Banque Nationale De Belgique Sa · EURONEXT:BNB
Banque Nationale De Belgique Sa — Technical Presentation (December 2025)
57 slides from Banque Nationale De Belgique Sa's technical presentation, December 2025
Slide 1: Measuring and Explaining Economic Uncertainty Across US States and Metropolitan Areas
Measuring and Explaining Economic Uncertainty Across US States and Metropolitan Areas Gerald D. Cohen, Eric Ghysels, Cody Morris, Xinglin Li, Jieyao Wang Kenan Institute University of North Carolina - Chapel Hill December 2025
Slide 2: Agenda
1 Introduction 2 Prior work 3 Empirical Models and Implementation for States 4 High-dimensional (mixed-frequency) time series and sg-LASSO 5 Comparison of cross-sectional aggregated state uncertainty measures with existing literature 6 Extended Metropolitan Areas 7 Application
Slide 3: Introduction
Introduction The U.S. exhibits substantial regional heterogeneity in economic performance. National uncertainty indices (e.g. Jurado, Ludvigson and Ng 2015 - henceforth JLN) may obscure local fluctuations. This paper develops new measures of uncertainty, inspired by JLN at the state and extended met
Slide 4: Introduction
Introduction The uncertainty measures constructed by JLN have three key ingredients: (1) a forecasting model for a large set of macroeconomic variables, (2) a conditional volatility model for the h-step ahead forecasting errors, (3) an aggregation scheme for the uncertainties specific to individual
Slide 5: Introduction
Introduction The uncertainty measures constructed by JLN have three key ingredients: (1) a forecasting model for a large set of macroeconomic variables, (2) a conditional volatility model for the h-step ahead forecasting errors, (3) an aggregation scheme for the uncertainties specific to individual
Slide 6: Challenges for standard factor models used by JLN
Challenges for standard factor models used by JLN Fitting a factor model for all states does not capture cross-sectional heterogeneity very well. Fitting a factor model for each state separately is difficult with sparse data. A group factor model might work, but how to form groups? Mixed frequency d
Slide 7: Comparison of adjusted R2 across forecasting models
Comparison of adjusted R 2 across forecasting models MIDAS refers to the sg-LASSO MIDAS regression, MIDAS-C refers to the sg-LASSO MIDAS regression with COVID-19 dummies, and Factor refers to the multi-factor model. The states on the x-axis are sorted in descending order based on adjusted R 2 of sg-
Slide 8: Agenda
1 Introduction 2 Prior work 3 Empirical Models and Implementation for States 4 High-dimensional (mixed-frequency) time series and sg-LASSO 5 Comparison of cross-sectional aggregated state uncertainty measures with existing literature 6 Extended Metropolitan Areas 7 Application
Slide 9: MIDAS Machine Learning Nowcasting
MIDAS Machine Learning Nowcasting Prior work: Andrii Babii, Eric Ghysels, and Jonas Striaukas (2022) Machine learning time series regressions with an application to nowcasting, Journal of Business and Economic Statistics, 40, 1094-1106. Andrii Babii, Ryan Ball, Eric Ghysels, and Jonas Striaukas (202
Slide 10: Challenges
Challenges Issues with LASSO Standard LASSO/elastic net regression may pick an ad hoc selection of high frequency regressors, and perform poorly out-of-sample in the mixed frequency settings; LASSO does not recognize data structures.
Slide 11: Challenges: Our solution: Sparse-group LASSO
Challenges Issues with LASSO Standard LASSO/elastic net regression may pick an ad hoc selection of high frequency regressors, and perform poorly out-of-sample in the mixed frequency settings; LASSO does not recognize data structures. Our solution: Sparse-group LASSO (sg-LASSO) Simon, Friedman, Hasti
Slide 12: Why sparse-group LASSO?
