of variables from which the size of the multiplier is calculated, such as the marginal propensity to consume (MPC), the marginal propensity to import, and the tax rate. When we apply the model to the world, it is important to realise that in practice there is no single multiplier—a number—that applies at all times.

If the MPC of the proportion of households in the economy that is credit constrained is equal to one and the MPC of the unconstrained (the rest of the households) is equal to zero, then the average MPC in an economy is just the share of credit-constrained households.

One modification follows directly from the discussion in Section 3.6, where we showed that households that are credit constrained will have an MPC close to one and households that are not will have an MPC close to zero: the MPC in the economy will depend on the share of each group in the economy. In a recession, after taking account of the effect of the automatic stabilizers, we would expect the share of credit-constrained households to rise, which implies that the average MPC in the economy would rise. A higher MPC increases the size of the multiplier and hence the effectiveness of discretionary fiscal stimulus in a recession.

With our assumptions so far, the multiplier in the model is always greater than one. We assume that output is determined solely by the level of aggregate demand and a change in aggregate demand directly changes output one-for-one and then indirectly by more in the subsequent rounds of expenditure, depending on the size of the multiplier.

However, the model can be extended in ways that mean the direct effect of a fiscal stimulus on output is less than one-for-one. This can result in an overall multiplier of less than one.

Crowding out

crowding out, crowded out
There are two quite distinct uses of the term. One is a negative effect that is observed when economic incentives displace people’s ethical or social motivations. In studies of individual behaviour, incentives may have a crowding out effect on social preferences. The second use of the term is to refer to the effect of an increase in government spending in reducing private spending, as would be expected for example in an economy working at full capacity utilization, or when a fiscal expansion is associated with a rise in the interest rate.

Suppose the economy is operating at full capacity utilization and there is very low unemployment. In such a situation, there may be little or no scope for output to rise. Then, a 1% increase in government spending on goods and services would displace or crowd out up to 1% of other spending in the economy. With complete crowding out, the multiplier would be zero. However, we would not normally expect a government to undertake a fiscal expansion when unemployment is very low—although it may do so in exceptional circumstances like war, as the US did in the later years of the Second World War and during the Vietnam War.

Another example of crowding out (and therefore, a lower multiplier) is if households think that higher government spending will be followed by higher taxes. In this case, some households may put aside more of their income to pay the extra taxes in the future. They save more now to keep their consumption path smoother. If this happened, the effect of the stimulus would be less.

The size of the multiplier will also depend on the expectations of firms and businesses. Households and firms not only react to policy changes, but also anticipate them. For example, if firms anticipate that the government will stabilize the economy following a negative shock, this will support business and consumer confidence, and the policymaker will be able to use a smaller stimulus. In this case, fiscal policy ‘crowds in’ private spending.

The multiplier and the financial crisis of 2007–2009

When the financial crisis in 2007–2009 led to the biggest fall in GDP in many economies since the Great Depression, the world’s policymakers expected an answer from economists: would fiscal policy help to stabilize the economy? The multiplier model, inspired by Keynes’ analysis of the Great Depression, suggested that it would. And despite scepticism among some economists, policymakers around the world embarked on fiscal stimulus programmes in 2008–2009. This prompt and decisive action was credited with helping to avert the persistent high unemployment of another Great Depression, as discussed in Unit 17 of The Economy 1.0.

The global financial crisis of 2008 revived interest in the multiplier. In 2012, a study published by economists Alan Auerbach and Yuriy Gorodnichenko showed how the multiplier varies in size according to whether the economy is in a recession or in an expansion.1

For the US, their study suggested a $1 increase in government spending in the US raises output by about $1.50 to $2.00 in a recession, but only about $0.50 in an expansion. Auerbach and Gorodnichenko extended their research to other countries and found similar results. They also found that the effect of autonomous increases in spending in one country had spillover effects on the countries with which they trade. These effects were about the same magnitude as the indirect effects of second, third, and further rounds of spending in the home country.

