Advances in Nowcasting Economic Activity

Transcription

1 Advances in Nowcasting Economic Activity Juan Antoĺın-Díaz 1 Thomas Drechsel 2 Ivan Petrella 3 XIII Annual Conference on Real-Time Data Analysis Banco de España October 19, Fulcrum Asset Management 2 LSE and Centre for Macroeconomics 3 Warwick Business School and CEPR

2 This paper This paper contributes to the literature on nowcasting economic activity. We propose a bayesian dynamic factor model (DFM), which takes seriously the features of the data: 1. Low-frequency variation in the mean and variance 2. Heterogeneous responses to common shocks (lead-lags) 3. Outlier observations and fat tails 4. Endogenous modeling of seasonality (today as an extension) We evaluate performance of the model and new features in a comprehensive out of sample real-time exercise, paying particular attention to density forecasts. The project builds on our earlier work: Antolin-Diaz, Drechsel, and Petrella (217 ReStat)

3 Preview of Results The results we show today are for the US The proposed improvements are successful at capturing important features of the data The real-time nowcasting performance is substantially improved across a variety of metrics (point and density) Capturing trends and SV improves nowcasting performance significantly Heterogeneous dynamics deliver substantial additional improvement Fat tails successfully capture outlier observations in an automated way and improve density forecasts of the monthly variables (these results are preliminary!).

4 Plan of the talk 1. The Model 2. Estimation Highlight features of the data Lay out how these are formally captured in the DFM Brief overview of data and algorithm 3. Setup of Real-Time Evaluation Exercise 4. Evaluation Results 5. Extension: Residual Seasonality 6. Conclusion

5 The Model

6 The Model Specification We start from the familiar specification of a DFM (see, e.g. Giannone, Reichlin, and Small, 28) Consider an n-dimensional vector of observables y t, which follows (y t ) = c + λf t + u t (1) (I Φ(L))f t = ε t (2) (1 ρ i (L))u i,t = η i,t, i = 1,..., n (3) ε t iid N(, Σε ) (4) η i,t iid N(, σ 2 ηi ), i = 1,..., n (5)

7 The Model Why explicitly model low frequency variation? 1 Gross Domestic Product (% 12 m change) and Long Run Trend (ADP 217)

8 The Model Specification Consider n-dimensional vector of observables y t, which follows (y t ) = c t + λf t + u t, (6) with and c t = [ B c ] [ at 1 ], (7) (I Φ(L))f t = ε t, (8) (1 ρ i (L))u i,t = η i,t, i = 1,..., n (9)

9 The Model Why model changes in volatility? SV in the common factor captures both secular (McConnell and Perez-Quiros, 2) and cyclical (e.g., Jurado et al., 214) movements in volatility.

10 The Model Specification Consider n-dimensional vector of observables y t, which follows (y t ) = c t + λf t + u t, (1) with and c t = [ B c ] [ at 1 ], (11) (I Φ(L))f t = σ εt ε t, (12) (1 ρ i (L))u i,t = σ ηi,t η i,t, i = 1,..., n (13) where the time-varying parameters will be specified as a random walk processes.

11 The Model Why allow for heterogeneous dynamics? 2-2 CARSALES ISMMANUF PAYROLL

12 The Model Specification (y t ) = c t + Λ(L)f t + u t, (14) where Λ(L) contains the loadings on the contemporaneous and lagged common factors. Camacho and Perez-Quiros (21) first noticed that survey data was better aligned with a distributed lag of GDP. D Agostino et al. (215) show that adding lags improves performance in the context of a small model.

13 The Model What do the heterogeneous dynamics achieve? 2 CARSALES ISMMANUF PAYROLL

14 The model What do the heterogeneous dynamics achieve?.6 Monotonic.4 Reversing.6 Hump Shaped GDP INVESTMENT INDPRO CONSUMPTION CARSALES PERMIT HOUSINGSTARTS NEWHOMESALES ISMMANUF CONSCONF PHILLYFED CHICAGO Months Months Months Result: There is substantial heterogeneity in the impulse responses.

15 The Model Why model fat tails? 5 Light Weight Vehicle Sales (% MoM change) Real Personal Disposable Income (% 1 m change) Civilian Employment (% 1 m change)

16 The Model Specification (y t o t ) = c t + Λ(L)f t + u t, (15) with o t as well as the innovations to u t following a t-distribution.

