Federal Reserve Bank of Philadelphia Launches Improved U.S. GDP Growth Series

Exciting news for empirical macroeconomics and finance: The Federal Reserve Bank of Philadelphia today released a new and improved \(GDP\) growth series, \(GDPplus\). It's an optimal blend of the BEA's expenditure-side and income-side estimates (call them \(GDP_E\) and \(GDP_I\), respectively). The \(GDPplus\) web page contains extensive background information and will be updated whenever new or revised data for \(GDP_E\) and/or \(GDP_I\), and hence \(GDPplus\), are released.

\(GDPplus\) (developed in Aruoba, Diebold, Nalewaik, Schorfheide and Song, "Improving GDP Measurement: A Measurement-Error Perspective," NBER Working Paper 18954, 2013) is based on a dynamic-factor model,

$$
\begin{pmatrix}
GDP_{Et} \\
GDP_{It}
\end{pmatrix}
=
\begin{pmatrix}
1 \\
1
\end{pmatrix}
GDP_t
+
\begin{pmatrix}
\epsilon_{Et} \\
\epsilon_{It}
\end{pmatrix}
$$
$$
GDP_{t} = \mu (1- \rho) + \rho GDP_{t-1} + \epsilon_{Gt},
$$
where \(GDP_E\) and \(GDP_I\) are noisy indicators of latent true \( GDP\), \(\epsilon_{E}\) and \(\epsilon_{I}\) are expenditure- and income-side stochastic measurement errors, and \(\epsilon_{G}\) is a stochastic shock to true \(GDP\). The Kalman smoother provides an optimal estimate of \(GDP\) based on the noisy indicators \(GDP_{E}\) and \(GDP_{I}\). That optimal estimate is \(GDPplus\). Note that \(GDPplus\) is not just a period-by-period simple average, or even a weighted average, of \(GDP_E\) and \(GDP_I\), because optimal signal extraction averages not only across the \(GDP_E\) and \(GDP_I\) series, but also over time.

The historical perspective on \(GDP\) provided by \(GDPplus\) complements the real-time perspective on the overall business cycle provided by the Aruoba-Diebold-Scotti (ADS) Index, also published by the Federal Reserve Bank of Philadelphia.

Moving forward, \(GDPplus\) will be updated at 2 PM on every day that new and/or revised \(GDP_E\) and/or \(GDP_I\) data are released. The next update will be November 7, the day of BEA's NIPA release for Q3 (delayed due to the government shutdown).