Business Cycles Chris Edmond NYU Stern Spring 2007 1
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
Trends and cycles Start by looking at quarterly US real GDP 3
Trends and cycles US log real GDP 9.25 8.75 8.25 7.75 7.25 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 4
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
Trends and cycles US log real GDP 9.25 8.75 8.25 smooth red line is the trend given by an HP filter 7.75 7.25 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 6
Business cycles 8.00 percent deviation from trend 6.00 4.00 2.00 0.00-2.00-4.00-6.00 standard deviation at business cycle frequencies = 1.69-8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 7
Business cycle jargon 8.00 percent deviation from trend 6.00 4.00 peak peak peak peak 2.00 peak 0.00-2.00 trough -4.00 trough trough trough -6.00 trough standard deviation at business cycle frequencies = 1.69-8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 8
Business cycle jargon 8.00 percent deviation from trend 6.00 4.00 contraction 2.00 contraction contraction 0.00-2.00-4.00-6.00 standard deviation at business cycle frequencies = 1.69-8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 9
Business cycle jargon 8.00 percent deviation from trend 6.00 4.00 2.00 0.00-2.00 expansion -4.00 expansion expansion -6.00 standard deviation at business cycle frequencies = 1.69-8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 10
NBER recessions 8.00 6.00 4.00 2.00 0.00-2.00-4.00-6.00-8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: National Bureau of Economic Research, 2006 11
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
Nondurables consumption 8.00 6.00 correlation at business cycle frequencies = 0.73 standard deviation relative to GDP = 0.65 4.00 2.00 0.00-2.00-4.00-6.00 GDP -8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 13
Services consumption 8.00 6.00 correlation at business cycle frequencies = 0.71 standard deviation relative to GDP = 0.42 4.00 2.00 0.00-2.00-4.00-6.00 GDP -8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 14
Durables consumption 30.00 correlation at business cycle frequencies = 0.59 standard deviation relative to GDP = 3.10 20.00 10.00 0.00-10.00-20.00-30.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 15
Investment 30.00 correlation at business cycle frequencies = 0.87 standard deviation relative to GDP = 4.70 20.00 10.00 0.00-10.00-20.00-30.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Economic Analysis, 2006 16
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
Labor markets Examples hours worked earnings per hour unemployment employment Cyclical properties positively correlated with GDP? smooth or volatile? leads or lags? 18
Hours worked 8.00 6.00 correlation at business cycle frequencies = 0.74 standard deviation relative to GDP = 0.27 4.00 2.00 0.00-2.00-4.00-6.00 GDP -8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Labor Statistics, 2006 19
Earnings per hour 8.00 6.00 correlation at business cycle frequencies = 0.58 standard deviation relative to GDP = 0.45 4.00 2.00 0.00-2.00-4.00-6.00 GDP -8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Bureau of Labor Statistics, 2006 20
Unemployment 8.00 6.00 correlation at business cycle frequencies = 0.76 standard deviation relative to GDP = 11.88 60.00 40.00 4.00 2.00 20.00 0.00 0.00-2.00-20.00-4.00-6.00-40.00-8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003-60.00 Source: Bureau of Labor Statistics, 2006 21
Employment 8.00 6.00 correlation at business cycle frequencies = 0.71 standard deviation relative to GDP = 1.48 60.00 40.00 4.00 2.00 20.00 0.00 0.00-2.00-20.00-4.00-6.00-40.00-8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003-60.00 Source: Bureau of Labor Statistics, 2006 22
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
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
S&P 500 30.00 correlation at business cycle frequencies = 0.40 standard deviation relative to GDP = 5.50 20.00 10.00 0.00-10.00-20.00-30.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Standard and Poor s, 2006 25
Term spread 8.00 6.00 correlation at business cycle frequencies = 0.40 standard deviation relative to GDP = 1.01 4.00 GDP 2.00 0.00-2.00-4.00-6.00 term spread = 10-year treasury fed funds -8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Federal Reserve Board of Governors, 2006 26