How economists learn from facts The Mafia and the multiplier

reverse causality
If we are looking for evidence that one variable (x) causes another (y) and find that the variables are correlated, the explanation may be the reverse: that y causes x. For example, if we find that people who attend university earn more, does that mean that university increased their earning ability? Could it be that people with high earning potential are more likely to attend university? See also: correlation.

Economists need estimates of the multiplier to design their policy interventions. But finding out its size directly from data on government spending and changes in output will run into the problem of reverse causality: a fall in output may have led the government to increase spending. To get at the ‘pure’ effect of a change in spending on output, economists have used the Italian government’s struggle against the Mafia where spending cuts took place for reasons quite unrelated to the business cycle.

natural experiment
An empirical study that exploits a difference in the conditions affecting two populations (or two economies), that has occurred for external reasons: for example, differences in laws, policies, or weather. Comparing outcomes for the two populations gives us useful information about the effect of the conditions, provided that the difference in conditions was caused by a random event. But it would not help, for example, in the case of a difference in policy that occurred as a response to something else that might affect the outcome.

Antonio Acconcia, Giancarlo Corsetti, and Saverio Simonelli2 adopted the natural experiment method to address the problem of reverse causality; they used data on Mafia-related dismissals of local politicians to isolate the variation in public spending that is not caused by variations in output.

After legal changes in 1991, the central government dismissed provincial councils in Italy that were revealed to have close links with the Mafia, and appointed new officials in their place. These technocrats cut local spending by 20% on average. The change in public spending was indirectly caused by Mafia infiltration, because that led to the replacement of government officials. However, because it was the change in government officials, rather than the involvement of Mafia, that led to spending cuts, the researchers can uncover the causal effect of a change in public spending on output. This situation is illustrated in Figure 5.9.

The flowchart illustrates the causal relationship examining the impact of Mafia-related government changes on output in Italy. It begins with Proximity to the Mafia, which leads to Replacement by technocrats. This replacement then leads directly to Spending cuts. It is shown that these spending cuts lead to Variation in output. Additionally, a line from Replacement by technocrats extends to the side with a label No direct effect, indicating no direct impact on the variation in output from the Proximity to the Mafia.
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https://www.core-econ.org/macroeconomics/05-macroeconomic-policy-07-multiplier-and-fiscal-policy.html#figure-5-9

Figure 5.9 Using Mafia infiltration to estimate the multiplier.

Using this method, the researchers were able to estimate multipliers of 1.5 at the local level.

Economists have used their ingenuity to come up with other methods of estimating the size of the multiplier and the implication of its operation for jobs in the context of the fiscal stimulus implemented in the US after the financial crisis (the American Recovery and Reinvestment Act of 2009, a $787 billion fiscal stimulus). The problem of reverse causality is very clear in this case. We are interested in how the stimulus affects output but measuring this is hard when output also affects the stimulus: US states that were more severely affected by the financial crisis would be expected to attract more stimulus money.

One approach to get around the problem of reverse causality is to make use of the fact that some of the spending in the US stimulus programme was distributed to US states using a formula that was unrelated to the severity of the recession experienced in each state. For example, some road repair expenditures funded by the stimulus package were based on the length of highway in each state.3

Given the formula for allocating road building funds and the fact that having more miles of highway has no direct effect on the change in unemployment, this allows us to answer the question: Were more jobs created in states that received more stimulus spending?4

The flowchart illustrates the causal relationship examining the impact of highway spending on employment in the US. It begins with more miles of highway, which leads to more stimulus spending. It is shown that these spending stimulus leads to change in unemployment. Additionally, a line from more miles of highway extends to the side with a label no direct effect, indicating no direct impact on the variation in employment from more miles of highway.
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https://www.core-econ.org/macroeconomics/05-macroeconomic-policy-07-multiplier-and-fiscal-policy.html#figure-5-10

Figure 5.10 Using US stimulus highway spending to estimate the multiplier.

The results of studies using this approach estimated a multiplier of 2, and suggest that the American Recovery and Reinvestment Act created between one million and three million new jobs.

Question 5.4 Choose the correct answer(s)

Read the following statements about the multiplier and choose the correct option(s).

