Economics 154. Investment Fall 2008

1. Economics 154. Investment Fall 2008 NOAA’s weather supercomputer PET Scan of PIB molecule

2. The Macroeconomics of Investment Capital • Produced, durable, used for further production • Examples: • tangibles (structures, equipment) • intangibles (software, patents) Basic role of investment in macro • Short run: most volatile part of aggregate demand • Recall decline of I in Great Depression • Long run: key determinant of growth of potential output and major way that governments affect economic growth.

3. Investment-GDP ratio

4. Investment decline in the Depression Note on data: Very convenient place is “FRED”: http://research.stlouisfed.org/fred2

5. Investment in information industries around the Internet bubble

6. Today’s housing crunch

7. The major theories of investment 1. Accelerator theory: states that investment is a function of change in output 2. Neoclassical theory: Desired capital stock a function of output and cost of capital 3. Q theory: Investment a function of Tobin’s Q (Q =ratio of market value of K to replacement cost): • In Mankiw and section, not in class

8. 1. Accelerator Theory • Oldest and simplest theory is the accelerator model. • Here, the idea is that there is a target capital-output ratio K* = v Y • Hence the desired change in investment is equal to the change in output (I is gross investment): • I* = ΔK* + δK = v Δ Y + δK • The actual investment might differ from the desired, but this is a simple and useful model. It shows why there is a close relationship between investment and output change.

9. I δK+vΔY δK ΔY Graph shows relation between investment and change in output (accelerator model)

11. What about models?

12. Role of Models in Economics and Policymaking:Transcript of House hearing on October 23, 2008 (slighted edited for brevity) REP. WAXMAN: Dr. Greenspan, … you had an ideology, and this is your statement, “I do have an ideology. My judgment is that free, competitive markets are by far the unrivaled way to organize economies. We've tried regulation. None meaningfully worked.” Do you feel that your ideology pushed you to make decisions that you wish you had not made? MR. GREENSPAN: Remember that what an ideology is; it is a conceptual framework with the way people deal with reality. Everyone has one. To exist, you need an ideology. The question is whether it is accurate or not. And what I'm saying to you is, yes, I've found a flaw. I don't know how significant or permanent it is. But I've been very distressed by that fact. [I found a] flaw in the model that I perceived as the critical functioning structure that defines how the world works…. I was shocked because I had been going for 40 years or more with very considerable evidence that it was working exceptionally well.

13. REP. WAXMAN: Well, where do you think you made a mistake, then? MR. GREENSPAN: I made a mistake in presuming that the self- interest of organizations, specifically banks and others, were such that they were best capable of protecting their own shareholders and their equity in the firms. And it's been my experience – having worked both as a regulator for 18 years and similar quantities in the private sector, especially 10 years at a major international bank – that the loan officers of those institutions knew far more about the risks involved in the people to whom they lent money than I saw even our best regulators at the Fed capable of doing.       So the problem here is, something which looked to be a very solid edifice, and indeed a critical pillar to market competition and free markets, did break down. And I think that, as I said, shocked me. I still do not fully understand why it happened. And obviously, to the extent that I figure out where it happened and why, I will change my views.

14. 2. Neoclassical Theory The mainstream theory is the neoclassical model. - This is closely related to the accelerator model. - The difference is that in the neoclassical model there is a variable capital-output ratio - Hence, K/Y depends upon relative factor prices, and in particular upon the user cost of capital and taxes. Using standard production theory Start with aggregate production function:Y = F(K,L) Next figure shows the difference of the accelerator and neoclassical models for an isoquant.

15. Isoquants with fixed capital - output ratio v. variable prop ortions L fixed K/L ratio in accelerator Cobb-Douglas in neoclassical K - fixed K/L corresponds to accelerator model - variable proportions (such as Cobb-Douglas) corresponds to neoclassical model

16. Investment Criteria There are a number of return concepts. • present value (V0 today) • internal rate of return (i0 per year) • rental price of capital ($ per apartment per month) • cost of capital (usually, “user cost of capita”) • Central concept in macro theories of investment • Def. Unit cost for the use of a capital asset for one period • Appropriate for perfect capital market. • Estimate as imputed in most circumstances because firms own capital (also for housing in NIPA)

17. Formula for cost of capital u ≈ (1+τ) pK [r + δ] whereu = cost of capitalpK = price of capital goodr = real interest rateδ = depreciation rateτ = effective rate of tax (or subsidy when negative) on capital goods Linkage to policy:- through real interest rate- through taxation of capital In practice, u is complicated to measure; off to B School!

