Unit 3 Aggregate demand and the multiplier model

3.10 Shocks to households and the limits to smoothing consumption

Figures 3.10a and 3.10b (in Section 3.5) show that, in the data, consumption is less volatile than investment and smoother than GDP as a whole. But it is by no means completely smooth. Indeed if it were completely smooth, as assumed in Figure 3.17, then the marginal propensity to consume (MPC)—which is the basis of our multiplier model—would be precisely zero! In this section, we examine the limitations of the strong assumptions made by the consumption-smoothing model, and demonstrate that this leads naturally to an aggregate consumption function with a strongly positive MPC, and therefore a multiplier of above one.

How do households respond to unexpected events—or shocks—to themselves, their family, and to the economy as a whole? They would like to smooth their consumption but may not be able to do so.

As discussed in Unit 1, the term ‘shock’ is used in economics to refer to an unexpected positive or negative event, whether it affects an individual, a sector or region, or the entire economy. As we know, people think about the future and anticipate that unpredictable events may occur. When anticipating shocks affecting their own household, they also act on these beliefs. In a modern economy, this is the basis of the insurance industry.

We can distinguish between two situations:

  • Good or bad fortune strikes the household: For example, when a family member who plays an important role in household income gets a bonus or is unable to work because of an injury. This is called an idiosyncratic shock.
  • Good or bad fortune strikes the economy as a whole: For example, when a new technology raises the productivity of a staple crop or when the price of a crucial imported input like oil goes up. This is called an economy-wide or common shock.

People use two strategies to deal with idiosyncratic shocks—shocks that are specific to their household:1

self-insurance
To maintain their consumption, households can use savings and borrowing to self-insure against a temporary fall in income or need for greater expenditure.
co-insurance
A co-insurance scheme enables households to pool savings so that individual households can maintain consumption when they experience a temporary fall in income or the need for greater expenditure.
  • Self-insurance: Households that encounter an unusually high income in some period will save, so that when their luck reverses, they can spend their savings. They may also borrow in bad times if they can. It is called self-insurance because other households are not involved.
  • Co-insurance: Households that have been fortunate during a particular period can help a household hit by bad luck. Sometimes this is done among members of extended families or among friends and neighbours. Since the mid-twentieth century, particularly in richer countries, co-insurance has taken the form of citizens paying taxes, which are then used to support individuals who are temporarily out of work or when there is an economy-wide shock (unemployment benefits, furlough payments in the pandemic).

Co-insurance at a local level between households is less effective if the bad shock hits everyone at the same time. In the case of an economy-wide shock, co-insurance at the level of the economy is necessary to help the households worst hit and least able to smooth the shock themselves. This was very evident in the COVID-19 pandemic.

In economics, we use the term ‘preferences’ when describing how people decide between different options. Their preferences reflect their own evaluation of the costs and benefits of the options they face.

preferences
A description of the relative values a person places on each possible outcome of a choice or decision they have to make.

Self-insurance and co-insurance reflect two important aspects of the preferences of many households:

  • Households prefer a smooth pattern of consumption: They dislike consumption that fluctuates as a result of bad or good shocks, so they will self-insure.
  • But they may have a bias towards the present: In some circumstances, households may prefer consuming their income now, rather than saving for the future.
  • Households are not solely selfish: They are willing to provide support to each other to help smooth the effect of good and bad luck. They often trust others to do the same, even when they do not have a way of enforcing this. Support for the tax and benefits system reflects the preference for smoothing.

Limits to consumption smoothing

What limits a household’s consumption smoothing? Many individuals and households are not able to make or implement long-term consumption plans. Making plans can be difficult because of a lack of information. Even if we have information, we may not be able to use it to predict the future with confidence. For example, it is often very hard to judge whether a change in circumstances is temporary or permanent.

Section 9.9 of the microeconomics volume discusses the reasons why many people, especially in poorer households, are credit constrained or excluded altogether from borrowing.

