Unit 3: Microfoundations
Unit 3.1: Consumption
In this unit, we will study the microeconomic foundations that underlie key pieces of the economy. While the goal of macroeconomics is to study aggregate economic activity, micro-level decisions underlie macroeconomic aggregates. For example, in understanding investment spending at the macroeconomic level, we need a good handle on how firms make investment decisions.
In this section, we will focus on the microfoundations of consumption spending. Consumption spending represents about 70% of aggregate expenditures / aggregate demand in the economy. We will first go through some basic stylized facts on consumption spending, and then we will study two different approaches to modeling consumption spending – the Keynesian approach and the life-cycle approach, which is more consistent with classical economics.
Stylized Facts on Consumption Spending
Here is a graph showing real GDP and real consumption spending in the US since 1960.
The key stylized fact is that consumption spending grows at approximately the same rate as GDP,
Recall that consumption spending is made up of durable goods, nondurable goods and services. Here is a graph showing US data on each component since 1960.
The key stylized fact here is that spending on nondurable goods and on services is more stable than spending on durable goods. We know that consumption spending is more stable than GDP overall, and now we see that the fluctuations that do exist tend to arise primarily because of fluctuations in spending on durable goods. In other words, spending on nondurables and on services is extremely
stable over the business cycle.
If you think practically about household budgeting, this makes good sense. Families still need to eat, buy gasoline and get haircuts during recessions, but they can postpone purchases of refrigerators, automobiles or couches.
Disposable Income and Spending – Automatic Stabilizers
Why is consumption spending so much more stable than income is? Doesn’t this invalidate the Keynesian postulate that consumption spending is just a function of income?
One important thing to note is that GDP represents all income in the economy. But, as we saw in unit 1, not all of this income ends up as disposable income in the pockets of consumers. Some of our national income is held by firms as retained profits, some is eaten up by depreciation and some is paid to the government as taxes. All in all, disposable income is only about 60% of GDP.
Why is disposable income so much more stable than total income (GDP)? Economists point to three main factors.
1. Progressivity of the tax system – The US income tax system is progressive. You pay a higher percentage of your income in taxes as your income rises. Because of this, when a family’s income rises, its disposable income may not rise as quickly as its income rises because the family will owe a higher percentage of its income in taxes. On the positive side, this feature of the tax system can buffer negative shocks. A family that suffers a decline in income won’t see its disposable income fall by the same proportion since it might find itself in a lower tax bracket.
2. Means-tested transfers – When income falls, more people qualify for government transfers like food stamps and assistance with medical care. This means that, during recessions,
disposable income will not fall by as much as income falls since some families suffering from income shocks will qualify for transfers. Conversely, when income rises, disposable income for a family might not rise by all that much if the family loses access to transfers.
3. Companies tend to reduce retained earnings during recessions but continue to pay dividends. Thus, dividend income to households does not fall by as much as GDP falls since firms are absorbing some of the GDP decline as a decline in retained earnings.
Keynesian Consumption Function
The Keynesian consumption function does not fit well when we model consumption spending as a function of GDP. But it fits better if we model consumption spending as a function of disposable
income. Here is a diagram that plots consumption spending and disposable every year since 1960.
The regression line is drawn in. If we run a regression of consumption spending on disposable income (in trillions), the Excel output is:
Writing out the estimated regression line:
Consumption spending = −0.2557 + 0.9358 ⋅ (Disposable Income)
Using this estimate derived from US data, the MPC is about 0.94. In other words, each $1 increase of disposable income is associated with about $0.94 of additional consumption spending. The coefficient is statistically significant at any conventional level since the p-value is almost zero.
While the data are somewhat noisy, the general pattern is that spending during economic downturns is higher than what the Keynesian consumption function would predict, and spending during good economic times is somewhat lower than what the Keynesian consumption function would predict. There must be something else going on here. The Keynesian consumption function, with spending as a function of current income, is inadequate for explaining all movements in consumption spending.
To summarize what we have argued so far, consumption spending fluctuates less than GDP, especially services and nondurables. The main reason is that disposable income fluctuates less than GDP due to automatic stabilizers. If we use US data to estimate a Keynesian consumption function of consumption spending on current disposable income, we obtain an MPC of about 0.94, but there are substantial deviations from this consumption function.
Life-Cycle Models
Inadequacies with the Keynesian consumption function led economists to study the determinants of consumer spending more deeply. Relying on micro-level theories of optimal consumption spending at the individual household level, we obtain a set of models that offer conclusions that are quite different from the Keynesian model.
The basic difference is this. Keynesian models postulate that individuals and households make consumption decisions based on current income. By contrast, life-cycle models postulate that people make consumption decisions based on an optimizing plan that incorporates their entire lives. The basic idea has had a number of different incarnations and labels – forward-looking consumption, permanent income theory (coined by Milton Friedman) and life-cycle theory (coined by Modigliani and Miller). The last one seems like the most descriptive, so we will call these models life-cycle models.
While the Keynesian model is based on a strong empirical regularity, life-cycle models are based more on economic theory – individuals plan out their consumption patterns to optimize their total happiness across their lives. That is, in making current consumption decisions, households not only consider their current incomes but also previous asset accumulation and future expectations. Important questions to consider are things like:
• How much income will I earn in the future?
• What are my assets? How much wealth will I need for the future?
• How much will I owe in taxes in the future?
people with the same $25,000 current income might spend different amounts if one is going to earn $25,000 a year for the rest of his life, but the other is going to earn a salary of $100,000 next year and forever thereafter.
Economic institutions allow consumers to take advantage of life-cycle consumption plans. You can “smooth” your income across your life by using financial assets – borrowing and saving. In other words, your consumption does not need to be tied closely to your current income. Income greater than consumption allows you to save and accumulate assets. Consumption spending greater than income can be financed through borrowing or through drawing down assets.
What does an optimal lifetime consumption plan look like? The basic idea is that most people like to keep their consumption spending fairly steady. In allocating income across their lives, most people do not want wild swings in their consumption spending. Economists call this pattern
consumption smoothing.
Why is consumption smoothing so important? Earned income varies considerably over a typical person’s life cycle. It’s low when we’re students and when we start our working careers. It’s high when we are in the prime of our careers. And then it drops to zero once we retire. But most people don’t want their consumption expenditures to vary that drastically, so they borrow and save to smooth it out. Think about it – most of us would rather live comfortably our whole lives than live in poverty, then live in riches, then live in poverty again.
Here is a diagram showing the pattern in earned income over a typical person’s life.
For a simple numerical example, suppose that Adam lives for 5 years. He earns no income during the first year, earns $100,000 a year for the next three years, and then earns no income during the last year when he is retired. The market interest rate is 10%. How should he allocate his lifetime income to keep consumption steady over his life?
To solve, we need to equate the present value of Adam’s income with the present value of his consumption spending. Income is given. Let consumption spending in each year be 𝐶𝐶. We assume that Adam plans to perfectly smooth his consumption over his life.
𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖= 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖𝑖𝑖𝑐𝑐𝑐𝑐𝑖𝑖𝑐𝑐𝑐𝑐𝑖𝑖𝑖𝑖𝑖𝑖
0
(1 + .1)1+(1 + .1)100,0002+(1 + .1)100,0003+(1 + .1)100,0004+(1 + .1)0 5=(1 + .1)𝐶𝐶 1+(1 + .1)𝐶𝐶 2+(1 + .1)𝐶𝐶 3+(1 + .1)𝐶𝐶 4+(1 + .1)𝐶𝐶 5
$226,077 =(1 + .1)𝐶𝐶 1+(1 + .1)𝐶𝐶 2+(1 + .1)𝐶𝐶 3+(1 + .1)𝐶𝐶 4+(1 + .1)𝐶𝐶 5
Solving the expression above for 𝐶𝐶 gives 𝐶𝐶 = $59,639. In words, Adam’s optimal plan is to borrow $59,639 in his first year, then repay the loan and accumulate some savings during the years when he is earning $100,000 a year. Finally, his accumulated assets allow him to spend $59,639 in his retirement year when he earns nothing.
One final point about life-cycle consumption plans – We have assumed here that the lifetime budget balances, in other words that the consumption stream exactly exhausts the income stream. Hardly anyone dies with a lot of debt, but some people do leave bequests. The speed at which people accumulate and spend down assets depends on this bequest motive. The nature of the bequest motive is an open question in the economic literature.1
Temporary and Permanent Income Shocks
We turn now to some testable implications of Keynesian and life-cycle consumption models.
By how much does an increase in disposable income raise consumption spending? In the Keynesian model, the answer would just be based on the MPC. In the life-cycle model, the answer depends crucially on whether the income shock is temporary or permanent.
Consider the impact of a $1000 tax cut. If the tax cut is permanent, then consumption spending would rise by $1000 every year to keep balance in the lifetime budget. The MPC would appear to be 1. By contrast, if the tax cut is temporary, then the one-time $1000 windfall would be smoothed over the consumer’s entire life, leading to a very low observed MPC in the year that the windfall arrives. In fact, if the interest rate is 5%, then perfect consumption smoothing would suggest
1 It might be charitable – people care about future generations. Or it might be selfish – people leave money to their
spending $50 a year (the residual lifetime income generated from investing the money), or perhaps a bit more to eat up the principal.
By contrast, consumption in the Keynesian model is based on current income, so it wouldn’t matter whether the income increase is temporary or permanent. This year’s spending is based on this year’s disposable income.
As a second example, consider a government that cuts taxes by $1000 this year and then plans to raise taxes by $1100 next year. Assume that the interest rate is 10%. In the Keynesian model, the consumer’s spending would rise this year and then fall next year based on his disposable income. In the life-cycle model, this tax policy would actually lead to no change in spending in either year because permanent income does not change. The $1000 windfall has to be fully “repaid” (with interest) next year. The policy point of this example is that, in life-cycle models, tax cuts might not increase spending by all that much if people expect that taxes are going to have to be raised in the future to pay off the debts that are accumulated.
Anticipated and Unanticipated Income Shocks
In life-cycle models, the response to anticipated income shocks is different from the response to unanticipated income shocks. Anticipated shocks can be planned for early. If you know you are getting a $1 million inheritance from your rich uncle in two years, you can start raising your spending now. This would reduce the observed MPC in the year that the income arrives. By contrast, an unanticipated shock can only become incorporated in your life plan once it arrives.
By contrast, the Keynesian consumption function is based on current income, so it makes no difference whether an income shock is anticipated or unanticipated.
Evidence
As we noted earlier, there are frequent deviations from the Keynesian consumption function. Can life-cycle models help to explain them?
Another piece of evidence in favor of life-cycle models is that the MPC from increases in asset value are much lower than the MPC from increases in earned income. This stylized fact is consistent with the life-cycle model because asset values fluctuate a lot but earned income increases (e.g. a raise at work) tend to be more permanent. Thus, people might be treating the former as a temporary shock but the latter as a permanent shock.
Sudden changes in tax policy a few decades ago also provide almost an experimental test. The government imposed a temporary tax surcharge in 1968 and a temporary tax reduction in 1974. But, contrary to the goals of the policy, these tax changes had little impact on consumption spending. Households mostly just saved less in 1968 and saved more in 1974. This is evidence in favor of life-cycle planning. However, households did spend some of this temporary income, and the short-run MPC from these temporary income shocks is much higher than the 0.05 than a life-cycle model would predict (assuming that the interest rate is 5%). Estimates of the short-run MPC tend to be between 0.3 and 0.5 for temporary income shocks.
Deficiencies in the Life-Cycle Model
The Keynesian model predicts that a high fraction (the MPC) of increases in current disposable income are spent. But that’s obviously wrong. Households smooth out temporary income changes. But life-cycle models are not perfect, either. Households consistently spend more out of temporary income shocks than what life-cycle models would predict.
Overall, life-cycle models fit the data better than models based on short-term income. But how can we explain deficiencies with the life-cycle model? Here are a few possibilities.
• Maybe people have a planning horizon of a few years, but not their entire lives. This would explain why people have a higher MPC than expected for temporary income shocks, but that the MPC is less than 1 for permanent income shocks.
• Maybe people don’t follow the news and they don’t realize that temporary tax changes aren’t permanent. This would explain a higher-than-expected MPC for short-term income shocks based on temporary tax changes.
Interest Rates and Consumption Spending
We finish this section with a brief discussion of the relationship between interest rates and consumption spending. We tell students in principles-level classes that higher interest rates lead to lower consumption spending because (1) borrowing is more expensive, and (2) accumulating assets generates a higher return. But it turns out that both theory and empirical evidence on this point are spotty, at best.
First of all, the theoretical relationship between interest rates and consumption spending is ambiguous. On one hand, higher interest rates make borrowing expensive and increase the value of saving money, suggesting that consumption spending should fall. This is the substitution effect
– consumers substitute saving for spending because saving is more valuable on the margin when the interest rate is higher. However, a higher interest rate also increases the permanent value of accumulated assets, suggesting that consumption spending should rise. This is the income effect
– consumers enjoy higher lifetime income at higher interest rates and can spend more. Overall, these contrary effects pull in opposite directions, and so the impact of higher interest rates on consumption spending is theoretically ambiguous.
Unit 3.2: Investment
Investment spending is about 15% of GDP. Unlike consumption spending, which is more stable than GDP, investment spending fluctuates more erratically than GDP does. In fact, Keynes argued that volatility in investment spending is the primary driver of business cycles. This volatility is one of the main reasons that investment spending is of so much interest to economists despite its relatively modest share in GDP. Furthermore, understanding investment spending is important for long-run growth models because today’s investments determine future growth.
Here is a plot of investment spending and GDP in the US since 1960. Note the high volatility of investment spending relative to GDP.
Composition of Investment Spending
Investment spending is divided into three major categories.
1. Nonresidental fixed investment – Business purchases of plant machinery and equipment. 2. Residential fixed investment – Construction of new houses and apartments.
3. Inventory investment – Increases and decreases in the stock of goods held in inventory by firms.
Here is a graph showing nonresidential and residential fixed investment in the US since 1960.
Firm Investment Decisions
Overall, the level of investment spending in the economy is an equilibrium phenomenon determined by the supply of investment funds (how much consumers save) and the demand for investment funds (how much businesses want to borrow). These investment funds flow through financial markets, typically in the form of bonds, stocks or bank loans. The supply of investment funds depends on consumer saving behavior, which we studied in the last unit. In this unit, we focus on demand for investment projects by firms.
Investment spending is a flow of new capital. The two questions that a firm faces are:
1. What is the firm’s desired level of capital stock? 2. How should the firm time its accumulation of capital?
We will treat each question in turn. We will begin with firms that rent their capital equipment and then extend the analysis to ownership.
