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					           Recession Outlook: An Analysis of Two ECRI Indicators
                                       Updated October 28th, 2011
                                            by Kevin Mabe


Summary

       Two indices by the Economic Cycle Research Institute provide strong collective
predictive power in determining months of recession (as defined by the National Bureau of
Economic Research). A binary logistic regression model indicates a 3.6% probability that a
recession began during the latest-modeled month of August, 2011. However, the model‟s
projections suggest an overall risk of a recession by December, 2011 at just over 79%,
indicating the occurrence of a recession by the end of the year.


Introduction

       The Economic Cycle Research Institute (ECRI) produces many economic indices,
including the publicly-available U.S. Weekly Leading Index Growth Rate and the monthly
U.S. Coincident Index Growth Rate.1 In addition, the National Bureau of Economic
Research (NBER) traditionally calls the beginning and ending months of business cycles.2
A September 20, 2010 NBER update affirmed that the most recent “Great Recession” ended
in June, 2009, nearly 15 months after the fact. Can we identify a recession more quickly?3
       Presuming that the NBER correctly identifies and designates the starting and
ending months of recessions, the following analysis uses the ECRI and NBER time series to
model the occurrence of past recessions and then provides a framework to predict the
possibility of a new recession from 2011 to mid-2012.


Methodology and Data

        Four main methodological steps comprise this small study.

        1) Determine the strongest empirical lead or lag of the two ECRI indicators with
           regard to NBER-defined recession-months
        2) Model the recession-months as a function of the empirically led/lagged indicators
        3) Test the model‟s robustness on a holdout sample
        4) Provide probabilistic guidance on the occurrence of a 2011/mid-2012 recession

       The monthly frequency of the ECRI data allows for the measurement of the NBER
recessions in monthly increments. The dependent variable takes a value of „1‟ for the
months of recession and „0‟ otherwise. This analysis models data from 1968 through


1 The ECRI keeps the formulation of these indices proprietary. Refer to www.businesscycle.com.
2 Refer to www.nber.org for information.
3 Designating an “official” recession admittedly represents little more than an academic exercise.

After all, to the typical consumer, his lost job still feels like a lost job, whether experienced during a
sluggish recovery or a deep depression.
November, 2007 and uses December, 2007 to August, 2011 data as a prediction sample.4
Although the model data includes just six recessions, those recessions span a total of 71
months alongside over 400 non-recession months, thus providing a substantial statistical
sample with which to model. The analysis tests the timing and longevity of recessions on a
month-by-month basis as the ECRI growth rates rise and fall.
       Because the ECRI produces the Leading Index Growth Rate weekly, but the ECRI
Coincident Index Growth Rate and the NBER Recession data appear monthly, this analysis
uses the Leading Index Growth Rate from a month‟s third week to proxy that month.5


Analysis and Results

       This analysis does not presume the empirical and correlative lead/lag of the two
ECRI indices with the NBER recessions. Because any direct correlation between the two
indices and the NBER recessions can lead to a spurious conclusion, ARIMA processes
extract white noise residuals for the three time series for use in cross-correlation analysis.6

               Series                                  ARIMA Process
               Leading Index (Growth Rate)                (1,1,1)
               Coincident Index (Growth Rate)             (2,1,0)
               NBER Recessions                            (1,0,0)

Cross-correlation between the NBER recession residuals and the residuals of the indices
determines the strength and timing of any correlation. The table below summarizes the
most statistically significant cross-correlation function (CCF) of the indices‟ residuals with
the NBER recession residuals (at the 1% level).

               Series                                  CCF (lead/lag)
               Leading Index (Growth Rate)             –0.14 (1-month lead)
               Coincident Index (Growth Rate)          –0.25 (1-month lag)

The results illustrate that a decrease in the Leading Index Growth Rate in month „t‟ shows
correlation with a recession month for month „t+1‟. Similarly, a decrease in the Coincident
Index Growth Rate in month „t‟ shows a correlation with a recession month for month „t–1‟.7



4 Model sample: n=478 (71 recession months, 407 non-recession months). Prediction sample: n=45
(19 recession months, non-recession months yet to be determined). NBER Recessions since 1968
include the following periods: Dec-1969 to Nov-1970; Nov-1973 to Mar-1975; Jan-1980 to Jul-1980;
Jul-1981 to Nov-1982; Jul-1990 to Mar-1991; Mar-2001 to Nov-2001; and Dec-2007 to Jun-2009.
5 Selection of a different week‟s Leading Index Growth Rate to represent its month did not

meaningfully change results.
6 Essentially, the ARIMA processes separate the trends from the underlying noise. The analysis

rests on the correlation of the time series‟ noise signals, not of the series themselves. The actual
ARIMA processes themselves yield little value in this particular analysis, other than to filter out the
white noise residuals. See “Time Series Correlation” (2010) by Kevin Mabe found on
www.kevinmabe.com/econometrics.html for an in-depth discussion on this methodology.
7 As a check, and as expected, the CCF between the noises of the Leading and Coincident Index