When faced with income shocks, the extent of smoothing also depends on:

credit constraints
Credit constraints are restrictions on the amounts or terms on which individuals can borrow.
credit market excluded
A description of individuals who are unable to borrow on any terms. See also: credit market constrained.
  • Credit constraints or credit market exclusion: This restricts a family’s ability to borrow in order to sustain consumption when income has fallen.
  • Limited co-insurance: Those with a fall in income can expect only partial support in sustaining their incomes from others more fortunate than them, including from the government’s co-insurance schemes.

Credit constraints

The amount a family can borrow is limited, particularly if it is not wealthy. Sometimes households with little money cannot borrow at all, or only at extraordinarily high interest rates. Therefore, the people who most need credit to smooth their consumption are often unable to borrow.

Figure 3.18 shows the reaction of two different types of household to an anticipated rise in income. Households that are able to borrow as much as they like are in the top panel. Credit-constrained households that are unable to get a loan or a credit card are in the bottom panel. Follow the analysis in Figure 3.18 to understand how the two households react differently to two key events:

  1. First, news is received that income will rise at a predictable time in the future (for example, a promotion or a bequest).
  2. Later, the household’s income actually rises (the promotion happens, the inheritance comes through).
This figure shows two diagrams. Both diagrams display the path of income and the path of consumption over time. Diagram 1 shows the path of income and consumption over time in consumption-smoothing households. The horizontal axis in diagram 1 shows the time and is split into two periods, namely, “News about rise in future income received” and “Actual income rises”. The vertical axis in diagram 1 shows income and consumption. The path of income remains constant at a low level until actual income rises, when it increases to a higher level and stays constant at that level. The path of consumption in starts at a low level and rises to a higher level when news about rise in future income is received, and stays constant at that higher level. The area between the income and consumption paths bounded by the time periods “News about rise in future income received” and “Actual income rises” when consumption exceeds income is shaded and labelled as “Borrowing”. In the time period after “Actual income rises” when income is higher than consumption, the area between the income and consumption paths is shaded and labelled as “Repaying debt”. Diagram 2 shows the path of income and consumption over time in credit-constrained households. The horizontal axis in diagram two also shows the time and is split into two periods, namely, “News about rise in future income received” and “Actual income rises”. The vertical axis in diagram two also shows income and consumption. The paths of income and consumption in credit-constrained households are the same. They start at a low level and stay constant until actual income rises, when both income and consumption rise the same amount to a higher level and remain constant for the remaining time.
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https://www.core-econ.org/macroeconomics/03-aggregate-demand-10-shocks-and-limits-to-consumption.html#figure-3-18

Figure 3.18 An anticipated rise in income: consumption smoothing and credit constraints.

Income over time: This figure shows two diagrams. Both diagrams display the path of income over time. Diagram 1 shows the path of income over time in consumption-smoothing households. The horizontal axis in diagram 1 shows the time and is split into two periods, namely, “News about rise in future income received” and “Actual income rises”. The vertical axis in diagram 1 shows income and consumption. The path of income remains constant at a low level until actual income rises, when it increases to a higher level and stays constant at that level. Diagram 2 shows the path of income over time in credit-constrained households. The horizontal axis in diagram 2 also shows the time and is split into two periods, namely, “News about rise in future income received” and “Actual income rises”. The vertical axis in diagram 2 also shows income and consumption. The path of income in credit-constrained households is identical to that in consumption-smoothing households; it remains constant at a low level until actual income rises, when it increases to a higher level and stays constant at that level.
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https://www.core-econ.org/macroeconomics/03-aggregate-demand-10-shocks-and-limits-to-consumption.html#figure-3-18a

Income over time

The blue lines on the figure show that the path of income over time is the same in both households.

