Monday, November 4, 2013

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).