# Forecasting recessions with economic indicators

Abstract

This study compares three economic indicators often used in forecasting recessions: the Yield Spread, the Chicago Index and the Leading index. We find that the latter two predict recessions well one and two quarters ahead, but fail in forecasting recessions on a longer time period. On the contrary, the Yield Spread performs better when forecasting recessions four and six quarters ahead.

# Introduction

There exist several ways to define an economic recession. In the United States, the National Bureau of Economic Research defines it as: ≪ *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*.≫ [NBoER, 2010]. In the United Kingdom and Europe, recession is generally defined as two consecutive quarters of negative economic growth, measured by the seasonal adjusted real GDP.

Whichever definition we chose to consider, it is clear that recessions have an effect on the overall economy, the inflation rate, the real prices the unemployment rate. As figure 1 shows, in December 2007, the national unemployment rate in the United States was 5.0%, and it had been at or below that rate for the previous 30 months. At the end of the recession, in June 2009, it was 9.5%. In the months after the recession, the unemployment rate peaked at 10.0% (in October 2009) [Hagedorn and al., 2013].

Moreover, a recent study found that the Great Recession of 2007-2009 affected the overall health of Americans, especially their mental health, increasing morbidity, psychological distress, and suicide. The study also found that health impacts were stronger among men than women and among racial minorities than white people. An important finding of this study was that European governments and strong social safety nets were able to save Europeans from a similar deterioration of health [Margerison-Zilko and al., 2016].

Furthermore, a recession can decrease economic output through several channels, decreases in the overall consumption, investment, government spending and net export activity are the attributes of a recession that reinforce one another. Psychological and confidence aspects are essentials in order to understand the underlying mechanism of a recession. If companies fear an economic slowdown, they are less likely to invest and they might reduce employment in order to save money. Such expectation can create a self-reinforcing vicious circle, worsening the recession. John Maynard Keynes used the term ≪ animal spirit ≫ in his 1936 book ≪ The General Theory of Employment, Interest and Money ≫ to describe the instincts and emotions that influence and guide human behavior, and which can be measured in terms of, for example, consumer confidence. It has since been argued by Robert J. Shiller, that trust is one of the ≪ animal spirits ≫, a change in consumer confidence can affect the overall economy of a country [Shiller, 2009]. Therefore, most economists believe that recessions are caused by inadequate aggregate demand in the economy, although high interest and/ or inflation rates can also trigger an economic downturn, while reduced consumer confidence and real wages get a blame too.

So, what to do if a country is in a recession? Government responses aim to help the economy recover desperately, especially as the administration gets usually blamed for the state of economy during its time. Furthermore, even if a country tries to walk out of a recession, the recovery takes months, sometimes years, during which almost everybody in the country, politicians, workers and even young graduates suffer the consequences.

Having seen the long-lasting economic and social effects of a recession, what would a government do to prevent one? Frankly speaking, it is just logic to say that a recession is one of the worst nightmare of a developed country, and so governments try their best to avoid them. Prevention starts by forecasting, and since the aim to be able to forecast an economic downturn is not only justified from a purely financial and economic, but also a social perspective, research have long tried to analyze the variables that possibly help us to predict a recession. In our study, we introduce three of these often-used methods, the Yield Spread, Leading and Chicago Index, and compare them through a Logit model.

# Theory and Literature Review

Although no one can claim to foresee the future, it is possible to analyse the economic cycle in its entirety in order to understand its different phases and more particularly that of the economic downturn. A natural question arises is, therefore, which financial variables are useful in anticipating economic growth. The use of asset prices (for instance stock or property prices, interest rate spreads, etc. with an informational content) may prove relevant as they adjust quickly to current and future economic conditions due to the nature of the markets in which they are determined. Part of the central banks’ activity would then consist in extracting the signals contained in certain indicators in order to detect future economic developments.

Among the multitude of financial variables considered in the literature, it appears that the spread between long-term interest rates, such as 10-year government bill rates, and short-term interest rates, generally the three-month interbank rate, is a relatively reliable indicator for predicting short-term economic activity over a 18-month horizon (1 to 6 quarters). In order to understand the concept of the Yield Curve Spread, we have to define the Yield Curve first[Estrella, 2005].