Consumption smoothing: This figure shows two diagrams. Both diagrams display the path of income and the path of consumption over time. Diagram 1 shows the path of income and consumption over time in consumption-smoothing households. The horizontal axis in diagram 1 shows the time and is split into two periods, namely, “News about rise in future income received” and “Actual income rises”. The vertical axis in diagram 1 shows income and consumption. The path of income remains constant at a low level until actual income rises, when it increases to a higher level and stays constant at that level. The path of consumption in starts at a low level and rises to a higher level when news about rise in future income is received, and stays constant at that higher level. The area between the income and consumption paths bounded by the time periods “News about rise in future income received” and “Actual income rises” when consumption exceeds income is shaded and labelled as “Borrowing”. In the time period after “Actual income rises” when income is higher than consumption, the area between the income and consumption paths is shaded and labelled as “Repaying debt”. Diagram 2 shows the path of income over time in credit-constrained households. The horizontal axis in diagram 2 also shows the time and is split into two periods, namely, “News about rise in future income received” and “Actual income rises”. The vertical axis in diagram 2 also shows income and consumption. The path of income in credit-constrained households is identical to that in consumption-smoothing households; it remains constant at a low level until actual income rises, when it increases to a higher level and stays constant at that level.
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https://www.core-econ.org/macroeconomics/03-aggregate-demand-10-shocks-and-limits-to-consumption.html#figure-3-18b

Consumption smoothing

The red line in the top panel shows that, in a consumption-smoothing household, consumption changes immediately once the household receives the news.

The effect of credit constraints: This figure shows two diagrams. Both diagrams display the path of income and the path of consumption over time. Diagram 1 shows the path of income and consumption over time in consumption-smoothing households. The horizontal axis in diagram 1 shows the time and is split into two periods, namely, “News about rise in future income received” and “Actual income rises”. The vertical axis in diagram 1 shows income and consumption. The path of income remains constant at a low level until actual income rises, when it increases to a higher level and stays constant at that level. The path of consumption in starts at a low level and rises to a higher level when news about rise in future income is received, and stays constant at that higher level. The area between the income and consumption paths bounded by the time periods “News about rise in future income received” and “Actual income rises” when consumption exceeds income is shaded and labelled as “Borrowing”. In the time period after “Actual income rises” when income is higher than consumption, the area between the income and consumption paths is shaded and labelled as “Repaying debt”. Diagram 2 shows the path of income and consumption over time in credit-constrained households. The horizontal axis in diagram two also shows the time and is split into two periods, namely, “News about rise in future income received” and “Actual income rises”. The vertical axis in diagram two also shows income and consumption. The paths of income and consumption in credit-constrained households are the same. They start at a low level and stay constant until actual income rises, when both income and consumption rise the same amount to a higher level and remain constant for the remaining time.
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https://www.core-econ.org/macroeconomics/03-aggregate-demand-10-shocks-and-limits-to-consumption.html#figure-3-18c

The effect of credit constraints

On the other hand, a credit-constrained household that cannot borrow has to wait until the income arrives before adjusting its standard of living.

A temporary change in income affects the current consumption of credit-constrained households more than it does that of the unconstrained.

Present bias

present bias
An individual or household with present bias puts more weight on present rather than future consumption. They may prefer to consume all of their current income now, even when they know that income will be lower in the future.

In Figure 3.19, an individual learns that income is going to fall in the future. This could be because of retirement or job loss. It could also be because the individual is becoming pessimistic. Perhaps the media predicts an economic crisis. In the top panel of Figure 3.19, we again show a household behaving in a forward-looking manner to smooth consumption. The bottom panel shows a household with present bias that consumes all its income today even though it implies a large reduction in consumption in the future.

This figure shows two diagrams. Both diagrams display the path of income and the path of consumption over time. Diagram 1 shows the path of income and consumption over time in consumption-smoothing households without present bias. The horizontal axis in diagram 1 displays the time and is split into 2 periods, namely, “News about fall in income received” and “Actual income falls”. The vertical axis in diagram 1 displays income and consumption. The path of income starts at a high level and remains constant until actual income falls, falling to a lower level and staying constant at that lower level for the remaining time. The path of consumption starts at the same high level as income, but once news about fall in income is received, consumption falls to a lower level, staying constant at that lower level for the remaining periods. The area between the income path and the consumption path bounded by the time periods “News about fall in income received” and “Actual income falls” when income is above consumption is shaded and labelled as “Saving”. The area between the income path and the consumption path after “Actual income falls” when consumption is above income is labelled as “Running down savings or borrowing”. Diagram 2 shows the path of income and consumption over time in credit-constrained households with present bias. The paths of income and consumption in credit-constrained households with present bias are the same. They both start at the same high level and remain constant until actual income falls, falling to a lower level and staying at the lower level for the remaining periods.
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https://www.core-econ.org/macroeconomics/03-aggregate-demand-10-shocks-and-limits-to-consumption.html#figure-3-19

Figure 3.19 Consumption when households demonstrate present bias: an anticipated fall in income.

