Survey Data as Coincident or Leading Indicators

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Survey Data as Coincident or Leading Indicators Frale C., Marcellino M., Mazzi G.L., Proietti T. 1st Macroeconomic Forecasting Conference ISAE Rome, March 27

Motivation Survey variables represent a very timely piece of economic information, but their role and quality is a bit controversial. In the U.S. none of them (neither the Consumer Sentiment index by the University of Michigan) is listed among the set of series that enter the Conference Board and the Stock and Watson (1989) coincident index; by contrast in EU surveys by the European Commission are featured in the Eurocoin indicator for the euro area produced by the CEPR. Frale, Marcellino, Proietti and Mazzi (FMMP) concluded that the survey variables did not contribute significantly to the factor based indicator of the euro area monthly GDP. It turns out that this evidence was in part the consequence of imposing a single common factor on the series, and of neglecting the timeliness of the economic data. We report a modification of FMMP that deals with the introduction of a second common factor, capturing the contribution of the survey variables as coincident indicators and allows for low frequency movements, still in a mixed frequency (monthly/quarterly) framework. We also compare the short term forecasting performance of the model, with respect to the original FMMP formulation and a more standard autoregressive distributed lag (ADL) model.

Results Looking ahead to the results, we anticipate that the second factor loads significantly on the survey variables for the Industry sector and for Exports. However, the resulting monthly measure of euro area GDP is very similar to that by FMMP. Instead, the forecasting performance of the survey based factor model improves substantially over both the single factor model and ADL specifications.

Outline Motivation Survey-based factor model Euro Area application Forecasting performance Conclusion Real time analysis Revisions

Extending FMMP FMMP: Disaggregation of the chain-linked quarterly value added at constant prices from the output side and from the expenditure side by using a parametric dynamic factor model at the monthly level and indicators of economic activity, taking the temporal aggregation constraint into account. The chained-linked total GDP results via a multistep procedure that exploits the additivity of the volume measures expressed at the prices of the previous year. The final estimate is obtained by combining the two estimates (output side and expenditure side) with weights reflecting their relative precision. The extensions of the original model specification in FMMP are twofold: 1 we bring in an additional common factor, which ex post will turn out to be driven by the survey variables. 2 We model the first common factor as an integrated modified high-order autoregressive process, referred to as ZAR(p), originally proposed by Morton and Tunnicliffe-Wilson (24) as a model with improved resolution at the low frequencies.

The two index SW model with surveys y t = ϑ µ t + ϑ 1 µ t 1 + ϑ µ t + ϑ 1 µ t 1 + γ t + X t β, t = 1,...,n, φ(l) µ t = (1 θl) p η t, η t NID(,ση), 2 φ(l) µ t = η t, η t NID(,σ 2 η ), D(L) γ t = δ + ξ t, ξ t NID(,Σ ξ ), (1 θl) p η t is the pre-specified MA(p) term which squeezes the spectrum in the interval (1 θ)/(1+θ) and therefore accounts for low frequency cycles (Morton & Tunnicliffe-Wilson, G. (2)). φ(l) and φ(l) are autoregressive polynomials of order p and p with stationary roots The matrix polynomial D(L) is diagonal and Σ ξ = diag(σ 2 1,...,σ2 N ). The disturbances η t, η t and ξ t are mutually uncorrelated at all leads and lags.

The two index SW model with surveys y t = ϑ µ t + ϑ 1 µ t 1 + ϑ µ t + ϑ 1 µ t 1 + γ t + X t β, t = 1,...,n, φ(l) µ t = (1 θl) p η t, η t NID(,ση), 2 φ(l) µ t = η t, η t NID(,σ 2 η ), D(L) γ t = δ + ξ t, ξ t NID(,Σ ξ ), (1 θl) p η t is the pre-specified MA(p) term which squeezes the spectrum in the interval (1 θ)/(1+θ) and therefore accounts for low frequency cycles (Morton & Tunnicliffe-Wilson, G. (2)). φ(l) and φ(l) are autoregressive polynomials of order p and p with stationary roots The matrix polynomial D(L) is diagonal and Σ ξ = diag(σ 2 1,...,σ2 N ). The disturbances η t, η t and ξ t are mutually uncorrelated at all leads and lags.

Estimation and time constraint procedure The estimation procedure and the disaggregation of the quarterly GDP is as in FMMP(28). The model involves mixed frequency data, e.g. monthly indicators and quarterly GDP. Following Harvey (1989) and Proietti(26), the state vector in the SSF is suitably augmented by using an appropriately defined cumulator variable in order to traslate the time constraint into a problem of missing observations. The model is cast in State Space Form and, under Gaussian distribution of the errors, the unknown parameters can be estimated by maximum likelihood, using the prediction error decomposition, performed by the Kalman filter. Filter and Smoother are based on the Univariate statistical treatment of multivariate models by Koopman and Durbin (2): very flexible and convenient device for handling missing values in multivariate models and reduce the time of convergence. The multivariate vectors y t, t = 1,...,n, where some elements can be missing, are stacked one on top of the other to yield a univariate time series {y t,i,i = 1,...,N,t = 1,...,n}, whose elements are processed sequentially.

