Research

Working Papers

1. Incorporating Micro Data into Macro Models Using Pseudo VARs

   Gary Koop, Stuart McIntyre, James Mitchell, and Ping Wu (2026)

   Federal Reserve Bank of Cleveland Working Paper
   Abstract

   This paper develops a method to incorporate micro data, available as repeated cross-sections, into macro VAR models to understand the distributional effects of macroeconomic shocks at business cycle frequencies. The method extends existing functional VAR models by "looking within" the micro distribution to identify the degree to which specific types of micro units are affected by macro shocks. It does so by creating a pseudo-panel from the repeated cross-section and adding these pseudo individuals into the macro VAR. Jointly modeling the micro and macro data leads to a large (pseudo) VAR, and we use Bayesian methods to ensure shrinkage and parsimony. Our application revisits Chang et al. (2024) and compares their functional VAR-based distributional impulse response functions with our proposed pseudo VAR-based ones to identify what types of individuals' earnings are most affected by business-cycle-type shocks. We find that the individuals exhibiting the strongest positive cyclical sensitivity are those in the lower tail of the earnings distribution, particularly men and those without a college education, as well as young workers.

Publications

1. Fast, Order-Invariant Bayesian Inference in VARs using the Eigendecomposition of the Error Covariance Matrix

   Ping Wu and Gary Koop (2025)

   Journal of Business and Economic Statistics, forthcoming
   Journal Version Working Paper

   Abstract

   Bayesian inference in Vector Autoregressions (VARs) involves manipulating large matrices which appear in the posterior (or conditional posterior) of the VAR coefficients. For large VARs, the computational burden of these manipulations can render empirical work impractical. In response to this, many researchers transform their VARs so as to allow for Bayesian estimation to proceed one equation at a time. This leads to a massive reduction in the computational burden. This transformation involves taking the Cholesky decomposition for the error covariance matrix. However, this strategy implies that posterior inference depends on the order the variables enter the VAR. In this paper we develop an alternative transformation, based on the eigendecomposition, which does not lead to order dependence. Beginning with an inverse-Wishart prior on the error covariance matrix, we derive and discuss the properties of the prior it implies on the eigenmatrix and eigenvalues. We then show how an extension of the prior on the eigenmatrix can allow for greater flexibility while maintaining many of the benefits of conjugacy. We leverage this flexibility to extend the prior on the eigenvalues to allow for stochastic volatility. The properties of the eigendecomposition approach are investigated in a macroeconomic forecasting exercise involving VARs with 20 variables.
2. Incorporating Short Data into Large Mixed-Frequency VARs for Regional Nowcasting

   Gary Koop, Stuart McIntyre, James Mitchell, Aubrey Poon and Ping Wu (2024)

   Journal of the Royal Statistical Society: Series A, 187(2), 477–495
   Journal Version Working Paper

   Abstract

   Interest in regional economic issues coupled with advances in administrative data is driving the creation of new regional economic data. Many of these data series could be useful for nowcasting regional economic activity, but they suffer from a short (albeit constantly expanding) time series which makes incorporating them into nowcasting models problematic. Regional nowcasting is already challenging because the release delay on regional data tends to be greater than that at the national level, and “short” data imply a “ragged edge” at both the beginning and the end of regional data sets, which adds a further complication. In this paper, via an application to the UK, we investigate various ways of including a wide range of short data into a regional mixedfrequency VAR model. These short data include hitherto unexploited regional VAT turnover data. We address the problem of the ragged edge at both the beginning and end of our sample by estimating regional factors using different missing data algorithms that we then incorporate into our mixed-frequency VAR model. We find that nowcasts of regional output growth are generally improved when we condition them on the factors, but only when the regional nowcasts are produced before the national (UK-wide) output growth data are published.
3. Should I Open to Forecast? Implications from a Multi-country Unobserved Components Model with Sparse Factor Stochastic Volatility

   Ping Wu (2023)

   International Journal of Forecasting, 40(3), 903–917
   Journal Version Working Paper

   Abstract

   In this paper, we assess whether and when multi-country studies pay off for forecasting inflation and output growth. Factor stochastic volatility is adopted to allow for cross-country linkages and model economies jointly. We estimate factors and rely on the post-processing, rather than expert judgement, to obtain an estimate for the number of factors. This is different from most existing two-step approach in the factor literature. Our approach is then used to extend the existing unobserved components model which assumes 34 economies are independent. The results suggest that allowing for cross-country linkages yields inflation and output growth forecasts that are highly competitive to estimating economies independently. Zooming into the forecast performance over time reveals that allowing for cross-country linkages is of particular importance when interest centers on forecasting periods of uncertainty. Another key finding is that the estimated global factors are correlated with the domestic business cycle. We interpret this as that part of the variation captured in global factors reflects a global business cycle.
4. A Time-Varying Phillips Curve with Global Factors: Are Global Factors Important?

   Alain Ntumba Kabundi, Aubrey Poon, and Ping Wu (2023)

   Economic Modelling, 126: 106423
   Journal Version Working Paper

   Abstract

   Increased globalization and trade have integrated the world, but whether they are the underlying drivers of the flattening of the Phillips curve slope is not clear. This problem is further complicated since time-varying parameters are empirically important in most applications as the role of global factors may change over time. This paper investigates empirically the role played by global and domestic factors in driving dynamics in inflation using a panel data comprising of 23 advanced (AEs) and 11 emerging market economies (EMEs), from 1995Q1 to 2018Q1. The results indicate the predominance and increasing importance of global factors in explaining inflation dynamics, especially for EMEs. The Phillips curve is flat for both groups, but it is flatter in AEs. The results are consistent with the theoretical view that increased globalization and trade are underlying factors behind the flattening of the Phillips curve.
5. Estimating the Ordering of Variables in a VAR using a Plackett-Luce Prior

   Ping Wu and Gary Koop (2023)

   Economics Letters, 230: 111247
   Journal Version Working Paper

   Abstract

   Estimating Bayesian Vector Autoregressions (VARs) involving the Cholesky decomposition is sensitive to the ordering of variables. We treat the ordering as unknown, develop a prior over variable orderings and Markov Chain Monte Carlo (MCMC) methods for posterior sampling over orderings.

Book Chapters

1. Measuring Sub-regional Economic Activity: Missing Frequencies and Missing Data

   Gary Koop, Stuart McIntyre, James Mitchell, Aubrey Poon and Ping Wu (2024)

   Recent Developments in Bayesian Econometrics and its Applications: Festschrift in Honour of Sune Karlsson (Springer)
   Chapter Version Working Paper

Work in Progress

• U.S. Economy and Global Stock Markets: Insights from a Distributional Approach
• A Panel Unobserved Components Model
• Time Series Analysis with Missing Data (with Sharada Nia Davidson)
• Variable Ordering in a Cholesky-MSV model (with Martina Danielova Zaharieva)