A Yield Curve plots bond yields (interest rates), against their time period to maturity, from very short-term interest rates to higher ones. As a reminder, the interest rate measures the price of liquidity lending and its fluctuations have a strong impact on the economy because they influence the behavior of lenders and borrowers, therefore of all economic agents’. The normal Yield Curve is the most common situation, in which the curve is positively sloped, meaning that long term interest rates are higher than shorter ones. For example, if two-year Treasury notes yield 3% and if five-year Treasury notes yield 5.5%, we observe a normal situation and the Yield curve takes approximately the form shown in Figure 2. This, of course, can be easily explained by the fact that in a healthy economy, if someone trust the government with his money for longer time, he expects a higher pay-off than to lend his money for a shorter period of time. Equally, this is explained by the expected future returns; if these are positive, the investor could lend his money for a shorter period of time today and then reinvest after the short-term bond has come to its maturity. To encourage investors to invest for a longer period of time, the return has to be higher[Yield Curve, Investopedia].

On the other hand, if this pattern is not followed, and short-term bonds pay higher returns than long-term ones, the Yield Curve is called an Inverted Yield Curve, and takes the approximate form shown in Figure 3. Intuitively, if a government pays higher interest rates for short-term bonds than for longer ones, it only does that because it has no other choice. Why would governments be forced to pay higher interest rates on short maturity bonds than longer ones? If for instance investors have no trust in the present government and the state of the economy, they refuse to invest in government debt. In order to incite investors to invest in the risky asset, they pay a premium return. For instance, Greek renewed short-term bond hit a record high return in 2015 when the government debt maturing in 2017 payed 27%. Figure 4. shows the Yield Spread throughout the observed period in the United States. The periods of recessions are the shaded areas on the graph. It is clear that Yield Spreads is relatively low (even negative) before each of these recessions.

How could we explain this phenomena between the Yield Spread and future recessions? Some early studies regarding the relationship between growth and the yield spread sug- gest that an inverted yield curve (and therefore a negative yield spread) could signal an impending recession. Harvey offered the first explanation in 1988, in discreet time. It is based on the consumer’s intertemporal maximization behaviour: some agents want to consume more today than in a year’s time; others prefer to save now and consume later. The interest rate is the price that ensures market balance between lenders and borrowers. However, households are assumed to aspire to stability in their consumption and to smooth their consumption throughout time. If, for example, they anticipate a loss of income in a year (a recession is therefore anticipated), they will want to save more in order to guarantee a certain level of consumption for bad days. This way, they will buy long-term stocks that will provide them with income during the recession. These purchases will be financed by sales of short securities. As the demand for long securities is increasing, their price increases and consequently their yield decreases. At the same time, demand for short securities is decreasing, resulting in lower prices and higher yields. The flattening of the slope of the rates results from these two movements.

James Stock and Mark Watson, in 1989, examined the information contained in a wide variety of economic variables in an attempt to construct a new index of leading indicators. They found that two interest rate spreads, the difference between the six-month commercial paper rate and the six-month Treasury bill rate, and the difference between the ten-year and one-year Treasury bond rates outperformed nearly every other variable as forecasters of the business cycle. The finding that interest rates and spreads contain a great deal of information is interesting, but it raises a number of questions. Possibly the most important of these is the question of why interest rates and spreads predict the course of the economy so well[Stock and Watson, 1989].

In line with Harvey and Stock and Watson’s pioneering work on the United States, Estrella and Hardouvelis as well as Estrella and Mishkin examined the predictive quality of the spread. Estrella and Hardouvelis (1991) popularized the Treasury spread as a predictor of future output growth and recessions as they found that it has a higher predictive power than the Leading indicator index and surpasses survey forecasts. They show that, although monetary policy actions are certainly a contributing factor, they cannot account for all of the predictive content of the term spread.

