\(GDPplus\) (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).

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