Board of Governors of the Federal Reserve System

Abstract:

This study assesses whether the introduction of the GSIB surcharge requirement resulted in GSIBs reducing the systemic risk posed by their activities. We find limited evidence of GSIBs managing their activities to avoid increases in their surcharges. For a sample of international banks, proximity to surcharge thresholds is associated to a decrease in the growth of intra-financial system liabilities, underwriting activities, and holdings of trading and available-for-sale securities. In the case of US GSIBs and the method 2 GSIB surcharge, we find some association between proximity to surcharge thresholds and a decrease in the growth of trading and available-for-sale securities and short-term wholesale funding.

Keywords: bank capital requirements, banking regulation, GSIB surcharge, systemic risk

DOI: https://doi.org/10.17016/FEDS.2025.029

Abstract:

We show that the secular decline in real interest rates in the United States, which began in the early 1980s and persisted for nearly four decades, reduced the labor’s share of output and the unemployment rate, and increased earnings inequality. We establish this link using a model of frictional labor markets, estimated from household-level data, in which unemployment risk is only partially insurable. Rising debt resulting from lower interest rates reduces the value of unemployment, leading to lower equilibrium wages relative to productivity and a lower unemployment rate. Wage dispersion also rises. The model is consistent with panel-data reduced-form evidence linking unemployment duration, assets, debt, and post-unemployment wages. In the model, a decline in the real interest rate of the magnitude observed in the data generates a decline in the labor’s share of 6 percentage points and in the unemployment rate of 0.3 percentage points. The variance of log earnings rises from 0.66 to 0.75.

Keywords: Labor Share, Household Indebtedness, Reservation Wage

DOI: https://doi.org/10.17016/FEDS.2025.028

Abstract:

Since the 1990s, monetary policy research has highlighted the properties of policy rules that stabilize inflation and economic activity, the role of inflation targeting in anchoring expectations, and the constraints posed by the effective lower bound (ELB). This paper combines these themes by examining whether explicitly responding to long-run inflation expectations improves policy effectiveness. Using both a small model for intuition and a large-scale policy model for quantitative evaluation, the analysis shows that the proposed approach reinforces inflation anchoring, reduces volatility from slow-moving inflationary forces, and mitigates ELB risks. The findings suggest that policy rules incorporating long-run inflation expectations enhance stability and complement makeup strategies by addressing ELB risks through different channels. Given that central banks already emphasize inflation expectations in their communications, this strategy aligns naturally with existing policy discussions.

Keywords: Monetary policy; inflation targeting; anchored inflation expectations; effective lower bound

DOI: https://doi.org/10.17016/FEDS.2025.027

Abstract:

Using a broad definition of energy consumption that includes both residential energy use and gasoline for transport, we identify 20% of households in the PSID as energy burdened (EB) based on a twice-the-median, income-based threshold. Logit analysis shows that being nonwhite, being single with dependents, receiving public assistance, having no post-secondary education, and being unemployed increase the probability of being EB. We document four key empirical facts: (1) EB/non-EB status is persistent; (2) EB households have significantly higher marginal propensities to consume and marginal propensities to consume energy compared to non-EB households; (3) EB households experience lower expected energy consumption growth despite having higher expected income growth relative to non-EB households; and (4) EB households face more volatile energy consumption and income than non-EB households. Lastly, we show that both consumption inequality and energy consumption inequality have risen more moderately than income inequality over the 1999 to 2021 period. Inequality in residential energy consumption increased until 2009, then declined, whereas inequality in gasoline consumption for transport has risen steadily, reaching a level 50% higher in 2021 than in 1999.

DOI: https://doi.org/10.17016/FEDS.2025.026

Abstract:

Since the initial launch of inflation targeting in the early 1990s in New Zealand and a few other countries, inflation targeting has become the predominant monetary policy strategy in large advanced and emerging market economies. Inflation targeting has been remarkably successful in anchoring inflation, likely owing to core elements of the framework across central banks. Its reaction process, which adjusts the monetary policy stance to ensure the return of inflation to target, allows it to flexibly incorporate a wide range of factors while limiting the discretionary biases that can contribute to excessive inflation. The emphasis on communications about the inflation outlook promotes transparency and accountability. As a result, inflation targeting central banks have, on balance, managed well the large shocks associated with the Global Financial Crisis and COVID. Even so, there are numerous challenges discussed in this paper that are associated with calibration and communications of forward guidance, quantitative easing/tightening, and financial stability.