According to Estrella and Mishkin, monetary policy influences both economic growth and the slope of the yield curve, as an increase in short-term interest rates simultaneously leads to a flattening of the yield curve and a slowdown in economic activity. The link between spread and GDP is linked to the direct effects of monetary policy on GDP developments, subject to a certain amount of time needed for the spread to constitute a leading indicator, independently of expectations. To consider the direct effects of monetary policy is to consider, for example, that a restrictive monetary policy has two successive effects: firstly, it leads to an increase in long-term interest rates, but more moderate than that of short-term rates, and secondly, the structure of rates is reversed. Then, as high interest rates reduce spending in credit-sensitive sectors, it leads to a decline in activity. Therefore, given the lags in the reaction of activity to a change in monetary policy stance, a monetary tightening (easing) translates into a tendency to reverse (increase) the slope of the yield curve, and then into a slowing (accelerating) economic activity. The direct effects of monetary policy are therefore an acceptable but still insufficient explanation.

The credit spread represents the degree to which monetary policy is tightened or loos- ened. Thus, when short-term rates rise, long-term rates rise but less than short-term rates and the spread decreases. (Estrella and Mishkin note that the greater the credibility of monetary policy, the smaller the change in long-term interest rates caused by a change in short-term interest rates.) This explanation suggests that a shallow yield curve (in response to restrictive monetary policy) indicates a declining economic activity and inflation.

Thus, the monetary policy variable (intervention rate or real rate) is often introduced in empirical tests. It serves principally to check whether the interest rate spread contains information other than monetary policy information. The effects of monetary policy should also be linked to the credit channel. Indeed, an increase in short-term rates translates into a smaller increase in long-term rates. The banks’ intermediation margin is decreasing. To maintain their profitability, banks eliminate the riskiest borrowers from their portfolios, which reduces investment and therefore activity. Mishkin and Estrella used a regression model in 1996 to assess changes in the spread following changes in monetary policy in the case of the United States over the period 1973-1995. The results show that monetary policy is one of the important determinants of the term structure of interest rates[Estrella and Mishkin, 1995].

On the other hand, the slope of the yield curve is also determined by financial market expectations about future short-term interest rates. Thus, the yield curve tends to flatten when financial markets anticipate a recession, with short-term interest rates generally at their lowest during periods of recession. This is none other than the pure theory of expectations which defines the long-term rate as a weighted average of the current and expected short-term rates. The link with activity is direct: if, for example, current monetary policy is deemed too restrictive by agents, they anticipate a slowdown in activity and therefore a fall in short-term rates once the economy has actually slowed.

An expectation of weak growth then corresponds to an inverted structure such that long-term rates, which already include future short-term rate cuts, are lower than their current level. The credit spread therefore represents the degree to which monetary policy is restricted or relaxed. Thus, when short-term rates increase, long-term rates increase to a lesser extent and the spread decreases. A recession is therefore anticipated with a high probability when the yield curve is called ”inverted”, i.e. when long-term rates are lower than short-term rates.

# Econometrics methods

## Maximum Likelihood estimation

The Maximum Likelihood estimation chooses as estimator of the parameter vector *θ* a value of* θ* that maximizes the likelihood of observing the actual sample. In the discrete case this likelihood is the probability obtained from the probability mass function; in the continuous case this is the density. As we proceed with Logit models, we consider the discrete case in what follows. If one value of *θ* implies that the probability of the observed data occurring is 0.0012, whereas a second value of *θ* gives a higher probability of 0.0014, then the second value of *θ* is a better estimator.

The joint probability mass function or density *f(y,X|θ)* is viewed here as a function of *θ* given the data (y, X). This is called the likelihood function and is denoted by *Ln(θ|y, X).* Maximizing *Ln(θ)* is equivalent to maximizing the log-likelihood function:

(We take the natural logarithm because in application this leads to an objective function that is the sum rather than the product of N terms.) Therefore, the maximum likelihood estimator solves the first order condition:

In case of the Logit model, we estimate the parameters with the maximum likelihood estimation method. Now we turn to the specific models.

