Using Survey Information for Improving the Density Nowcasting of U.S. GDP

Abstract

We provide a methodology that efficiently combines the statistical models of nowcasting with the survey information for improving the (density) nowcasting of U.S. real GDP. Specifically, we use the conventional dynamic factor model together with stochastic volatility components as the baseline statistical model. We augment the model with information from the survey expectations by aligning the first and second moments of the predictive distribution implied by this baseline model with those extracted from the survey information at various horizons. Results indicate that survey information bears valuable information over the baseline model for nowcasting GDP. While the mean survey predictions deliver valuable information during extreme events such as the Covid-19 pandemic, the variation in the survey participants’ predictions, often used as a measure of “ambiguity,” conveys crucial information beyond the mean of those predictions for capturing the tail behavior of the GDP distribution.

KEYWORDS:

• Bayesian inference
• Disagreement
• Dynamic factor model
• Predictive density evaluation
• Stochastic volatility
• Survey of professional forecasters

Supplementary Materials

The supplementary material contains details on the econometric model and related Bayesian inference, comparison with alternative specifications, analysis with alternative datasets, evaluation of the prediction performance using Probability Integral Transforms (PIT), comparison with alternative density combination methods, and finally, a detailed monthly analysis of the model performance during 2020.

Notes

1 Other popular methods used for nowcasting the GDP involve mixed frequency VARs, see, for example, Giannone, Reichlin, and Simonelli (2009) and Foroni, Ghysels, and Marcellino (2013), among others, or MIDAS and bridge equations, see, for example, Aastveit et al. (2014) and Schumacher (2016), among others, which make use of datasets at mixed frequencies.

2 We provide full details about the simulation-based inference of the competing models in Section A of the supplementary material for the sake of brevity.

3 Banbura et al. (2013) show that variables that are sampled at higher frequency than monthly provide little or no improvement for prediction of the GDP.

4 We also estimate models where monthly variables bear idiosyncratic stochastic volatility. This model provides less accurate predictions than the model with stochastic volatility structures in real GDP and factor error terms. The results of this specification search and the related discussion can be found in Section B of the supplementary material.

5 The timing for the release of survey-based predictions was also unclear before 1990. For the periods before the 2000s, survey-based predictions were released toward the end of the second month of the corresponding quarter, while after the 2000s it was released at the end of the second week rather than at the end of the month. Performing the predictions at the end of the month ensures that we do not use information that is not available in real-time. For the release dates of the survey information after the second quarter of 1990, see https://www.philadelphiafed.org/-/media/frbp/assets/surveys-and-data/survey-of-professional-forecasters/spf-release-dates.txt?la=en&hash=B00319

6 We also consider stochastic volatility structure in these alignment equations. Results are unaffected when we allow for time variation in ${\sigma }_{{\psi }_h}^2$, and frequently it does perform worse than the models without stochastic volatility. The results of this specification and the related discussion can be found in Section B of the supplementary material.

7 We provide our findings on comparing the two measures in Section C of the supplementary material.

8 Essentially, the output is measured as Gross National Product (GNP) until 1991 and Gross Domestic Product (GDP) after that. Still, the output is denoted as GDP for the whole sample period for the sake of demonstration.

9 As an alternative, we consider a much larger dataset using 135 variables obtained from the FRED-MD dataset of McCracken and Ng (2016). These models perform inferiorly compared to those using the dataset involving 16 variables. We provide details on this comparison in Section C of the supplementary material.