Model specification Based on two criteria: - statistical relevance of indicators: "general to specific" approach in combination with lag length selection on the BIC criterion. Every time the possibility of 1 or 2 factor model, with or without ZAR modification, is evaluated. - residual diagnostics: common approach in State Space Models of basing diagnostics and goodness of fit on the innovations. The double factor ZAR model encompasses the standard FMMP single index model only in two, but important, cases: Industry and Exports, which represents respectively 23% and 24% of the total GDP. Although the BIC criterion is in favour of a double index model in almost all cases, the survey based factor model outperform the standard FMMP in forecasting only in the two mentioned cases.

INDUSTRY Estimation results Parameters prod howk S.clime S.prod.exp S.price.exp Value added θ i.68.156 -.5 -.2 -.7.649 (.113) (.62) (.13) (.3) (.24) (.14) θ i.42.22.164.249.97.41 (.2) (.11) (.23) (.48) (.48) (.19) δ i.12 -.147.2.55.19.221 (.4) (.66) (.7) (.196) (.2) (.66) d i1.461 -.62 1.824.831.788 d i2.481 -.13 -.847 -.327.173 σ 2 η.274.274.31.119.23.3 ( 1.44L.41L 2) µ t = (1+.5L) 2 η t, η t N (,1) ( 1 1.36L+.41L 2) µ t = η t, η t N (,1) EXPORTS Parameters exp IP.int S.exp.order S.prodcap S.exp.expect S.comp NA θ i 1.17.621 -.1.321.425.13 1.543 (.28) (.22) (.17) (.321) (.518) (.278) (.71) θ i -.2.5.168 -.368.38.138.21 (.22) (.19) (.21) (.64) (.13) (.48) (.48) δ i.352.349.1 1.121.637.15.973 (.18) (.18) (.2) (.478) (.254) (.5) (.169) d i1.32 -.645 1.78 1.352.233 1.779 d i2 -.178 -.226 -.84 -.619.67 -.78 σ 2 η 1.142.595.1.95.74.133 1.1 ( 1.57L.43L 2) µ t = (1+.5L) 2 η t, η t N (,1) ( 1 1.35L+.371L 2) µ t = η t, η t N (,1)

INDUSTRY EXPORTS Industry Indicators Exports Indicators Climate 11 15 Hours worked 11 IP intermediate goods 2 1 1 95 1 1 3 9 2 1 1 11 1 Industrial production 1 Export order book Production capacity Price expectation Compatitive position Exports monthly index 12 2 9 1 1 1 2 3 8 13 Monthly Value added Industry Estimates Quartely 375 3 Monthly Exports Exports Estimates 8 Quartely 12 11 35 325 25 2 6 1 3 15 4 5 1 15 1 Monthly Value Added annual growth rates 2 Monthly Value Added monthly growth rates 15 1 CoInd1 CoInd2 5 DCoInd1 DCoInd2 5 5 2 5 CoInd1 CoInd2 2.5 DCoInd1 DCoInd2 5 5 5. rates. 25 2.5 2.5 5. 5 1. 2.5 GDP

1 Climate Industry Indicators 11 Hours worked 15 1 95 3 Price.exp 2 1 11 Industrial production 1 2 Prod.exp 1 1 9

3 2 1 Monthly Value added Industry Estimates Quartely 375 35 325 3 5 1 15 1 Monthly Value Added annual growth rates 2 Monthly Value Added monthly growth rates 5 2 2.5 CoInd1 CoInd2. 2.5 5. 5 DCoInd1 DCoInd2 5 1

Exports Indicators 11 IP intermediate goods 2 1 1 9 1 Export order book Production capacity Price expectation Compatitive position 12 Exports monthly index 1 1 2 3 8

5 Monthly Exports Exports Estimates 8 Quartely 6 5 15 CoInd1 CoInd2 1 5 5 annual growth rates 25 4 5 DCoInd1 DCoInd2 5 5. monthly growth rates 2.5. 2.5

1. Monthly Growth rate 5 Yealy growth rate.5 4 3. 2 FMMP FMMP survey based 1996 1998 2 22 24 26 28.1 Monthly Growth rate 1 FMMP survey based FMMP 1996 1998 2 22 24 26 28 Yealy growth rate.5...1 Difference between FMMP and FMMP2 1996 1998 2 22 24 26 28.5 Difference between FMMP and FMMP2 1996 1998 2 22 24 26 28 Figure: Estimated Monthly GDP: FMMP and FMMP survey-based