## General binary outcome models

For binary outcome data, the dependent variable y takes one of two values. We let:

A regression model is formed by parameterizing the probability p to depend on a regressor vector x, and vector of k parameters, β. The conditional probability that the dependent variable, y takes the value of 1 is given by:

where F(∆) is a specified function. The logit model arises if F(∆) is the cumulative distribution function of the logistic distribution, therefore with the probability defines as:

where (Λ) is the logistic cumulative distribution function, with e/(1 + e) = 1/(1 + e).

We can directly translate the sign of the coefficients obtained by the logit regression as the sign of the marginal effect, so that a positive (negative) sign indicates that an increase (decrease) in the independent variable increases (decreases) the probability that the dependent variable takes the value one. To know the exact marginal effect of a change in the dependent variable on the probability, however, we use the following transformation:

The odds ratio, p/(1 − p) measures the probability that y = 1 relative to the probability that y = 0.

# Data

In this study, we use data from the Federal Reserve Economic Data (FRED), a database maintained by the Research division of the Federal Reserve Bank of St. Louis, including more than 500,000 economic time series from 81 sources. The time series are compiled by the Federal Reserve and collected from government agencies such as the U.S. Census and the Bureau of Labor Statistics. Another source of data is represented by Federal Reserve Bank of Chicago, one of 12 regional Reserve Banks across the United States that, together with the Board of Governors in Washington, D.C., serve as the central bank for the United States.

The data used in this study is quarterly represented and covers the period of 36 years: from 1982 to the 3th quarter of 2017. The period covers the 4 following recessions in the United States:

- The economic recession of 1981–1982: consequences of Iranian Revolution and thereafter the 1979 energy crisis.
- The economic recession of the early 1990s: caused by the combination of false monetary policy, the 1990 oil price shock, the debt accumulation of the years of the 1980s and a growing consumer pessimism, all of those contributed to a weakened economy.
- The economic recession of the early 2000s: the collapse of the speculative dot-com bubble, a fall in business outlays and investments, and the September 11th attacks, brought the decade of growth to an end.
- The great recession of 2007-2009: notoriously known subprime mortgage crisis led to the collapse of the United States housing bubble. Falling housing related assets contributed to a global financial crisis, even as oil and food prices soared.

## Predictive indicators

In this study, we consider three base models with the following three predictive indicators:

• The Yield Curve Spread: As explained in Part 2., the Yield Spread is of the best indicator of future economic recessions. By analyzing information of the economic activity of United States for the last 36 years, this study aims to reveal the strength and possible weaknesses of yield curves as a predictor of future economic recession. The first models of this paper are therefore in the form:

(In what follows Model 1.1, Model 1.2, Model 1.3 and Model 1.4 for one, two, four and six quarters lagged Yield Spread variables respectively.)

• CFNAI-MA3: The Chicago Fed National Activity Index (CFNAI) is a weighted average of 85 monthly indicators of national economic activity. It provides a single summary measure of a common factor in these national economic data. As such, historical movements in this index track closely periods of economic expansion and contraction, as well as periods of increasing and decreasing inflationary pressure. Research studies by economists at Harvard University, Princeton University, and the Federal Reserve Bank of Chicago have shown that the CFNAI often provides early indications of business cycle turning points and changes in inflationary pressure[FRBC, 2016].

The economic indicators used for the CFNAI are drawn from four broad categories of data:

1. production and income (23 series),

2. employment, unemployment, and work hours (24 series), 3. personal consumption and housing (15 series), and

4. sales, orders, and inventories (23 series).

However, to find out a correct prediction, this study focuses on CFNAI-MA3 indicator which considers the three months moving average variation, and we refer to it as Chicago Index in what follows.

Methodologically, the Chicago Fed National Activity Index is similar to the index of economic activity developed by James Stock (Harvard University) and Mark Watson (Princeton University) in a 1999 article on inflation forecasting which we use as well in this study. Therefore, the second four models of this study are in the form:

• Leading Index: The leading index predicts for each state the six-month growth rate of the state’s coincident index. In addition to the coincident index, the models include other variables “leading” the economy, such as the state-level housing permits (1 to 4 units), the state initial unemployment insurance claims, the delivery times from the Institute for Supply Management (ISM) manufacturing survey, and the interest rate spread between the 10-year Treasury bond and the 3-month Treasury bill, constructed by stochastic time-series (Vector Autoregression). Therefore, it contains the same interest yield spread we use in our first model, and so provides un interesting comparison between these two[Stock and Watson, 1991].

