1. 4
INVESTMENT SPENDING & CAPITAL FORMATION

2. Income and Consumption—LCH
death
Saving
Consumption
Income
Dissaving T

3. Investment
Investment has always been high on the economics research agenda for many reasons. In particular:
In the short run, investment expenditures represent
a significant source of volatility in business cycle fluctuations. Fluctuations in investment account for much of the year-to-year change in GDP.
(2) In the long run, investment can be an "engine" of growth to greater productivity and wealth. Countries that invest a greater share of their GDP generally exhibit higher economic growth rates

4. Growth rates of real GDP, consump., investment
Percent change from 4 quarters earlier
Investment growth rate
Real GDP growth rate
Consumption growth rate
This graph shows consumption growth and GDP growth, the same data from the previous slide, but now the vertical axis has a much bigger scale to accommodate the addition of investment growth.
The point: Investment is far more volatile than GDP or consumption.
Source: FRED

5. International evidence on investment rates and income per person
Income per person in (log scale)
Figure 8.6, p.223.
This scatterplot shows the experience of 100 countries, each represented by a single point. The horizontal axis shows the country’s rate of investment, and the vertical axis shows the country’s income per person. High investment is associated with high income per person, as the Solow model predicts.
Source:
Alan Heston, Robert Summers and Bettina Aten, Penn World Table Version 7.1, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania, July 2012.
Investment as percentage of output (average )

6. Capital and Interest Investment and Capital
The capital stock is the total amount of plant, equipment, buildings, and inventories, or physical capital.
Gross investment is the purchase of new capital.
Depreciation is the wearing out of the capital stock.
Net investment equals gross investment minus depreciation, and net investment is the addition to the capital stock.
Definitions and the meaning of investment in economics. The student has met the key definitions of this section in Chapter 19, but to be absolutely sure that they are remembered, this chapter repeats them. It is worth emphasizing that in economics, “capital” and “investment” without any qualification mean physical capital and purchase of newly produced physical capital goods. Everyday usage of investment as the purchase of stocks or bonds can lead to confusion. So it is worth getting these matters clear right from the start.

7. Gross Investment, Net Investment, and Depreciation
Investment is the flow of spending that adds to the physical stock of real capital. We begin the year with some level of capital and we end the year at some different level:
Int = Kt – Kt where,
Int = net investment in period t
Kt = capital stock at the end of period t, and
Kt-1 = capital stock at the end of period t-1 (start of period t)
The above specification ignores depreciation. Physical capital wears out and becomes obsolete. Some additional investment spending must be directed to the replacement of depreciating capital.

8. Gross Investment, Net Investment, and Depreciation
The Commerce Department reports depreciation as "consumption of fixed capital."
A common assumption is that the depreciation rate is a fixed fraction of the level of capital (capital depreciates geometrically at a constant rate), and replacement investment is:
Irt = δ Kt-1
Irt = investment in replacement capital in period t
δ = depreciation rate
Total gross investment is the sum of net investment and replacement investment:
Igt = Int + Irt = Kt – Kt-1 + δ Kt-1 = Kt - (1 - δ ) Kt-1
Igt = gross investment in period t

9. Sources of Investment Saving
Saving is current income minus current expenditure, and in part finances investment. Investment is financed by national saving and borrowing from the rest of the world.
Personal saving is personal disposable income minus consumption expenditure.
Business saving is retained profits and additions to pension funds by businesses.
Government saving is the government’s budget surplus.
Any of these components can be negative.
The U.S. saving rate. The low U.S. saving rate, described in this chapter, is very interesting to students. They are also intrigued by the low level of personal saving and the high level of business saving. It is worth emphasizing that part of the reason for the low personal saving rate is that payroll deductions for employment pension plans are business savings.

10. Investment Expenditures
The National Income and Product Accounts (NIPA) includes these categories of investment expenditures:
Nonresidential fixed investment - goods used for future use in production processes, including:
Structures - factories, office buildings, warehouses, and other structures in which the production of goods and services takes place.
Equipment and software - any business equipment that is expected to last more than one year such as computers, office furniture, machinery, tools, cars, trucks, etc.
Residential fixed investment - new housing that people buy to live in and landlords buy to rent out.
Change in inventories - goods in storage that will be used to produce other goods, including raw materials, work-in-process, and finished products. A decline in inventories is recorded as negative investment.

