Academy of Economic Studies Bucharest Doctoral School of Finance and Banking DOFIN

1. Academy of Economic Studies BucharestDoctoral School of Finance and BankingDOFIN The Yield Curve in Predicting U.S. Recessions Supervisor: Professor Dr. Moisa Altar MSc Student: TIBERIU PIPIRIG Bucharest, July 2008

2. Contents • Conceptual considerations The Yield Curve as a Leading Indicator Defining Recessions Measuring the variables • Recession Prediction Using the Yield Curve: Alternative Probit Models Methodology Empirical Results Out of Sample Predictions of Recessions and Expansions Interpreting the signal Conclusions References Appendix 1

3. Motivation • In 1996, the Conference Board added the yield curve spread to its index of leading indicators, focusing on monthly changes in the spread. Note, however, that it announced in June 2005 that it would adjust its procedure so as to focus on the level of the spread and not on the change, and for this reason my analysis is focused on the level of the term spread. • The slope of the Treasury yield curve has often been cited as a leading economic indicator, with inversion of the curve being thought of as a harbinger of a recession. • Before each of the last six recessions, short-term interest rates rose above long term rates, reversing the customary pattern and producing what economists call a yield curve inversion. • In March 2007, Alan Greenspan stated that there is a 35 percent probability that the US economy enters a recession before the end of the year.

4. Literature Review • Analysis of the behaviour of interest rates of different maturities over the business cycle goes back at least to Mitchell (1913) and Kessel (1965); • Laurent (1988,1989) used term spread to predict GNP growth; • Fama (1990), Mishkin (1990) and Jorion (1991) show that spreads between long and short term interest rates contain information about future inflation; • Bernanke (1990) and Estrella and Hardouvelis (1991) showed that term spreads are useful for predicting future real economic growth; • The value of term spreads as an indicator of the likelihood of whether a recession, as defined by the NBER, will occur in the near future is forcefully demonstrated by Bernard and Gerlach (1998) and Estrella and Trubin (2006); • More supportive empirical evidence for this argument is recently provided by Stock and Watson (2003), Wright (2006), Swanson (2007), Estrella and Adrian (2007) and Rosenberg and Maurer (2008);

5. The Yield Curve as a Leading Indicator • Current monetary policy has a significant influence on the yield curve spread and hence on real activity over the next several quarters Tightening of monetary policy rise in short term interest rates  intended to lead to a reduction in inflationary pressures  pressures subside  lower interest rates  monetary tightening slows down the economy and flattens or inverts the yield curve • Changes in investor expectations can also change the slope of the yield curve Rise in short term interest rates  slowing economic activity  increasing the likelihood of a future easing in monetary policy  expected declines in short term rates would tend to reduce current long term rates This scenario is consistent with the observed correlation between the yield curve and recessions.

6. Defining Recessions • A recession is a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales (NBER). • The 2001 recession thus lasted 8 months, which is somewhat less than the average duration of recessions since World War II. The post-war average, excluding the 2001 recession, is 11 months. • The standard dating of U.S. recessions derives from the cyclical peaks and troughs identified by the National Bureau of Economic Research (NBER). To convert the NBER monthly dates into a monthly recession indicator, I classify as a recession every month between the peak and the subsequent trough, as well as the trough itself. The peak is not classified as a recession month because the economy would have grown from the previous month. • Other conventions may lead to different results, for example, Wright (2006) classifies peaks as recession periods.

7. Measuring the variables • Term spread measured as 10 years Treasury Bond less the 3 month Treasury Bill • Maximum accuracy and predictive power are obtained with the secondary market three month rate expressed on a bond equivalent basis, rather than the constant maturity rate, which is interpolated from the daily yield curve for Treasury securities. To convert the three month discount rate to a bond equivalent basis, I apply the transformation: where “discount” is the discount yield expressed in percentage points. • Historically, the nominal federal funds rate (annualized using a 360 day year) has exhibited a positive statistical relationship with the odds of a recession

8. Notes: The term spread in February 2007 was -0.45 percentage points. The shaded areas indicate periods designated national recessions by the National Bureau of Economic Research.