Based on the content of the leading index, we assume that it will show a good prediction power over the observed period. Therefore, the third model is in the form:

# Results

## Comparison of the 3 predictors by Logit model estimation

The goal of our research is to identify the prediction power of three economic indicators, the Yield spread, the Chicago Index and the Leading Index in forecasting economic recessions in the United States, based on an in-sample approach. The first stage was to run a simple logistic regression model for each explicative variable for one, two, four and six quarters ahead, with a unique explicative variable, the indicator in question. In each case, a logit model can be interpreted for marginal effects and the estimated probability of being in a future recession can be derived from the odds ratios, based on the value of the indicator for the observed period.

There are four methods that we employ in order to compare the models:

- The statistical significance of the indicator in question (Yield Spread, Chicago or Leading Index) by the Wald test statistic, that is used to test the significance of the parameter based on the sample estimate. Under the Wald-test, the maximum likelihood estimates of the parameter based on the sample is compared with the proposed value (0 under the null hypothesis), with the assumption that the dif- ference between the two will be approximately normally distributed. We can then compare the square of the difference to a Chi-squared distribution. We reject the null hypothesis (and therefore accept the significance of the estimated parameter) if the Wald-test is greater than the critical value of the Chi-square distribution at a threshold chosen (typically 5%), or if the respective p-value is smaller than this threshold (5%).
- Once we evaluate the significance of each model coefficient, we would like to evaluate a model against other ones in order to decide which model gives the best estimates of future recession probabilities. The Akaike Information Criterion (AIC) is a helpful measure for comparing models. The essential intuition is that there exists a tension between model fit, as measured by the maximized log-likelihood value, and the principle of parsimony that favors a simple model. The fit of the model can be improved by increasing model complexity. However, parameters should only be added if the resulting improvement in fit sufficiently compensates for the loss of parsimony. Therefore, the AIC is calculated as:

AIC = −2lnL + 2q

where q is the number of parameters and lnL is the log likelihood of the model with the estimated coefficients. The model with lowest AIC preferred.

- The likelihood ratio test (LR) can equally be used to evaluate nested models. The motivation for the LR test statistic is that if H0 is true, the unconstrained and constrained maxima of the log-likelihood function should be the same. This suggests testing the difference between ln
*L(θu)*(likelihood of the unrestricted model) and ln*L(θr)*(likelihood of the restricted model). The likelihood ratio test statistic is: -
Table 1 shows the results of the simple logit model that estimate the probability of an economic downturn with the one, two, four and six quarters lagged value of the Yield Spread, respectively.
We see that the Yield Spread is not statistically significant in Model 1.1. (in the model that estimate the probability of a recession one quarter ahead), however, it is significant at 5% in Model 1.2. (p-value is inferior to 5%), and at 1% in Models 1.3. and 1.4., as the p-value is less than 1%. Therefore, we conclude that although a one period lagged value of the Yield Spread is not a reliable predictor of the future state of the economy, it might be one for a longer time period. The AIC information reinforce this assumption, as it is the lowest in model 1.4., suggesting that the six-quarters-lagged value of the Yield Spread explains the future economic downturns the best. If we look at the Likelihood Ratio statistic, we see that it is significant at 1% when considering the model with two, four and six lagged values of the Yield Spread, moreover that it is the highest in the last model. We prefer therefore the 6 lagged Yield Spread to its other lags. Furthermore, the coefficient is negative in each model, meaning that an increase in the Yield Spread (so the increased difference between the long-term and short-term bonds) reduces the estimated probability of a future recession. (This coincides with the theory presented in part 2.)

The Appendix presents the results in the same fashion for the simple logistic models run with the lagged values of the Chicago index (Table 5.) and the Leading index (Table 6.). This leads us, however, to a very different conclusion: the models perform only on the shorter time period, while fail to reliably predict the future state of the economy four and six-quarters ahead. The coefficients are statistically significant only for one and two lagged values at 5%. In addition, the AIC is the lowest at the models with one lagged values, furthermore, that the Likelihood Ratio is significant at 1% in both models of the one and two period lags.