18. Derivation and example: • Buy a car, rent it for one period, and then sell at the end. No inflation or taxes. r = .05. • Pay $20,000 sell for 20,000(1-.1) = $18,000; collect rent u. • What cost of capital (u) would just break even? when pK = pK (1- δ)/(1+r) + u20,000 = 18,000/(1.05) + uu = 20,000 – 18,000/1.05 = 20,000 – 17,143 = 2857 ≈ pK (r+ δ) = 20,000(.15) = 3,000

19. Cost of capital with no taxes and P = 1 This is a slightly more realistic version that has both debt and equity capital.

20. Basic approach in the neoclassical model We start with a production function; and then derive the demand for capital. Demand for capital: Assume a Cobb-Douglas production function Y = A Kβ L1-β Then derive the MPK: MPK = ∂Y/∂K=βA Kβ-1L1-β = βY/K Finally, the firm sets its desired capital stock (K*) by equating the cost of capital to the MPK: u =∂Y/∂K=βY/K Now normalize prices = 1 for simplicity and ignore taxes: u = (r+δ) = βY/K

21. This yields a demand for capital (K*): K* = βY/(r+δ) Note the various components of the demand for capital • output (like accelerator) • interest rate (r) • depreciation rate (δ) • With taxes: K* = βY/[(r+δ) (1+τ)]

22. r demand for capital 0 K* δ Demand for capital schedule

23. Note that the impact of interest rates on investment is powerful but depends importantly on the lifetime of the capital: • Where biggest impacts? Housing • Where smallest? Computers and inventories

24. From demand for capital to demand for investment • How do we get investment demand (or equilibrium investment)? • Generally, go from demand for capital to demand for investment • Several approaches: • Costs of adjustment of investment • Capacity in the capital goods industry (Boeing aircraft) • Construction lags (power plants) • Internal funds constraint

25. 3. Q theory of investment Idea here is that investment is determined by relationship between the value of firms or houses and the cost of new or replacement capital. Keynes: “The daily revaluations of the Stock Exchange, though they are primarily made to facilitate transfers of old investments between one individual and another, inevitably exert a decisive influence on the rate of current investment. For there is no sense in building up a new enterprise at a cost greater than that at which a similar existing enterprise can be purchased; whilst there is an inducement to spend on a new project what may seem an extravagant sum, if it can be floated off on the Stock Exchange at an immediate profit.” Tobin: "It is common sense that the incentive to make new capital investments is high when the securities giving title to their future earnings can be sold for more than the investments cost, i.e., when q exceeds one."

27. More formally: Q = (market value of K)/(replacement cost of K) Example: - Cargo ships were selling for a Q of 3 last year - E.g., cost of production is $20 million, but ships sell for $60 million - How is this possible? • Inelastic supply and high demand → high rentals • Because of construction lags (formalized as adjustment costs in macro literature) will take time for rentals market to get back to equilibrium where rentals equal the cost of capital. How does Q affect investment? - Because Q > 1, firms can build ships and sell for more than cost - This promotes investment. - Therefore I/K = f(Q), f’(Q) > 0.

28. Rental of ships St+5 St “cost of capital” for ships Demand for shipping Number of ships 28

29. Example of rental on ships

30. Q I/K = f (Q) 1 I/K δ

31. Housing bubble: • Note that Q rose about 80 percent from mid-1990s. • Another 20 to 40 percent to go to get back to trend Q. • If that happens, substantial fraction of households will have prices that are “under water.”

32. Investment ratio and Q for housing

33. Summary of investment theory 1.. The major components of investment are residential, business plant and equipment, software, and inventories. 2. These are among the most volatile components of output in the short run. 3. In equilibrium, demand for capital determined where the cost of capital equals the marginal productivity of capital. 4. The major theories are the accelerator theory, the neoclassical theory, and the Q theory. These apply differently in different sectors. 5. Economic policy affects investment through both monetary and fiscal policy: • monetary policy through real interest rate and stock prices • fiscal policy through things like depreciation policy and investment tax credits.