The path of income: This figure shows two diagrams. Both diagrams display the path of income over time. Diagram 1 shows the path of income over time in consumption-smoothing households without present bias. The horizontal axis in diagram 1 displays the time and is split into 2 periods, namely, “News about fall in income received” and “Actual income falls”. The vertical axis in diagram 1 displays income and consumption. The path of income starts at a high level and remains constant until actual income falls, falling to a lower level and staying at that lower level for the remaining periods. Diagram 2 shows the path of income over time in credit-constrained households with present bias. The horizontal axis in diagram 2 displays the time and is split into the same 2 periods, namely, “News about fall in income received” and “Actual income falls”. The vertical axis in diagram 2 also displays income and consumption. The path of income in diagram 2 is the same as that of diagram 1; it starts at a high level and remains constant until actual income falls, falling to a lower level and staying at that lower level for the remaining periods.
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https://www.core-econ.org/macroeconomics/03-aggregate-demand-10-shocks-and-limits-to-consumption.html#figure-3-19a

The path of income

The blue lines in the figure show that income follows the same path in both sets of households.

Consumption smoothing: This figure shows two diagrams. Both diagrams display the path of income and the path of consumption over time. Diagram 1 shows the path of income and consumption over time in consumption-smoothing households without present bias. The horizontal axis in diagram 1 displays the time and is split into 2 periods, namely, “News about fall in income received” and “Actual income falls”. The vertical axis in diagram 1 displays income and consumption. The path of income starts at a high level and remains constant until actual income falls, falling to a lower level and staying constant at that lower level for the remaining time. The path of consumption starts at the same high level as income, but once news about fall in income is received, consumption falls to a lower level, staying constant at that lower level for the remaining periods. The area between the income path and the consumption path bounded by the time periods “News about fall in income received” and “Actual income falls” when income is above consumption is shaded and labelled as “Saving”. The area between the income path and the consumption path after “Actual income falls” when consumption is above income is labelled as “Running down savings or borrowing”. Diagram 2 shows the path of income over time in credit-constrained households with present bias. The horizontal axis in diagram 2 displays the time and is split into the same 2 periods, namely, “News about fall in income received” and “Actual income falls”. The vertical axis in diagram 2 also displays income and consumption. The path of income in diagram 2 is the same as that of diagram 1; it starts at a high level and remains constant until actual income falls, falling to a lower level and staying at that lower level for the remaining periods.
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https://www.core-econ.org/macroeconomics/03-aggregate-demand-10-shocks-and-limits-to-consumption.html#figure-3-19b

Consumption smoothing

The red line in the top panel shows the consumption path for a consumption-smoothing household. When it receives news of the imminent fall in income, it immediately starts saving to supplement consumption when income falls.

A household with present bias: This figure shows two diagrams. Both diagrams display the path of income and the path of consumption over time. Diagram 1 shows the path of income and consumption over time in consumption-smoothing households without present bias. The horizontal axis in diagram 1 displays the time and is split into 2 periods, namely, “News about fall in income received” and “Actual income falls”. The vertical axis in diagram 1 displays income and consumption. The path of income starts at a high level and remains constant until actual income falls, falling to a lower level and staying constant at that lower level for the remaining time. The path of consumption starts at the same high level as income, but once news about fall in income is received, consumption falls to a lower level, staying constant at that lower level for the remaining periods. The area between the income path and the consumption path bounded by the time periods “News about fall in income received” and “Actual income falls” when income is above consumption is shaded and labelled as “Saving”. The area between the income path and the consumption path after “Actual income falls” when consumption is above income is labelled as “Running down savings or borrowing”. Diagram 2 shows the path of income and consumption over time in credit-constrained households with present bias. The paths of income and consumption in credit-constrained households with present bias are the same. They both start at the same high level and remain constant until actual income falls, falling to a lower level and staying at the lower level for the remaining periods.
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https://www.core-econ.org/macroeconomics/03-aggregate-demand-10-shocks-and-limits-to-consumption.html#figure-3-19c