17 The Model Specification The laws of motion of the various components are specified as (I Φ(L))f t = σ εt ε t, (16) (1 ρ i (L))u i,t = σ ηi,t η i,t, i = 1,..., n (17) η i,t iid t(vη,i ), i = 1,..., n (18) o i,t iid t(vo,i ), i = 1,..., n (19) ε t iid N(, I) (2) The degrees of freedom of the t-distributions are estimated jointly with the other parameters of the model.

18 The Model Specification The model s time-varying parameters are specified to follow driftless random walks: a j,t = a j,t 1 + v aj,t, v aj,t iid N(, ω 2 a,j ) j = 1,..., r log σ εt = log σ εt 1 + v ε,t, v ε,t iid N(, ω 2 ε ) log σ ηi,t = log σ ηi,t 1 + v ηi,t, v ηi,t iid N(, ω 2 η,i ) i = 1,..., n

19 The model News Decompositions Banbura and Modugno (214) show in a Gaussian model that the impact of a new release on the nowcasts can be written as a linear function of the news: E(y k,tk Ω 2 ) E(y k,tk Ω 1 ) = w j (y j,tj E(y j,tj Ω)) w j = Λ k E ( (f tk f tk Ω)(f tj f tj Ω) ) Λ j ( ) Λ j E (f tj f tj Ω)(f tj f tj Ω) Λ j + σ2 η j,tj

20 The model News Decompositions.1 INDPRO.1 CARSALES.1 INCOME.1 RETAILSALES HOUSINGSTARTS NEWHOMESALES PAYROLL EMPLOYMENT CLAIMS ISMMANUF ISMNONMAN CONSCONF RICHMOND PHILLYFED CHICAGO EMPIRE Forecast Error (s.d.) Forecast Error (s.d.) Forecast Error (s.d.) Forecast Error (s.d.)

21 The model News Decompositions We show that with the Student-t distribution the weights are no longer linear, but depend on the value of the forecast error itself: E(y k,tk Ω 2 ) E(y k,tk Ω 1 ) = w j (y j,tj ) (y j,tj E(y j,tj Ω)) w j (y j,tj ) = Λ k E ( ( (f tk f tk Ω)(f tj f tj Ω) ) ) Λ j Λ j E (f tj f tj Ω)(f tj f tj Ω) Λ j +σ2 η j,tj δ j,tj δ j,tj = (((y j,tj E(y j,tj Ω)) 2 /σ 2 η j,tj + v o,j )/(v o,i + 1) Large errors are discounted as outlier observations containing less information.

22 The model What do the fat tails achieve?.1 INDPRO.1 CARSALES.1 INCOME.1 RETAILSALES HOUSINGSTARTS NEWHOMESALES PAYROLL EMPLOYMENT CLAIMS ISMMANUF ISMNONMAN CONSCONF RICHMOND PHILLYFED CHICAGO EMPIRE Forecast Error (s.d.) Forecast Error (s.d.) Forecast Error (s.d.) Forecast Error (s.d.)

23 Estimation

24 Estimation Data set Hard Indicators GDP (Chained $) GDI (Chained $) Consumption (Chained $, Non Dur. + Serv.) Investment (Chained $, Fixed + Cons. Dur.) Aggregate Hours Worked (Total Economy) Industrial Production Payroll Employment (Establishment Survey) Real Retail Sales Food Services Real Personal Income less Transfer Payments New Orders of Capital Goods Light Weight Vehicle Sales Real Exports of Goods Real Imports of Goods Building Permits Housing Starts New Home Sales Civilian Employment (Household Survey) Unemployed Initial Claims for Unemployment Insurance Soft Indicators Markit Manufacturing PMI ISM Manufacturing PMI ISM Non-manufacturing PMI Conference Board: Consumer Confidence University of Michigan: Consumer Sentiment Richmond Fed Mfg Survey Philadelphia Fed Business Outlook Chicago PMI NFIB: Small Business Optimism Index Empire State Manufacturing Survey Frequency Q Q Q Q Q M M M M M M M M M M M M M M M M M M M M M M M M

25 Estimation Algorithm (brief overview) Model is specified at monthly frequency. Observed growth rates of quarterly variables are related to the unobserved monthly growth rate using a weighted mean (see Mariano and Murasawa, 23) We use a hierarchical implementation of a Gibbs Sampler algorithm (Moench, Ng, and Potter, 213) which iterates between a small DFM on the outlier adjusted data and the univariate measurement equations. This leads to large computational gains due to parallelisation of this step. SVs are sampled following Kim et al. (1998).