  • Economists tend to agree on their estimates of the multiplier.
  • Reverse causation can be a problem when estimating the multiplier empirically.
  • If households anticipate that increased government spending will be funded by future tax increases, then the multiplier will be higher.
  • If firms anticipate that the government’s fiscal policy will be effective, then the multiplier will be higher.
  • Estimates of the multiplier vary widely.
  • If more fiscal stimulus is given to economies with higher unemployment then reverse causality can be a problem for estimates of the multiplier.
  • In this case, households may increase savings today in order to pay for the anticipated tax increases, reducing their marginal propensity to spend and hence reducing the multiplier.
  • Firms will increase investment if they believe the economy will recover quickly, increasing demand.

Exercise 5.5 Stimulus without more debt

Read ‘Stimulus, Without More Debt’ by Robert Shiller.

Assume the economy is in a recession. The government has a high level of debt and wants to set a balanced budget, that is, \(G = T\), where T is total tax revenue. How can the government achieve a fiscal stimulus effect on GDP while keeping the budget balanced?

To answer the question and show that the size of the balanced budget multiplier is exactly one, take the following steps:

  • Explain in words how the government can achieve a fiscal stimulus effect (with a multiplier of one) while keeping the budget balanced.
  • Derive the balanced budget multiplier using algebra. (Hint: Write down the increase in output arising from the increase in G: by how much does it rise as a result of the rise in G, because of the rise in consumption due to the higher incomes, and so on. Next, write down the change in output due to the effect of the higher taxation in depressing incomes. Compare the change in output in each case, remembering that G and T are the same size.)
  • More challenging is to show the result in a multiplier diagram: using squared paper helps. Make the diagram sufficiently accurate so that the exact size of the multiplier is visible. Try to label the diagram with the steps in the reasoning in the previous bullet.
  • Refer to Shiller’s article to comment briefly on disadvantages with the adoption of a balanced budget fiscal stimulus.

When working on this problem, make the following assumptions:

  • Assume a lump sum tax. This means that the tax does not depend on the level of income, \(T = T\), rather than our usual assumption that \(T = tY\) introduced in Section 3.9. The consumption function is now \(C = c_{0} + c_{1}(Y - T)\) rather than \(C = c_{0} + c_{1}(1 - t)Y)\).
  • Assume that there are no transfers.
  • Also assume that the country does not have any imports or exports.
  1. ‘How Powerful Are Fiscal Multipliers in Recessions?’ NBER Reporter. Updated 13 July 2015. 

  2. Antonio Acconcia, Giancarlo Corsetti, and Saverio Simonelli. 2014. ‘Mafia and Public Spending: Evidence on the Fiscal Multiplier from a Quasi-Experiment’. American Economic Review 104 (7): pp. 2185–2209. 

  3. Sylvain Leduc and Daniel Wilson. 2015. ‘Are State Governments Roadblocks to Federal Stimulus? Evidence on the Flypaper Effect of Highway Grants in the 2009 Recovery Act’. Federal Reserve Bank of San Francisco Working Paper 2013–16 (September). 

  4. Miguel Almunia, Agustín Bénétrix, Barry Eichengreen, Kevin H. O’Rourke, and Gisela Rua. 2010. ‘From Great Depression to Great Credit Crisis: Similarities, Differences and Lessons’. Economic Policy 25 (62): pp. 219–65.

    Tim Harford. 2010. ‘Stimulus Spending Might not Be as Stimulating as We Think’. The Financial Times. Updated January 2010.

    Paul Krugman. 2012. ‘A Tragic Vindication’. Paul Krugman, New York Times Blog. Updated 9 October 2012.

    Jonathan Portes. 2012. ‘What Explains Poor Growth in the UK? The IMF Thinks It’s Fiscal Policy’. National Institute of Economic and Social Research Blog. Updated 9 October 2012.

    Noah Smith. 2013. ‘Why the Multiplier Doesn’t Matter’. Noahpinion. Updated 7 January 2013.

    Simon Wren-Lewis. 2012. ‘Multiplier Theory: One Is the Magic Number’. Mainly Macro. Updated 24 August 2012.