A household with present bias

On the other hand, a household that demonstrates present bias will be reluctant to reduce their current consumption, keeping it at the initial level until income falls. At that point, consumption falls further than it does for the consumption-smoothing household who can now rely on the savings that were made ahead of the fall in income.

Although a household may want to avoid a sudden drop in consumption when income falls, the desire to postpone a fall in living standards (present bias) means they may not react to the news at all, and keep consumption high until income falls. The problem of not being able to save differs from the problem of not being able to borrow: there is no constraint on saving, and as a form of self-insurance it doesn’t involve anyone else. This feature of human behaviour is familiar to many of us. When the time comes, we often lack the willpower to implement a plan we made earlier. Economists refer to this as time-inconsistent behaviour. While there are other possible explanations for failing to save ahead of a known fall in income, time inconsistency is one for which there is evidence. (Read the box ‘How economists learn from facts: My diet starts tomorrow’.)

How economists learn from facts My diet starts tomorrow

Economists have conducted experiments to test for behaviour that would help to explain why we don’t save even when we can. For example, Daniel Read and Barbara van Leeuwen conducted an experiment with 200 employees at firms in Amsterdam. They asked them to choose today what they thought they would eat next week. The choice was between fruit and chocolate.

When asked, 50% of subjects replied that they would eat fruit next week. But, when next week came, only 17% actually chose to eat fruit. The experiment shows that, although people may plan to do something that they know will be beneficial (eat fruit, save money), when the time comes they often don’t do it.2

Question 3.12 Choose the correct answer(s)

The following diagram shows the path of income for a household that receives news about an expected rise and fall in future income at the depicted times.

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https://www.core-econ.org/macroeconomics/03-aggregate-demand-10-shocks-and-limits-to-consumption.html#

Assume that the household prefers to smooth out its consumption, if it can. Based on this information, read the following statements and select the correct option(s).

  • If the household is not credit constrained, then it will consume the same level after \(t = 1\).
  • If the household is credit constrained and has present bias, then its consumption will match precisely its income path.
  • If the household is not credit constrained but has present bias, then it will borrow at \(t = 1\) and save at \(t = 3\).
  • If the household is credit constrained but does not have present bias, then it will borrow at \(t = 1\) and save at \(t = 3\).
  • If the household is not credit constrained, then it can smooth consumption over the next three periods by borrowing at \(t = 1\), then repaying debt once income rises. Therefore it will not consume at the same level after \(t = 1\).
  • The fact that the household is credit constrained implies that it cannot borrow. The fact that it has present bias implies that it will not save. So income will be equal to consumption at all times.
  • A household with present bias will not save at \(t = 3\).
  • A credit-constrained household will not be able to borrow at \(t = 1\).

Limited co-insurance

Most households lack a network of family and friends who can help out in substantial ways over a long period when a negative income shock occurs. Unemployment benefits provide this kind of co-insurance—the citizens who turn out to be lucky in one year insure those who are unlucky. But in many societies, the coverage of these policies is very limited.3

A vivid demonstration of the value of smoothing through co-insurance is the experience of Germany during the drastic reduction in income that occurred there in the global financial crisis in 2007–2009. When the demand for firms’ products fell, workers’ hours of work were cut, but as a result of both government policy and agreements between firms and their employees, very few Germans lost their jobs, and many of those at work were still paid as if they were working many more hours than they did. The result was that although aggregate income fell, consumption did not—and unemployment did not increase. Employers ‘banked’ these hours and their employees worked the extra hours later when demand rebounded.

