Measuring Sub-Regional Economic Activity: Missing Frequencies and Missing Data

Bayesian mixed-frequency vector autoregressions (MF-VARs) are commonly used to produce timely and high-frequency estimates of low-frequency variables. A typical application uses quarterly data on output, for a given country, and monthly indicator data to produce monthly estimates of national output. But, when working at sub-national levels, data limitations preclude the use of standard MF-VARs. The frequency mismatch is more complicated, key variables can have missing data, and release delays can be substantial. In this paper, we develop a novel MF-VAR which addresses all these issues and use it to produce historical estimates of sub-regional output growth in the UK. The model combines information in the annual sub-regional data (when available) with data from the UK regions and the UK as a whole. The model is estimated using variational Bayesian methods with shrinkage priors, reflecting the “big data” setup. We use our model to produce a new database of quarterly estimates of sub-regional GVA growth back to the 1960s, that importantly, because the MFVAR imposes temporal and cross-sectional restrictions, is consistent with those official data that do exist. We illustrate the use of these new estimates by showing how they can used to characterize the considerable heterogeneity in sub-regional business cycle dynamics in the UK and contribute to our understanding of regional economic resilience.