Keywords: Inflation targeting, monetary policy, central banking, financial stability

DOI: https://doi.org/10.17016/FEDS.2025.025

Abstract:

Using the micro data underlying the U.S. CPI, we document several findings about firm price-setting behavior during and following the Covid-19 pandemic, a period with the highest levels of inflation seen in around forty years. 1) The frequency of price change increased substantially as inflation took off, and has declined markedly as inflation has receded. 2) The average size of price changes also increased as price increases became more common, while the absolute value changed little. 3) The dispersion of price changes did not fall, contrary to the prediction of state-dependent models. 4) A menu cost model fitted on pre-pandemic pricing data has difficulty matching the increase in the frequency of price changes post-pandemic, which was not the case for the high inflation period of the 1980s. A re-calibrated menu cost model with smaller menu costs and larger idiosyncratic shocks can match the elevated frequency seen in the post-pandemic period, but not the movements in the dispersion of price changes. Such a model also implies a faster pass-through of shocks to inflation than the model fitted to pre-pandemic data.

Keywords: Inflation, Microdata, Sticky prices

DOI: https://doi.org/10.17016/FEDS.2025.024

Abstract:

This paper examines the revival in the analysis of monetary policy rules that took place during the 1990s. The focus is on the role that John Taylor played in this revival. It is argued that Taylor’s role—most notably through his advancing the Taylor rule, developed in 1992−1993 and increasingly permeating discussions in research and policy circles over the subsequent several years—is usefully viewed as one of building bridges. In particular, Taylor created links between a monetary policy rules tradition closely associated with Milton Friedman and an interest-rate setting tradition long associated with central banks. The rules tradition had looked unfavorably on interest-rate setting, while the central bank tradition was unfavorably disposed toward policy rules. The Taylor rule helped create a compromise between the traditions, while also advancing an interest-rate reaction function that helped create a revival during the 1990s of economic research on monetary policy rules.

Keywords: Taylor rule, interest rate rules.

DOI: https://doi.org/10.17016/FEDS.2025.023

Abstract:

I provide evidence that investors' attention allocation plays a critical role in how financial markets incorporate macroeconomic news. Using intraday data, I document a sharp increase in the market reaction to Consumer Price Index (CPI) releases during the 2021-2023 inflation surge. Bond yields, market-implied inflation expectations, and other asset prices exhibit significantly stronger responses to CPI surprises, while reactions to other macroeconomic announcements remain largely unchanged. The joint reactions of these asset prices point to an attention-based explanation–an interpretation I corroborate throughout the rest of the paper. Specifically, I construct a measure of CPI investor attention and find that: (1) attention was exceptionally elevated around CPI announcements during the inflation surge, and (2) higher pre-announcement attention robustly leads to stronger market reactions. Studying investor attention in the context of Employment Report releases and Federal Reserve announcements, I document a similar importance of attention allocation for market reactions. Lastly, I find that markets tend to overreact to announcements that attract high levels of attention.

Keywords: Macroeconomic News Announcements, Investor Attention, Financial Markets, Inflation, Federal Reserve, High-frequency event study

DOI: https://doi.org/10.17016/FEDS.2025.022

Abstract:

I combine microdata on the intertemporal marginal propensity to consume with 10 structural macro shocks to identify the role of intertemporal substitution in consumption behavior. Although some of the structural shocks that I examine lead to large and persistent changes in real interest rates—which in many models would induce a large intertemporal substitution effect—I find no evidence that households shift the timing of their consumption in response to these interest rate changes. Indeed, changes to the expected path of income explain almost all the aggregate consumption response, leaving no role for intertemporal substitution.

Keywords: Intertemporal Substitution, HANK, Monetary Policy, Consumption

DOI: https://doi.org/10.17016/FEDS.2025.021

Abstract:

We develop a model of Ponzi schemes with asymmetric information to study Ponzi frauds. A long-lived agent offers to save on behalf of short-lived agents at a higher rate than they can earn themselves. The long-lived agent may genuinely have a superior savings technology, but may be an imposter trying to steal from short-lived agents. The model identifies when a Ponzi fraud can occur and what interventions can prevent it. A key feature of Ponzi frauds is that the long-lived agent builds trust over time and improves their reputation by keeping the scheme going.

