Federal Reserve Bank of St. Louis working papers are preliminary materials circulated to stimulate discussion and critial comment.
Bootstrapping out-of-sample predictability tests with real-time data
In this paper we develop a block bootstrap approach to out-of-sample inference when real-time data are used to produce forecasts. In particular, we establish its first-order asymptotic validity for West-type (1996) tests of predictive ability in the presence of regular data revisions. This allows the user to conduct asymptotically valid inference without having to estimate the asymptotic variances derived in Clark and McCracken’s (2009) extension of West (1996) when data are subject to revision. Monte Carlo experiments indicate that the bootstrap can provide satisfactory finite sample size and power even in modest sample sizes. We conclude with an application to inflation forecasting that adapts the results in Ang et al. (2007) to the presence of real-time data.
Impulse Response Functions for Self-Exciting Nonlinear Models
We calculate impulse response functions from regime-switching models where the driving variable can respond to the shock. Two methods used to estimate the impulse responses in these models are generalized impulse response functions and local projections. Local projections depend on the observed switches in the data, while generalized impulse response functions rely on correctly specifying regime process. Using Monte Carlos with different misspecifications, we determine under what conditions either method is preferred. We then extend model-average impulse responses to this nonlinear environment and show that they generally perform better than either generalized impulse response functions and local projections. Finally, we apply these findings to the empirical estimation of regime-dependent fiscal multipliers and find multipliers less than one and generally small differences across different states of slack.
Growth-at-Risk is Investment-at-Risk
We investigate the role financial conditions play in the composition of U.S. growth-at-risk. We document that, by a wide margin, growth-at-risk is investment-at-risk. That is, if financial conditions indicate U.S. real GDP growth will be in the lower tail of its conditional distribution, we know that the main contributor is a decline in investment. Consumption contributes under extreme financial stress. Government spending and net exports do not play a role.
How Much Should We Trust Regional-Exposure Designs?
Many prominent studies in macroeconomics, labor, and trade use panel data on regions to identify the local effects of aggregate shocks. These studies construct regional-exposure instruments as an observed aggregate shock times an observed regional exposure to that shock. We argue that the most economically plausible source of identification in these settings is uncorrelatedness of observed and unobserved aggregate shocks. Even when the regression estimator is consistent, we show that inference is complicated by cross-regional residual correlations induced by unobserved aggregate shocks. We suggest two-way clustering, two-way heteroskedasticity- and autocorrelation-consistent standard errors, and randomization inference as options to solve this inference problem. We also develop a feasible optimal instrument to improve efficiency. In an application to the estimation of regional fiscal multipliers, we show that the standard practice of clustering by region generates confidence intervals that are too small. When we construct confidence intervals with robust methods, we can no longer reject multipliers close to zero at the 95% level. The feasible optimal instrument more than doubles statistical power; however, we still cannot reject low multipliers. Our results underscore that the precision promised by regional data may disappear with correct inference.
Decomposing the Government Transfer Multiplier
We estimate the local, spillover and aggregate causal effects of government transfers on personal income. We identify exogenous changes in federal transfers to residents at the state-level using legislated social security cost-of-living adjustments between 1952 and 1974. Each effect is measured as a multiplier: the change in personal income in response to a one unit change in transfers. The local multiplier, i.e., the effect of own-state transfers on own-state income holding fixed other state's income, at a four-quarter horizon is approximately 3.4. The cross-state spillover multiplier is about -0.7, but not statistically different from zero. The aggregate multiplier, i.e., the sum of its local and spillover components, equals 2.7. More generally, our paper provides a template for conducting inference that decomposes an aggregate effect into its local and spillover components.
Systemic Tail Risk: High-Frequency Measurement, Evidence and Implications
We develop a new framework to measure market-wide (systemic) tail risk in the cross-section of high-frequency stock returns. We estimate the time-varying jump intensities of asset prices and introduce a testing approach that identifies multi-asset tail risk based on the release times of scheduled news announcements. Using high-frequency data on individual U.S. stocks and sector-specific ETF portfolios, we find that most of the FOMC announcements create systemic left tail risk, but there is no evidence that macro announcements do so. The magnitude of the tail risk induced by Fed news varies over the business cycle, peaks during the global financial crisis and remains high over different phases of unconventional monetary policy. We use our approach to construct a Fed-induced systemic tail risk (STR) indicator. STR helps explain the pre-FOMC announcement drift and significantly increases variance risk premia, particularly for the meetings without press conferences.
