Exploding Bubbles In a Macroeconomic Model. Narayana Kocherlakota

Transcription

1 Bubbles Exploding Bubbles In a Macroeconomic Model Narayana Kocherlakota presented by Kaiji Chen Macro Reading Group, Jan 16,

2 Bubbles Question How do bubbles emerge in an economy when collateral is scarce and entrepreneurs are borrowing constrained? How do bubbles and burst of bubbles a ect the aggregate economy? 2

3 Bubbles This paper construct a model where housing is bubble assets, which provide no utility services ows but serves as store of values and collateral against borrowing. Burst of bubbles have persistent e ects on aggregate productive e ciencies by distorting the allocation of capital. Discuss government intervention after burst of bubbles. 3

4 1. MODEL ECONOMY Bubbles 1 Model Economy Environment In nite horizon, closed economy unit measure of entrepreneurs and unit measures of workers Each worker supplies one unit of labor inelastically, and consume their labor income each period. 4

5 1. MODEL ECONOMY Bubbles Heterogeneity of Entrepreneurs Each entrepreneur has a production technology y t+1 = A t+1 k t+1 n1 t+1 A t+1 is stochastic, i.i.d over both entrepreneurs and over time. with probability, it equals to 1 and probability 1, equals to 0: news about A t+1 arrives at time t, before k t+1 is installed. Call entrepreneurs receiving good news about A t+1 as "investors", and bad news as "savers". 5

6 1. MODEL ECONOMY Bubbles Each entrepreneur is endowed with a house, which is in nitely divisible. He can buy and sell houses. The entrepreneur can save or borrow against housing using one-period risk-free bonds. Housing provides no utility service for entrepreneurs. 1X t=1 t 1 ln (c t ) 6

7 1. MODEL ECONOMY Bubbles Entrepreneur s Constraints Budget constraint c t A t+1 + p t h t+1 A t+1 + b t+1 A t+1 + k t+1 A t+1 + w t n t A t+1 b t A t (1 + r t ) + A t k t A t nt A t (1 ) kt A t + p t h t A for all t; A t. Borrowing constraint b t+1 A t+1 (1 + r t+1 ) p t+1 h t+1 A t+1 b 1 = 0; h 1 = 1, and the nonnegativity for c t ; k t+1 ; h t : 7

8 1. MODEL ECONOMY Bubbles De nition A speci cation of prices (p; r; w) and entrepreneurial quantities (c; h; b; k; n) form an equilibrium if (c; h; b; k; n) maximizes the entrepreneur s utility subjects to constraints, and markets clear X Pr A t+1 n t A t+1 = 1 A t+1 X Pr A t+1 c t A t+1 + X Pr A t+1 k t+1 A t+1 A t+1 A t+1 = (1 ) X Pr A t k t A t + X Pr A t+1 A t k t A t nt A t+1 1 A t A t+1 3. X Pr A t+1 h t+1 A t+1 = 1 A t+1 8

9 1. MODEL ECONOMY Bubbles 4. X Pr A t+1 b t+1 A t+1 = 0. A t+1 9

10 2. TWO STEADY-STATE EQUILIBRIUM Bubbles 2 Two Steady-State Equilibrium No Bubbles (p = 0) Neither investors or savers can borrow (autarkic equilibrium) De ne wealth of entrepreneur as W t = A t kt n1 t + (1 ) k t + b t then for all entrepreneurs c t = (1 ) W t ; k t+1 = W t : The gross return for bad project is 1 ; (note that the return is less than the growth rate of the economy, provide a potential role for bubble). 10

11 2. TWO STEADY-STATE EQUILIBRIUM Bubbles The equilibrium interest rate r 2 ( 1; ] ; so that no entrepreneurs want to buy or sell bonds (self-ful lling expectation). per capital wealth W NB = (MP K NB + 1 ) W NB + (1 ) (1 ) W NB marginal returns to capital MP K NB in good projects. MP K NB = [1 (1 ) (1 )] Note the higher is ; the larger is MP K NB, as investors are more nancially constrained (by self nancing). 11