Keywords: Ponzi scheme, asymmetric information, reputation, fraud

DOI: https://doi.org/10.17016/FEDS.2025.020

Abstract:

This paper was written for the academic conference held in celebration of the 100th anniversary of the Division of Research and Statistics (R&S) of the Federal Reserve Board. The work of the Federal Reserve turns strongly on empirical efforts to understand the structure and state of the economy, and R&S can be thought of as operating a large factory for discovering and developing data and analytical methods to provide evidence relevant to the mission of the Board. This paper, as signaled by its title, illustrates how the measurement research component of the R&S factory often looks far beyond current conventions to meet the needs of the Board—and has done so since its earliest days. It would take a far longer paper to provide a complete history and evolution of measurement activities in R&S; here, we provide an indicative review focusing on selected areas from which, we believe, it is easy to conclude that R&S has been—and likely will continue to be—an important innovator in economic measurement.

Keywords: Data collection methods and estimation strategies; Business cycles, productivity, and price measurement; Financial accounts and financial data; the Survey of Consumer Finances; Blended data.

DOI: https://doi.org/10.17016/FEDS.2025.019

Abstract:

This study examines the demographic characteristics of U.S. state border counties, comparing them with those of nonborder counties. The demographic representativeness of border counties is essential for the interpretation of the results in state border-county difference-in-difference analyses, used in state policy evaluations. Our findings reveal that border counties generally have higher proportions of White, older, and disabled populations. We also see occasional instances of wide demographic differences across state boundaries. These differences potentially undermine the external validity and identification of policy evaluations. We illustrate the implications of these finding through a case study, highlighting the need for robustness checks and demographic considerations in border-county policy research.

Keywords: Demographics, Difference-in-Difference Estimates, Event Studies, Natural Experiments, Policy Experiments, US state border counties

DOI: https://doi.org/10.17016/FEDS.2025.018

Abstract:

Payment fraud has been high in recent years, and as criminals gain access to capability-enhancing generative AI tools, there is a growing need for innovative fraud detection research. However, the pace, diversity, and reproducibility of such research are inhibited by the dearth of publicly available payment transaction data. A few payment simulation methodologies have been developed to help narrow the payment transaction data gap without compromising important data privacy and security expectations. While these simulation approaches have enabled research advancements, more work is needed to generate datasets that reflect diverse and evolving fraud tactics. This paper introduces CardSim, a flexible, scalable payment card transaction simulation methodology that extends the small but emerging body of simulators available for payment fraud modeling research. CardSim is novel in the extent to which it is calibrated to publicly available data and in its Bayesian approach to associating payment transaction features with fraud. The simulator’s modular structure, which is operationalized in a corresponding software package, makes it easy to update based on new evidence about payment trends or fraud patterns. After laying out the simulation methodology, I show how outputs can be used to test and evaluate machine learning workflows, modeling approaches, and interpretability frameworks that are relevant for payment card fraud detection.

Keywords: Payment cards, Fraud detection, Bayesian analysis, Simulation, Machine learning

DOI: https://doi.org/10.17016/FEDS.2025.017

Abstract:

Filtered historical simulation (FHS)—a simple method of calculating Value-at-Risk that reacts quickly to changes in market volatility—is a popular method for calculating margin at central counterparties. However, FHS does not address how correlation can vary through time. Typically, in margin systems, each risk factor is filtered individually so that the computational burden increases linearly as the number of risk factors grows. We propose an alternative method that filters historical returns using latent risk factors derived from principal component analysis. We compare this method's performance with "traditional" FHS for different simulated and constructed portfolios. The proposed method performs much better when there are large changes in correlation. It also performs well when that is not the case, although some care needs to be taken with certain concentrated portfolios. At the same time, the computational requirements can be reduced significantly. Backtesting comparisons are performed using data from 2020 when markets were stressed by the COVID-19 crisis.

Keywords: Portfolio risk, Value-at-Risk, Margin, CCPs, Principal component analysis (PCA), historical simulation, FHS

DOI: https://doi.org/10.17016/FEDS.2025.016

Abstract:

The Federal Reserve’s discount window is a tool that can provide reserves to banks at a rate set by the Federal Reserve, the discount rate. During the past several years, there have been large fluctuations in the level of reserves in the banking system and in the level discount rate relative to other interest rates. In this paper, we explore how banks’ holdings of reserves, especially relative to the amount of reserves that banks prefer to hold, and the interest rate available at the discount window influence borrowing at the window. We find that banks borrow more when their reserves are low and when the discount rate is relatively attractive, although the size of these effects depends on a bank’s size, FHLB membership status, and financial condition.