Mind Your Language: Market Responses to Central Bank Speeches
Researchers have carefully studied post-meeting central bank communication and have found that it often moves markets, but they have paid less attention to the more frequent central bankers’ speeches. We create a novel dataset of US Federal Reserve speeches and develop supervised multimodal natural language processing methods to identify how monetary policy news affect financial volatility and tail risk through implied changes in forecasts of GDP, inflation, and unemployment. We find that news in central bankers’ speeches can help explain volatility and tail risk in both equity and bond markets. Our results challenge the conventional view that central bank communication primarily resolves uncertainty and indicate that markets attend to speech signals more closely during abnormal GDP and inflation regimes. Our analysis also reveals that the views of Fed members (i.e., hawkish versus dovish) tend to play a marginal role in terms of the strength of the speech signals. Looking at the speeches by the Fed Chair, we find that the Chair signals produce a larger tail risk compared to non-Chair signals, and the estimated magnitude of the market responses depends on the position of the officials (i.e., the Fed Chair or other Fed member).
The Evolution of Regional Beveridge Curves
The slow recovery of the labor market in the aftermath of the Great Recession highlighted mismatch, the misallocation of workers across space or across industries. We consider the historical evolution of regional mismatch. We construct MSA-level unemployment rates and vacancy data using techniques similar to Barnichon (2010) and a new dataset of online help-wanted ads by MSA. We estimate regional Beveridge curves, identifying the slopes by restricting them to be equal across locations with similar labor market characteristics. We find that the 51 U.S. cities in our sample have four groupings which are influenced by industry classification, union membership, and geographic proximity. Additionally, allowing for a structural break suggests match efficiency increased across regions after adoption of the internet.
Financial market reactions to the Russian invasion of Ukraine
This article analyzes financial market reactions to the Russia-Ukraine war with a focus on the opening weeks. Markets did not completely anticipate the war and asset price reactions strengthened from the first week—when there were hopes for a quick resolution—to the second week, when prices generally peaked and began to partially revert to pre-war values. Exposure to commodity trade and trade with Russia-Ukraine determined market perceptions of the riskiness of equity and foreign exchange assets. Credit default swap prices on sovereign debt and breakeven inflation rates indicate that markets saw the war as a measurable fiscal risk even for non-belligerents.
Age and Gender Differentials in Unemployment and Hysteresis
We use a time-varying panel unobserved components model to estimate unemployment gaps disaggregated by age and gender. Recessions before COVID affected men's labor market outcomes more than women's; however, the reverse was true for the COVID recession, with effects amplified for younger workers. The aggregate Phillips curve flattens over time and hysteresis is countercyclical for all groups. We find heterogeneity in both the Phillips curve and hysteresis coefficients, with wages responding more to workers with an outside option (high school- and retirement-age) and larger effects of hysteresis for younger workers.
The Sine Aggregatio Approach to Applied Macro
We develop a method to use disaggregate data to conduct causal inference in macroeconomics. The approach permits one to infer the aggregate effect of a macro treatment using regional outcome data and a valid instrument. We estimate a macro effect without (sine) the aggregation (aggregatio) of the outcome variable. We exploit cross-equation parameter restrictions to increase precision relative to traditional, aggregate series estimates and provide a method to assess robustness to departures from these restrictions. We illustrate our method via estimating the jobs effect of oil price changes using regional manufacturing employment data and an aggregate oil supply shock.