Challenges Issues with LASSO Standard LASSO/elastic net regression may pick an ad hoc selection of high frequency regressors, and perform poorly out-of-sample in the mixed frequency settings; LASSO does not recognize data structures. Our solution: Sparse-group LASSO (sg-LASSO) Simon, Friedman, Hasti
Slide 13: Agenda
1 Introduction 2 Prior work 3 Empirical Models and Implementation for States 4 High-dimensional (mixed-frequency) time series and sg-LASSO 5 Comparison of cross-sectional aggregated state uncertainty measures with existing literature 6 Extended Metropolitan Areas 7 Application
Slide 14: Empirical Models and Implementation for States
Empirical Models and Implementation for States The goal is to predict state GDP growth. The samples cover 2007Q1 to 2023Q4. The generic Mixed Data Sampling (MIDAS) regression for forecasting a low frequency (quarterly) target yi,t+1 at one horizon, with high frequency covariates is: J K yi,t+1 = αi
Slide 15: Empirical Models and Implementation
Empirical Models and Implementation To examine the role of different predictors, we consider three sets of explanatory variables: (a) State-only: Models only using state-level variables. (b) State + Adjacent States: Models that include both state-level and adjacent state variables. (c) State + Adjac
Slide 16: Econometric Methodology
Econometric Methodology Regularization: sparse-group LASSO for variable and lag selection. Stochastic Volatility (SV) models applied to forecast errors to extract uncertainty. To account for the economic disruptions caused by COVID-19, we introduce two COVID-19 dummy variables corresponding to Q2 an
Slide 17: Comparison of adjusted R2 across forecasting models
Comparison of adjusted R 2 across forecasting models MIDAS refers to the sg-LASSO MIDAS regression, MIDAS-C refers to the sg-LASSO MIDAS regression with COVID-19 dummies, and Factor refers to the multi-factor model. The states on the x-axis are sorted in descending order based on adjusted R 2 of sg-
Slide 18: Agenda
1 Introduction 2 Prior work 3 Empirical Models and Implementation for States 4 High-dimensional (mixed-frequency) time series and sg-LASSO 5 Comparison of cross-sectional aggregated state uncertainty measures with existing literature 6 Extended Metropolitan Areas 7 Application
Slide 19: High-dimensional (mixed-frequency) time series regression
High-dimensional (mixed-frequency) time series regression 1 K predictors, each measured at j ∈ [m] (high-frequency if m > 1) over T time periods {xt−(j−1)/m,k , k ∈ [K ], j ∈ [m], t ∈ [T ]}, where [p] = {1, 2, . . . , p} for p ∈ N. 2 Predictive regression/projections K 1 m (j) yt+h = α + ∑ ∑ βk xt−(
Slide 20: High-dimensional (mixed-frequency) time series regression
High-dimensional (mixed-frequency) time series regression Dimensionality reduction 1 Parametrize slope coefficients via MIDAS approach (j) j −1 βk = ω ; βk , j ∈ [m] m for some weight function ω : [0, 1] × RL → R. 2 Sparse approximation to MIDAS weight function L ω(t; βk ) ≈ ∑ βk,l wl (t), l=1 where
Slide 21: High-dimensional (mixed-frequency) time series regression
High-dimensional (mixed-frequency) time series regression Choice of dictionary 1 Orthogonal Legendre polynomials is one possibility: universal approximation for any continuous function. 2 Preferred to non-orthogonalized Almon (algebraic) polynomial due to better numerical properties: reduced multico
Slide 22: Sparse-group LASSO regression/projection
Sparse-group LASSO regression/projection Estimator 1 sg-LASSO solves argminb∈Rp ∥y − Xb∥2T + 2λ Ωγ (b) with regularization parameter λ ≥ 0 and penalty K Ωγ (b) = γ|b|1 + (1 − γ) ∑ |bk |2 , k=0 b = (b0⊤ , . . . , bK⊤ )⊤ ∈ Rp and where γ ∈ [0, 1] is relative weight, |.|i is ℓi norm, i = 1, 2. 2 Easy a
Slide 23: sg-LASSO and dependent data
sg-LASSO and dependent data New Fuk-Nagaev type inequality Theorem (Babii et al. [2022]) Suppose that (ξt )t∈Z is a centered stochastic process in Rp such that each coordinate j ∈ [p] has (i) tails: supt E|ξt,j |q ≤ C < ∞ with q > 2; (ii) τ-mixing coefficients: τk ≤ dk −a with a > (q − 1)/(q − 2). T
Slide 24: sg-LASSO and dependent data
sg-LASSO and dependent data Convergence rates Theorem (Babii et al. [2022]) Under tail/dependence conditions and bounded restricted eigenvalue of Σ = E[X⊤ X/T ] r ! ˆ sp2/κ log p |β − β |1 = OP ∨s T 2−2/κ T ! sp 1/κ log p ∥X(βˆ − β )∥T = OP 2 ∨s . T 2−2/κ T Comments: 1 OLS/QMLE requries p/T = o(1),
Slide 25: Panel data regressions
Panel data regressions Linear projection Consider the baseline linear projection panel data model yit = α + xit⊤ β + uit , E[uit xit ] = 0, i ∈ [N], t ∈ [T ].