Choosing how much capital to acquire is a basic marginal benefit / marginal cost calculation. The marginal benefit of acquiring additional capital is the money that the firm saves by being able to reduce its use of other inputs. Specifically, suppose the firm needs 𝑁𝑁 workers to produce its desired level of output, but a new investment can reduce labor requirements to 𝑁𝑁′. Each unit of labor is paid a wage of 𝑤𝑤. Then the marginal benefit for investing in the new capital is the savings in labor costs.
The marginal benefit relationship will typically feature diminishing returns – the marginal benefit of adding additional capital falls as more and more capital is accumulated.
Now, on the cost side, the marginal cost of renting a unit of capital is 𝑅𝑅𝐾𝐾. Thus, the firm will continue to rent additional capital up to the point where marginal benefit is equal to marginal cost.
Now, what will the rental rate for capital be in a competitive market? To answer this question, suppose that you own a $1000 machine and you rent it out to a firm for a year. What are the costs of this rental to you?
• Opportunity cost of the lost interest – You could have had your $1000 in the bank instead of tied up in the machine. If the interest rate is 5%, this is $50 of lost interest.
• Depreciation – If the depreciation rate is 10%, the value of the machine drops by $100 over the course of the year due to its use by the renter.
Thus, your zero-profit, break-even rental price for the machine is $150. And, of course, in a competitive market we know that prices are driven down to the zero-profit level.
Summarizing, if the value of a piece of capital is 𝑃𝑃𝐾𝐾, the interest rate is 𝑟𝑟 and the depreciation rate is 𝛿𝛿, then the competitive rental rate for a piece of capital 𝑅𝑅𝐾𝐾 is:
Using this analysis, combined with the diagram given above, we can derive a few conclusions about firm demand for capital.
• Firm demand for capital rises when planned output rises because the marginal benefit of capital rises.
• Firm demand for capital rises when the wage rate rises because the marginal benefit of capital rises.
• Firm demand for capital falls when the price of new equipment rises because the rental rate (the marginal cost of capital) rises.
• Firm demand for capital falls when the interest rate rises because the rental rate (the marginal cost of capital) rises.
As a sidenote, this way of thinking about optimal investment decisions is equivalent to net present value analysis from finance. The two give the same answers mathematically, it’s just that finance people are used to thinking in terms of total cash flows whereas economists are used to thinking in terms of marginal conditions. At the end of the day, the results are the same. A project’s net present value is positive when the marginal benefit of the investment exceeds marginal cost.
The analysis above was for a firm that rented its capital equipment, but it would be exactly the same if the firm purchased its capital equipment. If the firm uses its own money to buy capital, the cost of holding the capital is exactly the same as the competitive rental price – the opportunity cost of the lost interest from money tied up in capital and the depreciation expenses.
The Accelerator
The previous section answers our first question – how a firm determines its optimal capital stock. In this section, we will address the second question – investment spending, or the flow process by which the firm acquires capital to reach its desired capital stock.
In the simplest setup, the firm invests each year to reach its desired capital stock. Let 𝐾𝐾 be the firm’s desired capital stock now and let 𝐾𝐾𝑐𝑐−1 be the firm’s previous capital stock. Then, if the firm instantaneously acquires the capital it wants, its investment spending is:
𝐼𝐼 = 𝐾𝐾 − 𝐾𝐾𝑐𝑐−1
Now, the desired capital stock in any given year is a function of output in that year (𝑌𝑌), so:
If we substitute this back into the investment function, we can see that investment in any year is given by:
𝐼𝐼 = 𝐾𝐾 − 𝐾𝐾𝑐𝑐−1
= 𝜆𝜆𝑌𝑌 − 𝜆𝜆𝑌𝑌𝑐𝑐−1
= 𝜆𝜆(𝑌𝑌 − 𝑌𝑌𝑐𝑐−1)
= 𝜆𝜆 ⋅ Δ𝑌𝑌
The key result of this model is that investment spending does not depend on the level of output, but on the change in the level of output from one year to the next. While consumption spending depends on the level of output, investment spending depends on the change in output. This critical property of the behavior of investment spending is known as the accelerator.
The accelerator explains a lot of why investment spending is erratic and why small fluctuations in the business cycle lead to exaggerated changes in the business cycle. For example, suppose output suddenly rises by 5% but then stays at this new level. There will be a large burst of new investment when output rises, but then investment spending will drop once the desired level of capital is attained. In other words, even though output remains high, investment spending drops because the firm does not need to add any more capital once it has reached its desired capital stock for producing the new level of output. By contrast, consumption spending would remain high because it depends on the level of output. To reiterate, investment spending is volatile because it depends on the change in output, not on the level of output.
In reality, the accelerator is not quite as strong as these simple equations would suggest. We assumed that investment spending is structured for the firm to jump immediately to its optimal capital stock. But, practically, most firms cannot immediately put new capital in place. As a result, most firms will experience a lag between the time that optimal capital decisions are made and when investment spending is actually realized. Generic things like trucks and tools can be accumulated quickly, but specialized and expensive equipment could involve a longer lag. These lags slow the adjustment of investment in capital stock and reduce the magnitude of the accelerator.
Let’s finish this section with a numerical example. Suppose that a firm’s optimal capital stock is given by 𝐾𝐾∗ = 2𝑌𝑌. The firm produces 𝑌𝑌 = 200 units of output in year 1 and starts off at its optimal capital stock 𝐾𝐾 = 400. In year 2, the firm’s output suddenly rises to 𝑌𝑌 = 250 units and stays there forever after. How does the firm’s capital stock adjust?
Year 𝑲𝑲∗ 𝑲𝑲−𝟏𝟏 𝑰𝑰 𝑲𝑲
1 400 400
2 500 400 500 − 400 = 100 400 + 100 = 500
3 500 500 500 − 500 = 0 500 + 0 = 500
4 500 500 500 − 500 = 0 500 + 0 = 500
5 500 500 500 − 500 = 0 500 + 0 = 500
In year 2, the firm’s optimal capital stock rises from 400 to 500, and it immediately invests 100 in new capital and reaches its desired capital stock. Its investment spending drops to 0 in subsequent years since the firm attained its desired level of capital immediately.
This example illustrates how investment spending can feature volatile swings. There is a huge burst of investment in the year that the desired capital stock rises, and then investment drops to zero thereafter because the new optimal capital stock is attained.
But what if we modify the model to include a lag? Specifically, suppose that the firm’s investment function is 𝐼𝐼 = 0.5(𝐾𝐾∗− 𝐾𝐾−1). In other words, the firm can only get halfway to reaching its desired capital stock each year. The table below shows the firm’s optimal capital stock, level of investment and level of capital attained each year.
Year 𝑲𝑲∗ 𝑲𝑲−𝟏𝟏 𝑰𝑰 𝑲𝑲
1 400 400
2 500 400 0.5(500 − 400) = 50 400 + 50 = 450
3 500 450 0.5(500 − 450) = 25 450 + 25 = 475
4 500 475 0.5(500 − 475) = 12.5 475 + 12.5 = 487.5
5 500 487.5 0.25(500 − 487.5) = 6.25 487.5 + 6.25 = 493.75
In both cases, the firm is shooting for its new optimal capital stock of 𝐾𝐾 = 500. The difference is that, in the first case, there is a large burst of investment and the firm reaches its desired capital stock immediately. In the second case, the firm adds capital slowly and its investment spending slowly tapers off as the firm gets closer and closer to its optimal capital stock.