Credit spread 8.00 6.00 correlation at business cycle frequencies = 0.43 standard deviation relative to GDP = 0.45 4.00 GDP 2.00 0.00-2.00-4.00-6.00 credit spread = moody s BAA 10-year treasury -8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Federal Reserve Board of Governors, 2006 27
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
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
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
Business cycle indicators and forecasting Statistical forecasts properties of good leading indicators regression methods Market forecasts leading example: yield curve other examples? 31
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
Index of leading indicators INDICATOR WEIGHT Average weekly hours, manufacturing 0.1946 Average weekly initial claims for unemployment insurance 0.0268 Manufacturers new orders, consumer goods and materials 0.0504 Vendor performance, slower deliveries diffusion index 0.0296 Manufacturers new orders, non-defense capital goods 0.0139 Building permits, new private housing units 0.0205 Stock prices, 500 common stocks 0.0309 Money supply, M2 0.2775 Interest rate spread, 10-year Treasury bonds less fed funds 0.3364 Index of consumer expectations 0.0193 Source: Conference Board 33
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
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
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
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
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
Euro yield curve 6 annual percentage 5 4 yields y m 3 2 1 0 maturity m (in years) 1 2 3 4 5 6 7 8 9 10 Source: Euro zero-coupon yield curve, Feb 2006 39
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 1 1 + f m = p m p m+1 40
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) 1 2 3 4 5 y m (%) 3.018 3.215 3.315 3.386 3.441 p m (per 100) 97.07 93.87 90.68 87.53 84.44 f m 1 (%) 3.018 3.412 3.517 3.600 3.660 41
Euro yield curve 6 annual percentage 5 forwards f m 1 4 yields y m 3 2 1 0 maturity m (in years) 1 2 3 4 5 6 7 8 9 10 Source: Euro zero-coupon yield curve, Feb 2006 42
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
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
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
Numerical example current data historical average f m f 0 m (years) f m,t (%) f m (%) risk premium 0 1 2 3 4 3.018 3.412 3.517 3.600 3.660 3.221 3.716 4.161 4.502 4.779 0.000 0.495 0.940 1.281 1.558 46
Euro yield curve 6 annual percentage historical average f m 1 5 4 forwards f m 1 3 yields y m 2 1 0 maturity m (in years) 1 2 3 4 5 6 7 8 9 10 Source: Euro zero-coupon yield curve, Feb 2006 47
Euro yield curve 6 annual percentage historical average f m 1 5 4 forwards f m 1 3 yields y m estimated risk premium f m 1 f 0 2 1 0 maturity m (in years) 1 2 3 4 5 6 7 8 9 10 Source: Euro zero-coupon yield curve, Feb 2006 48
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
Numerical example current data f m f 0 expected future short m (years) f m,t (%) risk premium E t {y 1,t+m } 0 1 2 3 4 3.018 3.412 3.517 3.600 3.660 0.000 0.495 0.940 1.281 1.558 3.018 2.917 2.577 2.319 2.102 50
Euro yield curve 6 annual percentage historical average f m 1 5 4 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) 1 2 3 4 5 6 7 8 9 10 Source: Euro zero-coupon yield curve, Feb 2006 51
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
Recall: term spread 8.00 6.00 correlation at business cycle frequencies = 0.40 standard deviation relative to GDP = 1.01 4.00 GDP 2.00 0.00-2.00-4.00-6.00 term spread = 10-year treasury fed funds -8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Euro zero-coupon yield curve, Feb 2006 53
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
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 = 0.045 55
Recall: credit spread 8.00 6.00 correlation at business cycle frequencies = 0.43 standard deviation relative to GDP = 0.45 4.00 GDP 2.00 0.00-2.00-4.00-6.00 credit spread = moody s BAA 10-year treasury -8.00 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 Source: Euro zero-coupon yield curve, Feb 2006 56
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