Equity prices around the world have fallen sharply in recent weeks, raising alarm about the possibility of a double-dip recession in some advanced economies. Several factors may have played a role in the drop in equity prices:

- The sovereign debt problems in the Eurozone,
- A downgrade of US federal government debt, and
- The limited room for policy manoeuvre by advanced economies that are facing a weaker than expected economic recovery.

To the extent that such factors simultaneously affect confidence and equity prices, an equity price drop can indicate a greater risk of recession, reflecting falling earning expectations. Accordingly, many think that a double-dip recession in the US and other advanced economies has become more likely, particularly as uncertainty has increased (Bloom 2011). But others have noted that equity price drops have not always been good predictors of recessions. As Paul Samuelson (1966) famously remarked, “The stock market has forecast nine of the last five recessions.”

This column examines the performance of equity prices as coincident predictors of a new recession in the G7 economies. The beginnings of new recessions – which coincide with cyclical peaks – are identified using the algorithm introduced by Harding and Pagan (2002), as implemented by Claessens *et al* (2011). We find that real equity prices in France, Japan, the UK, and the US are useful predictors of recessions. In contrast with the existing literature, there is some evidence of important nonlinearities in the relationship between real equity prices and recessions for the UK and the US. For Canada and Germany, there is no evidence that real equity prices aid in predicting recessions, whereas for Italy, their predictive power is consistently superseded by the inclusion of additional financial market variables.

# Predicting the probability of a new recession

While real-time recession prediction remains an elusive endeavour, important progress in forecasting the onset of a recession has been achieved using simple probabilistic models. These models take advantage of the fact that cyclical peaks can be modelled as binary indicators (with a value of one when the economy has reached its peak and zero otherwise). The most important finding of this literature is that the term spread (the difference between the long-term interest rate and the short-term interest rate) is an important predictor of recessions in the Eurozone and the US. A number of these studies also find that domestic equity prices can be useful in predicting recessions.^{1}

Building on this literature, this column explores how real equity price changes help predict new recessions in the G7. The explanatory variables included in our simple, baseline logit model are the contemporaneous quarterly growth rate of the economy’s average real equity price index, an indicator variable for whether the equity price index dropped quarter-over-quarter by 5% or more, and the interaction (product) of these two variables. This model allows us to explore the relevance of nonlinearities in the information conveyed by real equity price changes about the likelihood of a recession. In particular, sharp drops in real equity prices are more likely to be followed by a new recession, reflecting both the destruction of private-sector wealth and possible underlying weaknesses in the macroeconomy.

The following findings stand out:

- In the UK and the US, there is evidence of important nonlinearities in the information that equity prices convey about the probability of a new recession. This is evident in the statistical significance of equity price growth, the equity price-drop indicator, and their interaction as predictors of a new recession (Table 1). The in-sample performance of the baseline model for these economies is very strong, as reflected by AUC statistics of 0.85 and 0.90, respectively.
^{2}As seen in Table 1, column 3, the average probability of a new recession occurring in any quarter, conditional upon observing a drop in equity prices of 5% or more, is around 20%. By contrast, if no equity price drop is observed, the estimated average probability is insignificantly different from zero. - Interestingly, this nonlinearity in the predictive power of equity prices is not evident for France and Japan. Instead, there appears to be a robust, linear relationship between equity price growth and the likelihood of a new recession—large equity price drops do not appear to convey any more information than small drops. The in-sample performance of this model is also strong, as reflected in an AUC of 0.82 for France and 0.91 for Japan (Table 1). The marginal effect of a 1% fall in equity prices is associated with a rise in the probability of a new recession of between 0.5 and 0.6% for France and 0.6 and 0.9% for Japan.
- These findings are generally robust to the inclusion of other real-time financial variables (such as the term spread, house prices, and credit) and oil prices. Despite the statistical significance of some of the additional financial variables, the in-sample performances (as measured by the AUC statistic) are not statistically significantly different from the baseline models for France, Japan, the UK, and the US.
- Equity prices do not help predict the onset of a new recession in Canada and Germany. In Italy, the relation between equity prices and the onset of a new recession is not robust, as equity prices are encompassed as predictors of a new recession by other financial variables.