Taxation and Investment Spending
Suppose that firms renting out capital pay a tax of 𝑢𝑢 on each dollar of rental income. But capital producers receive a subsidy of 𝑧𝑧 for each dollar of capital produced. Both are features of the US economy. In particular, production subsidies and tax credits for new capital are substantial.
Remember that the original competitive rental cost of capital was 𝑅𝑅𝐾𝐾 = 𝑃𝑃𝐾𝐾 ⋅ (𝑟𝑟 + 𝛿𝛿). After we take into account the taxes and subsidies, the new rental cost is:
𝑅𝑅𝐾𝐾 = �1 − 𝑧𝑧
1 − 𝑢𝑢� �𝑃𝑃𝐾𝐾⋅ (𝑟𝑟 + 𝛿𝛿)�
It’s fairly intuitive to see that an increase in the subsidy 𝑧𝑧 reduces the rental cost of capital, while an increase in taxes on rental income 𝑢𝑢 increases the rental cost of capital. For example, if 𝑢𝑢 = 0.5 and 𝑧𝑧 = 0, then the tax system doubles the cost of renting capital. But if 𝑢𝑢 = 0.5 and 𝑧𝑧 = 0.4, then the offsetting subsidy means that the tax system raises the cost of capital only by 20%.
Turning to empirical evidence, the government in 1985 announced the repeal of a 10% investment tax credit, to be take effect in 1986. The effect was a 19% increase in investment in the just last quarter of 1985, and then about the same offsetting decline in 1986. The lesson is that the use of investment tax changes to stabilize the economy is problematic if firms can anticipate these changes in advance.
The capital gains tax is a tax on capital income. Reductions in capital gains taxes theoretically should stimulate investment. The reason is simple benefit/cost analysis – firm profits can either be capitalized into the company (increasing stock prices) or paid out directly as dividends. If the capital gains tax falls, shareholders prefer that the profits go towards increasing the stock value (taxed at the capital gains rate) than to paying out dividends (taxes as regular income).
From 1996 to 2003, policymakers reduced the tax rate on capital gains almost in half – from 28% to 15%. Evidence suggests that, at least in the short-term, that each 1% cut in the capital gains tax rate increases investment by about 1%.2
Residential Investment
A key stylized fact is that residential investment is much more sensitive to interest rates than business capital investment is. How can we explain this? Remember that the rental cost of capital, business or housing, is 𝑅𝑅 = 𝑃𝑃 ⋅ (𝑟𝑟 + 𝛿𝛿). Firm capital depreciates at a rate of about 𝛿𝛿 = 0.1 each
2 There is some evidence that the rate reduction may even increase total tax revenues collected because it encourages
year. By contrast, housing doesn’t depreciate much at all, its depreciation rate being closer to 𝛿𝛿 = 0.02. Thus, the real interest rate 𝑟𝑟 is a much more important factor for housing investment than for business capital investment. Because depreciation is only a small issue, the opportunity cost of lost interest is far more important. In other words, most of what you are paying to your landlord every month is compensation for the capital that he has tied up in buildings. Thus, higher interest rates reduce housing investment.
The accelerator principle applies to housing investment as well. It depends on the change in income, not on the absolute level of income. A family that experiences a jump in its income might build a new house, but once it has the house it wants, there is no new investment in housing even if the family’s income remains high. It would take another change in income for the family to build a new house.
Inventory Investment
Inventory stocks are large – about $0.14 for every $1 of GDP. Nevertheless, inventory investment
in any given year is quite small because additions and reductions in inventories approximately balance out. They don’t exactly balance out, though, and remember in the Keynesian setup that inventory accumulation or decumulation is an important indicator of an imbalance between GDP and aggregate expenditures.
There are two basic reasons for firms to hold inventories.
• The pipeline stock is about 2/3 of inventories and represents output in transit or in the production process. Think of oil in refineries or unfinished cars.
• The buffer stock is about 1/3 of inventories and represents finished goods that firms hold to accommodate changes in demand. Think of unsold food on the shelf or cars sitting on the car lot.
The buffer stock is the more volatile of the two, and can change unexpectedly when sales rise or fall faster than expected.
Overall, inventory investment is higher when output is higher, mainly because of the pipeline stock. Firms that produce more output have more output in the pipeline at any point in time.
Unit 3.3: Government
The government impacts the macroeconomy in many ways. Here are some of the more important ones.
• Government purchases contribute to aggregate demand.
• Transfer payments add to disposable income.
• Taxes reduce disposable income.
• Interest paid on the debt adds to income and impacts financial markets.
Most macroeconomic models treat government spending as exogenous – determined by policymakers outside of our model. This is probably not entirely accurate because transfers and taxes themselves depend on GDP and are therefore endogenous to GDP formation. In other words, the government’s fiscal position is not exogenous but is intertwined with the rest of the economy.
The “how and why” of government spending and revenue collection is the subject of courses in public finance. Our purpose here is more narrow – to understand the way in which the government is intertwined with macroeconomic activity.
Government Expenditures and Revenues
The things that the government spends money can be sorted into three broad categories.
1. Purchases of goods and services 2. Transfer payments
3. Interest on the debt
Here is some terminology. The distinction between these is a source of much confusion.
• Government spending is (1). This is 𝐺𝐺 from the GDP identity.
• Government outlays are (1) + (2)
• Government expenditures are (1) + (2) + (3)
Importantly, only government spending contributes to GDP directly. Government spending in 2016 was $3.27 trillion, about 18% of GDP. State and local governments account for about 62% of total spending, with the federal government accounting for the other 38%. Within the federal government’s share, about 59% is military spending and about 41% is nonmilitary spending.
While government spending by the federal government is lower than spending by state and local governments, government expenditures are higher on the federal side because of the large outlay by the federal government on transfer payments, which are not counted as government spending.
Composition of Expenditures and Revenues
The federal government collected $3.45 trillion of revenue in 2016. Here is the composition.
Transfer payments are the largest component of government expenditures. Here is a breakdown of government transfers at all levels of government.3
As for state and local governments, different states collect revenue in a variety of different ways. Here is a breakdown of Pennsylvania’s tax collection. States also receive substantial grants from the federal government, but these are not included here. Also, property taxes in Pennsylvania are collected by individual school districts, not at the state level, so these are not included here.4
On the spending side, here is a breakdown of spending at the state level. Again, a lot of the money for K-12 spending is allocated at the school district level, so that is not included here.
3 Note that, despite public perception, cash “welfare” payments are quite small and represent only about 2.4% of
transfers. A 1996 overhaul of the welfare infrastructure limited cash benefits to a substantial extent. A “welfare” program that permanently provides income for able-bodied adults does not presently exist in the United States.
To close this section, we need to touch on two accounting issues.
First, social security is technically “off-budget”, which can lead to drastic discrepancies in numbers reported by different sources. Most economists disregard this as an accounting gimmick and look at an integrated federal budget that includes social security.
Second, and a point that we will revisit later, only some spending is discretionary – allocated by law each year. Much of the federal government’s spending is mandatory or nondiscretionary – meaning that it is mandated by laws that have already been passed (e.g. social security payments).