DOI: https://doi.org/10.17016/FEDS.2025.015

Abstract:

Analysis of market liquidity often focuses on measures of the current cost of trading. However, investors and policy-makers also care about what would happen to liquidity in the event of an adverse shock. If liquidity were to deteriorate rapidly at times when investors were seeking to rebalance portfolios, this could amplify the effects of shocks to the financial system even if liquidity is high most of the time. We examine the potential for such fragility of liquidity in the Treasury market. We show that a reduction in the availability of resting orders to trade ("market depth") increases liquidity fragility, likely because lower depth increases the dependence of low trading costs on prompt replenishment of resting orders. Our results apply to all major benchmark Treasury securities individually, which enables us to establish analogous conclusions for market-wide liquidity fragility.

Keywords: liquidity, fragility, Treasury market, price impact, volatility, market depth, hidden Markov model

DOI: https://doi.org/10.17016/FEDS.2025.014

Abstract:

We develop a model of the repo market with strategic interactions among dealers who compete for funding in a decentralized over-the-counter market and have access to a centrally cleared interdealer market. We show that such “wiring” of the repo market combined with imperfect competition in dealer funding results in market inefficiencies and instability. The model allows us to disentangle supply and demand factors, and we use these factors to estimate supply and demand elasticities. Our estimates suggest that the instability of the market in September 2019 was driven by a large supply shock facing inelastic dealer funding demand, amplified by strategic interactions among dealers. We evaluate different interventions for market functioning and efficiency, including the Standing Repo Facility.

Keywords: market efficiency, over-the-counter markets, Standing Repo Facility, centrally cleared markets, networked markets, repo market

DOI: https://doi.org/10.17016/FEDS.2025.013

Abstract:

Modern payments systems are critical infrastructure for the US and global economy, and they all utilize computing systems to facilitate transactions. These computing systems can be vulnerable to failures and an outage of a payment system could cause a serious ripple effect throughout the economy it supports.

Commonly used designs in existing distributed computer systems often lack a built-in defense against certain types of failures (e.g., malicious attacks and silent data corruption) and rely on preventing these failures from happening in the first place via techniques external to the system itself. These computer system failures can cause downtime in the systems (e.g., modern payments systems) that rely on them. Byzantine Fault Tolerant (BFT) systems have the potential of improved resiliency and security. BFT systems can tolerate a larger range of failure modes than contemporary designs but suffer from performance challenges. Our work sought to design and evaluate a scalable BFT architecture and compare its properties to other database architectures used in payments infrastructure. This analysis is intended to better understand technical tradeoffs and is agnostic to broader policy or operational considerations.

In this paper, we present Heraclius, a parallelizable leader-based, BFT key-value store that could be extended for use in payment systems. Heraclius executes transactions in parallel to achieve high transaction volumes. We analyze the scalability of the protocol, bottlenecks and potential solutions to the bottlenecks. We ran the prototype implementation with up to 256 nodes and achieved a transactional volume of 110 thousand operations per second with a transaction latency 0.2 seconds.

Keywords: BFT systems, Payment systems

DOI: https://doi.org/10.17016/FEDS.2025.012

Abstract:

This paper introduces a novel measure of firm-level Artificial Intelligence (AI) Research & Development—the AIR Index—derived from the semantic similarity between earnings conference call transcripts and leading AI research papers. The AIR Index varies widely across industries, with sustained strength in computer and electronic manufacturing, and accelerating growth in computing infrastructure and educational services seen after the introduction of ChatGPT in November 2022. I find that the AIR Index is associated with an immediate increase in Tobin's Q and can help explain the cross-section of cumulative absolute returns following the conference call, suggestive of investors valuing substantive AI discussions in the near-term. A sharp rise in the AIR Index leads to persistent increases in year-over-year capex growth, lasting about a year before tapering off, indicative of the life cycle of AI-induced capital deepening. However, I find no significant effects of AI R&D on productivity or employment. Using industry level survey data from Census, I find that recent growth in the AIR Index correlates with broader AI adoption trends. The positive association of the AIR Index with capex and valuation holds across previous time periods, suggesting that Generative AI may be the latest form of an ongoing technical innovation process, albeit at an accelerated pace.

