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STS544 Baoline C. et al.
of the first and third estimates of the of detailed PCE services from the 2009Q2
to 2017Q4 vintages; monthly data include percentage changes in population,
average wage earnings for the relevant PCE services, and the corresponding
consumer and producer price indices (CPI and PPI) from the 2009M7 to
2017M12 vintages. Each vintage of the quarterly data include four lagged
quarterly growth rates and each vintage of the monthly indicators includes
lagged values to compute 4 lagged quarterly growth rates of the monthly
indicators.
For estimation using bridge equations, we allow a maximum of 4 lagged
growth rates of the third quarterly estimate of the PCE services and the current
and a maximum of 4 lagged quarterly growth rates of the monthly indicators.
For estimation of the bridging with factors model, a monthly factor model is
first estimated using a total of 92 monthly indicators designated for the
components in the 9 sub-groups of PCE services. Two common factors are
selected according to the Bai-Ng criterion. Like estimation with bridge
equations, we allow a maximum of 4 lagged quarterly growth rates of the
target quarterly variable and the current and 4 lagged quarterly growth rates
of the selected common factors aggregated from the monthly factors.
The estimation and nowcasting exercise is done in three steps: 1) in-
sample estimation using 75% of the sample; 2) one-step-ahead pseudo out-
of-sample predictions using the remaining 25% of the sample; and 3)
comparison of the proposed methods with the current method. To fully utilize
the information from our small samples, we choose the recursive approach to
compute out-of-sample predictions. The in-sample estimation is conducted
using the STATA program VSELECT and the number of explanatory variables
for each PCE service component is determined according to the Akaike
information criteria corrected for small samples (AICC).
To examine the impact of the outliers on estimation results, we also
estimate models with the outliers (| − | ≥ 3) removed. Thus, we evaluate
four models: bridge equation (M1), bridge equation without outliers (M2),
bridging with factors (M3), and bridging with factors without outliers (M4). We
measure improvements in accuracy by comparing model root mean squared
revisions (RMSR) with those from the current method.

4. Results from In-Sample Estimation and Out-of-Sample Predictions
4.1 Results from in-sample estimation
Results from the in-sample estimation validate the choices of using bridge
equations and bridging with factors models to compile advance estimate of
detailed PCE services. Table 1 shows results for selected PCE service
components from the estimated bridge equations. Column 1 identifies the
regression models. Columns 2 and 3 identify the PCE services components and
the service groups they belong to. Columns 4 to 8 display the estimated

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