Growth Rates shows a statistically-significant positive correlation at the 1% level. The Leading
Index Growth Rate empirically leads the Coincident Index Growth Rate by about four months.
        The next step in the analysis includes a binary logistic regression model of the
NBER recession-months as a function of the two appropriately lagged/led index growth
rates. The full model results appear in the Appendix.8
        Both index growth rates show the expected signs with strong statistical significance.
As each index growth rate decreases, the probability of a recession increases. The
coefficients imply that a one-point change in the Coincident Index Growth Rate impacts the
probability of a recession over three times as much as a one-point change in the Leading
Index Growth Rate. The media has often lauded the Leading Index Growth Rate as a sure-
fire indicator of recession, particularly if it drops to –10.0. However, the model suggests
that any change of the Coincident Index Growth Rate plays a stronger role.
        The high sensitivity and specificity indicate a low number of false-positive and false-
negative months.9 The six false positives and eleven false negatives occur either in months
leading up to a known recession (thus producing an early or late call to a recession‟s
beginning) or following the end of one (thus producing a late or early call to a recession‟s
completion). The model gives no false prediction of a recession that the NBER never called.
Figure 1 illustrates the model‟s fit against the historical recessions. Visually, the predicted
recessions track nicely with actual recessions. Note the anomalies of slightly early/late
calls and over/underestimation of recession lengths.
        Figure 2 represents the relationship between the two indices and their combined
modeled effect on the predicted probability of a recession. This „heat map‟ indicates that for
negative values of both indices, the chances of a recession increase dramatically. Figure 2
provides contrary evidence to the aforementioned media-popular “rule of thumb” that a
Leading Index Growth Rate of lower than –10.0 necessarily portends an oncoming
recession. The Coincident Index Growth Rate plays a necessary and significant role. Even
the ECRI plays down the –10.0 threshold and did not call for a double-dip in 2010.10
        Applying the model to data to the holdout sample period of December, 2007 through
August, 2011 predicts that the “Great Recession” began in February, 2008 and ended in
August, 2009. In reality, the NBER designated the beginning of the “Great Recession” in
December, 2007 (two months earlier than the model) and designated its end in June, 2009
(two months earlier than the model). Note in Figure 3 that the model also indicated a
period of economic distress in the fall of 2010 (as evidenced by increasing probabilities of a
recession) concurrent with media attention on a “double-dip” recession. However, economic
indicators (and the model) suggested the risk waned leading into 2011. Since the model‟s
probabilities fell below 50%, the model indicated no double-dip recession for those months.
        An alternative model, using data from 1968 to 2000 (five recessions inclusive) and
predicting 2001 onward (two recessions inclusive), shows highly similar results to the above
primary model as evidenced by statistically indistinguishable coefficients and similar by-
month fitted probabilities. Hit rates, sensitivities, and specificities matched quite well.
The remainder of this analysis uses only the primary model and leaves the alternative
model as a loose demonstration of this analysis‟ robustness.




8 Output comes from MiniTab version 15. See www.minitab.com for algorithm documentation.
Model diagnostics measured as follows: Hit rate = 0.964, sensitivity and specificity = 0.845 and
0.985 respectively, and an adj-count R² of 0.761.
9 For any month, any fitted or predicted value that equals or exceeds 0.50 counts as a „hit‟ (recession).

Any value that falls below 0.50 counts as a „no hit‟ (no recession).
10 See the “Resources” section of the ECRI website (www.businesscycle.com) for several articles.
                                                                                             Recessions: Actual vs. Predicted

                                                                                                                                                    Recession
                                                                                                                                                    NBER Actual
                                                                                                                                                    Predicted



                                                    1.0
  Predicted probability of a recession




                                                    0.8


                                                    0.6


                                                    0.4


                                                    0.2


                                                    0.0

                                                          Jan-68    Jan-72        Jan-76       Jan-80    Jan-84      Jan-88     Jan-92    Jan-96   Jan-00    Jan-04    Nov-07

                                                                                                                  Month-Year

Figure 1: Actual NBER recessions versus predicted recessions




                                                                   Heat Map of Predicted Probability of Recession vs. ECRI Indices
                                                                                                                                                                       Predicted
                                                                                                                                                                      Recession
                                                    20                                                                                                                     < 0.1
                                                                                                                                                                      0.1 – 0.3
         Leading Index Growth Rate (1-month lead)




                                                                                                                                                                      0.3 – 0.5
                                                                                                                                                                      0.5 – 0.7
                                                    10                                                                                                                0.7 – 0.9
                                                                                                                                                                           > 0.9


                                                     0




                                                    -10




                                                    -20




                                                                             -5                             0                         5                     10
                                                                                           Coincident Index Growth Rate (1-month lag)


