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).