Size of the Government
While the government has certainly grown in real terms, the whole economy has grown too. A more informative way to look at the evolution is government spending is to look at it as a percentage of GDP. A graph is shown below. There, we see that government spending has remained fairly constant at about 20% of GDP and, if anything, has been trending down.
What about government expenditures, which includes transfer payments and interest on the debt, as well as purchases? Here we see a different picture. The graph below shows federal government expenditures as a percentage of GDP since 1950. The most important feature is the upward trend in transfer payments
The Government and Economic Fluctuations
Consumption spending and investment spending both fluctuate cyclically – they rise when GDP rises and fall when GDP falls, with consumption spending more stable and investment spending more volatile. By contrast, a main motivation for government in the economy is that government activity can be countercyclical – rising when GDP falls and falling when GDP rises. In other words, the government can potentially help to offset the business cycle, at least in part.
Government spending (purchases of goods and services) does not fluctuate strongly in synchronicity with GDP one way or the other. Most of these fluctuations are due to changes in defense spending. And, while there are stimulus programs during recessions, they are mostly small and can take years to get started.
The diagram below plots government spending and the unemployment rate each year since 1950. The unemployment rate is a good indicator of business cycle fluctuations, but government spending does not appear to be strongly correlated with the unemployment rate.
On the other hand, government transfers are strongly countercyclical. They fluctuate in the opposite direction as the economy and therefore act as automatic stabilizers that offset the economic cycle. Most of these changes in transfers are automatic. For example, more people qualify for unemployment payments, Medicaid, food stamps and cash transfers when the economy is not doing well. No government action is needed.
Taxes are also an automatic stabilizer because they rise and fall together with GDP changes. When GDP is low, tax collection is mechanically low, and vice versa when GDP is high. In other words, when the economy is not doing well, tax collection falls, which puts more money into the pockets of consumers and raises aggregate expenditures.
The diagram below shows taxes as a percentage of GDP and the unemployment rate since 1950. Tax payments fall when the unemployment rate rises and rise when the unemployment rate falls.
Another reason for the automatic stabilizer effect of taxes is deliberate policy. For example, George W. Bush implemented some temporary tax changes to stimulate the economy in the 2001 recession, and Barack Obama reduced social security payroll taxes following the 2008 recession.
To reiterate, the countercyclical nature of the government is one of the most important features of government involvement in the economy. Much of the government’s role here is baked into consumption spending as well – as we noted earlier, disposable income fluctuates only about 40% as much as GDP fluctuates because of tax and transfer changes, which keeps consumption spending relatively stable. From a macroeconomic perspective, this countercyclical structure is one of the most important rationales for government involvement in the economy.
Deficits and Economic Fluctuations
During a recession, tax payments will fall and government expenditures naturally rise, especially because of transfers. With low tax payments and high expenditures, it is normal and expected for the government to operate with a deficit during recessions. Even economists who support balanced budgets tend to believe that the budget should be balanced long-term over the business cycle, not in every single year. If the government had to operate with a balanced budget every year, it would have no ability to act countercyclically, which again is one of the most important functions of government in the macroeconomy.
The important feature is that the budget deficit rises in bad economies when the unemployment rate rises. But the deficit falls again when the economy is healthy. Note that the federal government’s budget was actually in surplus in 2000. The government collected more in taxes than what it spent.
Now, part of the deficit is structural and part is cyclical.
• The structural deficit is the part of the deficit that would have existed even if the economy were operating at full employment.
• The cyclical deficit is the part of the deficit that is due to an underperforming economy.
At the height of the last recession, the government’s deficit was $1.1 trillion. But estimates are that the deficit would have been only $500 billion if the economy had been operating at full employment because tax revenues would have been $450 billion higher and expenditures would have been $150 billion lower. Thus, we can say that the structural deficit is $500 billion, but the other $600 billion is cyclical – attributable to business cycle fluctuations.
Deficits and Interest Rates
One concern about government budget deficits is crowding out. High government spending and low taxes shift the IS curve right, which increases interest rates and crowds out some investment spending. In reality, this link is not borne out in the data. The interest rate does not tend to rise when the deficit rises. If anything, the relationship appears to be the opposite of what theory would predict. Interest rates have actually been lower when the US has had high budget deficits.
The empirical problem with estimating this relationship is the same problem we had when we tried to look at the relationship between interest rates and consumption spending. The deficit tends to be high when the economy is doing badly, so it’s hard to figure out what piece of the interest rate change is due to the deficit and what piece is due to economic fluctuations. In other words, low interest rates are probably not caused by high deficits, but they do tend to happen together.
The National Debt
Before anything else, make sure that you are using terminology properly.
• The deficit is the government’s shortfall (expenditures – tax receipts) in any given year. The 2016 government budget deficit was $697 billion. There is a surplus if taxes are higher than expenditures.
• The debt is the total amount of money owed by the government. It represents the accumulated stock of previous deficits. The national debt is currently almost $20 trillion.
In order to run deficits, the government has to borrow money from the public. To whom do we owe $20 trillion? The diagram below breaks it down.
About 29% of the national debt is owed internally to other government accounts, mostly to social security.5 The largest foreign holders of US government debt are the governments of Japan and China.
Is the magnitude of our national debt a problem? Surely you have seen an apocalyptic figure like the following, which shows federal government debt since 1950.
5 Until recently, the social security trust fund accumulated large surpluses since social security taxes far exceeded
First of all, anything expressed in nominal dollars is meaningless. Second of all, the correct way to think about debt burden is our national debt as a percentage of GDP. This is just like a household. A $1 million debt might not be a problem for a household with an annual income of $500 million.
Here is a diagram showing national debt as a percentage of GDP since 1940, which gives us a very different picture.
While different economists have different views, the overall consensus is that economists tend to be less concerned about the national debt than the general public and journalists are.
First of all, nearly all economists agree that cyclical deficits are OK. The government can borrow money at much lower interest rates than any private citizen or firm, so it is in a better position than any other entity in the economy to act countercyclically and spend to offset bad economic times.
Another crucial point is that adding debt can actually generate a profit if the return on investment is higher than interest on the debt. Again, the analogy to a firm is straightforward. If a company can borrow money at a 2% interest rate and invest it in a project that generates a 5% return, then the company increases its profit by continuing to borrow and roll over its debt.
Ricardian Equivalence
According to the principle of Ricardian Equivalence, deficits have no impact on the economy and so countercyclical policy is doomed to fail. The rationale is classical in nature – tax cuts that are financed by deficits are not really tax cuts at all. The government is just rescheduling taxes until some later date when the bills come due.
Thus, according to forward-looking theories of life-cycle consumption, such tax cuts (and transfers) do not impact permanent income and should not impact household behavior. Families that get tax cuts and transfers today know that they money has to be paid back tomorrow. Of course, the underlying assumption here is that households have rational expectations and that they are forward-looking as far into the future as needed.
But does a household really disregard a tax cut or transfers today because someone (their grandkids?) might have to pay taxes 50 years from now? There is disagreement about the impact of debt on the economy, and many economists dispute whether Ricardian Equivalence holds.
First, as a practical matter households weight the present more than the future in making decisions. They feel better off and spend more when they benefit from these tax cuts and transfers because they do not fully incorporate the future repayment that will be required. Thus, even short-term tax cuts and transfer boosts might increase aggregate demand because the repayment is too far away for anyone to take it into account in making decisions.