12. U.S. Investment and its components, 1970–2014
Total investment
Business fixed investment
Residential investment
Change in inventories
Billions of current dollars
Similar to Figure 17-1, p.508.
What we learn from this graph:
1. Business fixed investment is the largest of the three types of investment
2. Investment varies with the business cycle, rising in booms and falling in recessions.
Also interesting is the behavior of residential investment in the period.
Source: U.S. Dept of Commerce, obtained from
Series:
GPDI – total investment
PNFI – business fixed investment
PRFI – residential fixed investment
CBI – inventory investment

13. Understanding business fixed investment
The standard model of business fixed investment: the neoclassical model of investment Shows how investment depends on:
MPK
interest rate
tax rules affecting firms 13

14. Two types of firms
For simplicity, assume two types of firms:
1. Production firms rent the capital they use to produce goods and services.
2. Rental firms own capital, rent it to production firms.
In this context, “investment” is the rental firms’ spending on new capital goods.
Note: Many students find it easier to learn the following material by separating the investment decision from the production decision.
Of course, the lessons apply to real-world firms that actually do both functions. 14

15. The capital rental market
capital stock
real rental price, R/P
capital supply
Production firms must decide how much capital to rent.
Recall that Competitive firms rent capital to the point where MPK = R/P.
capital demand (MPK)
equilibrium rental rate
The graph of the rental market for capital is review from chapter 3. As you present it to your students, it might be worthwhile to briefly review each piece (why the supply curve is vertical, why demand = MPK). 15

16. Factors that affect the rental price
For the Cobb-Douglas production function,
the MPK (and hence equilibrium R/P ) is
The equilibrium R/P would increase if:
K (e.g., earthquake or war)
L (e.g., pop. growth or immigration)
A (technological improvement, or deregulation)
(It might be worth reminding students that A represents the level of technology, and  is a number between 0 and 1 that equals capital’s share of national income.)
We use the C-D function for two reasons: First, we can make the ideas here more concrete with a specific functional form, and second, because the C-D function will be familiar to most students from earlier chapters (Chapter 3 and the economic growth chapters).
If students are wondering where the MPK equation comes from, either refer them to Chapter 3, or, if they are acquainted with basic calculus, take the derivative of the C-D production function with respect to K.
Regarding the impact of an increase in A on R/P: We usually associate A with technology. However, A represents anything that affects the amount of output that can be produced from a given bundle of inputs. For example, firms use resources (in this context, L and/or K) to comply with regulations (some labor time is used to fill out forms; some capital is used to reduce emissions of nasty things into the air or rivers). A relaxation of regulations would allow firms to divert these resources from compliance with regulations to production, causing output to increase. Hence, a deregulation could cause A to rise. 16

17. Neoclassical Investment Model
The neoclassical investment model takes a more rigorous approach to estimating the desired level of capital.
Building from the microeconomic model of the firm's production function and profit-maximizing behavior we can relate the desired level of capital and investment to product prices (demand) and interest rates.
We also improve on the simple accelerator model by explicitly accounting for the reality that it takes time to build new plant and equipment.

18. Rental firms’ investment decisions
Rental firms invest in new capital when the benefit of doing so exceeds the cost.
The benefit (per unit capital): R/P, the income that rental firms earn from renting the unit of capital to production firms. 18

19. The cost of capital
Components of the cost of capital:
interest cost: i PK, where PK = nominal price of capital
depreciation cost:  PK, where  = rate of depreciation
capital loss:  PK (a capital gain, PK > 0, reduces cost of K )
The total cost of capital is the sum of these three parts:
Notes:
Interest cost-- If firms borrow in the loanable funds market (from chapter 3) to finance their purchases of capital, then they incur interest. But even if firms use their own funds, they incur an opportunity cost equal to the interest they could have earned had they purchased Pk worth of bonds instead of spending Pk to buy a piece of capital.
Depreciation cost--
Remind students that  is the depreciation rate, the percentage of capital that wears out each period. If the firm starts the period with $1000 worth of capital and the depreciation rate = 0.03, then at the end of the period, the value of the firm’s capital equals (1-0.03)$1000 = $970. 19

20. Nominal cost of capital
The cost of capital
Nominal cost of capital
Example: car rental company (capital: cars)
Suppose PK = $10,000, i = 0.10,  = 0.20, and PK/PK = 0.06
Then, interest cost = depreciation cost = capital loss = total cost =
$1000
If the price of capital, Pk, falls during the period, then firm incurs a capital loss, which increases its cost of capital.
In this example, the price of capital rises, so the “capital loss” is negative. (Or, there’s a capital gain which we subtract from the cost, because the increase in the price of new capital reduces the cost of capital.)
$2000
 $600
$2400 20

21. The cost of capital
For simplicity, assume PK/PK = . Then, the nominal cost of capital equals PK(i +   ) = PK(r + )
and the real cost of capital equals
The assumption in the first line says that the price of capital rises as fast as the general price level.
The real cost of capital equals the nominal cost divided by the price level, just as the real wage equals the nominal wage divided by P.
The real cost of capital depends positively on:
the relative price of capital
the real interest rate
the depreciation rate 21

22. The rental firm’s profit rate
A firm’s net investment depends on its profit rate:
If profit rate > 0, then increasing K is profitable
If profit rate < 0, then the firm increases profits by reducing its capital stock (i.e., not replacing capital as it depreciates)
In plain English, the profit rate equals
(the rental price of capital) minus (the user cost of capital) 22