Slide 26: Panel data regressions
Panel data regressions Linear projection Consider the baseline linear projection panel data model yit = α + xit⊤ β + uit , E[uit xit ] = 0, i ∈ [N], t ∈ [T ]. Mixed frequency panel data model K yit = α + ∑ ψ(L1/m ; βk )xit,k + uit , k=1 with the high-frequency lag polynomial m ψ(L1/m ; βk )xit,k = 1
Slide 27: sg-LASSO
sg-LASSO Estimators Pooled panel data sg-LASSO estimator min ∥y − aι − Xb∥2NT + 2λ Ωγ (b), (a,b)∈R×Rp where ι ∈ RNT is the vector of ones.
Slide 28: sg-LASSO
sg-LASSO Estimators Pooled panel data sg-LASSO estimator min ∥y − aι − Xb∥2NT + 2λ Ωγ (b), (a,b)∈R×Rp where ι ∈ RNT is the vector of ones. Fixed effects sg-LASSO estimator min ∥y − Ba − Xb∥2NT + 2λ Ωγ (b), (a,b)∈RN ×Rp where B = IN ⊗ ι. Some notation Z = (B, X), IN is N × N identity matrix, ι ∈ RT a
Slide 29: Theory
Theory New Fuk-Nagaev type inequality for panel data Theorem (Babii et al. [2024a]) Suppose that (ξi,t )i∈N,t∈Z is an array of centered random vectors such that {(ξi,1 , . . . , ξi,T ) : i ∈ N} are i.i.d. and for each i ≥ 1, (ξi,t )t∈Z is a stationary stochastic process in Rp such that (i) tails: ma
Slide 30: Theory
Theory Pooled panel data sg-LASSO Theorem (Babii et al. [2024a]) Under maintained assumptions and provided that q > 2 ! sp 2/κ s log p ∥Z(ρ̂ − ρ)∥2NT = OP ∨ (NT )2−2/κ NT and r ! sp1/κ log p |ρ̂ − ρ|1 = OP ∨s . (NT )1−1/κ NT p is the total number of parameters, N is the total number of units, T is t
Slide 31: Theory
Theory Fixed effects sg-LASSO Theorem (Babii et al. [2024a]) Under maintained assumptions and provided that q > 2 ! (s ∨ N)(p2/κ ∨ N) (s ∨ N) log(p ∨ N) ∥Z(ρ̂ − ρ)∥2NT = OP ∨ . N 1−2/κ T 2−2/κ NT The number of fixed effects have a similar impact on prediction accuracy as the number of time-varying c
Slide 32: Agenda
1 Introduction 2 Prior work 3 Empirical Models and Implementation for States 4 High-dimensional (mixed-frequency) time series and sg-LASSO 5 Comparison of cross-sectional aggregated state uncertainty measures with existing literature 6 Extended Metropolitan Areas 7 Application
Slide 33: Comparison of cross-sectional aggregated state uncertainty measures with existing literature
Comparison of cross-sectional aggregated state uncertainty measures with existing literature The plotted series include the adjusted state-level average uncertainty measure from this study, JLN Uncertainty, and the state-level Economic Policy Uncertainty (EPU) index from Baker, Davis and Levy 2022.
