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Federal Reserve Bank of St. Louis working papers are preliminary materials circulated to stimulate discussion and critial comment.

Applied Econometrics

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.

Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors

We develop uncertainty measures for point forecasts from surveys such as the Survey of Professional Forecasters, Blue Chip, or the Federal Open Market Committee''''s Summary of Economic Projections. At a given point of time, these surveys provide forecasts for macroeconomic variables at multiple horizons. To track time-varying uncertainty in the associated forecast errors, we derive a multiple-horizon specification of stochastic volatility. Compared to constant-variance approaches, our stochastic-volatility model improves the accuracy of uncertainty measures for survey forecasts.

Debt and Stabilization Policy: Evidence from a Euro Area FAVAR

The Euro-area poses a unique problem in evaluating policy: a currency union with a shared monetary policy and country-specific fiscal policy. Analysis can be further complicated if high levels of public debt affect the performance of stabilization policy. We construct a framework capable of handling these issues with an application to Euro-Area data. In order to incorporate multiple macroeconomic series from each country but, simultaneously, treat country-specific fiscal policy, we develop a hierarchical factor-augmented VAR with zero restrictions on the loadings that yield country-level factors. Monetary policy, then, responds to area-wide conditions but fiscal policy responds only to its country level conditions. We find that there is broad quantitative variation in different countries'''' responses to area-wide monetary policy and both qualitative and quantitative variation in responses to country-specific fiscal policy. Moreover, we find that debt conditions do not diminish the effectiveness of policy in a significant manner, suggesting that any negative effects must come through other channels.

Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book

An extensive empirical literature documents a generally negative correlation, named the “leverage effect,” between asset returns and changes of volatility. It is more challenging to establish such a return-volatility relationship for jumps in high-frequency data. We propose new nonparametric methods to assess and test for a discontinuous leverage effect — i.e. a relation between contemporaneous jumps in prices and volatility. The methods are robust to market microstructure noise and build on a newly developed price-jump localization and estimation procedure. Our empirical investigation of six years of transaction data from 320 NASDAQ firms displays no unconditional negative correlation between price and volatility cojumps. We show, however, that there is a strong relation between price-volatility cojumps if one conditions on the sign of price jumps and whether the price jumps are market-wide or idiosyncratic. Firms’ volatility levels strongly explain the cross-section of discontinuous leverage while debt-to-equity ratios have no significant explanatory power.

Systematic Cojumps, Market Component Portfolios and Scheduled Macroeconomic Announcements,

This study provides evidence of common bivariate jumps (i.e., systematic cojumps) between the market index and style-sorted portfolios. Systematic cojumps are prevalent in book-to-market portfolios and hence, their risk cannot easily be diversified away by investing in growth or value stocks. Nonetheless, large-cap firms have less exposure to systematic cojumps than small-cap firms. Probit regression reveals that systematic cojump occurrences are significantly associated with worse-than-expected scheduled macroeconomic announcements, especially those pertaining to the Federal Funds target rate. Tobit regression shows that Federal Funds news surprises are also significantly related to the magnitude of systematic cojumps.

Nonlinearities, Smoothing and Countercyclical Monetary Policy

Empirical analysis of the Fed’s monetary policy behavior suggests that the Fed smooths interest rates— that is, the Fed moves the federal funds rate target in several small steps instead of one large step with the same magnitude. We evaluate the effect of countercyclical policy by estimating a Vector Autoregression (VAR) with regime switching. Because the size of the policy shock is important in our model, we can evaluate the effect of smoothing the interest rate on the path of macro variables. Our model also allows for variation in transition probabilities across regimes, depending on the level of output growth. Thus, changes in the stance of monetary policy affect the macroeconomic variables in a nonlinear way, both directly and indirectly through the state of the economy. We also incorporate a factor summarizing overall sentiment into the VAR to determine if sentiment changes substantially around turning points and whether they are indeed important to understanding the effects of policy.

