1 Economics 122. Investment Fall 2013 PET Scan of PIB molecule NOAA’s weather supercomputer

Midterm results Overall: bimodal distribution. Many of you are apparently engaged in irrational procrastination and suboptimal study habits: –Problem sets –Lectures Grade distribution. Roughly evenly distributed within segments. 2

3 The Macroeconomics of Investment Capital Produced, durable, used for further production Examples: –tangibles (structures, equipment) –intangibles (software, human capital) Basic role of investment in macro Short run: most volatile part of aggregate demand –See next slides Long run : key determinant of growth of potential output and major way that governments affect economic growth –In growth theory

r = real interest rate Investment (I) I(r) E Why is investment an inverse function of r?

5 National accounts include only a small part of “investment-like” spending: 12% of 40%. Gross Investment, US, 2010 Counted as investment in National Accounts Sector2010% of GDP GROSS DOMESTIC PRODUCT15, Total, investment type39.6 Residential/Household1, Durable goods1,146 Residential structures339 Gross busines domestic investment1, Fixed investment1,480 Structures405 Equipment and software1,075 Change in private inventories37 Government gross investment Federal National defense109 Nondefense52 State and local320 Other investment-type private spending2, Health1,752 Private education252 Research and development480

Investment decline in the Depression 6 Note on data: Very convenient place is “FRED”:

7 This is only gross domestic private investment. Investment in the Great Recession

Today’s housing depression 8

Housing and interest rates with tight money 9

10 The major theories of investment 1. Neoclassical theory : Desired capital stock a function of output and cost of capital 2. Q theory : Investment a function of Tobin’s Q (Q =ratio of market value of K to replacement cost)

11 - L K Cobb-Douglas in neoclassical Production underlying neoclassical theory

12 Investment Criteria User cost of capital, uc Central concept in macro theories of investment Definition. Cost of renting capital for one period Appropriate for perfect capital market where Q=1* Estimate as imputed in most circumstances because firms own capital (also for housing in NIPA) * We will see later that Q = market value/replacement cost.

13 Formula for cost of capital uc ≈ (1+τ) p K [r + δ] where uc = user cost of capital p K = price of capital good r = real interest rate δ = depreciation rate τ = effective rate of tax (or subsidy when negative) on capital goods Linkage to policy: - through real interest rate - through taxation of capital In practice, uc is complicated to measure; off to B School!

14 Derivation and example : Buy a car, rent it for one period, and then sell at the end. No inflation or taxes. Real interest rate = 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 p K = p K (1- δ)/(1+r) + u 20,000 = 18,000/(1.05) + u uc = 20,000 – 18,000/1.05 = 20,000 – 17,143 = 2857 ≈ p K (r+ δ) = 20,000(.15) = 3,000

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

Derivation of Basic Theory Define the user or rental cost of capital as uc = (r+δ) P K as implicit rental on capital. Assume that Y is given by short-run aggregate demand Cobb-Douglas for simplicity and p K = p = 1. So the demand for investment is; – proportional to output –inverse to the user cost of capital, and therefore also to the interest rate. 16

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

18 From demand for capital to demand for investment Note that this is the demand for capital out of equilibrium. Generally, go from demand for capital to demand for investment Several approaches: -Costs of adjustment of investment (standard in modern macro) -Capacity in the capital goods industry (Boeing aircraft) -Construction lags (power plants) -Internal funds constraint

Now a major puzzle for neoclassical model: housing and interest rates 19 Tight money ? Housing price crash

20 The major theories of investment 1. Neoclassical theory : Desired capital stock a function of output and cost of capital 2. Q theory : Investment a function of Tobin’s Q (Q =ratio of market value of K to replacement cost)

21 A glut of cargo ships in 2009

Airplanes in mothballs (Tucson, Arizona) 22

23 More formally: Q = (market value of K)/(replacement cost of K) Example: - Cargo ships are selling for a Q of E.g., cost of production is $20 million, but ships sell for $5 million - How is this possible? Inelastic supply and high demand for cargo → low rentals PV of ships is low. Therefore, little to no shipbuilding, and the stock gradually depreciates or is scrapped How does Q affect investment? - Because Q < 1, shipping firms buy old ships rather than build new ones - This depresses investment. - Therefore I/K = f(Q), f’(Q) > 0.

24 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."

25 Q I/K 1 δ I/K = f (Q) Investment and Q

Housing market collapse, 2006 –

27 Housing bubble: 1.Note that Q rose about 50 percent from mid-1990s. 2. Note huge decline in residential construction (I) Investment ratio and Q for housing

Housing Q and housing starts, 2006:m1 – 2010:m7 28

29 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 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 unconventional policies (buying mortgage backed securities) fiscal policy through things like depreciation policy and investment tax credits.