23. Net investment & gross investment
Hence,
where In[ ] is a function that shows how net investment responds to the incentive to invest.
Total spending on business fixed investment equals net investment plus replacement of depreciated K:
The equation in the yellow box simply states “net investment depends on the profit rate.”
It might be useful to remind students that gross investment is simply net investment plus depreciation. 23

24. The investment functionr
An increase in r :
raises the cost of capital
reduces the profit rate
and reduces investment: r2
Finally, we see where our familiar investment function comes from. I1 r1 I2 24

25. The investment function
An increase in MPK or decrease in PK/P
increases the profit rate
increases investment at any given interest rate
shifts I curve to the right. I r
Here’s a challenge for particularly bright students:
Ask what happens to the investment curve given an increase in the depreciation rate. Tell them to justify their answer based on the investment equation we have derived.
Answer: The impact on the curve is ambiguous.
The depreciation rate appears in two different places in the equation.
First, it appears in the expression for the profit rate, which is the argument of the net investment function. An increase in the depreciation rate would raise the cost of capital and hence reduce the profit rate and the incentive to invest (*net* investment). This would tend to shift the curve left.
Second, the depreciation rate appears as a coefficient on K. An increase in the depreciation rate means that more investment (*gross* investment) is needed to replace depreciating capital and keep the total capital stock at its optimal level. This effect would shift the curve right.
The net impact of the two opposing forces is ambiguous, without knowing the specific form of the In( ) function.
Note: This exercise is simply for practice, and does not correspond to a real-world policy example. I1 r1 I2 25

26. Taxes and investment Corporate income tax Investment tax credit
Two of the most important taxes affecting investment:
Corporate income tax
Investment tax credit 26

27. Tobin’s q
numerator: the stock market value of the economy’s capital stock.
denominator: the actual cost to replace the capital goods that were purchased when the stock was issued.
If q > 1, firms buy more capital to raise the market value of their firms.
If q < 1, firms do not replace capital as it wears out.

28. Relation between q theory and neoclassical theory
The stock market value of capital depends on the current & expected future profits of capital.
If MPK > cost of capital, then profit rate is high, which drives up the stock market value of the firms, which implies a high value of q.
If MPK < cost of capital, then firms are incurring losses, so their stock market values fall, so q is low.

29. The stock market and GDP
Reasons for a relationship between the stock market and GDP:
1. A wave of pessimism about future profitability of capital would:
cause stock prices to fall
cause Tobin’s q to fall
shift the investment function down
cause a negative aggregate demand shock

30. The stock market and GDP
Reasons for a relationship between the stock market and GDP:
2. A fall in stock prices would:
reduce household wealth
shift the consumption function down
cause a negative aggregate demand shock

31. Models of Investment Four models of investment:
Net Present Value - this is one of the standard "Business School" approaches to how individuals compare different opportunities when making investment decisions. While it is not a model that can be directly applied to macroeconomic models it does provide insight into the relationships of investment to demand, prices and interest rates.
Simple Accelerator Model - one of the most basic macroeconomic investment models, the simple accelerator model relates investment (changes in the level of the capital stock) to changes in demand. This model of investment is frequently applied to modeling inventory behavior.
Neoclassical with Flexible Accelerator Model - a more rigorous approach to determining the desired level of capital stock and the rate of investment to reach that desired level of capital. The resulting flexible accelerator model is similar to the simple accelerator model, but adds interest rates and expected inflation to demand as explanatory variables.
q-Theory - economists don't completely ignore the stock market. One of the problems in estimating investment models and forecasting is that some variables are not directly observable. We generally know how much capital costs, but how much is capital worth? The stock market provides an indication.

32. The Simple Accelerator Model
Attempts to capture some measure of current business conditions (growth of the economy or lack of it), and use that to explain the level of investment.
It is a model of business investment that in its simplest form relates the level of investment to the rate of change in output.
The desired capital stock is proportional to the level of output:

33. Accelerator Model
We assume that whatever the capital stock ended up being last period was the level of capital that businesses actually wanted:

34. Accelerator Model This allows us to rewrite: As
Thus investment is related to the rate of change in output.
If the economy is growing rapidly, then investment grows rapidly.
If the economy is not growing, then investment slows, and net investment (after depreciation) may actually be negative.

35. The Flexible Accelerator Model
As a result of adjustment costs and practical time-to-build considerations, the entire adjustment to the desired capital stock may not be done in one period. The firms may only finance a partial adjustment.
Let  be the fraction of the gap between the desired and actual capital stock that the firms pursue. This leads to:

36. Tobin’s q
The neoclassical model provides insight on how to estimate the cost of capital using observable variables but provides little guidance on how to determine the benefit of using real capital. The neoclassical model assumes that the technology, or the marginal product of capital, is known. Unfortunately for economists this usually isn't the case.
Nobel laureate James Tobin suggested a possible solution--use the value of capital as revealed in the stock market. If the total market value of a firm's stocks and bonds exceeds the cost of replacing all of the capital it owns, this implies the value of its capital is greater than the cost of acquiring it.
Tobin's q - the market value of installed capital divided by the replacement cost of installed capital.

37. THE END