Business Cycles. Chris Edmond NYU Stern. Spring 2007

Transcription

1 Business Cycles Chris Edmond NYU Stern Spring

2 Overview Business cycle properties GDP does not grow smoothly: booms and recessions categorize other variables relative to GDP look at correlation, volatility, leads and lags, etc Business cycle indicators statistical forecasts market forecasts 2

3 Trends and cycles Start by looking at quarterly US real GDP 3

4 Trends and cycles US log real GDP Source: Bureau of Economic Analysis,

5 Trends and cycles Start by looking at quarterly US real GDP want to isolate trend from cycle many ways to do this filtering we use something called the Hodrick-Prescott (HP) filter has the effect of drawing a smooth curve through the data 5

6 Trends and cycles US log real GDP smooth red line is the trend given by an HP filter Source: Bureau of Economic Analysis,

7 Business cycles 8.00 percent deviation from trend standard deviation at business cycle frequencies = Source: Bureau of Economic Analysis,

8 Business cycle jargon 8.00 percent deviation from trend peak peak peak peak 2.00 peak trough trough trough trough trough standard deviation at business cycle frequencies = Source: Bureau of Economic Analysis,

9 Business cycle jargon 8.00 percent deviation from trend contraction 2.00 contraction contraction standard deviation at business cycle frequencies = Source: Bureau of Economic Analysis,

10 Business cycle jargon 8.00 percent deviation from trend expansion expansion expansion standard deviation at business cycle frequencies = Source: Bureau of Economic Analysis,

11 NBER recessions Source: National Bureau of Economic Research,

12 Co-movement and volatility Many macro variables comove with GDP which are positively correlated with GDP? which are volatile? which are smooth? Variables to look at national income accounts: consumption, investment, etc labor markets: hours, earnings, unemployment financial markets: stock prices, interest rates 12

13 Nondurables consumption correlation at business cycle frequencies = 0.73 standard deviation relative to GDP = GDP Source: Bureau of Economic Analysis,

14 Services consumption correlation at business cycle frequencies = 0.71 standard deviation relative to GDP = GDP Source: Bureau of Economic Analysis,

15 Durables consumption correlation at business cycle frequencies = 0.59 standard deviation relative to GDP = Source: Bureau of Economic Analysis,

16 Investment correlation at business cycle frequencies = 0.87 standard deviation relative to GDP = Source: Bureau of Economic Analysis,

17 Co-movement and volatility Consumption nondurables and services: pro-cyclical, relatively smooth durables: a bit less pro-cyclical, but much more volatile Investment extremely pro-cyclical and volatile similar to durables consumption 17

18 Labor markets Examples hours worked earnings per hour unemployment employment Cyclical properties positively correlated with GDP? smooth or volatile? leads or lags? 18

19 Hours worked correlation at business cycle frequencies = 0.74 standard deviation relative to GDP = GDP Source: Bureau of Labor Statistics,

20 Earnings per hour correlation at business cycle frequencies = 0.58 standard deviation relative to GDP = GDP Source: Bureau of Labor Statistics,

21 Unemployment correlation at business cycle frequencies = 0.76 standard deviation relative to GDP = Source: Bureau of Labor Statistics,

22 Employment correlation at business cycle frequencies = 0.71 standard deviation relative to GDP = Source: Bureau of Labor Statistics,

23 Labor markets Hours worked pro-cyclical, relatively smooth Earnings per hour pro-cyclical, relatively smooth Unemployment counter-cyclical and extremely volatile Employment pro-cyclical, somewhat volatile a lagging indicator? 23

24 Financial markets Examples S&P 500 index term spread (long return short return) credit spread (risky return safe return) Cyclical properties positively correlated with GDP? smooth or volatile? leads or lags? What do you think? 24

25 S&P correlation at business cycle frequencies = 0.40 standard deviation relative to GDP = Source: Standard and Poor s,

26 Term spread correlation at business cycle frequencies = 0.40 standard deviation relative to GDP = GDP term spread = 10-year treasury fed funds Source: Federal Reserve Board of Governors,