10 The original dataset of Banbura et al. (2013) includes some variables at daily and weekly frequency as well, including return on the market index at the daily frequency and initial jobless claims at the weekly frequency. They note that the daily and weekly variables do not provide further information beyond the monthly variables for nowcasting GDP. We follow this practice to exclude the variables at higher than monthly frequency. This structure also facilitates the computation substantially for the recursive out-of-sample exercise without deteriorating the model’s overall performance. We also consider alternative model strategies where the survey information is used as typical data as in Equation (5)(5) $$\begin{array}{ccc}{y}_t^q& =& {\lambda }^q{f}_t^q+{\epsilon }_t^q\mathrm{\hspace{1em}}\mathrm{\hspace{1em}}\text{for}\mathrm{}t=3k\mathrm{}\text{and}\mathrm{}k=1,2\dots ,K\\ y_t^m& =& {\lambda }^m{f}_t^m+{\epsilon }_t^m\hspace{1em}\text{for}\mathrm{}t=1,2,\dots ,T\\ f_t^m& =& \varphi f_{t-1}^m+u_t\end{array}$$(5) with using the alignment equations as in Equation (12)(12) $$\begin{array}{c}{E}_t^S\left[y_{t+1}^q\right]={\lambda }^q(\varphi f_t^m+2f_t^m+3f_{t-1}^m+2f_{t-2}^m+f_{t-3}^m)+{\psi }_{1,t}\\ E_t^S\left[y_{t+h}^q\right]={\lambda }^q\left(\sum _{s=0}^4{w}_s{\varphi }^{h-s}\right)f_t^m+{\psi }_{h,t}\\ \mathrm{\hspace{1em}}\mathrm{\hspace{1em}}\text{with}\hspace{1em}h=3k+1\mathrm{}\text{for}\mathrm{}k=1,2,3,4.\end{array}$$(12) . These models perform inferiorly compared to our framework. We provide details on this comparison in Section B of the supplementary material.

11 https://www.philadelphiafed.org/research-and-data/real-time-center/survey-of-professional-forecasters

12 The stochastic volatility structures in our model framework also lead to nonlinearities as the dependence structure of the log-volatilities to the data is through the exponential function. In these cases, we use the approach of Omori et al. (2007) where we approximate the model using a mixture of Normals. We provide details on the estimation of volatility in the Section A of the supplementary material.

13 Details on the computations of these measures are provided in Section A of the supplementary material.

14 Here we do not display the fitted values obtained from (BMSV + S) type of models for the clarity of the demonstration as these are very similar to those displayed in Figure 3.

15 We display the graph of the evolution of predictive likelihoods for predictions performed in the first month of the current quarter in Section E of the supplementary material as it is very similar to Figure 6.

16 We conduct a detailed analysis for exploring the underlying reasons for this inferior performance at the onset of the evaluation sample. Results indicate that this limited performance is partly due to the inferior performance of surveys predictors during the 1970s, where we observe extreme turmoils. Combined with the lack of data at the sample’s onset, this poor performance led to considerable deterioration of the predictions toward the end-1970s. Interestingly, this substantially poor performance of the surveys seems unique to this period. Essentially, we do not observe such performance of survey participants for latter turmoil periods. On the contrary, as discussed in Section 5 survey participants react pretty promptly to the changing conditions during the Covid-19 pandemic induced recession of 2020. We display those results in Section E of the supplementary material.

17 Since the fourth quarter of 2020 is relatively more in parallel with the pre-pandemic periods, here we do not provide details on the fourth quarter of 2020. We provide a complete analysis, including the fourth quarter of 2020 and the corresponding nowcast distributions obtained at the end of each month in Section G of the supplementary material.

18 We only include the BMSV model for the sake of brevity. The evidence in earlier sections shows that the BMSV model has superior predictive ability compared to the BM model, and thus the conclusions drawn in the section remain unaffected if we also include BM in the comparison of methods.

19 For BMA, we approximate the SPF predictions using a parametric specification, allowing us to compute the predictive likelihood. We provide the details on this model and on forecast combination methods in Section F of the supplementary material.

20 We also consider the Entropic Tilting (ET) method in comparison to our model framework. In the ET method, the combined distribution is obtained by minimizing the relative entropy, that is, the Kullback–Leibler divergence, between the candidate distribution and the predictive distribution obtained by the BMSV model subject to the constraints that the moment conditions of the candidate should be identical to those from the SPF, see, for example, Krüger, Clark, and Ravazzolo (2017) and Tallman and Zaman (2019). Unlike our models, where the moments from both sources could occasionally deviate from each other, the moments are perfectly identical in our case for the ET methods. This equality implies that the conclusions that we draw using RMSFEs in Section 4.4 for comparison between the SPF and the BMSV model also apply here. While analytical expressions for predictive likelihoods are not available, we evaluate the ET method in comparison to our model framework using other metrics, which are displayed in Section F of the supplementary material.