Does the term spread predict a US recession?
Many commentators suggest that a negative term spread (inverted yield curve) in the US may signal an imminent recession, but other data is more positive. In this post, I use an R program jointly with the FRED data base to shed some light on the risk of a US recession.
To show this, let us first look at some simulated data. I simulated 1,000 observations for three persistent time series:
Spurious correlation and a test for leading indicators
Before we delve into data analysis, I want to emphasize a problem when eyeballing leadlag relationships between GDP growth and potential leading indicators. If two timeseries are persistent, meaning that they exhibit longlasting cycles, we may wrongly conclude that one leads the other. In fact, if two timeseries are persistent, we will likely find spurious correlation between the two when in fact there is no relationship.To show this, let us first look at some simulated data. I simulated 1,000 observations for three persistent time series:
y(t) = 0.8y(t1)+0.1x(t1)+0.3e(t)
x(t) = 0.9x(t1)+0.3v(t)
z(t) = 0.9z(t1)+0.3n(t)
e(t), v(t), n(t) ~ i.i.d. N(0,1)
By construction, x is a leading indicator for y, but z is independent of y and x. Figure 1 shows an excerpt of the three timeseries and the crosscorrelation with y at various leads and lags. When just looking at the data, we are prone to find some leadlag relationship between the three series. At least in the first part, all three seem to be positively correlated. When looking at the crosscorrelation function, x seems to lead y. Note that the blue dashed lines give confidence intervals. Values outside of these intervals indicate that the crosscorrelations are statistically significantly different from zero. However, we also find positive crosscorrelations for s<0, implying that y leads x. The crosscorrelation function with z is even more misleading. We may conclude that z is a countercyclical leading indicator, meaning the crosscorrelation is negative, with a lead of 10 to 30 periods. But we know that the two variables are independent by construction.
To avoid this spurious correlation problem, Neusser (2016), proposes to “prewhiten” the data before calculating the crosscorrelation function. This means that we fit a timeseries model to the data and compute the crosscorrelation with the residuals, which are by construction not persistent. So we are less likely to find spurious crosscorrelation between the variables.
Indeed, when looking at the crosscorrelation between y and z using the prewhitened data, we do not see any clear leadlag relationship (Figure 2). However, we find a significant crosscorrelation between y and x at a lead of one period, exactly how we simulated the data. This shows that the approach is useful to detect the true underlying leadlag relationship between a leading indicator and a target variable when the time series are persistent
Let’s apply this idea to US data, in particular, to the term spread. What I want to examine is whether the term spread is a good leading indicator for quarteronquarter US GDP growth. I therefore aggregate the term spread to quarterly frequency and calculate the crosscorrelation function using the original and the prewhitened data.
Looking at the original data, we see that the term spread is relatively persistent, as shown in the autocorrelation function in the lower left panel of Figure 3. The crosscorrelation with GDP growth exhibits many significant lags. Actually, we may conclude that GDP growth is a leading indicator for the term spread! In addition, the relationship is negative meaning that a decline in GDP growth is followed by an increase in the term spread. This is a consequence of the spurious correlation problem.
If we compute the crosscorrelation function with prewhitened data, we see that the term spread leads GDP growth by two quarters (Figure 4). In addition, as intuition and theory suggest, the term spread is a procyclical indicator, meaning a decline in the term spread signals a decline in economic activity.
Based on this data set, we can then construct a composite leading indicator (CLI). I normalize all the indicators with a clear leading relationship with GDP growth, shift the indicators in time so that they exhibit the same lead on GDP growth, multiply them with 1 if they are countercyclical, and then take an unweighted average.
Figure 5 shows that the leading indicator (in red) tracks the major movements of GDP growth rather well (in blue). The shortterm fluctuations, however, are not captured by the CLI. As the main purpose of the indicator is to signal recessions, we can compare it to the official dating by the NBER (lower panel). We see that the CLI declined strongly before all NBER recessions. In addition, there are few “false positives”, meaning that the indicator declined strongly where in fact there was no recession.
Focusing on the recent period, we see that this leading indicator has declined, but remains around its longrun average (red dashed line). Notably it remains much higher than during the Great Recession or the burst of the dotcom bubble in the early 2000s. This means that, although the term spread may point to a recession, other indicators paint a more benign picture of economic activity in the US.
PS: Do not hesitate to use the R program for your own purposes. If you do and find ways to improve it, please let me know in the comments.
x(t) = 0.9x(t1)+0.3v(t)
z(t) = 0.9z(t1)+0.3n(t)
e(t), v(t), n(t) ~ i.i.d. N(0,1)
By construction, x is a leading indicator for y, but z is independent of y and x. Figure 1 shows an excerpt of the three timeseries and the crosscorrelation with y at various leads and lags. When just looking at the data, we are prone to find some leadlag relationship between the three series. At least in the first part, all three seem to be positively correlated. When looking at the crosscorrelation function, x seems to lead y. Note that the blue dashed lines give confidence intervals. Values outside of these intervals indicate that the crosscorrelations are statistically significantly different from zero. However, we also find positive crosscorrelations for s<0, implying that y leads x. The crosscorrelation function with z is even more misleading. We may conclude that z is a countercyclical leading indicator, meaning the crosscorrelation is negative, with a lead of 10 to 30 periods. But we know that the two variables are independent by construction.
Fig. 1: Original data and crosscorrelation 
To avoid this spurious correlation problem, Neusser (2016), proposes to “prewhiten” the data before calculating the crosscorrelation function. This means that we fit a timeseries model to the data and compute the crosscorrelation with the residuals, which are by construction not persistent. So we are less likely to find spurious crosscorrelation between the variables.
Indeed, when looking at the crosscorrelation between y and z using the prewhitened data, we do not see any clear leadlag relationship (Figure 2). However, we find a significant crosscorrelation between y and x at a lead of one period, exactly how we simulated the data. This shows that the approach is useful to detect the true underlying leadlag relationship between a leading indicator and a target variable when the time series are persistent
Fig. 2: Prewhitened data and crosscorrelation 
What does the term spread tell us about US GDP growth?
Let’s apply this idea to US data, in particular, to the term spread. What I want to examine is whether the term spread is a good leading indicator for quarteronquarter US GDP growth. I therefore aggregate the term spread to quarterly frequency and calculate the crosscorrelation function using the original and the prewhitened data.Looking at the original data, we see that the term spread is relatively persistent, as shown in the autocorrelation function in the lower left panel of Figure 3. The crosscorrelation with GDP growth exhibits many significant lags. Actually, we may conclude that GDP growth is a leading indicator for the term spread! In addition, the relationship is negative meaning that a decline in GDP growth is followed by an increase in the term spread. This is a consequence of the spurious correlation problem.
Fig. 3: Term spread and GDP growth, with auto and crosscorrelation 
If we compute the crosscorrelation function with prewhitened data, we see that the term spread leads GDP growth by two quarters (Figure 4). In addition, as intuition and theory suggest, the term spread is a procyclical indicator, meaning a decline in the term spread signals a decline in economic activity.
Fig. 4: Prewhitened term spread and GDP growth, with auto and crosscorrelation 
A composite leading indicator for the US
Of course, we can repeat this for other indicators as well (See the R file and FRED for sources and a detailed description of the data). Table 1 shows a summary of all the indicators that I examine:
Indicator