Keywords: artificial intelligence, capital expenditure, corporate finance, natural language processing, productivity

DOI: https://doi.org/10.17016/FEDS.2025.011

Abstract:

The annual Survey of Household Economics and Decisionmaking (SHED) receives substantial research attention for topics related to household finances and economic well-being. To assess the reliability of data from the SHED, we compare aggregate statistics from the SHED with prominent, nationally representative surveys that use different survey designs, sample methodologies, and interview modes. Specifically, we compare recent statistics from the SHED with similar questions in U.S. Census Bureau surveys, including the Current Population Survey (CPS) and the American Community Survey (ACS). Overall, aggregate responses to the SHED benchmark well against nationally representative surveys, particularly for questions with nearly identical wording. However, we also note that subtle differences in wording of survey questions for broadly similar indicators can prompt moderate variations across data sources.

Keywords: SHED, Survey methodology, Census Bureau: CPS, ACS, Demographic, Employment, Homeownership, Health insurance, Food insufficiency

DOI: https://doi.org/10.17016/FEDS.2025.010

Abstract:

Regulating bank risk-taking is challenging since banks know more than regulators about the risks of their portfolios and can make adjustments to game regulations. To address this problem, I build a tractable model that incorporates this information asymmetry. The model is flexible enough to encompass many regulatory tools, although I focus on taxes. These taxes could also be interpreted as reflecting the shadow costs of other regulations, such as capital requirements. I show that linear risk-sensitive taxes should not generally be set more conservatively to address asymmetric information. I further show the efficacy of three regulatory tools: (1) not disclosing taxes to banks until after portfolio selection, (2) nonlinear taxes that respond to information contained in banks' portfolio choice, and (3) taxes on banks' realized pro ts that incentivize banks to reduce risk.

DOI: https://doi.org/10.17016/FEDS.2025.009

Abstract:

The Medicaid continuous enrollment provision, which ensured uninterrupted coverage for beneficiaries during the COVID-19 pandemic, was ended in March 2023. This unwinding process has led to large-scale Medicaid disenrollments, as states resumed their standard renewal process to evaluate enrolled individuals' eligibility status. Our analysis investigates whether resumption of states' renewal process has led to an increase in the risk of becoming uninsured for adults aged under 65 and affected their household economic well-being. Using state-month variation in the timing of the first round of disenrollments, we first document a 6-12 percent decline in total Medicaid enrollments after states resumed their renewal process. Next, based on nationally representative samples of adults younger than age 65, we do not find statistically relevant effects on the probability of being without any health coverage. However, looking at different demographic groups, we see a one percentage point increase in the likelihood of becoming uninsured for adults who have a college education but do not have a bachelor's or higher degree.

Keywords: Continuous enrollment provision; COVID-19 pandemic; Medicaid; health insurance; policy analysis

DOI: https://doi.org/10.17016/FEDS.2025.008

Abstract:

The equity market’s reaction to macroeconomic news is consistent with the propagation of news into the real economy. We embody all the macro news in an activity news index and a price news index that together explain 34% of the quarterly stock price returns variation. When those indexes capture a stream of favorable macroeconomic surprises, publicly traded firms experience increases in revenues, profitability, financing, and investment activities. The firm-level results lead up to an expansion of the real side of the whole U.S. economy. Our findings, taken together, show that stock prices’ reactions to macro news have a strong association with firm-level and economy-wide growth.

Keywords: Macroeconomic News, Equity Markets, Real Activity

DOI: https://doi.org/10.17016/FEDS.2025.007

Abstract:

The correlation of the spatial distribution of banking exposures with changes in spatial patterns of economic activity (e.g., internal migration, changes in agglomeration patterns, climate change, etc.) may have financial stability implications. We therefore study the spatial distribution of large U.S. banks' commercial and industrial (C&I) lending portfolios. We construct a novel dataset that augments FR Y-14Q regulatory data with borrower microdata for a more granular understanding of where banks' exposures are located by looking beyond headquarters to the location of facilities. We find that banks are exposed to almost all U.S. counties, with clustered exposure in certain geographies. We then use our dataset for a climate-related application by analyzing what fraction of C&I loans have been extended to firms that operate in areas vulnerable to physical risks, identifying, for example, counties where both (i) banks are highly exposed via their lending portfolios, and (ii) physical risks have historically resulted in large losses. Results of this kind can help inform risk management and be used to improve resilience to future stresses.

Keywords: bank lending to firms, climate risks, mapping of firm facilities, spatial lending patterns

DOI: https://doi.org/10.17016/FEDS.2025.006

Abstract:

Using a novel data collection, we examine the impact of the Volcker Rule on trading revenue of the 21 largest U.S. trading firms during the 100 day stress period centered on the COVID-19 financial crisis. We find that despite the market volatility, trading profits were consistent with volume-driven fees, commissions, and widening of the bid-ask spread. This work adds to the growing body of evidence that a consequence of the Volcker Rule on firm revenue associated with trading is increased financial stability and decreased risk exposure to market shocks.

