Speculative Growth and Overreaction to Technology Shocks

Transcription

1 Speculative Growth and Overreaction to Technology Shocks Kevin J. Lansing Federal Reserve Bank of San Francisco June 5, 2009

2 Overview Excess volatility of asset prices may a ect capital accumulation, growth, and welfare. The price-dividend ratio in standard RBC models is nearly constant. But U.S. price-dividend ratio is highly volatile.

3 Overview Excess volatility of asset prices may a ect capital accumulation, growth, and welfare. The price-dividend ratio in standard RBC models is nearly constant. But U.S. price-dividend ratio is highly volatile. This paper: Introduce excess volatility (overreaction to technology shocks) in an RBC model with endogenous growth. In making forecasts, speculative agents behave like rational agents with very low risk aversion.

4 Overview Excess volatility of asset prices may a ect capital accumulation, growth, and welfare. The price-dividend ratio in standard RBC models is nearly constant. But U.S. price-dividend ratio is highly volatile. This paper: Introduce excess volatility (overreaction to technology shocks) in an RBC model with endogenous growth. In making forecasts, speculative agents behave like rational agents with very low risk aversion. Misspeci ed forecast rule alters dynamics in a way that tends to con rm the stronger technology response.

5 Overview Excess volatility of asset prices may a ect capital accumulation, growth, and welfare. The price-dividend ratio in standard RBC models is nearly constant. But U.S. price-dividend ratio is highly volatile. This paper: Introduce excess volatility (overreaction to technology shocks) in an RBC model with endogenous growth. In making forecasts, speculative agents behave like rational agents with very low risk aversion. Misspeci ed forecast rule alters dynamics in a way that tends to con rm the stronger technology response. Speculation generates asset price bubbles that coincide with improved technology, investment booms, and faster growth.

6 Overview Excess volatility of asset prices may a ect capital accumulation, growth, and welfare. The price-dividend ratio in standard RBC models is nearly constant. But U.S. price-dividend ratio is highly volatile. This paper: Introduce excess volatility (overreaction to technology shocks) in an RBC model with endogenous growth. In making forecasts, speculative agents behave like rational agents with very low risk aversion. Misspeci ed forecast rule alters dynamics in a way that tends to con rm the stronger technology response. Speculation generates asset price bubbles that coincide with improved technology, investment booms, and faster growth. Speculation can improve welfare if CRRA 1 and agents underinvest relative to socially-optimal level.

7 Overview Excess volatility of asset prices may a ect capital accumulation, growth, and welfare. The price-dividend ratio in standard RBC models is nearly constant. But U.S. price-dividend ratio is highly volatile. This paper: Introduce excess volatility (overreaction to technology shocks) in an RBC model with endogenous growth. In making forecasts, speculative agents behave like rational agents with very low risk aversion. Misspeci ed forecast rule alters dynamics in a way that tends to con rm the stronger technology response. Speculation generates asset price bubbles that coincide with improved technology, investment booms, and faster growth. Speculation can improve welfare if CRRA 1 and agents underinvest relative to socially-optimal level. When CRRA > 1, the welfare cost of speculation can be large.

8 U.S. Price-Dividend Ratio is Volatile and Highly Persistent S&P 500 Index: Price Dividend Ratio

9 Four Major Run-ups in U.S. Stock Prices Real S&P 500 Index (in logarithms)

10 Shiller (2000): Price Run-ups and "New Era" Enthusiasm Early 1900s: High-speed rail travel, transatlantic radio, long-line electrical transmission.

11 Shiller (2000): Price Run-ups and "New Era" Enthusiasm Early 1900s: High-speed rail travel, transatlantic radio, long-line electrical transmission. 1920s: Mass-produced autos, travel by highways and roads, commercial radio broadcasts, widespread electri cation of manufacturing.

12 Shiller (2000): Price Run-ups and "New Era" Enthusiasm Early 1900s: High-speed rail travel, transatlantic radio, long-line electrical transmission. 1920s: Mass-produced autos, travel by highways and roads, commercial radio broadcasts, widespread electri cation of manufacturing. 1950s and 60s: Widespread introduction of television, advent of the suburban lifestyle, space travel.