27 Credit spread correlation at business cycle frequencies = 0.43 standard deviation relative to GDP = GDP credit spread = moody s BAA 10-year treasury Source: Federal Reserve Board of Governors,

28 Financial markets S&P 500 index weakly pro-cyclical, massively volatile Term spread (long return short return) weakly counter-cyclical, same volatility as GDP a leading indicator? Credit spread (risky return safe return) weakly counter-cyclical, smooth 28

29 What have we learned so far? GDP does not grow smoothly: booms and recessions investment and durables consumption are even more volatile than GDP; nondurables and services consumption are less volatile consumption, investment, employment, and stock market all pro-cyclical unemployment, term and credit spreads counter-cyclical some indicators seem to lead the cycle (term spread?) while others lag the cycle (employment?) Lead/lag relationships might help with forecasting 29

30 Business cycle indicators and forecasting Some variables seem to lead the business cycle can we exploit these indicator variables to forecast GDP movements? Market prices aggregate information/beliefs of market participants can we use prices/returns to infer market forecasts? 30

31 Business cycle indicators and forecasting Statistical forecasts properties of good leading indicators regression methods Market forecasts leading example: yield curve other examples? 31

32 What s a good indicator Correlated with variable of interest strength of correlation important sign of correlation not important Leads variable of interest Timely available quickly Stable no significant revisions that would make in-sample assessments unreliable 32

33 Index of leading indicators INDICATOR WEIGHT Average weekly hours, manufacturing Average weekly initial claims for unemployment insurance Manufacturers new orders, consumer goods and materials Vendor performance, slower deliveries diffusion index Manufacturers new orders, non-defense capital goods Building permits, new private housing units Stock prices, 500 common stocks Money supply, M Interest rate spread, 10-year Treasury bonds less fed funds Index of consumer expectations Source: Conference Board 33

34 Regression-based forecasting Example k-period ahead GDP growth γ Y,t+k vector of indicator variables observed at time t X t regression γ Y,t+k = α + βx t + ε t (gives estimates of α and β coefficients) 34

35 Regression-based forecasting Regression γ Y,t+k = α + βx t + ε t Sources of forecast error large residual error (low R 2 ) imprecise estimates of α or β (large standard errors) unstable relationship between γ Y and X unstable data, revisions 35

36 Information aggregation How do we combine information from many sources? adjust for differing degrees of quality or reliability? Market data basic idea: prices aggregate information of market participants 36

37 Reading the yield curve: overview Long bond yields contain information about expected future bond market conditions Why? If you buy a 10-year Treasury bond the yield should compensate you for expected changes in short rates over time if we expect short rates to rise, long yield should be higher Insight can try to reverse engineer this process infer expected future short rates from yield curve Difficulty separating risk premia on long bonds from expected future short rates 37

38 Bond yields Look at zero-coupon bonds ( zeros ) Notation p m = price of $100 in m-periods y m = yield on m-period bond (maturity m) Price and yield related by present value formula p m = 100 (1 + y m ) m (since prices are in dollars, yields are nominal) Yield curve ( term structure of interest rates ) is a plot of y m against m 38

39 Euro yield curve 6 annual percentage 5 4 yields y m maturity m (in years) Source: Euro zero-coupon yield curve, Feb

40 Convert yields to forward rates Notation f m = 1-period return on investment made in m periods (forward rate) Yields apply to all periods until maturity, so $100 = p m (1 + y m ) m Forwards apply one period at a time, so $100 = p m (1 + f 0 )(1 + f 1 )... (1 + f m 1 ) Compute forwards from yields by comparing these relations, leads to 1 + f 0 = 1 + y f m = p m p m+1 40

41 Numerical example Bond prices p m = Forward rates 100 (1 + y m ) m 1 + f 0 = 1 + y 1 then 1 + f m = p m p m+1 m (years) y m (%) p m (per 100) f m 1 (%)

42 Euro yield curve 6 annual percentage 5 forwards f m 1 4 yields y m maturity m (in years) Source: Euro zero-coupon yield curve, Feb