On the Real-Time Predictive Content of Financial Conditions Indices for Growth
We provide evidence on the real-time predictive content of the National Financial Conditions Index (NFCI), for conditional quantiles of U.S. real GDP growth. Our work is distinct from the literature in two specific ways. First, we construct (unofficial) real-time vintages of the NFCI. This allows us to conduct out-of-sample analysis without introducing the kind of look-ahead biases that are naturally introduced when using a single current vintage. We then develop methods for conducting asymptotic inference on tests of equal tick loss between nested quantile regression models when the data are subject to revision. We conclude by evaluating the real-time predictive content of NFCI vintages for quantiles of real GDP growth. While our results largely reinforce the literature, we find gains to using real-time vintages leading up to recessions — precisely when policymakers need such a monitoring device.
Reconsidering the Fed's Inflation Forecasting Advantage
Previous studies show the Fed has a forecast advantage over the private sector for inflation, either because it devotes more resources to forecasting or because it has an informational advantage. We evaluate the Fed's forecast advantage to determine how much of it results from the Fed's knowledge of future monetary policy. We develop two tests -- an instrumental variable encompassing test and a path-dependent encompassing test -- to equalize the Fed's information set with the private sector's. We find that Fed forecasts do not encompass those of the private sector when the latter has knowledge of the future of monetary policy. Further, we find that between 20 and 30 percent of the difference between the Fed's and the private sector's mean squared forecast error can be explained by monetary policy.
International trade and labor reallocation: misclassification errors, mobility, and switching costs
International trade has increased at a rapid pace in the last decades, altering production and labor demand in different sectors of the economy. The estimated effects of trade on employment and welfare critically depend on data about workers’ reallocation patterns, which is typically plagued with coding errors. I show that the estimated employment and welfare effects of international trade, and the estimated structural parameters of standard models are biased when the analysis uses data subject to misclassification errors. I develop an econometric framework to estimate misclassification probabilities, corrected mobility matrices, and structural parameters, and show that the estimated employment and welfare effects of a trade shock are different from those estimated with uncorrected data, raising an important warning about conclusions drawn from data with coding errors.
The Impact of Health and Economic Policies on the Spread of COVID-19 and Economic Activity
This paper empirically investigates the causal linkages between COVID-19 spread, government health containment and economic support policies, and economic activity in the U.S. up to the introduction of vaccines in early 2021. We model their joint dynamics as generated by a structural vector autoregression and estimate it using U.S. state-level data. We identify structural shocks to the variables by making assumptions on their short-run relation consistent with salient epidemiological and economic features of COVID-19. We isolate the direct impact of COVID-19 spread and policy responses on economic activity by controlling for demand fluctuations using disaggregate exports data. We find that health containment and economic support policies are highly effective at curbing the spread of COVID-19 without leading to a long-term contraction of economic activity.
Supply and demand shifts of shorts before Fed announcements during QE1–QE3
Cohen, Diether, and Malloy (Journal of Finance, 2007), find that shifts in the demand curve predict negative stock returns. We use their approach to examine changes in supply and demand at the time of FOMC announcements. We show that shifts in the demand for borrowing Treasuries and agencies predict quantitative easing. A reduction in the quantity demanded at all points along the demand curve predicts expansionary quantitative easing announcements.
Tests of Conditional Predictive Ability: Existence, Size, and Power
We investigate a test of conditional predictive ability described in Giacomini and White (2006; Econometrica). Our main goal is simply to demonstrate existence of the null hypothesis and, in doing so, clarify just how unlikely it is for this hypothesis to hold. We do so using a simple example of point forecasting under quadratic loss. We then provide simulation evidence on the size and power of the test. While the test can be accurately sized we find that power is typically low.
FRED-SD: A Real-Time Database for State-Level Data with Forecasting Applications
We construct a real-time dataset (FRED-SD) with vintage data for the U.S. states that can be used to forecast both state-level and national-level variables. Our dataset includes approximately 28 variables per state, including labor market, production, and housing variables. We conduct two sets of real-time forecasting exercises. The first forecasts state-level labor-market variables using five different models and different levels of industrially-disaggregated data. The second forecasts a national-level variable exploiting the cross-section of state data. The state-forecasting experiments suggest that large models with industrially-disaggregated data tend to have higher predictive ability for industrially-diversified states. For national-level data, we find that forecasting and aggregating state-level data can outperform a random walk but not an autoregression. We compare these real-time data experiments with forecasting experiments using final-vintage data and find very different results. Because these final-vintage results are obtained with revised data that would not have been available at the time the forecasts would have been made, we conclude that the use of real-time data is essential for drawing proper conclusions about state-level forecasting models.