13 Shiller (2000): Price Run-ups and "New Era" Enthusiasm Early 1900s: High-speed rail travel, transatlantic radio, long-line electrical transmission. 1920s: Mass-produced autos, travel by highways and roads, commercial radio broadcasts, widespread electri cation of manufacturing. 1950s and 60s: Widespread introduction of television, advent of the suburban lifestyle, space travel. Late 1990s: Widespread availability of the internet, innovations in computers and information technology, emergence of web-based business model.

14 Comparing Two Bubble Episodes 100 Real S&P 500 Index During Two 20 year Periods (each series normalized to 100 at stock market peak)

15 Technology and the late-1990s Stock Market Bubble When we look back at the 1990s, from the perspective of say [w]e may conceivably conclude from that vantage point that, at the turn of the millennium, the American economy was experiencing a once-in-a-century acceleration of innovation, which propelled forward productivity, output, corporate pro ts, and stock prices at a pace not seen in generations, if ever.

16 Technology and the late-1990s Stock Market Bubble When we look back at the 1990s, from the perspective of say [w]e may conceivably conclude from that vantage point that, at the turn of the millennium, the American economy was experiencing a once-in-a-century acceleration of innovation, which propelled forward productivity, output, corporate pro ts, and stock prices at a pace not seen in generations, if ever. Alternatively, that 2010 retrospective might well conclude that a good deal of what we are currently experiencing was just one of the many euphoric speculative bubbles that have dotted human history. And, of course, we cannot rule out that we may look back and conclude that elements from both scenarios have been in play in recent years.

17 Technology and the late-1990s Stock Market Bubble When we look back at the 1990s, from the perspective of say [w]e may conceivably conclude from that vantage point that, at the turn of the millennium, the American economy was experiencing a once-in-a-century acceleration of innovation, which propelled forward productivity, output, corporate pro ts, and stock prices at a pace not seen in generations, if ever. Alternatively, that 2010 retrospective might well conclude that a good deal of what we are currently experiencing was just one of the many euphoric speculative bubbles that have dotted human history. And, of course, we cannot rule out that we may look back and conclude that elements from both scenarios have been in play in recent years. Federal Reserve Chairman Alan Greenspan, January 13, 2000.

18 Business Investment and Stock Prices 140 Real Business Investment and Real S&P 500 Index (each series normalized to 100 at the investment peak) Real Business Investment Real S&P 500 Index

19 Rise and Fall of the "New Economy Potential GDP Growth and Detrended Stock Price Index CBO 4 Qtr Potential Output Growth (left scale) Real S&P 500, Deviation from HP Filter Trend (right scale)

20 Technology and the mid-2000s Housing Market Bubble [T]he nancial services sector has been dramatically transformed by technology...with these advances in technology, lenders have taken advantage of credit-scoring models and other techniques for e ciently extending credit to a broader spectrum of consumers.

21 Technology and the mid-2000s Housing Market Bubble [T]he nancial services sector has been dramatically transformed by technology...with these advances in technology, lenders have taken advantage of credit-scoring models and other techniques for e ciently extending credit to a broader spectrum of consumers....where once more-marginal applicants would simply have been denied credit, lenders are now able to quite e ciently judge the risk posed by individual applicants and to price that risk appropriately. These improvements have led to rapid growth in subprime mortgage lending.

22 Technology and the mid-2000s Housing Market Bubble [T]he nancial services sector has been dramatically transformed by technology...with these advances in technology, lenders have taken advantage of credit-scoring models and other techniques for e ciently extending credit to a broader spectrum of consumers....where once more-marginal applicants would simply have been denied credit, lenders are now able to quite e ciently judge the risk posed by individual applicants and to price that risk appropriately. These improvements have led to rapid growth in subprime mortgage lending. Federal Reserve Chairman Alan Greenspan, April 8, 2005.