**Table 1.** Predicting new recessions with financial market variables (logit model, dependent variable -- new recession starts in quarter *t* (1 if true and 0 if false).

*Sources: Datastream; Haver Analytics; IMF, International Financial Statistics; Claessens, Kose, and Terrones (2011); and authors' calculations. Note: Robust standard errors are in parentheses underneath the estimates. Statistical significance is denoted by * for 10% level, ** for 5% level, and *** for 1% level. ** *

# What does this mean going forward?** **

An application of the baseline model paints a sobering picture about the likelihood of a double-dip recession in France, the UK, and the US in light of the recent sharp drop in equity prices. As seen in Figure 1, the historical or unconditional probabilities of a new recession starting in the third quarter of 2011 are about 3½% for France and the UK and about 4½% for the US. Assuming that the recent behaviour of the equity markets in these economies during the third quarter of 2011 continues, the predicted likelihood of a new recession rises about fivefold for France and the UK (to about 18% and 17%, respectively) and eightfold for the US (to about 38%). By contrast, the model for Japan indicates that there has been essentially no change in the likelihood of a new recession there.^{3}

**Figure 1.** Predicted probability of a new recession in a quarter

*Sources: Claessens et al (2011), Haver Analytics, and authors’ calculations. Note: The equity price indices used in the estimation are: S&P 500 for the United States, FTSE All Shares for the UK, CAC All-Tradable for France, and the Nikkei 225 for Japan. The Claessens et al (2011) recession indicator is used for the starts of recessions. Probability estimates are derived from a simple logit model for the recession indicator over the period 1970:Q1 to 2011:Q2, excluding periods where the economy is already in recession and the quarter just after a recession concludes. The logit model takes as arguments the real equity price change, a dummy for large drops (>5%) and their interaction. To calculate the average for 2011:Q3, we assume that the last, daily equity price index extends to the end of the quarter. We then calculate the quarterly average level for 2011:Q3 over these daily observations. Latest data are for 24 August 2011.*

The analysis of this column suggests that policymakers should be mindful of sharp equity price drops, as they may foreshadow a substantial rise in the probability of a new recession. This may reflect how falling equity prices can be a drag on consumption and investment through the destruction of private wealth and worsened economic prospects. Current estimates suggest that a number of advanced economies, home to some of the largest equity markets in the world, are facing a rising risk of a new recession.

*Editor’s Note: The views expressed in this column are those of the authors and do not necessarily represent those of the IMF or IMF policy.*

# References** **

Berge, Travis and Òscar Jordà (2011) “Evaluating the Classification of Economic Activity into Recessions and Expansions,” *American Economic Journal: Macroeconomics*, 3(2): 246-77.

Bloom, Nicholas (2011) “The Uncertainty Shock From the Debt Disaster Will Cause a Double-dip Recession,” VoxEU.org, 22 August.

Claessens, Stijn, M. Ayhan Kose, and Marco Terrones (2011) “How Do Business and Financial Cycles Interact?” IMF Working Paper No. 11/88. 1 April.

Estrella, Arturo and Frederic S. Mishkin (1998) “Predicting US Recessions: Financial Variables as Leading Indicators,” *Review of Economics and Statistics*, 80(1): 45-61.

Harding, Don and Adrian Pagan (2002) “Dissecting the Cycle: A Methodological Investigation,” *Journal of Monetary Economics*, 49: 365-81.

Samuelson, Paul (1966) “Science and Stocks,” *Newsweek*, 9 September: 92.

^{1} Estrella and Mishkin (1998) is an important early contribution in this literature.

^{2} The AUC statistic is the area under the receiver operating characteristic (ROC) curve. This curve is just a plot of the true positive rate versus the false positive rate. The predictive value of a model is given by the extent this curve falls above the 45-degree line—which reflects the predictive power of a coin toss. The AUC is thus indicative of how well the model classifies the start of a recession versus the absence of recession observations in-sample, relative to a fair coin toss (which would have a 50% chance of correctly classifying the situation). A perfect classifier would have an AUC statistic of 1. Berge and Jorda (2011) offer a detailed discussion of this method and an application to the US business cycle.

^{3} Predicted probabilities are based on data as of 24 August 2011.