Finally, we are interested in reviewing the quality of estimation in the in-sample period, that is, the percentage that was well-estimated. Figures 5, 6 and 7 shows the ROC curves of the 3 economic indicators, the Yield Spread, the Chicago Index and the Leading index respectively, for one, two, four and six quarters ahead. We can see the following pattern emerging: although the two indices can predict recessions one quarters ahead remarkably well, they lose their capacity four and six quarters ahead. On the contrary, the Yield Spread can predict recessions poorly with one and two-period-lagged values, however, it is the most reliable predictor four and six quarters ahead. The difference arises from the reactiveness of the indicators for the economic environment, we can see that the two indices react simply too late. Therefore, we find the first strength of the Yield Spread in predicting recessions: it seems to look further ahead than other indicators and therefore it is the first indicator to detect an economic downturn, furthermore, it provides a valuable advance to Central Banks and Governments to avoid one.

## Estimating the probability of a recession

As explained in part 3., the predicted probabilities of being in a recession can be derived from the odds ratios. Table 2. shows the average predicted probabilities of being in a future recession for the three models, one for each indicator (we deliberately chose the models that gave the best results per indicator). Thus, the second column presents the estimated probabilities of the model only with one explicative variable, the Yield Spread six quarters ahead (Model 1.4. in part 5.1.), while the third and fourth columns show the predicted probabilities from the models with only the Chicago index and Leading index one quarter ahead, (Models 2.1. and 3.1. respectively).

The easiest way to present the way of interpreting the Table 2. is through some examples. In October, 1999, we observe a low value of the Yield Spread, 0.48. According to our table, this value predicted the probability of a recession in six quarters, that is in April, 2001 at 20% to 25%. Indeed, as history tells us, the collapse of the speculative dot-com bubble induced a recession in the second quarter of 2001. Following the same reasoning, the Yield Spread stood at the value of 3.12 in July, 1986. This high value predicts the probability of a future recession at 5%. Indeed, no economic downturn was observed one quarter later. Lastly, to take the Leading Index as an example, three months before the 2007-2009 recession, the index took the value of 0.49, that indicates a more than 15% predicted probability of a future recession.

We can conclude, therefore, the following information from Table 2: the lower the Yield Spread is (that is the smallest the difference is between the long-term maturity bonds and the short-term ones), the highest is the estimated probability of a future recession. When there is almost no difference between these two, the model predicts 40-50% recession probability while it predicts an even higher probability if the spread is negative (that is the short-term bond yields more than the long-term ones). This finding corresponds remarkably well to the theory presented in part 2. We observe the same pattern for the Chicago and Leading Index, the estimated probability of being in a recession increases as the indices decrease. As mentioned before, the main disadvantage of these indicators is the timing: they forecast an economic downturn simply too late.

As a last comparison of this section, we present the estimated probabilities graphically. Figure 8. shows the estimated probabilities through the observed period for the three models throughout the observed time period. The years of recessions are indicated by grey shaded areas. We see that for one and two quarters ahead, the probabilities of the two indices change more than the Yield Spread during recessions, suggesting that an increased probability predicts better the future state of the economy. We have to be careful, however, with this kind of interpretation for two reasons. First of all, the fact that the two indices show an increased estimated probability compared to the Yield Spread say nothing about the accuracy of the models; it can be easily the case that a 15-20% probability estimated by the lagged Spread values is equivalent to a 30% estimated probability by the indices. Secondly, we can clearly see a pattern emerging: while the spread estimated probabilities are higher before the recessions, the probabilities estimated by the two indices stay high after the recessions also, suggesting that these last ones react too late to the economic conditions. Finally, the level of probability after that we can expect a recession seems to be around 30% for the two indices and only a minor increase, around 15% for the Yield Spread. We refer to this probability as the “probability threshold” in what follows.

