[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120506-en":3,"doc-seo-120506-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120506,13056703019662,"Evangeline","https://ap-avatar.wpscdn.com/avatar/be000253a8e92610077?_k=1778726343310543188",8,"Research & Report","Forecasting With Machine Learning Shadow-Rate VARs - Research Article","Interest rates play a core role in macroeconomic modeling, especially when policy rates approach the effective lower bound (ELB). This study proposes shadow-rate VARs that treat interest rates as a latent variable near the ELB and estimates shadow-rate values using machine learning priors. The analysis extends Bayesian LASSO and shadow-rate VARs to homoscedastic and stochastic volatility settings, and integrates vintage-specific long-run assumptions from the Survey of Professional Forecasters (SPF). Using real-time U.S. data from 2005–2019, the paper evaluates predictive accuracy for point and density forecasts across 16 shadow-rate VARs and 20 variables, finding improvements for short- and longer-horizon outcomes and potential value for central banks.","Journal of Forecasting   \n RESEARCH ARTICLE  OPEN ACCESS   \nForecasting With Machine Learning Shadow-Rate VARs  \nMichael Grammatikopoulos   \nMoody's Analytics, University of Strathclyde, Glasgow, UK  \nCorrespondence: Michael Grammatikopoulos ([Michael.Grammatikopoulos@moodys.com](Michael.Grammatikopoulos@moodys.com))  \nReceived: 21 June 2024 | Revised: 22 September 2025 | Accepted: 25 September 2025  \nKeywords: effective lower bound | forecasting | generalized impulse responses | shadow rates | steady states | structural VAR | variable selection  \nABSTRACT  \nInterest rates are fundamental in macroeconomic modeling. Recent studies integrate the effective lower bound (ELB) into vector autoregressions (VARs). This paper studies shadow-rate VARs by using interest rates as a latent variable near the ELB to estimate their shadow-rate values. The study explores machine learning models, such as the Bayesian LASSO, and extends the analysis to include homoscedastic and stochastic volatility shadow-rate VARs. It also examines the integration of shadow rate with vintagespecific long-run assumptions derived from the Survey of Professional Forecasters (SPF) . The paper analyzes 16 shadow-rate VARs with 20 US variables, using real-time data from 2005 to 2019 and assesses their predictive accuracy for both point and density forecasts. The findings indicate that shadow-rate models can enhance predictive accuracy for both short-term and longer term horizons across macroeconomic and financial variables. These models could be of use for central banks and policymakers.  \n1 | Introduction  \nBayesian methods have been employed in economic forecasting since the 1980s. Vector autoregressions (VARs), introduced by Sims (1980), are widely used by academics and policymakers for analyzing economic activity. Traditional maximum likelihood VARs often suffer from the curse of dimensionality and can yield imprecise results when data quality is suboptimal. Bayesian VAR models gained prominence following the work of Doan et al. (1984) and Litterman (1986), who demonstrated that Bayesian shrinkage improves forecast accuracy.  \nA key aspect of forecasting involves modeling interest rates, particularly during recessions when rates may stabilize at their effective lower bound (ELB) . For instance, the Federal Open Market Committee (FOMC) maintained a 0–25 basis points federal funds rate range during both the Great Recession (2009– 2015) and the COVID-19 pandemic (2020–2022) . Similarly, the European Central Bank set its deposit rate at −50 bps. Several central banks have adopted negative interest rate policies (NIRPs), keeping policy rates near zero. Under NIRP, these rates tend to remain slightly above zero, as observed in estimates for the euro area by Wu and Zhang (2019) .  \nThis paper builds on recent advancements in Bayesian VARs, specifically those that incorporate stochastic volatility (SV) . The use of equation-by-equation estimation, as demonstrated by Carriero et al. (2019), has shown significant gains in computational efficiency for these models. Extending this approach, Gefang et al. (2023), hereafter GKP, developed a computationally efficient MCMC algorithm for structural VAR (SVAR) models by applying the equation-by-equation estimation framework toa range of machine learning priors, including Bayesian LASSO (BLASSO) and stochastic search variable selection (SSVS) .  \nThis paper extends the computationally efficient MCMC algorithm proposed by GKP (2023) because its equationby-equation estimation and triangular algorithm provide a significant advantage for our current application. This framework allows us to efficiently handle the high-dimensional parameter space that arises when combining shrinkage priors with the shadow-rate estimation proposed by Carriero et al. (2025), hereafter CCMM. To the best of our knowledge, the application of shrinkage priors and long-run assumptions within shadow-rate VAR models is an unexplored area in the literature. There","cbCaicXMhILhCQ2R","https://ap.wps.com/l/cbCaicXMhILhCQ2R","pdf",6144760,1,17,"English","en",105,"# Introduction\n## Bayesian VARs and forecasting\n## Effective lower bound and interest-rate modeling\n## Shadow-rate VARs and machine learning priors\n## VSLR assumptions and real-time forecasting setup","[{\"question\":\"What are shadow-rate VARs in this paper?\",\"answer\":\"They model interest-rate dynamics near the effective lower bound by treating interest rates as a latent variable and estimating corresponding shadow-rate values within a VAR framework.\"},{\"question\":\"Which machine learning and Bayesian methods are used?\",\"answer\":\"The paper studies machine learning/Bayesian approaches such as Bayesian LASSO, and it also considers extensions including homoscedastic and stochastic volatility shadow-rate VARs.\"},{\"question\":\"How are vintage-specific long-run assumptions incorporated?\",\"answer\":\"The approach uses vintagespecific long-run (VSLR) assumptions drawn from the Survey of Professional Forecasters (SPF), with prior means informed by SPF and prior variances modeled via a mixture of normals.\"}]","Forecasting With Machine Learning Shadow-Rate VARs - Research Article | PDF",1785730404,43,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"forecasting-with-machine-learning-shadow-rate-vars-research-article","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/forecasting-with-machine-learning-shadow-rate-vars-research-article/120506/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-05","2026-08-03",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What are shadow-rate VARs in this paper?","Question",{"text":76,"@type":77},"They model interest-rate dynamics near the effective lower bound by treating interest rates as a latent variable and estimating corresponding shadow-rate values within a VAR framework.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which machine learning and Bayesian methods are used?",{"text":81,"@type":77},"The paper studies machine learning/Bayesian approaches such as Bayesian LASSO, and it also considers extensions including homoscedastic and stochastic volatility shadow-rate VARs.",{"name":83,"@type":74,"acceptedAnswer":84},"How are vintage-specific long-run assumptions incorporated?",{"text":85,"@type":77},"The approach uses vintagespecific long-run (VSLR) assumptions drawn from the Survey of Professional Forecasters (SPF), with prior means informed by SPF and prior variances modeled via a mixture of normals.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]