9. Recession Prediction Using the Yield Curve: Alternative Probit Models • Model A where is the dummy that takes on a value 1 if and only if there is an NBER defined recession at some point during months or quarters t+1 through t+h, inclusive, denotes the average ten year over three month constant maturity Treasury term spread during quarter t and denotes the standard normal cumulative distribution function. • Model B where the denotes the average effective federal funds rate during month or quarter t. Each of the monthly models is estimated using data from Jul 1960 to Jul 2007 The quaterly model is estimated using data from Q3:1960 to Q2: 2007.

10. Measure of fit • The measure of fit used, that is, the pseudo R2, is calculated from a formula proposed in Estrella (1995) • where is the value of the likelihood of the estimated model and is the value of a model containing only the constant term .

11. Empirical Results • Chart shows that the estimated probability of recession exceeded 27 percent in the case of each recession and ranged as high as 98 percent in the 1981-82 recession. • Model A now puts the odds of a recession in the next twelve months at over 30 percent, starting from October 2007 until April 2008. Model B predict odds of a recession of around 20 percent, which is actually in the range of the unconditional probability of a recession in any twelve months period. • At the most recent Survey of Professional Forecasters (May 2008) the forecasters see a 49 percent chance of negative growth this quarter, up from 43 percent in the last survey

12. 12 Months Horizon • Charts show the fitted probabilities of a recession from models A and B, at the 12 months ahead horizon. Both models have generally quite good fit, with actual recessions following periods when the fitted probability of a recession was high. • In model A, the coefficient on the ten year over the three month term spread is statistically highly significant at the 12 months horizon, reaffirming the underlying historical statistical association. In model B, both the federal funds rate and term spread are highly significant. The fit of the regression, judging from the pseudo R-squared andMcFadden R-squared is better than using the term spread alone. Note: ***Statistically significant at the 1 percent level

13. 4 Quarters Horizon Estimated Recession Probabilities for Probit Model Using the Yield curve Spread Four Quarters Ahead

14. Out of Sample Predictions of Recessions and Expansions • Danger of overfitting • For each model, and each horizon, I recursively compute predicted recession probabilities in each month or quarter, beginning with the forecast made in 1980. I then consider the root mean square error of these predictions. That is, if is the fitted probability of a recession between month or quarter t and t+h, estimated using data available at time t, then the root mean square prediction error is: where is the total number of pseudo out of sample forecasts Out of Sample Root Mean Square Prediction Errors, 1981-2007 Q2

15. Interpreting the signal • The tallest bar from the right panel shows that the value of the spread was between 2 and 3 percentage points in about 35% of the cases • In the left panel the level of the spread was between -1 and 0 percentage points in almost 50% of the cases • The left panel suggests that, of the observations followed by a recession twelve months later, 67% (the sum of the bars to the left of zero) are negative • Note: the frequency distributions is estimated using data from 1968 to 2006

16. Short End versus Long End Changes • Charts display the level of the three month Treasuries and the change in their rates over the 18 months leading to peak recession signal since 1968. The timing of the peak signals corresponds to the low monthly average spread levels reported in table. • We could think of every yield curve inversion as resulting at least partly from a rise at the short end.

17. Conclusions • Defining recessions as the periods between NBER peaks and troughs, counting the throughs but not the peaks produces clear results. • Treasury rates are most likely to produce accurate forecasts • The best maturity combination may be the three months and ten years. The three month rate is best represented by the secondary market rate, expressed on a bond equivalent basis to match the ten year rate. • The ten year constant maturity rate produces good results. • The results obtain from a model using both variables are encouraging and suggest that the yield curve spread can have a useful role in macroeconomic predictions, particularly with longer lead times. Probit models forecasting recessions that use both the level of the federal funds rate and the term spread give better out of sample performance than models with the term spread alone. The shape of the yield curve that has historically been the strongest predictor of recessions involves an inverted yield curve with a high level of the nominal funds rate. While a probit model using the term spread alone predicts high odds of a recession in the next four quarters, the other probit model that I estimate, which controls for the level of the funds rate do not. • Further analysis of the correlations between the shape of the yield curve and growth in foreign industrialized countries is an important topic that is left for future research.

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20. Appendix 1