Page 280 - Special Topic Session (STS) - Volume 3

STS544 Baoline C. et al.
(1)

= + ∑ + ∑ ∑ ̅ + ,
−

, ,−

=1 =1 =1
where is a constant, p is the number of autoregressive parameters, k is the
number of lags of the indicator variables, and ~ ( , ).
2

Although bridge equations allow for multiple high-frequency indicator
variables, our small sample size limits the number of high-frequency variables
that could practically be included in the bridge equation. To be able to utilize
information from a much larger set of monthly indicators in a parsimonious
regression framework, we also consider the bridging with factors model, which
replaces the monthly indicators in the bridge equation framework with a small
number of common factors to capture the main co-movement of a much
larger set of indicators (Giannone, Reichlin and Small, 2008).
Let = ( , , … , ) be the vector of common factors from monthly
′

1,
,
2,
factor models aggregated to the quarterly frequency, where ≪ min (, ), n
is the number of monthly indicator variables and T is the number of quarterly
observations in the sample. For each PCE services component, bridging with
factor model can be expressed as

(2)

= + ∑ + ∑ ∑ + ,

, ,−

−
=1 =1 =0
where is a constant, is the number of autoregressive parameters, is the
number of lags of factor ; and ~ ( , ). The number of factors is
2

determined according to the Bai-Ng criterion proposed by Bai and Ng (2002).
The added advantage of the bridging with factors model is that it allows
us to extract common factors from all available monthly indicators for all PCE
services and use them in the estimation. Because we have insufficient number
of designated monthly indicators for all detailed PCE service components,
bridging with factors also allows us to incorporate information on the general
business conditions of the service sector via extracted common factors in the
estimation.

3. Application: Bridge Equation and Bridging with Factors Models for
Estimation of PCE Services
We apply the bridge equation framework and the bridging with factors
model outlined in the previous section to compile advance estimate of
detailed PCE services using real time data from the U.S. national accounts. 121
detailed components from 9 sub-groups of PCE services are included in the
application. To be able to compare revisions with the current extrapolation
method, we use the real-time data that were used to compile the advance
estimate of detailed PCE services from 2009Q2 to 2017Q4, a maximum of 34
quarters. Quarterly data used in the application include quarterly growth rates

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