Second, and as a result, consumption is too high and so these tax reductions and transfers result in a misallocation of resources towards consumption and away from investment. In this way, debt might not be neutral. It could displace productive capital, leading to an efficiency loss.
Unit 3.4: Net Exports
There are courses devoted to models dealing with international trade, financial flows and exchange rates. This is an extremely rich and multifaceted area. Our goal in this section is much more limited. We want to study the way in which imports and exports impact our model of economic fluctuations, and the basic microfoundations of why these relationships exist. Be aware that we are touching on only a tiny piece of an extensive body of knowledge.
In the standard IS/LM model, we regard net exports 𝑁𝑁𝑁𝑁 to be exogenous. But the truth is that net exports are endogenous. In fact, they depend both on GDP and on the interest rate. In this section, we will modify our IS/LM model to accommodate this feature and study the consequences.
Net Exports, Interest Rates and Income – Microfoundations
Here are the two basic relationships underlying the way in which an open economy impacts our model of macroeconomic fluctuations. Remember that net exports are defined as exports minus imports. It is a component of aggregate expenditures.
• Net exports fall when GDP 𝑌𝑌 rises.
• Net exports fall when the interest rate 𝑟𝑟 rises.
The first relationship is straightforward. When income rises, people are going to spend at least some of this income on imports. Rich countries can afford more imports than poor countries can. Thus, from an aggregate expenditures perspective, higher income 𝑌𝑌 reduces net exports.
The second relationship is intermediated by the exchange rate. Remember that the exchange rate is the value of the US dollar in terms of a foreign currency. When the exchange rate rises, we say that the dollar appreciates, meaning that it is more valuable in terms of a foreign currency. When the exchange rate falls, we say that the dollar depreciates, meaning that it is worth less in terms of a foreign currency.
Why do net exports fall when the interest rate rises? There are two steps to the argument.
2. When the exchange rate rises, two things happen. First, US exports become more expensive for foreigners to buy and so exports fall. Second, the US dollar becomes more valuable overseas and so imports of foreign goods by Americans rise. Overall, an increase in the exchange rate leads to a decline in net exports and a decline in aggregate expenditures on American goods and services.
To summarize, higher GDP means more income for Americans and means that Americans buy more imports. Thus, net exports fall as GDP rises. Higher interest rates mean that the US dollar appreciates, which makes American exports expensive and makes foreign imports cheap. Thus, net exports also fall as the interest rate rises.
Augmented IS/LM Model
From the previous section, net exports fall as GDP rises and they fall as the interest rate rises. Thus, rather than treating net exports as exogenous, we will model net exports as a function of GDP and of the interest rate.
𝑁𝑁𝑁𝑁 = 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑛𝑛𝑟𝑟
Here, 𝑁𝑁 is the exogenous intercept. Net exports decline as income 𝑌𝑌 rises and they decline as the interest rate 𝑟𝑟 rises. The parameters 𝑚𝑚 and 𝑛𝑛 are the sensitivity of these relationships. When they are small, changes in 𝑌𝑌 and 𝑟𝑟 do not have a large impact on net export spending. As they become larger, changes in 𝑌𝑌 and 𝑟𝑟 have more impact on net exports.
We will solve for the IS/LM equilibrium with this new addition to the model. The four components of aggregate expenditures are as follows:
• 𝐶𝐶 = 𝑎𝑎 + 𝑏𝑏(𝑌𝑌 − 𝑇𝑇) • 𝐼𝐼 = 𝐼𝐼0− 𝑑𝑑𝑟𝑟
• 𝐺𝐺 is exogenous
• 𝑁𝑁𝑁𝑁 = 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑛𝑛𝑟𝑟
𝑌𝑌 = 𝐴𝐴𝐴𝐴
𝑌𝑌 = 𝐶𝐶 + 𝐼𝐼 + 𝐺𝐺 + 𝑁𝑁𝑁𝑁
𝑌𝑌 = [𝑎𝑎 + 𝑏𝑏(𝑌𝑌 − 𝑇𝑇)] + [𝐼𝐼0− 𝑑𝑑𝑟𝑟] + 𝐺𝐺 + [𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑛𝑛𝑟𝑟]
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0 − 𝑑𝑑𝑟𝑟 + 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑛𝑛𝑟𝑟
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0 + 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − 𝑑𝑑𝑟𝑟 − 𝑛𝑛𝑟𝑟
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0 + 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − (𝑑𝑑 + 𝑛𝑛)𝑟𝑟
The LM curve is the standard LM curve that equates supply and demand for money.
𝑀𝑀
𝑃𝑃 = 𝑚𝑚0− ℎ𝑟𝑟 + 𝑘𝑘𝑌𝑌
Solving the LM relationship for 𝑟𝑟 gives:
𝑟𝑟 =𝑚𝑚ℎ −0 ℎ𝑃𝑃 + �𝑀𝑀 𝑘𝑘ℎ� 𝑌𝑌
To solve for the IS/LM equilibrium, we substitute this expression for 𝑟𝑟 back into the IS curve:
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − (𝑑𝑑 + 𝑛𝑛)𝑟𝑟
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − (𝑑𝑑 + 𝑛𝑛) �𝑚𝑚ℎ −0 ℎ𝑃𝑃 + �𝑀𝑀 𝑘𝑘ℎ� 𝑌𝑌�
We solve this expression for 𝑌𝑌 to find the equilibrium GDP.
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − (𝑑𝑑 + 𝑛𝑛) �𝑚𝑚ℎ −0 ℎ𝑃𝑃 + �𝑀𝑀 𝑘𝑘ℎ� 𝑌𝑌�
𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑌𝑌 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − 𝑚𝑚𝑌𝑌 − �𝑑𝑑 + 𝑛𝑛ℎ � 𝑚𝑚0+ �𝑑𝑑 + 𝑛𝑛ℎ � �𝑀𝑀𝑃𝑃 � − �(𝑑𝑑 + 𝑛𝑛)𝑘𝑘ℎ � 𝑌𝑌
𝑌𝑌 − 𝑏𝑏𝑌𝑌 + 𝑚𝑚𝑌𝑌 + �(𝑑𝑑 + 𝑛𝑛)𝑘𝑘ℎ � 𝑌𝑌 = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − �𝑑𝑑 + 𝑛𝑛ℎ � 𝑚𝑚0+ �𝑑𝑑 + 𝑛𝑛ℎ � �𝑀𝑀𝑃𝑃 �
𝑌𝑌 �1 − 𝑏𝑏 + 𝑚𝑚 +(𝑑𝑑 + 𝑛𝑛)𝑘𝑘ℎ � = 𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − �𝑑𝑑 + 𝑛𝑛ℎ � 𝑚𝑚0+ �𝑑𝑑 + 𝑛𝑛ℎ � �𝑀𝑀𝑃𝑃 �
𝑌𝑌∗= � 1
1 − 𝑏𝑏 + 𝑚𝑚 + (𝑑𝑑 + 𝑛𝑛)𝑘𝑘ℎ � �𝑎𝑎 − 𝑏𝑏𝑇𝑇 + 𝐼𝐼0+ 𝐺𝐺 + 𝑁𝑁 − � 𝑑𝑑 + 𝑛𝑛
ℎ � 𝑚𝑚0+ � 𝑑𝑑 + 𝑛𝑛
ℎ � � 𝑀𝑀
𝑃𝑃 ��
Economic Policy in an Open Economy
In the standard IS/LM model, where net exports are exogenous, the IS/LM spending multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝐺𝐺 =
1 1 − 𝑏𝑏 + 𝑑𝑑𝑘𝑘ℎ
In our enhanced IS/LM model, with endogenous net exports, the IS/LM spending multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕𝐺𝐺 =
1
1 − 𝑏𝑏 + 𝑚𝑚 + (𝑑𝑑 + 𝑛𝑛)𝑘𝑘ℎ
The denominator is larger for our new enhanced model. Thus, the IS/LM spending multiplier is
lower in the model with endogenous net exports than it is in the standard model.
