\(GDPplus\) (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).

Cool DFM application. Their chart says it's QoQ annualized and the excel only provides that rate. I saw in the paper where they explain why they do it that way instead of levels (basically for the reasons I expected). I think a levels estimator would be better, but I won't throw stones.

ReplyDeleteI'm not sure why a levels estimator would be "better" (or "worse"). But I certainly agree that it would be a useful complement. We are presently working on a co-integrated levels version.

ReplyDelete