Figure 2: Heat Map (contour plot) of predicted recession vs. two ECRI indices
                                                                          December, 2007 Recession and Beyond
                                                                                           Actual vs. Predicted

                                                 1.0
                                                                                                                                        Recession Periods
                                                                                                                                        Actual (NBER)
                                                                                                                                        Predicted
                                                 0.8
          Predicted Probability of a Recession




                                                 0.6



                                                 0.4



                                                 0.2



                                                 0.0

                                                       Jan-07   Jul-07   Jan-08   Jul-08        Jan-09       Jul-09   Jan-10   Jul-10       Jan-11

                                                                                                  Month-Year



       Figure 3: Actual vs. predicted recession/non-recession months since January, 2007


        Naïve statistical projection of both the Coincident Index and Leading Index Growth
Rates11  provide insight into the month-by-month probabilities of a new recession beginning
in late 2011 or early 2012. Figure 4 plots the modeled history from January, 2010 to
August, 2011 as well as three projections of risk: 50% (mean forecast), 20%, and 5%. The
modeled mean forecast (dark dashed red line) suggests the economy will experience a
recession by November, 2011, with a probability of 73% for that month. The graph also
illustrates a 20% risk of a recession beginning in October, 2011. The current recovery from
the Great Recession appears tenuous at best and Figure 4 suggests that the U.S. economy
poses a moderate risk, around 79%, of returning to recessionary conditions by December.
Simply put, evidence indicates a recession will begin before year-end. Indeed, the ECRI
publicly stated that “the U.S. Economy is tipping into a new recession”.12 The model then
indicates the new recession will last at least through the first half of 2012.


Conclusion

       This analysis confirms the strong correlative power between two proprietary ECRI
Growth Rates and the NBER-designated economic recessions. The strongly-predictive
model provides a framework to ascertain the presence of a recession well ahead of final
NBER attribution. The model now indicates a 79% chance of a new recession by the end of
the year that will last through at least June, 2012.

11 The forecast for the Coincident Index Growth Rate stems from a double-exponential smoothing
model. The forecast for the Leading Index Growth Rate stems from an ARIMA (2,0,0)x(0,1,1)3 model.
Neither necessarily reflects economic consensus, only statistical continuation of each time series.
12 See www.businesscycle.com for further detail (Bloomberg, September 30th, 2011).
                                      Projected Recession Risk for 2011 to mid-2012
                                                 with one-sided 5%, 20% and 50% risk curves



                               100%

                                                                                        5% Risk   20% Risk


                                            Recession prediction threshold
  Probability of a Recession




                                                                                                       50% Risk

                               50%



                                           Modeled History




                                0%
                                      Dec-10




                                      Dec-11
                                      Feb-10




                                      Aug-10
                                      Sep-10




                                      Feb-11




                                      Aug-11
                                      Sep-11




                                      Feb-12
                                       Jan-11
                                       Jan-10




                                      Jun-10
                                        Jul-10




                                      Jun-11
                                        Jul-11




                                       Jan-12




                                      Jun-12
                                      Apr-10




                                      Nov-10




                                      Apr-11




                                      Nov-11




                                      Apr-12
                                      Mar-10

                                      May-10




                                      Oct-10




                                      Mar-11

                                      May-11




                                      Oct-11




                                      Mar-12

                                      May-12
                                                                    Month-Year


Figure 4: Projected risk of recession for late 2011 into 2012.
Appendix

Recession Risk Model

Variable        Value     Count
NBERRecession   1            71   (Event)
                0           407
                Total       478
                                                             Odds      95% CI
Predictor           Coef       SE Coef          Z       P   Ratio   Lower Upper
Constant        -1.23937      0.309690      -4.00   0.000
LeadIndexLead1 -0.285611     0.0613268      -4.66   0.000    0.75   0.67   0.85
CoincIndexLag1 -0.913326      0.148109      -6.17   0.000    0.40   0.30   0.54

Log-Likelihood = -54.916
Test that all slopes are zero: G = 291.841, DF = 2, P-Value = 0.000


Goodness-of-Fit Tests
Method                 Chi-Square        DF       P
Pearson                   1241.79       475   0.000
Deviance                   109.83       475   1.000
Hosmer-Lemeshow              1.22         8   0.996
Brown General Alternative   23.50         2   0.000
Brown Symmetric Alternative 2.56          1   0.109


Measures of Association: (Between the Response Variable and Predicted Probabilities)

Pairs        Number     Percent   Summary Measures
Concordant    28437        98.4   Somers' D                 0.97
Discordant      432         1.5   Goodman-Kruskal Gamma     0.97
Ties             28         0.1   Kendall's Tau-a           0.25
Total         28897       100.0


Hit rate        0.964
Sensitivity     0.845
Specificity     0.985
Adj R² count    0.761

				
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