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This presentation includes two explanatory models to attempt to predict recessions. The first one is a logistic regression. The second one is a deep neural network (DNN). Both use the same set of independent variables: the velocity of money, inflation, the yield curve, and the stock market. As usual, the DNN fits the historical data a bit better than the simpler logistic regression. But, when it comes to testing or predicting, both models are pretty much even.

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economics | econometrics | logistic regression | deep neural network | Bayesian statistics

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Are We in a Recession? PowerPoint Presentation

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Are We in a Recession? Presentation Transcript

Slide 1 - Are we in a Recession?Predicting recessions with Logit Regression and DNNs Gaetan Lion, June 21, 2022
Slide 2 - 2 Are we already in a recession? Maybe … 2022 Q1 GDP growth was already negative. And, 2022 Q2 may very well be [negative] when the released data comes out. The majority of the financial media believes we are already in a recession because of the stubbornly high inflation (due to supply chain bottlenecks) and the Federal Reserve aggressive monetary policy to fight inflation. The policy includes a rapid rise in short-term rates, and a reversing of the Quantitative Easing bond purchase program (reducing the Fed’s balance sheet and taking liquidity & credit out of the financial system). The Bearish stock market also suggests we are currently in a recession. On the other hand, Government authorities including the President, the Secretary of the Treasury (Janet Yellen), and the Federal Reserve all believe that the US economy can achieve a “soft landing” with a declining inflation rate, while maintaining positive economic growth. I developed a couple of models to attempt to predict recessions using historical data.
Slide 3 - 3 The Federal Reserve most recent forecast The Fed anticipates that they will raise the Fed Funds rate to above 3% by the end of 2022. And, that economic growth will remain positive through 2024 ranging from 2% to 2.5% on an annualized basis. Notice that in 2022 Q1, the Fed forecast is already off. While they forecasted real economic growth of + 2% on an annualized basis, actual results came in at negative – 1.5%.
Slide 4 - 4 Modeling project basics Objective Attempting to predict recessions. Here I am focused on recessionary periods. And, any quarterly period with negative RGDP growth is considered part of a recessionary period. Dependent variable modeled It is a binomial variable (0, 1). If the quarter shows negative economic growth it equals 1, otherwise 0. Independent variable tested I tested numerous macroeconomic variables going back to early 1960s to capture as many recessionary periods as possible while still having access to an adequate pool of explanatory macroeconomic variables. Independent variable transformations I considered several transformations: a) quarterly % change; b) quarterly first difference (for rate variables); c) yearly % change; d) level variables. I used d) when a variable level was constrained (oscillating within a finite range). Model structures I developed two competing models: 1) a logistic regression; 2) a Deep Neural Network model. Used R software. Data I extracted economic variables from FRED going back to 1960. I extracted S&P 500 data from Robert Shiller at Yale.
Slide 5 - 5 The Logistic Regression Model rec. This is the binomial (0, 1) dependent variable. It is 1 if quarterly RGDP growth is negative, otherwise it is 0. velo. It is the quarterly first difference in the Velocity of Money (GDP/M2). cpi. Quarterly % change in the Consumer Price Index. curveL. Level of the Yield Curve. The spread between the 10 Year Treasury and Fed Funds. sp12. Yearly % change in S&P 500.
Slide 6 - 6 Logistic Regression Model rational A foundational equality: Price x Quantity = Money x Velocity of money The logistic regression to predict regression includes Price (cpi) and Velocity (velo). This model also includes the yield curve, a well established variable to predict recession. Notice that this variable is not quite statistically significant (p-value 0.14). But, the sign of the coefficient is correct. It does inform and improve the model. And, is well supported by economic theory. The model includes the stock market that is by nature forward looking in terms of economic outlook. This makes it a most relevant variable to include in a regression model to predict recessions.
Slide 7 - 7 The underlying directional relationships Focusing on standardized coefficients, as Velocity goes up, the probability of a recession goes down. As the CPI goes up, the probability of a recession goes up. As the yield curve widens, the probability of a recession goes down. As it narrows, the probability of a recession goes up. As the stock market goes up, the probability of a recession goes down. As it goes down, the probability of a recession goes up. Based on the standardized coefficients, Velocity has much more influence on the probability of recession. And, the yield curve has a lesser influence than the other variables.
Slide 8 - 8 Is our model spurious by including variables from the P x Q = M x V equality? I don’t think so. The actual correlations with probabilities of a recession or the actual binomial variable (0, 1) are rather modest as shown below. Also, none of the independent variables are multicollinear, as shown by the low Variance Inflation Factors below. All VIFs are below 2.5. I also tested the residuals for stationarity and unit root issues. And, the residuals were not deemed non-stationary. In view of the above, the model specifications and variable selection seem fine. Notice that the original correlations signs are consistent with the regression coefficient signs.
Slide 9 - 9 The DNN model The DNN model has two hidden layers with 3 neurons in the first one, and 2 neurons in the second one. Number of neurons is nearly predetermined as hidden layers must have fewer neurons than the input layer and more neurons than the output layer. The activation function is Sigmoid, which is the same as a Logistic Regression. And, the output function is also Sigmoid. This makes this DNN consistent with the Logistic Regression model.