On the graphs c) and d) of Figure 8. we see, however, that on a longer time period, the Yield Spread is the only indicator that can successfully predict all future recessions of the study, the two indices react only once the recessions started. We also conclude that the probability threshold is around 20% for this indicator, meaning that if the estimated probability of a future recession is superior to this level, we most certainly can expect a future recession. As timing is an important factor in predicting recessions, we conclude that the best indicator seems the Spread Yield, 6 quarters ahead.

## Multivariable Logit Model

So far, this study compared three important indicators in forecasting recessions in simple logistic models. Nevertheless, not all economic indicators can be captured by a single explicative variable, therefore, we can easily improve our model by adding additional information. Thus, we identify a multivariable logit model in this section.

The first step of the analysis is the appropriate selection of variables based on the Step-Wise method. This procedure allows us to choose the variables that contribute the most to an increased pseudo R2 by successively adding and subtracting variables according to their significance. We introduce the Yield Spread, Leading and Chicago Index, the GDP, the Money Supply, the Unemployment, the Initial Claims, the Oil Price, the Consumer Confidence Index, the Consumer Price Index, the Capitalisation-Weighted Index and the Nonfinancial corporate business indicator at the same lagged value for one, two, four and six quarters ahead. If a variable does not improve the fit of the Logit model, and if it is not significant, it is removed. Following the Stepwise procedure, we find that the proposed model has only 3 variables, the Yield Spread, the Oil price and the Consumer Price Index (CPI), all of them with the four quarters lagged values. (Table 3. presents the results).

We find again a negative sign for the variable, Yield Spread, meaning that an increase in the difference between the long-term and short-term bond reduces the estimated probability of a future recession. Furthermore, the variables Oil price and CPI both have a positive sign, suggesting that an increase in the Oil price or in the CPI increases the probability of a future recession.

What is the relationship between the oil price and a future recession? In a developed nation like the United States, every single aspect of business life requires some form of oil, almost all production is dependent on it. A higher oil price increases the trade deficit of the US. This increased export bill leads to a weaker state of the dollar currency. A weak dollar in turn pulls up the international prices of dollar denominated commodities. This allows a further increase in the oil price to exorbitantly higher oil prices. A market crash then becomes inevitable. Analysis shows that there is a cyclical process where market health and oil prices modulate each other in opposite direction. In other terms the oil prices affect the global economic health adversely while at the same time, being greatly affected by it. As oil price can actually increase a recession, we expect that increased oil prices increase the estimated probability of a future economic downturn[Austin, 2010].

And how do we explain the positive coefficient of the Consumer Price Index (CPI)? As a reminder, CPI is a hypothetical “market basket” of the goods and services that a typical consumer purchases. Prices of individual items in the CPI rise and fall with the forces of supply and demand. Thus, when the economy is growing in its expansionary phase, people are confident of their income and spend accordingly. Strong demand pushes prices higher. The Federal Reserve expands the money supply to accommodate growth, and more money in circulation stimulates spending and rising prices. Conversely, when there is an economic contraction supply initially outpaces demand. This would suggest that there would be downward pressure on prices. However, this pattern is not verified these days: prices for most goods and services don’t go down and neither do wages. Some economists suggest that it can be explained by consumer psychology-related factors that prevent prices from decreasing during a recession, more specifically, firms may be reluctant to decrease prices if they feel that customers will get upset when they increase prices back to their original levels at a later point in time. Of course, an increase in the CPI alone could not predict a recession cycle, but together with a decrease of Yield Spread and a rise in Oil Price, a high CPI represents the uncertainty of consumers about the economic stability, which is expressed by an increase in a demand for primary goods. Therefore, we expect the coefficient of the CPI also positive.

All three variables are significant, this, however, is no surprise, as we employed the StepWise method to choose them. Now, we compare the multivariable model presented in this section and Model 1.4. presented in part 5.1. (that is the simple logistic model only with a six-quarter lagged value of the Yield Spread). In model 1.4., the Likelihood Ratio is around 32.4 while in the multivariable logit model it is approximately 40.268, therefore we would deduce that the multivariable logit gives us a better estimation. However, the AIC is lower in model 1.4. When we recall that the Akaike Information Criterion takes into account the number of coefficients estimated (and penalizes for it), we gain a comprehension between these results: even though the multivariable logit model gives us a slightly better fit, the cost of this better fit is the estimation of two additional parameters.