Forecast performance We check empirically the forecasting performance of the survey based model by comparing the forecast accuracy of: a naive model ( ADL in differences), the FMMP single index model and the FMMP-survey specification of this paper. Dimensions: level or growth rates; Month of the quarter; horizon of forecast; real time indicators; revisions 1 Forecast error 2 DM test equal accuracy 3 revisions

1. Forecast error Results are very clear: The ADLD model is almost always outperformed by the multivariate models, between which the FMMP-survey model makes globally the lowest forecast error, with a few exceptions. This evidence is stronger as the forecast horizon increases and the information set shrinks (1st month), especially for Exports. The gains from the survey-based model emerge both for Exports and Industry, in level as in growth rates, slightly greater in the latter case. We run a similar forecasting experiment for Investment, focusing for simplicity on the MSFE measure. It turns out that the FMMP-survey is systematically worse than FMMP, even if it was better in terms of BIC. Similar results hold for the other components of GDP.

Table: Industry-Statistics on forecast performance with estimated parameters for 36 rolling estimates (23M1-26M8). LEVELS ADL(1,1)D Model FMMP FMMP survey 1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step ME 1 st M -961-3214 -5466-67 -736-1578 24-21 -237 2 nd -516-254 -4899 93-453 -1277 19 64 2 3 rd -176-441 -6277-356 -1192-1954 -23-225 -449 MAE 1 st M 1665 3716 5755 733 165 2629 697 1595 2579 2 nd 199 2898 5291 811 1779 2638 773 1627 2456 3 rd 271 4423 637 1265 2764 3753 1215 2284 393 smape 1 st M.48 1.6 1.63.21.47.74.2.46.74 2 nd.32.83 1.51.23.51.75.22.47.7 3 rd.59 1.26 1.8.36.78 1.6.35.65.88 RMSFE 1 st M 1845 4311 6677 965 198 313 99 1844 2857 2 nd 1468 3511 595 924 247 36 866 1914 2861 3 rd 2379 4894 725 1548 3184 4212 1544 284 3729 mrae 1 st M.44.47.42.36.38.35 2 nd.73.59.4.85.47.32 3 rd.6.63.52.46.38.31 The smallest values for each measure are underlined, unless for mrae where the benchmark is 1.

Table: Industry-Statistics on forecast performance with estimated parameters for 36 rolling estimates (23M1-26M8). GROWTH RATES ADL(1,1)D Model FMMP FMMP survey 1-step 2-step 3-step 1-step 2-step 3-step 1-step 2-step 3-step ME 1 st M -.27 -.64 -.64 -.2 -.19 -.23.1 -.1 -.6 2 nd -.15 -.58 -.67.3 -.15 -.23.1.1 -.1 3 rd -.49 -.66 -.63 -.1 -.23 -.21 -.5 -.6 MAE 1 st M.48.67.72.21.36.46.2.35.42 2 nd.32.61.71.23.37.46.22.33.42 3 rd.59.71.7.36.46.43.35.4.43 smape 1 st M 2 193 24 263 234 137 121 16 99 2 nd 335 417 179 2 129 137 743 9 98 3 rd 594 193 217 17 137 134 9 19 11 RMSFE 1 st M.53.77.82.28.45.54.26.44.52 2 nd.42.7.82.27.47.54.25.46.52 3 rd.68.82.8.44.53.53.45.49.53 mrae 1 st M.44.4.54.36.45.38 2 nd.73.44.54.85.21.34 3 rd.6.55.51.46.42.53 The smallest values for each measure are underlined, unless for mrae where the benchmark is 1.

2. DM test We assess the statistical significance of the differences in forecast accuracy for Industry and Exports by means of the Diebold and Mariano (1995) test. Although the FMMP and FMMP-survey models are nested, rolling estimation validates the applicability of the Diebold-Mariano test. It turns out that there is strong evidence of significant differences in MSE between multivariate factor models and univariate ADLD model, while the performance of the FMMP and FMMP-survey is not statistically different, with few exception for Exports growth rate forecast. To conclude, overall this forecasting evaluation provides support for multivariate models, especially the FMMP-survey that includes timely information from survey data.