26 Estimation Model Settings and Priors Number of lags in polynomials Λ(L), φ(l), and ρ(l): Set to m = 1, p = 2, and q = 2 Minnesota -style priors applied to coefficients in Λ(L), φ(l) and ρ i (L). Details Variance on priors set to τ h 2, where τ governs tightness of prior, and h ranges over lag numbers 1 : p, 1 : q, 1 : m + 1. Following D Agostino et al. (215), we set τ =.2, a value which is standard in the Bayesian VAR literature. Shrink ω 2 a, ω 2 ε and ω 2 η,i towards zero (standard DFM). For ω2 a set IG prior with one d.f. and scale 1e-3. For ω 2 ɛ and ω 2 η,i set IG prior with one d.f. and scale 1e-4 (see Primiceri, 25).

27 Real-time out of sample evaluation

28 Real-time out of sample evaluation Details of data base construction We construct a real-time data base for the US and other G7 countries: Germany, France, Italy, Canada, UK, and Japan. We consider 2744 data vintages since 11 January 2 to 31 December 215. For each vintage, sample start is Jan 196, appending missing observations to any series which starts after that date. Sources: (1) ALFRED, (2) Bloomberg, (3) Haver Analytics, (4) OECD Main Economic Indicators. Use appropriate deflators for nominal-only vintages. Splice data for series with methodological changes. Apply seasonal adjustment in real time for survey data.

29 Real-time out of sample evaluation Implementation of the exercise The model is fully re-estimated every time new data is released/revised. The out of sample exercise starts in January 2 and ends in December 215. For the US, on average there is a data release on 15 different dates every month. This means 2744 vintages of data. Thanks to efficient implementation of the code, it takes just 2 hours to run 8 iterations of the Gibbs sampler. But this would mean 7 months of computations! Made feasible by using Amazon Web Services cloud computing platform.

30 Evaluation Results

31 Evaluation Results What we show In the following slides: Model = Baseline DFM Model 1 = Trend + SV Model 2 = Trend + SV + heterogeneous dynamics Model 3 = Trend + SV + heterogeneous dynamics + fat tails We will consider the following metrics 1. RMSE / MAE 2. Probability Integral Transform (PITs) 3. Log Score 4. Continuous Rank Probability Score (CRPS) Everything is for US GDP (1st release)

32 Results Forecasts vs. actual over time Actual Model Model 1 GDP: Model forecasts vs realizations, day before release The addition of the long run trend eliminates the upward bias in GDP forecasts after the crisis...

33 Results Forecasts errors over time Model Model 1 4 GDP: Forecast error density, day before release and SV leads to better calibrated density forecasts.

34 Results Forecasts vs. actual over time Actual Model 1 Model 2 Model 3 GDP: Model forecasts vs realizations, day before release Heterogeneous dynamics capture recoveries more accurately

35 Results GDP: Root mean squared error (RMSE) across horizons Model Model 1 Model 2 Model Forecast Nowcast Backcast Note: Results with MAE very similar.

36 Results Root mean squared error (RMSE), Rolling Model Model 1 Model 2 Model Note: Results with MAE very similar.

37 Results Logscore -1.5 Forecast Model Model 1 Model 2 Model 3 Nowcast Backcast

38 Results CRPS Model Model 1 Model 2 Model Forecast Nowcast Backcast

39 Results Monthly Variables RMSE LogScore CRPS M M1 M2 M3 M M1 M2 M3 M M1 M2 M3 INDPRO ** NEWORDERS ** ***.92***.95*** ***.9***.94*** CARSALES *.89* INCOME ** ***.92***.96** RETAILSALES.99.98*.98.96* *.5.91***.93***.91*** EXPORTS **.99**.98** ***.89***.88*** ***.88***.86*** IMPORTS **.9***.9*** ***.87***.88*** PERMIT HOUSINGSTARTS NEWHOMESALES PAYROLL.12.96*.87***.89*** ***.82***.85*** EMPLOYMENT