Slide 10 - 10 Logistic Regression DNN ROC Curves, using the entire data, do not differentiate much between models AUROC = 0.954 AUROC = 0.947 When using the entire data, the difference between the two models is fractional. They both provide much lift in information vs. a naïve model that would just use the overall proportion of recessionary periods as the one constant probability of recession.
Slide 11 - 11 Kolmogorov - Smirnov plots do not differentiate much the two models Logistic Regression DNN Both models depict a tremendous lift or added information vs. a naïve model that would just use the mean proportion as a constant probability of a recession. The KS test in both cases is associated with a p-value of 0.000 that the model’s fit could be due to randomness. As shown, the KS Plot don’t facilitate a clear ranking between the two models.
Slide 12 - 12 This graph more clearly differentiates the two models Logistic Regression DNN The graphs above show recessionary quarters in green; And, the other quarters in red. On this count, the DNN model clearly differentiates itself by assigning probabilities very close to 1 for the vast majority of the recessionary quarters, and very close to 0 for the other quarters. The logistic regression model shows a more continuous range of probabilities between the 0 and 1 boundaries. Notice that both models do make a few errors
Slide 13 - 13 Confusion Matrix (using the entire data) Logistic Regression DNN
Slide 14 - 14 Summary output The main difference between the two models is that the DNN captures correctly 23 recessionary quarters out of 31. Meanwhile, the logistic regression captures 21 recessionary quarters out of 31. Most of the differences in accuracy measures sown above emanate from that difference.
Slide 15 - 15 A Bayesian representation using frequencies: Logistic Regression Think of a recession as a disease, and the model as a disease screening test (like a COVID test). And, given a disease prevalence (recession prevalence) and a model sensitivity and specificity, we can reconstruct the entire data from the Confusion Matrix.
Slide 16 - 16 A Bayesian representation using frequencies: DNN
Slide 17 - 17 Summary comparison using the Bayesian framework As shown, not much separates the models using these measures. However, we should remember that the DNN was more deterministic in its probabilities output with the majority of its quarterly probabilities estimates being close to either 0 or 1. This differentiation is not captured in the shown measures of accuracy.
Slide 18 - Testing Section 18 Here we are truly testing these models by truncating the data so that several recessionary periods are out-of-sample or Hold Out sample. Thus, the mentioned recessionary periods are treated as new data. Within such recessionary periods, we include two quarters before and after the recessionary quarters to capture enough economic turns in the data. And, check if the models can accurately forecast such economic turns into their respective recession probabilities estimates.
Slide 19 - 19 The 1980s Recessions The DNN made smaller Average and Median expected errors. Both models missed 2 recessionary quarters out of 6 (orange cells). The Logistic Regression model generated 3 false positives (purple) vs. only 1 for the DNN model.
Slide 20 - 20 The 1980s Recessions. Confusion Matrix The DNN model was superior in detecting non-recessionary quarters during the 1980s Recessions.
Slide 21 - 21 Great Recession Here, the Logistic Regression performed a lot better than the DNN as it captured 4 out of 5 recessionary quarters. Meanwhile, the DNN captured only 2 out of 5.
Slide 22 - 22 Great Recession. Confusion Matrix The Logistic Regression was twice as accurate in predicting recessionary quarters than the DNN during the Great Recession.
Slide 23 - 23 COVID Recession Both models have a perfect record during the 6 quarters including the 2 quarters of the COVID Recession.
Slide 24 - 24 COVID Recession. Confusion Matrix. That’s what a perfect prediction looks like
Slide 25 - 25 Adding the 3 Recessionary Periods together. Confusion Matrix When we add the three periods together, the Logistic Regression model is much better at capturing the recessionary quarters (10 out of 13, vs. 8 out of 13 for the DNN). On the other hand, the DNN generates fewer false positives (1 vs. 3 for the Logistic Regression model).
Slide 26 - 26 The three recessionary periods. Visual Bayesian representation. Logistic Regression
Slide 27 - 27 The three recessionary periods. Visual Bayesian representation. DNN
Slide 28 - 28 Bayesian comparison The DNN very marginal superiority when using the entire data set, did not translate in any superiority when testing both models using Hold Out or out-of-sample recessionary periods. Additionally, while the Logistic Regression model is easy to understand, including communicating the relative influence of the independent variables (standardized coefficient), the DNN is a rather opaque black box. Even, if we would publish the relative weights of each layer’s submodels, the overall depiction is very challenging to interpret.
Slide 29 - 29 Can these models predict the current prospective recession? No, they can’t. That is for a couple of reasons: First, both models have already missed out 2022 Q1 as a recessionary quarter. Even using the historical data (not true testing), the Logistic Regression model assigned a probability of a recession of only 6% for 2022 Q1; and the DNN assigned a probability of 0%. Remember, the DNN is always far more deterministic in its probability assessments. So, when it is wrong, it is far more off than the Logistic Regression model. Second, for the models to be able to forecast accurately going forward, you would need to have a crystal ball to accurately forecast the 4 independent variables. And, that is a general shortcoming of all econometrics models. Practitioners often believe that Vector Auto Regression (VAR) model structures can overcome this situation. But, it can’t. Resolving this situation entails resolving a bunch of circular functions, which is not possible.