The key insight is that net exports reduce the value of the spending multiplier and thus they reduce the susceptibility of the economy to spending shocks. Exports and imports modulate the impact of spending shocks on the economy. In brief, net exports act as an automatic stabilizer.
The economic intuition is easy to understand in an IS/LM framework. When there is a spending increase (a rightward shift of the IS curve), GDP and the interest rate increase. But both the GDP increase and the interest rate increase reduce net exports. This reduction offsets some of the initial increase in GDP, and so overall the multiplier effect of the spending shock on GDP is dampened. For negative spending shocks, the opposite is true. The reduction in interest rates and GDP will raise net exports and, at least in part, offset some of the negative impact on GDP.
However, this stabilizing effect of net exports is not necessarily the case for monetary shocks. In the standard model, the money multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕 �𝑀𝑀𝑃𝑃 �= � 𝑑𝑑 ℎ� �
1 1 − 𝑏𝑏 + 𝑑𝑑𝑘𝑘ℎ �
But, in our augmented model with endogenous net exports, the money multiplier is:
𝜕𝜕𝑌𝑌∗
𝜕𝜕 �𝑀𝑀𝑃𝑃 �= � 𝑑𝑑 + 𝑛𝑛
ℎ � �
1
The numerator is larger in the new model with endogenous net exports, but the denominator is larger also. Thus, the new money multiplier could be higher or lower than the original multiplier.
Again, the intuition is straightforward in an IS/LM framework. When the money supply rises, the LM curve shifts right, causing GDP to rise and the interest rate to fall. The increase in GDP causes net exports to fall, but the reduction in interest rates causes net exports to rise. Overall, the impact of the open economy on a monetary shock could be to partially offset the increase in GDP, or it could be to reinforce and strengthen it.
The Open Economy in the United States
To finish with some perspective, the diagram below shows exports and imports in the US since 1947. Our trade position was basically balanced (exports and imports approximately equal) until the 1980’s, and since then imports have exceeded exports. The difference between the two exploded in the late 1990’s and early 2000’s, creating large trade deficits that have persisted ever since. In 2016, the US exported $2.21 trillion of goods and services but we imported $2.74 trillion of goods and services, leading to a $521 billion trade deficit with the rest of the world
Unit 3.5: Money
In this section, we will cover the foundations of the role that money plays in macroeconomic models. We will first cover the demand side, then we will cover the supply side, and finally we will analyze the relationship between money and price levels. The money supply in each country is actively managed by its central bank. In the United States, the central bank is called the Federal Reserve Board. In a later section, we will cover optimal management of the money supply from a policy perspective. The purpose of this section is to provide an overview of the role of money in the macroeconomy.
Money Demand
Why hold money?
On its face, money seems like a stupid way to hold wealth. After all, other financial assets like bonds pay some interest, but holding money generates zero return. Why then do we hold any of our wealth in the form of money? Classical macroeconomics offers three reasons:
1. Transactions motive – Income arrives periodically, but you have to buy things regularly. Thus, you need to keep some stock of money to buy things.
2. Precautionary motive – People might keep a stock of money in case they have an emergency need for quick, liquid funds. This is not much of an issue in the US since there are interest-bearing assets like CD’s that can be liquidated quickly and serve this precautionary function.
3. Speculative motive – If financial markets are unstable, people might want to hold some of their wealth as money just to avoid risk.
Among these, the most important by far is the transactions motive. Practically, this is the reason that most of us keep stocks of money.
Transactions motive – Portfolio balance problems
money stock that is too low makes it inconvenient and costly to get money every time you need to spend it. But maintaining a money stock that is too high is costly because of the foregone interest.
Here is a simple model of how to choose the optimal stock of money to hold. Suppose you earn an income of 𝑌𝑌 each month, paid once a month. If you want your average money stock to be 𝑀𝑀, then number of withdrawals you need every month is:
withdrawals =2𝑀𝑀𝑌𝑌
For example, if your income is $8000 a month and you want to have an average money balance of $4000, then you only need 𝑌𝑌
2𝑀𝑀= 8000
2⋅4000= 1 withdrawal. Your $8000 will be depleted at the end of
the month, so your average money holdings over the month will be $4000.
But if you want to reduce your average money balance to $2000, then you need 𝑌𝑌
2𝑀𝑀= 8000 2⋅2000= 2
withdrawals each month. In this case, you withdraw your $8000 twice a month ($4000 each), which would mean that you average a $2000 money balance over the month.
The cost of each withdrawal is 𝑞𝑞. This cost includes the inconvenience, time cost and monetary cost associated with making withdrawals.
total cost of withdrawals = 𝑞𝑞 �2𝑀𝑀�𝑌𝑌
Choosing to keep a higher money balance 𝑀𝑀 reduces the total cost of withdrawals since you don’t have to visit the bank as often.
On the other hand, a higher money balance also increases the opportunity cost associated with the foregone interest. If the interest rate is 𝑟𝑟, then the opportunity cost associated with maintaining an average money balance of 𝑀𝑀 is:
opportunity cost of money balance = 𝑟𝑟𝑀𝑀
Combining the two pieces, the total cost associated with choosing to hold an average money balance 𝑀𝑀 is given by:
Now you can see the tradeoff. Higher money balances reduce transactions costs but they increase opportunity cost of lost interest. The objective is to choose a money balance 𝑀𝑀 to minimize the total cost associated with money holdings. To find the value of 𝑀𝑀 that minimizes total costs, we take the derivative of the expression with respect to 𝑀𝑀 and set it equal to zero.
𝑑𝑑 𝑑𝑑𝑀𝑀 = −
𝑞𝑞𝑌𝑌
2𝑀𝑀2+ 𝑟𝑟 = 0
𝑟𝑟 = 𝑞𝑞𝑌𝑌 2𝑀𝑀2
𝑀𝑀2 = 𝑞𝑞𝑌𝑌
2𝑟𝑟
𝑀𝑀 = �𝑞𝑞𝑌𝑌2𝑟𝑟
This model rationalizes the LM relationship that we developed earlier in the course. Money demand rises when income rises but money demand falls when the interest rate rises. Now we see why – at higher incomes, people spend more, so they keep higher money balances. But at higher interest rates, the opportunity cost of holding money balances is high, so people hold lower money balances and hold more of their wealth as interest-bearing assets.
Money Supply
Definition of money
Money is a special kind of asset that is extremely liquid. There are many kinds of assets. Stocks, bonds, property, artwork, etc… are all assets with value, but these are at least somewhat illiquid. Out of all financial assets in the economy, only two things are considered to be money.