We present the estimated probabilities in the in-sample approach of the multivariable logit model in Figure 9 to evaluate therefore the performance of the multivariable logit model. We see that indeed, before each past recession, our model predicts a future recession with a minimum estimated probability of 15-20 %. Therefore, we conclude that the “probability threshold”, that is the estimated probability from which we can expect the future recession is 15-20% for this model, and that the model captured well the recessions.

## Prediction of a future recession

This study started by pointing out why it is essential to predict a future economic recession. We constructed several models and evaluated them according to their prediction power. As a last step, we can use our models to actually predict a future recession (or lack of recession) in an out-sample approach. We call it “out-sample”, because our dataset does not cover the period, for which we estimate these probabilities. Therefore, using our last available data for the Yield Spread from July, 2017, and the estimated coefficients from the multivariable logit model presented in Part 5.3., we estimate the probability of a future recession for one, two, four and six quarters later, presented in Table 4. As we concluded previously, the probability threshold is around 15-20%, however, no estimated probability is higher than 9.71%. Therefore, we state that no economic recession is expected is the near future according to our regression model.

We equally estimated the probability of a future recession by all models presented in this study and not one of them was higher than 10%. Therefore, we expect no economic recession for the near future.

# Conclusion

In this study, we compare 3 indicators often used in assessing the future probability of being in a recession, the Yield Spread, the Chicago and the Leading indices. We find that one and two quarters ahead, the two indices predict better the future recessions than the Yield Spread, however, this latter is much better four and six quarters ahead. Therefore, we conclude that this indicator is the most reliable when forecasting future recessions.

Then, we construct a multinomial logit model, in which we identify the explicative variables that predict the best the future state of the economy. We find that a model with the Yield Spread, the Oil price and the CPI explains future recessions the best, however, we find also that this model does not perform much better than a simple logit model with the six quarters lagged Yield Spread variable.

Finally, we estimate the probability of being in recession one, two, four and six quarters ahead, with all the models that we previously identified. We find that the probability that we will be in recession is negligible (lower than the probability threshold of 15-20%), and therefore our study concludes that according to our estimations, we cannot expect a recession in the near future.

# Appendices

# References

[1] Austin, S., Do Rising Oil Prices Predict Another Economic Recession? Available from: www.oil-price.net/en/articles/rising-oil-prices-predict -economic-recession.php/

[2] Estrella, A., Mishkin, F.,S. (1995) Predicting U.S. recessions: Financial variables as leading indicators. Federal Reserve Bank of New York

[3] Estrella, A. (2005) The Yield Curve as a Leading Indicator: Frequently Asked Questions.

[4] Federal Reserve Bank of Chicago, Background on the Chicago Fed National Activity Index.

[5] Hagedorn, M., Karahan, F., Manovskii, I., Mitman, K. (2013) Unemployment ben- efits and unemployment in the great recession: the role of macro effects. National bureau of economic research

[6] Investopedia, Yield Curve. Available from: https://www.investopedia.com/terms/y/yieldcurve.asp/

[7] Margerison-Zilko, C., Goldman-Mellor, S., Falconi, A., Downing, J. (2016) Health Impacts of the Great Recession: A Critical Review. National Institutes of Health.

[8] Medcalc Statistical Software, ROC curve analysis . Available from: https://www.medcalc.org/manual/roc-curves.php

[9] National Bureau of Economic Research (2010), Business Cycle Expansions and Con- tractions.

[10] Shiller, R., J. (2009) Animal Spirits Depend on Trust. The Wall Street Journal.

[11] Stock, J., H. and Watson, M., W. (1989) New Indexes of Coincident and Leading Economic Indicators. NBER Macroeconomics Annual 1989, Volume

[12] Stock, J., H. and Watson, M., W. (1991) A Procedure for Predicting Recessions with Leading Indicators: Econometric Issues and Recent Experience. National Bureau of Economic Research.