23 Residential Investment and House Prices 110 Real Residential Investment and Real House Price Index (each series normalized to 100 at investment peak) Real Residential Investment Real S&P Case Shiller Index

24 Related Literature (partial list) Rational Bubbles and Endogenous Growth (OLG Models) Caballero, Farhi, and Hammour (2006) Olivier (2000) Grossman and Yanagawa (1993) King and Ferguson (1993)

25 Related Literature (partial list) Rational Bubbles and Endogenous Growth (OLG Models) Caballero, Farhi, and Hammour (2006) Olivier (2000) Grossman and Yanagawa (1993) King and Ferguson (1993) Non-Fundamental Asset Price Movements and Investment Chirinko and Schaller (2001, 2007) Gilchrist, Himmelberg, and Huberman (2005) Dupor (2002, 2005) Panageas (2005) Johnson (2007) Angeletos, Lorenzoni, and Pavan (2007)

26 Related Literature (partial list) Rational Bubbles and Endogenous Growth (OLG Models) Caballero, Farhi, and Hammour (2006) Olivier (2000) Grossman and Yanagawa (1993) King and Ferguson (1993) Non-Fundamental Asset Price Movements and Investment Chirinko and Schaller (2001, 2007) Gilchrist, Himmelberg, and Huberman (2005) Dupor (2002, 2005) Panageas (2005) Johnson (2007) Angeletos, Lorenzoni, and Pavan (2007) Behavioral RBC Model (Optimism and Overcon dence) Jaimovich and Rebelo (2007)

27 RBC Model with Endogenous Growth & Adjustment Costs Along the lines of Barlevy (AER, 2004). The representative agent (or capitalist-entrepreneur) maximizes c E 0 β t 1 α t=0 1 α c t + i t = y t t 1, α = CRRA φ 1 α y t = A exp (z t ) k θ t h 1 θ t h t = K t, θ 2 (0, 1] k t+1 = B kt 1 λ it λ λ 2 (0, 1] z t+1 = ρz t + ε t+1 ε t+1 N 0, σ 2 ε

28 Adjustment Cost Formulation Mapping to formulation of Jermann (JME, 1998) and Barlevy (AER, 2004). k ψ1 λ t+1 it it = 1 δ + ψ k 0 ' B t k t k t λ = ψ 0 ψ 1( g i /k) ψ 1 1 δ + ψ 0 ( g i /k) ψ 1 B = 1 δ + ψ 0( g i /k) ψ1 ( g i /k) λ (Taylor Coe cients)

29 Adjustment Cost Formulation Mapping to formulation of Jermann (JME, 1998) and Barlevy (AER, 2004). k ψ1 λ t+1 it it = 1 δ + ψ k 0 ' B t k t k t λ = ψ 0 ψ 1( g i /k) ψ 1 1 δ + ψ 0 ( g i /k) ψ 1 B = 1 δ + ψ 0( g i /k) ψ1 ( g i /k) λ (Taylor Coe cients) i t /λ {z} p t = E t β ct+1 c t 2 3 α 6 7 4θy t+1 i {z t+1 + i } t+1 /λ5 (FOC) {z } d p t+1 t+1 x t i t /λ c t = p t c t ) p t d t = x t θ (1 θ) λ x t, (Stationary)

30 Model Solution Investment-consumption ratio depends on technology shock (except for log utility). x 1 λφ t exp[(1 λ)φ z t ] (1+λx t ) (1 λ)φ = E t eβ h [θ+xt+1 (1 λ+λθ)] exp(φ z t+1 ) (1+λx t+1 ) φ {z } w t+1 i (FOC) x t i t /λ c t = p h i t φ, φ 1 CRRA, eβ β (Aλ) λ B c t

31 Model Solution Investment-consumption ratio depends on technology shock (except for log utility). x 1 λφ t exp[(1 λ)φ z t ] (1+λx t ) (1 λ)φ = E t eβ h [θ+xt+1 (1 λ+λθ)] exp(φ z t+1 ) (1+λx t+1 ) φ {z } w t+1 i (FOC) x t i t /λ c t = p h i t φ, φ 1 CRRA, eβ β (Aλ) λ B c t Solution: x t = ex exp (γ z t ) ) w t = ew exp (m z t ) Forecast: E t w t+1 = ew exp mρ z t m2 σ 2 ε, m = m (CRRA) Nonlinear Allocation Rule: c t = y t 1 + λx t, y t = A exp (z t ) k t