1. Currency (cash and coins)
2. Demand deposits (checking accounts)
Let 𝐶𝐶𝐶𝐶 designate the amount of currency outstanding and let 𝐷𝐷 be the total amount of demand deposits outstanding. The money supply (𝑀𝑀) is the amount of money in the hands of the public at any given time. Formally:
Fractional reserve system and the monetary base
Banks operate using a fractional reserve system, meaning that only a fraction of the total deposits at the bank are actually held in reserve. The banks lend the rest of the money out. Thus, much of what people think they have on deposit is illusory in a sense. If everyone tried to reclaim their demand deposits at the same time, a bank run ensues, which collapses the banking system.
The monetary base, sometimes called high-powered money, is the amount of hard money that is outstanding at any point in time (not the money that exists only on bank balance sheets). The monetary base consists of currency in the hands of the public (𝐶𝐶𝐶𝐶) and bank reserves (𝑅𝑅𝐴𝐴).
𝑀𝑀𝑀𝑀 = 𝐶𝐶𝐶𝐶 + 𝑅𝑅𝐴𝐴
The deposit multiplier
Banks are required by law to keep a fraction of their demand deposits on reserve. This is called the required reserve ratio (𝑟𝑟). In the US, 𝑟𝑟 = 0.1. Formally, reserves are:
𝑅𝑅𝐴𝐴 = 𝑟𝑟𝐷𝐷
Generally, people don’t want to have all of their money tied up in the bank. People want to hold some ratio 𝑐𝑐 of currency to demand deposits. Thus, currency holdings are:
𝐶𝐶𝐶𝐶 = 𝑐𝑐𝐷𝐷
Now, going back to the definition of the money supply, we substitute in the models above:
𝑀𝑀 = 𝐶𝐶𝐶𝐶 + 𝐷𝐷 = 𝑐𝑐𝐷𝐷 + 𝐷𝐷 = (1 + 𝑐𝑐)𝐷𝐷
Similarly, substitute in the models above for the definition of the monetary base:
𝑀𝑀𝑀𝑀 = 𝐶𝐶𝐶𝐶 + 𝑅𝑅𝐴𝐴 = 𝑐𝑐𝐷𝐷 + 𝑟𝑟𝐷𝐷 = (𝑐𝑐 + 𝑟𝑟)𝐷𝐷
𝑀𝑀 𝑀𝑀𝑀𝑀 =
(1 + 𝑐𝑐)𝐷𝐷 (𝑐𝑐 + 𝑟𝑟)𝐷𝐷 𝑀𝑀 = �1 + 𝑐𝑐𝑟𝑟 + 𝑐𝑐� 𝑀𝑀𝑀𝑀
The coefficient 1+𝑖𝑖
𝑟𝑟+𝑖𝑖 is called the deposit multiplier. The deposit multiplier is the change in the
total money supply that results from each $1 increase in the monetary base by the Fed. Importantly, when the Fed injects an additional dollar into the monetary base, the injection increases the money supply by more than $1 because of the subsequent rounds of loans and deposits it creates.
Say the Fed injects $1000 into the monetary base. The money initially ends up deposited in Bank A. Bank A will lend out a chunk of the money, and that money will eventually end up deposited in Bank B. Bank B will lend out a chunk of the money, and that will end up deposited in Bank C, which can lend some of it out, etc… Thus, the total increase in demand deposits at banks is much greater than $1000. Of course, if everyone tried to go back and redeem their demand deposits at the same time, there would be a bank run since there is only $1000 of monetary base backing up all of these demand deposits.
For example, suppose 𝑟𝑟 = 0.1 and 𝑐𝑐 = 0. In this case, the deposit multiplier is:
1 + 𝑐𝑐 𝑟𝑟 + 𝑐𝑐 =
1 + 0 0.1 + 0 = 10
The multiplier is intuitive in this case. If each bank keeps only 10% of its deposits and there is no currency sucked out of the system, then the total deposits will be 10 times the monetary base.
But, suppose instead that 𝑟𝑟 = 0.1 and 𝑐𝑐 = 0.2. In this case, the deposit multiplier is:
1 + 𝑐𝑐 𝑟𝑟 + 𝑐𝑐 =
1 + 0.2 0.1 + 0.2 = 4
In this case, when bank deposits increase, people want to hold some of their new wealth as currency, so not all of the subsequent loans end up re-deposited in banks. Some of the funds are simply held as currency. This currency drain reduces the deposit multiplier.
Managing the Money Supply
Practically, how does the Fed implement these changes to the monetary base? The traditional way for the Fed to manage the supply of money is through open market operations, where the Fed exchanges bonds with banks.
• When the Fed buys bonds from banks, it creates new money to do so. This new money increases bank reserves and so the money supply rises, and with a multiplier. Banks lend out some of the money, spurring subsequent rounds of deposits and loans.
• When the Fed sells bonds to banks, the banks use money to pay for the bonds. The Fed destroys the money, which reduces the monetary base and so the money supply falls, again with a multiplier effect. Because this action reduces bank money reserves, banks are forced to cut back on their lending.
In essence, when the Fed buys bonds from banks, it creates new money on the banks’ balance sheets. When the Fed sells bonds to banks, it takes money out of the public’s hands.
There are some other ways that the Fed can control the money supply. The discount rate is the rate at which private banks can borrow reserves from the Fed. If the Fed reduces the discount rate, banks borrow more reserves from the Fed, which increases the monetary base and the money supply. If the Fed raises the discount rate, banks are less likely to borrow reserves from the Fed, which reduces the monetary base and the money supply.
Additionally, the Fed can change the reserve ratio 𝑟𝑟. Lower reserve ratios increase the money multiplier as banks are free to lend out more of their deposits, which raises the money supply. Higher reserve ratios reduce the money multiplier because banks are forced to hold more of their deposits in reserve. This reduces the money supply.
The most prominent feature is the extremely large increases in the monetary base that occurred between 2008 and 2014 as a result of the Fed’s quantitative easing policy. We will talk about this recent episode in detail in the section on optimal monetary policy. An important thing to note is that the money multiplier appears to be significantly lower over this recent period – increases in the monetary base were not anywhere near matched by proportionate increases in the money supply, and in fact at this point the monetary base actually exceeds the money supply. The main reason is that banks held on to much of this new money as reserves.
Quantity Theory of Money
The relationship between money and economic activity is a long-standing question in economics with a deep intellectual history. In essence, the classical view is that money is completely neutral and has no impact on real economic activity. Keynesians dispute this proposition and claim that money can have real effects. Let’s go into more detail.
The Equation of Exchange
The basis for studying the relationship between money and economic activity is the basic equation of exchange. The four variables involved are:
• 𝑀𝑀 – the money supply
• 𝑃𝑃 – the velocity of money (number of times a dollar changes hands in 1 year)6
• 𝑃𝑃 – the price level
• 𝑌𝑌 – the level of output (real GDP)
The equation of exchange states that:
𝑀𝑀𝑃𝑃 = 𝑃𝑃𝑌𝑌
The equation of exchange is an accounting identity. It does not by itself express any economic theory. The left side of the equation is money circulation and the right side is the value of goods and services exchanged. To understand why the two must be identically equal, let’s consider a simple numerical example.
An economy sells output 𝑌𝑌 = 500 widgets, with each widget sold for price 𝑃𝑃 = 2. This is $1000 worth of goods and services traded. Obviously, $1000 of money has to circulate somehow in order to support these trades. If the money supply is 𝑀𝑀 = 200, then if each dollar circulates 𝑃𝑃 = 5 times, that’s $1000 of money circulation, which exactly balances out. $1000 of goods and services traded has to identically equal $1000 of money exchanged.