Table: Diebold-Mariano test (p-values) of equal forecast accuracy by horizon of forecast (1,2,3 quarters) and month of the prevision (1st, 2nd, 3td of the quarter). LEVELS Industry 1-step 2-step 3-step FMMP vs ADLD... FMMP-survey vs ADLD..1. FMMP-survey vs FMMP.243.344.393 1 st Month 2 nd Month 3 rd Month FMMP vs ADLD.11.7.17 FMMP-survey vs ADLD.39.35.5 FMMP-survey vs FMMP.721.698.449 GROWTH RATES Industry 1-step 2-step 3-step FMMP vs ADLD... FMMP-survey vs ADLD.2.1. FMMP-survey vs FMMP.121.228.212 1 st Month 2 nd Month 3 rd Month FMMP vs ADLD.2.1.11 FMMP-survey vs ADLD.34.75.5 FMMP-survey vs FMMP.361.349.27

Table: Diebold-Mariano test (p-values) of equal forecast accuracy by horizon of forecast (1,2,3 quarters) and month of the prevision (1st, 2nd, 3td of the quarter). LEVELS Exports 1-step 2-step 3-step FMMP vs ADLD... FMMP-survey vs ADLD.51.. FMMP-survey vs FMMP.138.94.535 1 st Month 2 nd Month 3 rd Month FMMP vs ADLD... FMMP-survey vs ADLD... FMMP-survey vs FMMP.316.362.496 GROWTH RATES Exports 1-step 2-step 3-step FMMP vs ADLD... FMMP-survey vs ADLD.38.. FMMP-survey vs FMMP.252.352.45 1 st Month 2 nd Month 3 rd Month FMMP vs ADLD... FMMP-survey vs ADLD... FMMP-survey vs FMMP.73.752.45

3.Revisions We attempt to isolate the news content of each block of series used in the estimation of GDP, namely survey data and hard data, by using vintages of time series from the Euro area Real Time database (EABCN). As for the forecast exercise, we consider 36 rolling forecasts staring from 23M1, so that the last estimated quarter is 27Q2. The model is run more than once per month, and in particular every time a block of indicators is made available. Since we consider only two blocks of variables, hard and soft data, twice per month a new estimate of the value added is calculated and compared with the previous one.

Table: Industry: Averaged size of the news in the estimation and Forecast errors, real time vintages for 36 rolling forecasts (23M1-26M8). INDUSTRY FMMP FMMP-survey Information set news* 1-step 2-step 3-step 1-step 2-step 3-step SURVEY ARRIVE 1 st Month.3.15.26 2 nd.1.7.17 3 rd..4.11 HARD DATA ARRIVE 1 st Month.24.3.31.23.31.3 2 nd.11.21.22.1.21.21 3 rd.1.29.27..3.26 RMSFE respect to first National Accounts vintage 1 st Month 7651 11657 15755 7668 11645 15599 2 nd 7678 11778 15921 7653 1168 15684 3 rd 912 8331 12333 858 8286 1247 RMSFE respect to last National Accounts vintage 1 st Month 28138 28744 29396 2884 28246 28429 2 nd 28214 28939 2959 28216 28589 28783 3 rd 2659 26765 27143 26527 26487 26219 (*) The news is measured by the Mean Absolute Relative difference between two consecutive vintages : 1 abs[(y 1 Y)/Y ]

Table: Exports: Averaged size of the news in the estimation and Forecast errors, real time vintages for 36 rolling forecasts (23M1-26M8). EXPORTS FMMP FMMP-survey Information set news* 1-step 2-step 3-step 1-step 2-step 3-step SURVEY ARRIVE 1 st Month.35.55.74 2 nd.19.4.57 3 rd.28.48.59 HARD DATA ARRIVE 1 st Month.39.36.36.61.8 1.3 2 nd.14.2.2.47.69.82 3 rd.13.27.28.5.85.99 RMSFE respect to first National Accounts vintage 1 st Month 19892 24913 3478 2365 26322 37627 2 nd 19825 2689 35498 2722 2886 36798 3 rd 1618 22144 27486 12349 23738 28219 RMSFE respect to last National Accounts vintage 1 st Month 49726 52718 5884 51127 54833 6383 2 nd 5159 54331 58951 52434 55922 6616 3 rd 4694 4987 53138 45168 4735 4942 (*) The news is measured by the Mean Absolute Relative difference between two consecutive vintages : 1 abs[(y 1 Y )/Y ]

Summary and conclusion This paper deals with the timely estimation and forecasting of low frequency variables in the presence of higher frequency information, such as quarterly GDP growth for whose components several monthly indicators are available. The aim is to explore whether the inclusion of the high frequency data might improve estimation accuracy and forecast ability. The methodology we propose for the estimation of Euro Area GDP at the monthly level is based prominently on the disaggregation procedure developed by FMMP (27). However, we suggest to extend their framework to allow for more than one common factor, survey based, and to correct for low frequency cycles. We also assess the forecasting performance of the model, evaluate the role of data revisions, and examine the news content in each block of survey and hard data. We find evidence in favour of the inclusion of a second survey based factor in two important components of GDP, namely, the Industry sector and the Exports demand component. The dominance of the two factor model is evident both in sample and out of sample. As far as the news content of data is concerned, information from survey matters, but mostly as long as hard data do not become available.

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