32 Rational Forecast versus Speculative Forecast Speculative agent knows law of motion of technology, but not optimal response. Rational Forecast: E t w t+1 = ew exp mρ z t m2 σ 2 ε Speculative Forecast: be t w s,t+1 = ew s exp m s ρ z t m2 s σ 2 ε

33 Rational Forecast versus Speculative Forecast Speculative agent knows law of motion of technology, but not optimal response. Rational Forecast: E t w t+1 = ew exp mρ z t m2 σ 2 ε Speculative Forecast: be t w s,t+1 = ew s exp m s ρ z t m2 s σ 2 ε Overreaction: jm s j > jmj Approximation Point: log ( ew s ) = E [log (w s,t )] m s is calibrated to match std. dev. of p t d t in U.S. data.

34 Calibrating the Speculation Model to Fit U.S. Data Rational model uses same parameter values. Parameter Value Empirical Target θ 0.4 Capital share of income. α 1.5 Degree of risk aversion. A Mean k t /y t = 3. λ Mean i t /y t = B Mean consumption growth = 2.06 %. σ ε Std. dev. consumption growth = 3.56 %. ρ 0.95 Corr (p t /d t, p t 1 /d t 1 ) = β Mean p t /d t = 26. m s Std. dev. p t /d t = 13. m Rational model value (endogenous).

35 Overreaction Behavior Tends to be Self-Con rming Perceived versus Actual Response to Technology Shocks Actual Coefficient from Law of Motion Actual Law of Motion for CRRA =1.5 Actual Law of Motion for CRRA = degree Line m s = m s = Perceived Coefficient Used in Forecast Rule, m s

36 Convergence to the Rational Equilibrium Can Be Very Slow Real Time Learning Paths Estimated Response Coefficient ms m ,200 1,600 2,000 Periods

37 Model Simulations Speculative bubbles coincide with economic booms and excess capital formation. p/d log(i) log(k) Price Dividend Ratio 0 Speculation Model Rational Model Periods Investment Speculation Model Rational Model Periods Capital Stock Speculation Model Rational Model Periods R 1(percent) log(c) log(d) Net Equity Returns Speculation Model Rational Model Periods Consumption Speculation Model Rational Model Periods Dividends Speculation Model Rational Model Periods

38 Business Cycle Behavior Speculation magni es investment volatility but reduces consumption volatility. 16 Detrended Output 16 Detrended Consumption Pct. deviation from trend Speculation Model Rational Model Periods Pct. deviation from trend Speculation Model Rational Model Periods 16 Detrended Investment 16 Detrended Dividends Pct. deviation from trend Speculation Model Rational Model Periods Pct. deviation from trend Speculation Model Rational Model Periods

39 Unconditional Moments: Model versus Data Statistic U.S. Data Rational Model Speculation Model Mean p t /d t Std. Dev Skew Kurt Corr. Lag Mean p err t 0.00 % 0.18 % Mean err 2 t 2.66 % 4.87 % Corr (err t, err t 1 ) Corr (err t, err t 2 ) Corr (err t, err t 3 ) Computed from 10,000 period simulation with θ = 0.4, CRRA = 1.5.

40 Intuition for Welfare Results Fluctuations (due to speculation or business cycles) can a ect the mean and volatility of consumption growth.

41 Intuition for Welfare Results Fluctuations (due to speculation or business cycles) can a ect the mean and volatility of consumption growth. Decreased consumption growth implies less resources devoted to investment, and hence a higher initial consumption E (c 0 ).

42 Intuition for Welfare Results Fluctuations (due to speculation or business cycles) can a ect the mean and volatility of consumption growth. Decreased consumption growth implies less resources devoted to investment, and hence a higher initial consumption E (c 0 ). Higher initial consumption can mitigate the welfare costs of slower growth.