Collaboration in Bipartite Networks, with an Application to Coauthorship Networks
This paper studies the impact of collaboration on research output. First, we build a micro founded model for scientific knowledge production, where collaboration between researchers is represented by a bipartite network. The equilibrium of the game incorporates both the complementarity effect between collaborating researchers and the substitutability effect between concurrent projects of the same researcher. Next, we develop a Bayesian MCMC procedure to estimate the structural parameters, taking into account the endogenous matching of researchers and projects. Finally, we illustrate the empirical relevance of the model by analyzing the coauthorship network of economists registered in the RePEc Author Service.
Forecasting Low Frequency Macroeconomic Events with High Frequency Data
High-frequency financial and economic indicators are usually time-aggregated before computing forecasts of macroeconomic events, such as recessions. We propose a mixed-frequency alternative that delivers high-frequency probability forecasts (including their confidence bands) for low-frequency events. The new approach is compared with single-frequency alternatives using loss functions for rare-event forecasting. We find: (i) the weekly-sampled spread improves over the monthly-sampled to predict NBER recessions, (ii) the predictive content of financial variables is supplementary to economic activity for forecasts of vulnerability events, and (iii) a weekly activity index can date the 2020 business cycle peak in real-time using a mixed-frequency filtering.
A Local-Spillover Decomposition of the Causal Effect of U.S. Defense Spending Shocks
This paper decomposes the causal effect of government defense spending into: (i) a local (or direct) effect, and (ii) a spillover (or indirect) effect. Using state-level defense spending data, we show that a negative cross-state spillover effect explains the existing simultaneous findings of a low aggregate multiplier and a high local multiplier. We show that enlisting disaggregate data improves the precision of aggregate effect estimates, relative to using aggregate time series alone. Moreover, we compare two-step efficient GMM with two alternative moment weighting approaches used in existing research.
Measuring Labor Supply and Demand Shocks during COVID-19
We measure labor demand and supply shocks at the sector level around the COVID-19 outbreak by estimating a Bayesian structural vector autoregression on monthly statistics of hours worked and real wages. Most sectors were subject to historically large negative labor supply and demand shocks in March and April, with substantial heterogeneity in the size of shocks across sectors. Our estimates suggest that two-thirds of the drop in the aggregate growth rate of hours in March and April 2020 are attributable to labor supply. We validate our estimates of supply shocks by showing that they are correlated with sectoral measures of telework.
FRED-QD: A Quarterly Database for Macroeconomic Research
In this paper we present and describe a large quarterly frequency, macroeconomic database. The data provided are closely modeled to that used in Stock and Watson (2012a). As in our previous work on FRED-MD, our goal is simply to provide a publicly available source of macroeconomic “big data” that is updated in real time using the FRED database. We show that factors extracted from this data set exhibit similar behavior to those extracted from the original Stock and Watson data set. The dominant factors are shown to be insensitive to outliers, but outliers do affect the relative influence of the series as indicated by leverage scores. We then investigate the role unit root tests play in the choice of transformation codes with an emphasis on identifying instances in which the unit root-based codes differ from those already used in the literature. Finally, we show that factors extracted from our data set are useful for forecasting a range of macroeconomic series and that the choice of transformation codes can contribute substantially to the accuracy of these forecasts.
Predicting Benchmarked US State Employment Data in Real Time
US payroll employment data come from a survey and are subject to revisions. While revisions are generally small at the national level, they can be large enough at the state level to alter assessments of current economic conditions. Users must therefore exercise caution in interpreting state employment data until they are “benchmarked” against administrative data 5–16 months after the reference period. This paper develops a state-space model that predicts benchmarked state employment data in real time. The model has two distinct features: 1) an explicit model of the data revision process and 2) a dynamic factor model that incorporates real-time information from other state-level labor market indicators. We find that the model reduces the average size of benchmark revisions by about 11 percent. When we optimally average the model’s predictions with those of existing models, the model reduces the average size of the revisions by about 14 percent.