Slide 34: Cross-sectional dispersion state uncertainty
Cross-sectional dispersion state uncertainty Empirical cross-sectional percentiles of state uncertainty
Slide 35: Average Uncertainty by State - Sample: 2007Q1 - 2023Q4
Average Uncertainty by State - Sample: 2007Q1 - 2023Q4
Slide 36: Pre-COVID, COVID, Post-COVID
(a) P RE -COVID (b) COVID (c) P OST-COVID
Slide 37: HAC-based inference
HAC-based inference Debiased CLT Suppose that p2/(κ−2) /T → 0. Then under mild conditions √ d T (βˆG + BG − βG ) − → N(0, ΞG ). bias correction BG = Θ̂G X⊤ (y − Xβˆ )/T , where Θ̂ estimates Θ = Σ−1 . long run variance: ΞG = limT →∞ Var √1T ∑Tt=1 ut ΘG Xt . application of Wald test to test low-dimens
Slide 38: sg-LASSO and dependent data
sg-LASSO and dependent data HAC estimator 1 Estimating the asymptotic variance k Ξ̂G = ∑ K Γ̂k , |k|<T MT −k with Γ̂k = Θ̂G T1 ∑Tt=1 ⊤ ût Xt ût+k Xt+k Θ̂⊤ ⊤ G , Γ̂−k = Γ̂k , and ût are sg-LASSO residuals. 2 K is the kernel function, see Newey and West (1986) and Andrews (1991). 3 MT is the lag tr
Slide 39: sg-LASSO and dependent data
sg-LASSO and dependent data HAC estimator Theorem (Babii et al. [2024c]) Under suitable regularity conditions r ! ! sp1/κ log p s2 p2/κ s3 p5/κ −ς ∥Ξ̂G − ΞG ∥ = OP MT ∨s + 2−3/κ + 4−5/κ + MT + T −(ς ∧1) . T 1−1/κ T T T 1 optimal bandwidth MT depends on the number of covariates p, tails, and weak dep
Slide 40: Explaining State-Level Differences
Explaining State-Level Differences Panel and cross-sectional regressions with 59 explanatory variables. ↗ uncertainty: Economic Policy Uncertainty Index, Economics Condition Indicator standard deviation, Oil-related GSP (Gross State Product) share, Domestic migration share, the standard deviation of
Slide 41: Agenda
1 Introduction 2 Prior work 3 Empirical Models and Implementation for States 4 High-dimensional (mixed-frequency) time series and sg-LASSO 5 Comparison of cross-sectional aggregated state uncertainty measures with existing literature 6 Extended Metropolitan Areas 7 Application
Slide 42: Extended Metropolitan Areas
Extended Metropolitan Areas We define Extended Metropolitan Areas (EMAs) as the fundamental unit of analysis, incorporating both Combined Statistical Areas (CSAs) and Metropolitan Statistical Areas (MSAs) that are not part of any CSA. The dataset spans the period 2007Q1 to 2023Q4 and includes 130 EM
Slide 43: EMA Uncertainty
EMA Uncertainty gi I + = ri meh Vers EE . we + my < ” “ ~ oe" = DA
Slide 44: Pre-COVID, COVID, Post-COVID
(a) P RE -COVID (b) COVID (c) P OST-COVID
Slide 45: Cross-Sectional Regression of Uncertainty Measures across EMAs
Cross-Sectional Regression of Uncertainty Measures across EMAs Variable Coefficient P-Values HPBA per capita 0.670 0.000 Oil-related GSP share (S) 0.434 0.000 Leisure & entertainment share 0.361 0.000 Transportation & warehousing share 0.116 0.088 Educational services share -0.143 0.057 GSP to US GD
Slide 46: Cross-Sectional Regression of Uncertainty Measures across EMAs
Cross-Sectional Regression of Uncertainty Measures across EMAs Variable Coefficient P-Values HPBA per capita 0.670 0.000 Oil-related GSP share (S) 0.434 0.000 Leisure & entertainment share 0.361 0.000 Transportation & warehousing share 0.116 0.088 Educational services share -0.143 0.057 GSP to US GD
Slide 47: Cross-Sectional Regression of Uncertainty Measures across EMAs