But most empirical evidence shows that credit constraints, present bias, and limited co-insurance mean that, for many households, a change in income results in an equal change in consumption. In the case of a negative income shock such as the loss of a job, this means that the income shock will now be passed on to other families who would have produced and sold the consumption goods that are now not demanded.

Figures 3.10a and 3.10b showed that consumption in middle-income countries was more volatile than in high-income countries. This reflects a combination of more widespread credit constraints and more limited government systems of co-insurance.

Exercise 3.7 Health insurance

  1. Think about the health insurance system in your country. Is this an example of co-insurance or self-insurance?
  2. Can you think of other examples of both co-insurance and self-insurance? In each case, consider what kinds of shocks are being insured against and how the scheme is financed.
  3. Would you expect insurance companies to provide ‘pandemic insurance’?

You may find it useful to refer to the discussion in Section 10.10 of the microeconomics volume in your answers.

Consumption behaviour and the multiplier model

Whether or not households are able or willing to smooth consumption is crucial for the multiplier model set out in Sections 3.7 and 3.8.

We can think of the multiplier model as applying to an economy that consists of two types of households. Some households smooth their consumption by borrowing and saving: we can think of these as having an MPC of zero \((c_1 = 0)\). But others, due to some combination of credit constraints and present bias, have an MPC of 1 \((c_1 = 1)\).

If we average across the two types of households to find the aggregate consumption function, this gives an average MPC between 0 and 1 as in the multiplier model. Whether the aggregate MPC is high or low therefore depends on the proportion of households in each group.

Shifts in the proportion who are credit constrained and therefore have a high MPC affect the size of the multiplier. This helps explain why the multiplier is found to be higher in deep recessions than it is in booms.

Exercise 3.8 Changes in income, changes in consumption

Consider a credit-constrained household type and a consumption-smoothing household type.

  1. For each household type, use a figure with time on the horizontal axis and income and consumption on the vertical axis to explain the relationship between the change in income and the change in consumption when income returns to normal after an unexpected temporary decline.
  2. Based on this analysis, explain the predicted relationship between temporary changes in income and consumption for an economy with a mixture of the two household types.

Question 3.13 Choose the correct answer(s)

Consider a €2.5 billion increase in investment in an economy with no taxation, exports, or imports. There are two scenarios:

  • Scenario A: 80% of households are credit constrained and 20% are not.
  • Scenario B: 20% of households are credit constrained and 80% are not.

Based on this information and the two scenarios, read the following statements and select the correct option(s).

  • The multiplier in Scenario A is 5.
  • The MPC in Scenario A is five times larger than the MPC in Scenario B.
  • In the new goods market equilibrium, aggregate demand increases by €3.125 billion in Scenario B.
  • In the new goods market equilibrium, aggregate demand would be €10 billion higher in Scenario A than Scenario B.
  • Credit constrained households have an MPC of 1 and households that are not credit constrained have an MPC of 0, so the MPC in scenario A is (\(0.8 \times 1 + 0.2 \times 0) = 0.8\). Then, given that the MPC is 0.8, we can calculate the multiplier as \(\frac{1}{1 \ - \ 0.8}=5\).
  • The MPC in Scenario A is 0.8, which is four times larger than the MPC in Scenario B (0.2).
  • Aggregate demand increases by \(2.5 \times \frac{1}{1 \ - \ 0.2}\) = €3.125 billion in Scenario B.
  • In Scenario A, aggregate demand increases by \(2.5 \times \frac{1}{1 \ - \ 0.8}\) = €12.5 billion, which is €9.375 billion more than in Scenario B.
  1. ‘New Cradles to Graves’. The Economist. Updated 8 September 2012. 

  2. Daniel Read and Barbara van Leeuwen. 1998. ‘Predicting Hunger: The Effects of Appetite and Delay on Choice’. Organizational Behavior and Human Decision Processes 76 (2): pp. 189–205. 

  3. OECD. 2010. Employment Outlook 2010: Moving Beyond the Jobs Crisis