Tax Progressivity, Economic Booms, and Trickle-Up Economics
We propose a method to decompose changes in the tax structure into orthogonal components measuring the level and progressivity of taxes. Similar to tax shocks found in the existing empirical literature, the level shock is contractionary. The tax progressivity shock is expansionary: Increasing tax progressivity raises (lowers) disposable income at the bottom (top) end of the income distribution by shifting the tax burden from the bottom to the top. If agents' marginal propensity to consume falls with income, the rise in consumption at the bottom more than compensates for the decline in consumption at the top. The resulting increase in output and consumption leads to rising capital gains for those at the high end of the income distribution that more than offsets their losses from higher income taxes. The net result is that an increasing progressivity leads to an increase in income inequality, contrary to what conventional wisdom might suggest. We interpret these results as evidence in favor of trickle up, not trickle down, economics.
While conditional forecasting has become prevalent both in the academic literature and in practice (e.g., bank stress testing, scenario forecasting), its applications typically focus on continuous variables. In this paper, we merge elements from the literature on the construction and implementation of conditional forecasts with the literature on forecasting binary variables. We use the Qual-VAR [Dueker (2005)], whose joint VAR-probit structure allows us to form conditional forecasts of the latent variable which can then be used to form probabilistic forecasts of the binary variable. We apply the model to forecasting recessions in real-time and investigate the role of monetary and oil shocks on the likelihood of two U.S. recessions.
Diverging Tests of Equal Predictive Ability
We investigate claims made in Giacomini and White (2006) and Diebold (2015) regarding the asymptotic normality of a test of equal predictive ability. A counterexample is provided in which, instead, the test statistic diverges with probability one under the null.
We analyze the propagation of recessions across countries. We construct a model that allows for multiple qualitative state variables in a vector autoregression (VAR) setting. The VAR structure allows us to include country-level variables to determine whether policy also propagates across countries. We consider two different versions of the model. One version assumes the discrete state of the economy (expansion or recession) is observed. The other assumes that the state of the economy is unobserved and must be inferred from movements in economic growth. We apply the model to Canada, Mexico, and the United States to test if spillover effects were similar before and after the North American Free Trade Agreement (NAFTA). We find that trade liberalization has increased the degree of business cycle propagation across the three countries.
Tests of Conditional Predictive Ability: Some Simulation Evidence
In this note we use simple examples and associated simulations to investigate the size and power properties of tests of predictive ability described in Giacomini and White (2006; Econometrica). While we find that the tests can be accurately sized and powerful in large enough samples we identify details associated with the tests that are not otherwise apparent from the original text. In order of importance these include (i) the proposed test of equal finite-sample unconditional predictive ability is not asymptotically valid under the fixed scheme, (ii) for the same test, but when the rolling scheme is used, very large bandwidths are sometimes required when estimating long-run variances, and (iii) when conducting the proposed test of equal finite-sample conditional predictive ability, conditional heteroskedasticity is likely present when lagged loss differentials are used as instruments.
An Empirical Investigation of Direct and Iterated Multistep Conditional Forecasts
When constructing unconditional point forecasts, both direct- and iterated-multistep (DMS and IMS) approaches are common. However, in the context of producing conditional forecasts, IMS approaches based on vector autoregressions (VAR) are far more common than simpler DMS models. This is despite the fact that there are theoretical reasons to believe that DMS models are more robust to misspecification than are IMS models. In the context of unconditional forecasts, Marcellino, Stock, and Watson (MSW, 2006) investigate the empirical relevance of these theories. In this paper, we extend that work to conditional forecasts. We do so based on linear bivariate and trivariate models estimated using a large dataset of macroeconomic time series. Over comparable samples, our results reinforce those in MSW: the IMS approach is typically a bit better than DMS with significant improvements only at longer horizons. In contrast, when we focus on the Great Moderation sample we find a marked improvement in the DMS approach relative to IMS. The distinction is particularly clear when we forecast nominal rather than real variables where the relative gains can be substantial.