43 Expectations hypothesis Basic idea: forward rate includes market expectation of future short rates Notation y m,t = yield on m-period bond contract at t f m,t = 1-period return on investment at m agreed at t Expectations hypothesis f m,t = E t {y 1,t+m } + risk premium m (E t { } means expectations of { } at date t ) Risk premium constant across time, varies across maturity m 43

44 Intuition for expectations hypothesis Compare strategies for investing over two periods: rollover strategy: reinvesting in short bonds rollover return = (1 + y 1,t )(1 + y 1,t+1 ) buy and hold strategy: buy a two-period bond buy and hold return = (1 + y 2,t )(1 + y 2,t ) = (1 + y 1,t )(1 + f 1,t ) If y 1,t+1 known at t, market forces should equalize returns (so, y 1,t+1 = f 1,t ) But y 1,t+1 not known at t, so weaker conclusion f 1,t = E t {y 1,t+1 } + risk premium 44

45 Expectations hypothesis Estimating risk premia f m,t = E t {y 1,t+m } + risk premium m Simple method to estimate risk premium terms T risk premium m = 1 T t=1 {f m,t y 1,t } = f m f 0 (risk premium is average forward average short) Calculate from historical data over long horizon T 45

46 Numerical example current data historical average f m f 0 m (years) f m,t (%) f m (%) risk premium

47 Euro yield curve 6 annual percentage historical average f m forwards f m 1 3 yields y m maturity m (in years) Source: Euro zero-coupon yield curve, Feb

48 Euro yield curve 6 annual percentage historical average f m forwards f m 1 3 yields y m estimated risk premium f m 1 f maturity m (in years) Source: Euro zero-coupon yield curve, Feb

49 Reverse engineering the yield curve Expectations hypothesis forward rate = expected short rate + risk premium So if we have market forward rates plus estimates of risk premia, then we can compute expected short rate = forward rate risk premium 49

50 Numerical example current data f m f 0 expected future short m (years) f m,t (%) risk premium E t {y 1,t+m }

51 Euro yield curve 6 annual percentage historical average f m forwards f m 1 3 yields y m estimated risk premium f m 1 f 0 2 expected future short E t {y 1,t+m } 1 0 maturity m (in years) Source: Euro zero-coupon yield curve, Feb

52 Comments Historical yield/forward curve is upward sloping, so risk premium increases with maturity so an inverted (downward sloping) yield/forward curve surely gives falling expected future short rates but also flat yield/forward curve also gives falling expected future short rates Consequences of falling expected future short rates? lower GDP growth and/or lower inflation 52

53 Recall: term spread correlation at business cycle frequencies = 0.40 standard deviation relative to GDP = GDP term spread = 10-year treasury fed funds Source: Euro zero-coupon yield curve, Feb

54 Reading the yield curve: recap Summary convert yields to forward rates use historical forward rates to estimate risk premium subtract estimate of risk premium result: market-based forecast of future short rate What can go wrong? bad/unstable estimates of risk premium market pricing based on non-risk factors 54

55 Credit spreads and default probabilities Similarly, can use credit spreads to infer market default probabilities Basic idea borrower s default probability α lender gets zero if borrower defaults lender gets return R if borrower does not default risk free return R f Market forces or R f = α0 + (1 α)r α = R Rf R Observe credit spreads R R f, so infer market α Example: R = 1.10, R f = 1.05 then α =

56 Recall: credit spread correlation at business cycle frequencies = 0.43 standard deviation relative to GDP = GDP credit spread = moody s BAA 10-year treasury Source: Euro zero-coupon yield curve, Feb

57 Business cycle properties What have we learned today? GDP does not grow smoothly: booms and recessions investment and durables more volatile than GDP; nondurables and services less volatile consumption, investment, employment, and stock market all pro-cyclical unemployment, term and credit spreads counter-cyclical Business cycle indicators regression-based forecasting yield curve reflects market forecasts of future rates inverted/flat yield curve implies falling GDP growth (and/or lower inflation) 57