12 2. TWO STEADY-STATE EQUILIBRIUM Bubbles Constant Bubble (p > 0) Housing and bond are completely equivalent. Hence, the return for bubble r = 0, which is the growth rate of the economy. Assume all entrepreneurs keeps their housing h t = 1: De ne wealth of entrepreneur as W t = A t kt n1 t + (1 ) k t + b t + p 12

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14 2. TWO STEADY-STATE EQUILIBRIUM Bubbles Allocation in Bubble Economy Investors (those who receiving good news) will borrow as much as possible to nance production next period. b t+1 = p and k t+1 = W t : Savers will save in bond and housings, which return is higher than the return in capital. b t+1 + p = W t : per capital wealth W BUB = (MP K BUB + 1 ) W BUB + (1 ) W BUB return to capital MP K BUB = [1 (1 ) ]

15 2. TWO STEADY-STATE EQUILIBRIUM Bubbles Bond market clearings (1 ) W BUB p = p 14

16 2. TWO STEADY-STATE EQUILIBRIUM Bubbles Aggregate productive e ciency in the two steady states MP K NB > MP K BUB ; implying a larger gap of return to assets between investors and savers in the no-bubble economy W BUB > W NB ; which means that per capital consumption, output, and wages all higher in the bubble economy. Welfare ln (1 + MP K BUB )+(1 ) log (1) > ln (1 + MP K NB )+ (1 ) ln (1 ) k NB > k BUB 15

17 2. TWO STEADY-STATE EQUILIBRIUM Bubbles Intuition In the non-bubble steady state, in order to self- nance good projects in the future, entrepreneurs who receives bad news have to save in physical capital, though it provides a low return. On the other hand, in the bubble steady state, bubble serves two roles: Allows savers to transfer wealth intertemporally at a higher return than ine cient investment. Allows investors to borrow against bubbles, therefore channels resources from the saver (with relatively lower returns) to the borrower (with relatively higher returns). 16

18 2. TWO STEADY-STATE EQUILIBRIUM Bubbles This increases the aggregate productive e ciencies with a lower aggregate capital stock. 17

19 3. STOCHASTIC BUBBLES Bubbles 3 Stochastic Bubbles Each period, allow a small chance "; that houses are worth zero, p = 0 (i.i.d asset pricing shocks or sunspots) if p = 0, then housing prices equals 0 forever. experiment with a burst of bubble, i.e. p = 0 from time t on. 18

20 3. STOCHASTIC BUBBLES Bubbles Thought Experiments after Bubble Bursting No borrowing and lending any more. All of the load back by houses will not be repaid. Leave the wealth of the investor unchanged The savers lose all their wealth, except for a small amount they had invested in capital to guard against this low-probability event. 19

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22 Figure 1: Output Before and After A Bubble Burst 15

23 3. STOCHASTIC BUBBLES Bubbles Government Intervention After bubble burst, sell one period government bond (promise to deliver one unit of goods tomorrow) to savers in the economy. Distribute the proceeds of bond selling evenly to all entrepreneurs. Allow investors to have p units of consumption goods used for tomorrow s capital. Tomorrow roll over debt to repay the outstanding debt. solve two problems: bond o er a higher returns than the prevailing one (providing a way to transfer resources); lump-sum transfer to entrepreneur. 20

24 3. STOCHASTIC BUBBLES Bubbles 21

25 4. FINAL REMARK Bubbles 4 Final remark The presence of bubbles relies on the two key assumptions bad project delivers a return less than the growth rate of the economy (making bubble a better storage of wealth than capital). No productive assets serves as collateral (making bubble serves as the only collateral in the economy). Interesting to see how quantitatively important is bubble generating and bursting for the resource reallocation (capital and labor) described in this paper for the TFP dynamics (e.g. Great Depression). 22

26 4. FINAL REMARK Bubbles Open Questions How to understand the counterpart of housing in real economy? holdings? Cash What if rms can issue equity? Or what kind of frictions prevent rms to issue equity at recession (liquidity shocks)? What is the source of bubble bursting? Pure expectation or fundamentals? 23