Cyclicality

Lead/Lag

Term spread 10Y2Y

Procyclical

+2q

Bond spread AAA10Y

Countercyclical

+1q

Bond spread BAA10Y

Countercyclical

+1q

Manufacturing ord. (EC)

Procyclical

+1q

Manufacturing prod. (EC)

Procyclical

+1q

Inflation expectations (EC)

?

?

Housing starts

Procyclical

+1q

Initial claims

Countercyclical

+1q

Inflation exp. (Michigan)

Procyclical

1q

TED spread

?

?

Consumer sentiment (Michigan)

Procyclical

+1q

EPU

?

?

EPU (Equity)


VIX

?

?

Capacity utilization

Procyclical

+1q

Figure 5 shows that the leading indicator (in red) tracks the major movements of GDP growth rather well (in blue). The shortterm fluctuations, however, are not captured by the CLI. As the main purpose of the indicator is to signal recessions, we can compare it to the official dating by the NBER (lower panel). We see that the CLI declined strongly before all NBER recessions. In addition, there are few “false positives”, meaning that the indicator declined strongly where in fact there was no recession.
Focusing on the recent period, we see that this leading indicator has declined, but remains around its longrun average (red dashed line). Notably it remains much higher than during the Great Recession or the burst of the dotcom bubble in the early 2000s. This means that, although the term spread may point to a recession, other indicators paint a more benign picture of economic activity in the US.
Fig. 5: Comparison of CLI with GDP growth and recessions 
Conclusion
This analysis showed that the term spread is a useful leading indicator. However, we should not only look at the bond market. Early available surveys and hard data also contain useful information and this information points to more robust GDP growth than the term spread.PS: Do not hesitate to use the R program for your own purposes. If you do and find ways to improve it, please let me know in the comments.
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