40 Results Summary of insights from real-time exercise Trend and SV deliver significant improvement Substantial additional improvement from heterogeneous dynamics Fat tails improve density forecasts of monthly variables

41 Extension: Residual Seasonality

42 Modeling residual seasonality Motivation Standard practice: Take seasonally adjusted data directly from statistical agency or adjust using off-the-shelf package outside of model (see e.g. Camacho, Lovcha, Perez-Quiros, 212). Recent data has sparked debate on whether standard methods are vulnerable to residual seasonality (see Rudebusch et al., 215, Stark, 215, Wright, 213). Not studied in detail: Impact of seasonal adjustment errors in the presence of ragged edge, i.e. the fact that in real time only a few observations are available at the end of the sample

43 Modeling residual seasonality Formal treatment Modify observation equation to include s t : (y t s t o t ) = c t + Λ(L)f t + u t, where and s i,t = 11 j=1 s t j + σ εs,tε s t, i = 1,..., n log σ s η i,t = log σ s η i,t 1 + v s η i,t, v s η i,t iid N(, ω 2 η,s,i ) i = 1,..., n

44 % Annualized Growth % Annualized Growth % Annualized Growth % Annualized Growth Modeling residual seasonality Results for GDP and GDI Posterior Estimate of Time-Varying Seasonal Effect by Quarter 2 Quarter 1 2 Quarter 2 2 Quarter 1 2 Quarter Quarter 3 2 Quarter 4 2 Quarter 3 2 Quarter

45 % Annualized Growth % Annualized Growth Modeling residual seasonality Results for GDP and GDI Fan Chart with seasonal effect Note: In both panels, the black line represents the actual data. The red line is the underlying measure of economic activity extracted from the DFM. The residual seasonality is shown by the orange line. The blue line is the forecast with the fan charts capturing the uncertainty in the forecast horizon.

46 Conclusion

47 Conclusion Summary of our contribution We propose a bayesian DFM, which incorporates: 1. Low-frequency variation in the mean and variance 2. Heterogeneous responses to common shocks 3. Outlier observations and fat tails 4. Endogenous modeling of seasonality (extension) The real-time nowcasting performance is substantially improved across a variety of metrics Capturing trends and SV improves nowcasting performance significantly Heterogeneous dynamics deliver substantial additional improvement Fat tails improve density forecasts of monthly variables (more to be done)

48 References Antolin-Diaz, J., T. Drechsel, and I. Petrella (217): Tracking the slowdown in long-run GDP growth, Review of Economics and Statistics, 99. Banbura, M. and M. Modugno (214): Maximum Likelihood Estimation of Factor Models on Datasets with Arbitrary Pattern of Missing Data, Journal of Applied Econometrics, 29, Camacho, M. and G. Perez-Quiros (21): Introducing the euro-sting: Short-term indicator of euro area growth, Journal of Applied Econometrics, 25, D Agostino, A., D. Giannone, M. Lenza, and M. Modugno (215): Nowcasting Business Cycles: A Bayesian Approach to Dynamic Heterogeneous Factor Models, Tech. rep. Giannone, D., L. Reichlin, and D. Small (28): Nowcasting: The real-time informational content of macroeconomic data, Journal of Monetary Economics, 55, Jurado, K., S. C. Ludvigson, and S. Ng (214): Measuring Uncertainty, American Economic Review, Forthcoming. McConnell, M. M. and G. Perez-Quiros (2): Output Fluctuations in the United States: What Has Changed since the Early 198 s? American Economic Review, 9, Moench, E., S. Ng, and S. Potter (213): Dynamic hierarchical factor models, Review of Economics and Statistics, 95,

49 Appendix Slides

50 Appendix Details on Priors For AR coefficients of factor dynamics, φ(l), prior mean is set to.9 for first lag, and zero in subsequent lags. Reflects a belief that factor captures highly persistent but stationary business cycle process. For factor loadings, Λ(L), prior mean is set to 1 for first lag, and zero in subsequent lags. Shrinks model towards factor being the cross-sectional average, see D Agostino et al. (215). For AR coefficients of idiosyncratic components, ρ i (L) prior is set to zero for all lags, shrinking model towards no serial correlation in u i,t. Back to main slides