43 Intuition for Welfare Results Fluctuations (due to speculation or business cycles) can a ect the mean and volatility of consumption growth. Decreased consumption growth implies less resources devoted to investment, and hence a higher initial consumption E (c 0 ). Higher initial consumption can mitigate the welfare costs of slower growth. Higher initial consumption is less desirable when agents underinvest, i.e., when θ < 1.

44 Intuition for Welfare Results Fluctuations (due to speculation or business cycles) can a ect the mean and volatility of consumption growth. Decreased consumption growth implies less resources devoted to investment, and hence a higher initial consumption E (c 0 ). Higher initial consumption can mitigate the welfare costs of slower growth. Higher initial consumption is less desirable when agents underinvest, i.e., when θ < 1. As CRRA increases, consumption growth volatility becomes more costly.

45 Intuition for Welfare Results Fluctuations (due to speculation or business cycles) can a ect the mean and volatility of consumption growth. Decreased consumption growth implies less resources devoted to investment, and hence a higher initial consumption E (c 0 ). Higher initial consumption can mitigate the welfare costs of slower growth. Higher initial consumption is less desirable when agents underinvest, i.e., when θ < 1. As CRRA increases, consumption growth volatility becomes more costly. Which of these e ects dominates depends on parameter values.

46 Intuition for Welfare Results (continued) Speculation increases mean growth at low levels of actual risk aversion, but the reverse holds true for higher risk aversion. Mean and Volatility of Consumption Growth (with θ = 0.4) Deterministic Rational Speculation α Statistic Model Model Model Mean Std. Dev Mean Std. Dev Mean Std. Dev Note: In percent. Statistics are averages from a 10,000 period simulation.

47 Welfare Costs (in percent of per-period consumption) 1 percent of consumption = $100 billion in 2007 dollars. Welfare Cost of Speculation α θ = 0.4 θ = 0.6 θ =

48 Welfare Costs (in percent of per-period consumption) 1 percent of consumption = $100 billion in 2007 dollars. Welfare Cost of Speculation α θ = 0.4 θ = 0.6 θ = Welfare Cost of Business Cycles In Speculation Model α θ = 0.4 θ = 0.6 θ =

49 Welfare Costs Costs increase rapidly with risk aversion when agents underinvest.

50 Conclusion Periods of major technological innovation have typically been accompanied by speculative bubbles.

51 Conclusion Periods of major technological innovation have typically been accompanied by speculative bubbles. Many economists consider technology shocks to be a fundamental driving force for business cycles.

52 Conclusion Periods of major technological innovation have typically been accompanied by speculative bubbles. Many economists consider technology shocks to be a fundamental driving force for business cycles. Behavioral RBC model: speculative agents forecast like rational agents who have low risk aversion.

53 Conclusion Periods of major technological innovation have typically been accompanied by speculative bubbles. Many economists consider technology shocks to be a fundamental driving force for business cycles. Behavioral RBC model: speculative agents forecast like rational agents who have low risk aversion. Overreaction tends to be self-con rming; forecast errors are not persistent.

54 Conclusion Periods of major technological innovation have typically been accompanied by speculative bubbles. Many economists consider technology shocks to be a fundamental driving force for business cycles. Behavioral RBC model: speculative agents forecast like rational agents who have low risk aversion. Overreaction tends to be self-con rming; forecast errors are not persistent. Even from the narrow perspective of a theoretical model, it remains an open question whether speculative behavior is harmful to society.

55 Conclusion Periods of major technological innovation have typically been accompanied by speculative bubbles. Many economists consider technology shocks to be a fundamental driving force for business cycles. Behavioral RBC model: speculative agents forecast like rational agents who have low risk aversion. Overreaction tends to be self-con rming; forecast errors are not persistent. Even from the narrow perspective of a theoretical model, it remains an open question whether speculative behavior is harmful to society. For higher degrees of risk aversion, the welfare costs of speculation and business cycles can be large.