Banbura 2013 - Partial Models and the Empirical GDP Application

Summary

Bridge equations aggregate monthly predictors to the target frequency (filling the ragged edge with auxiliary AR/VAR forecasts); MIDAS regressions use predictors at native frequency with parsimonious lag polynomials. Both lack a joint model and hence news. In the real-time US GDP exercise (1995-2010) the factor-model benchmark beat bridge equations, surveys mattered, and daily/weekly variables added little.

Overview

Partial models regress the target on predictors without a joint model, so the ragged edge needs auxiliary models or separate parameter sets per vintage. They remain common in policy institutions.

Main Content

Bridge equation

$y_t^{k_1}=\alpha +\beta (L)x_t^{k_1}+e_t$ where $x_t^{k_1}$ is a predictor aggregated to the target frequency; the missing months of the current quarter are forecast with ARMA/VAR models. OLS estimation; forecast combination across many bridge equations; bottom-up (aggregate component nowcasts through national-accounts identities). Giannone-Reichlin-Small’s approach is “bridging with factors”.

MIDAS regression

$y_t^{k_1}=\alpha +\beta \Gamma (L,\theta )y_{t-h_n,n}+e_t$ with a parsimonious lag polynomial such as the exponential Almon, $\Gamma (L,\theta )={\sum }_m\gamma (m,\theta )L^m$, $\gamma (m,\theta )=\exp ({\theta }_{1}m+{\theta }_2{m}^2)/{\sum }_j\exp ({\theta }_{1}j+{\theta }_2{j}^2)$ (Ghysels et al. 2003). Ragged edge is handled by re-aligning each series to its latest observation (a different set of coefficients per release pattern).

Data (Table 1). 24 series, only GDP quarterly: industrial production, labour market, surveys (e.g. Philadelphia Fed), prices (CPI), housing, trade, consumption; two weekly (initial claims, Bloomberg consumer comfort); daily financial (S&P 500, interest rates, effective exchange rate, oil). Publication delays recorded for January 2011; surveys appear earlier than hard data (negative delays = released before the reference month ends). Only headline series are used; disaggregates add little precision and do not hurt, so variable pre-selection is unnecessary.

Design. Benchmark: one-factor daily model with temporally aggregated loadings (EM estimation); alternatives: monthly factor model without weekly/daily data; a small five-hard-indicator monthly factor model (NBER BCDC set: GDP, IP, real disposable income, retail sales, employment); bridge equations (23 separate regressions, AR forecasts for missing months, BIC lags); Survey of Professional Forecasters. Evaluated by RMSFE over 1995-2010, four times per month for four months.

Findings

• Accuracy improves as information on the quarter accumulates; the benchmark beats bridge equations and is competitive with the SPF.
• Surveys improve accuracy at all points; the hard-data-only model is worse.
• Daily and weekly variables do not significantly improve the GDP nowcast (low-frequency financial components relate to activity, daily fluctuations carry wrong signals). By-product: a daily index of economic activity that explains most of GDP dynamics but little of daily stock-price movement.

Limitations / extensions. Point nowcasts only; density nowcasts (Aastveit et al. 2011; Marcellino et al. 2012); nowcast combination; bottom-up national-accounts coherence; Liebermann (2012) for other releases; Modugno (2013) for inflation.

Examples

Bridge vs joint model on day 20

Month 2 of the quarter: industrial production for month 1 only. A bridge equation must forecast months 2 and 3 with an AR, ignoring the survey already released; the joint factor model uses the month-2 survey immediately through the shared factor.

Connections

Similarity to Bayesian structural time series with regressors (Bayesian Structural Time-Series Model); shrinkage for large VARs links to Global-Local Shrinkage Priors.

See Also

Banbura et al 2013 - Now-casting and the Real-Time Data Flow - Overview