Cross-Sectional Regression of Uncertainty Measures across EMAs Variable Coefficient P-Values HPBA per capita 0.670 0.000 Oil-related GSP share (S) 0.434 0.000 Leisure & entertainment share 0.361 0.000 Transportation & warehousing share 0.116 0.088 Educational services share -0.143 0.057 GSP to US GD
Slide 48: Cross-Sectional Regression of Uncertainty Measures across EMAs
Cross-Sectional Regression of Uncertainty Measures across EMAs Variable Coefficient P-Values HPBA per capita 0.670 0.000 Oil-related GSP share (S) 0.434 0.000 Leisure & entertainment share 0.361 0.000 Transportation & warehousing share 0.116 0.088 Educational services share -0.143 0.057 GSP to US GD
Slide 49: Cross-Sectional Regression of Uncertainty Measures across EMAs
Cross-Sectional Regression of Uncertainty Measures across EMAs Variable Coefficient P-Values HPBA per capita 0.670 0.000 Oil-related GSP share (S) 0.434 0.000 Leisure & entertainment share 0.361 0.000 Transportation & warehousing share 0.116 0.088 Educational services share -0.143 0.057 GSP to US GD
Slide 50: Agenda
1 Introduction 2 Prior work 3 Empirical Models and Implementation for States 4 High-dimensional (mixed-frequency) time series and sg-LASSO 5 Comparison of cross-sectional aggregated state uncertainty measures with existing literature 6 Extended Metropolitan Areas 7 Application
Slide 51: Application
Application The cross-section of EMA uncertainty features interesting heterogeneity to study many socioeconomic phenomena. We conclude the paper with providing an illustrative example of the many potential applications. We focus on the connection between economic uncertainty and health, in particula
Slide 52: Application
Application Using data for England and Wales (2001–2019), Kawachi et al. [2023] report that higher economic uncertainty, measured by the EPU index, is associated with short-run increases in deaths from diseases of the circulatory system, even after controlling for unemployment and other macro indica
Slide 53: Economic Uncertainty and Cardiovascular Disease
Economic Uncertainty and Cardiovascular Disease Figure: EMA Uncertainty and cardiovascular disease outcomes: stroke, high cholesterol, high blood pressure and coronary heart disease.
Slide 54: Conclusion
Conclusion Developed novel state and EMA-level measures of economic uncertainty. Used MIDAS machine learning techniques to produce forecasts/nowcasts of state/EMA GDP growth. Drivers differ across states and EMAs: policy, sectoral, and credit factors matter. Implications: localized measures inform b
Slide 55: Thank You!
THANK YOU!
Slide 56: References I
References I Andrii Babii, Eric Ghysels, and Jonas Striaukas. Machine learning time series regressions with an application to nowcasting. Journal of Business and Economic Statistics, 40 (3):1094–1106, 2022. Andrii Babii, Ryan T. Ball, Eric Ghysels, and Jonas Striaukas. Machine learning panel data re
Slide 57: References II
References II Andrii Babii, Luca Barbaglia, Eric Ghysels, and Jonas Striaukas. Nowcasting and aggregation: Why small euro area countries matter. arXiv preprint arXiv:2509.24780, 2025. Wei Huang, Xiaoyan Lei, and Miao Yu. Economic policy uncertainty, health status, and mortality. Social Science and M
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