Keywords: Bank Trading, Supervision and regulation of financial markets and institutions, Systemic Risk, Volcker Rule

DOI: https://doi.org/10.17016/FEDS.2025.005

Abstract:

This paper studies the estimation and inference of time-varying impulse response functions in structural vector autoregressions (SVARs) identified with external instruments. Building on kernel estimators that allow for nonparametric time variation, we derive the asymptotic distributions of the relevant quantities. Our estimators are simple and computationally trivial and allow for potentially weak instruments. Simulations suggest satisfactory empirical coverage even in relatively small samples as long as the underlying parameter instabilities are sufficiently smooth. We illustrate the methods by studying the time-varying effects of global oil supply news shocks on US industrial production.

Keywords: Time-varying parameters, Nonparametric estimation, Structural VAR, External instruments, Weak instruments, Oil supply news shocks, Impulse response analysis

DOI: https://doi.org/10.17016/FEDS.2025.004

Abstract:

In this paper, we assemble the most comprehensive dataset to date on the characteristics of colleges and universities, including dates of operation, institutional setting, student body, staff, and finance data from 2002 to 2023. We provide an extensive description of what is known and unknown about closed colleges compared with institutions that did not close. Using this data, we first develop a series of predictive models of financial distress, utilizing factors like operational revenue/expense patterns, sources of revenue, metrics of liquidity and leverage, enrollment/staff patterns, and prior signs of significant financial strain. We benchmark these models against existing federal government screening mechanisms such as financial responsibility scores and heightened cash monitoring. We document a high degree of missing data among colleges that eventually close and show that this is a key impediment to identifying at risk institutions. We then show that modern machine learning techniques, combined with richer data, are far more effective at predicting college closures than linear probability models, and considerably more effective than existing accountability metrics. Our preferred model, which combines an off-the-shelf machine learning algorithm with the richest set of explanatory variables, can significantly improve predictive accuracy even for institutions with complete data, but is particularly helpful for predicting instances of financial distress for institutions with spotty data. Finally, we conduct simulations using our estimates to contemplate likely increases in future closures, showing that enrollment challenges resulting from an impending demographic cliff are likely to significantly increase annual college closures for reasonable scenarios.

Keywords: higher education, college, university, enrollment, tuition, revenue, budget, closure, fiscal challenge, demographic cliff

DOI: https://doi.org/10.17016/FEDS.2025.003

Abstract:

Using inflation swap prices, we study how changes in expected inflation affect firm-level credit spreads and equity returns, and uncover evidence of a time-varying inflation sensitivity. In times of "good inflation," when inflation news is perceived by investors to be more positively correlated with real economic growth, movements in expected inflation substantially reduce corporate credit spreads and raise equity valuations. Meanwhile in times of "bad inflation," these effects are attenuated and the opposite can take place. These dynamics naturally arise in an equilibrium asset pricing model with a time-varying inflation-growth relationship and persistent macroeconomic expectations.

Keywords: Inflation Sensitivity, Time Variation, Asset Prices, Stock-Bond Correlation

DOI: https://doi.org/10.17016/FEDS.2025.002

Abstract:

Replacing faulty measurements with missing values can suppress outlier-induced distortions in state-space inference. We therefore put forward two complementary methods for enhanced outlier-robust filtering and forecasting: supervised missing data substitution (MD) upon exceeding a Huber threshold, and unsupervised missing data substitution via exogenous randomization (RMDX).

Our supervised method, MD, is designed to improve performance of existing Huber-based linear filters known to lose optimality when outliers of the same sign are clustered in time rather than arriving independently. The unsupervised method, RMDX, further aims to suppress smaller outliers whose size may fall below the Huber detection threshold. To this end, RMDX averages filtered or forecasted targets based on measurement series with randomly induced subsets of missing data at an exogenously set randomization rate. This gives rise to regularization and bias-variance trade-off as a function of the missing data randomization rate, which can be set optimally using standard cross-validation techniques.

We validate through Monte Carlo simulations that both methods for missing data substitution can significantly improve robust filtering, especially when combined together. As further empirical validation, we document consistently attractive performance in linear models for forecasting inflation trends prone to clustering of measurement outliers.

Keywords: Kalman filter, outliers, Huberization, missing data, randomization

DOI: https://doi.org/10.17016/FEDS.2025.001