Estimating Border Effects: the Impact of Spatial Aggregation

Trade data are typically reported at the level of regions or countries and are therefore aggregates across space. In this paper, we investigate the sensitivity of standard gravity estimation to spatial aggregation. We build a model in which initially symmetric micro regions are combined to form aggregated macro regions. We then apply the model to the large literature on border effects in domestic and international trade. Our theory shows that larger countries are systematically associated with smaller border effects. The reason is that due to spatial frictions, aggregation across space increases the relative cost of trading within borders. The cost of trading across borders therefore appears relatively smaller. This mechanism leads to border effect heterogeneity and is independent of multilateral resistance effects in general equilibrium. Even if no border frictions exist at the micro level, gravity estimation on aggregate data can still produce large border effects. We test our theory on domestic and international trade flows at the level of U.S. states. Our results confirm the model’s predictions, with quantitatively large effects.

Real-Time Forecasting with a Large, Mixed Frequency, Bayesian VAR

We assess point and density forecasts from a mixed-frequency vector autoregression (VAR) to obtain intra-quarter forecasts of output growth as new information becomes available. The econometric model is specified at the lowest sampling frequency; high frequency observations are treated as different economic series occurring at the low frequency. We impose restrictions on the VAR to account explicitly for the temporal ordering of the data releases. Because this type of data stacking results in a high-dimensional system, we rely on Bayesian shrinkage to mitigate parameter proliferation. The relative performance of the model is compared to forecasts from various time-series models and the Survey of Professional Forecaster''s. We further illustrate the possible usefulness of our proposed VAR for causal analysis.

A State-Level Analysis of Okun's Law

Okun''s law is an empirical relationship that measures the correlation between the deviation of the unemployment rate from its natural rate and the deviation of output growth from its potential. This relationship is often referred to by policy makers and used by forecasters. In this paper, we estimate Okun''s coefficients separately for each U.S. state using an unobserved components framework and find variation of the coefficients across states. We exploit this heterogeneity of Okun''s coefficients to directly examine the potential factors that shape Okun''s law, and find that indicators of more flexible labor markets (higher levels of education achievement in the population, lower rate of unionization, and a higher share of non-manufacturing employment) are important determinants of the differences in Okun''s coefficient across states.

Tests of Equal Accuracy for Nested Models with Estimated Factors

In this paper we develop asymptotics for tests of equal predictive ability between nested models when factor-augmented regression models are used to forecast. We provide conditions under which the estimation of the factors does not affect the asymptotic distributions developed in Clark and McCracken (2001) and McCracken (2007). This enables researchers to use the existing tabulated critical values when conducting inference despite the presence of estimated predictors. As an intermediate result, we derive the asymptotic properties of the principal components estimator over recursive windows. We provide simulation evidence on the finite sample effects of factor estimation and apply the tests to the case of forecasting excess returns to the S&P 500 Composite Index.

The Evolution of Scale Economies in U.S. Banking

Continued consolidation of the U.S. banking industry and a general increase in the size of banks has prompted some policymakers to consider policies that discourage banks from getting larger, including explicit caps on bank size. However, limits on the size of banks could entail economic costs if they prevent banks from achieving economies of scale. This paper presents new estimates of returns to scale for U.S. banks based on nonparametric, local-linear estimation of bank cost, revenue and profit functions. We report estimates for both 2006 and 2015 to compare returns to scale some seven years after the financial crisis and five years after enactment of the Dodd-Frank Act with returns to scale before the crisis. We find that a high percentage of banks faced increasing returns to scale in cost in both years, including most of the 10 largest bank holding companies. And, while returns to scale in revenue and profit vary more across banks, we find evidence that the largest four banks operate under increasing returns to scale.

Estimation of Dynastic Life-Cycle Discrete Choice Models

This paper explores the estimation of a class of life-cycle discrete choice intergenerational models. It proposes a new semiparametric estimator. It shows that it is root-n-consistent and asymptotically normally distributed. We compare our estimator with a modified version of the full solution maximum likelihood estimator (MLE) in a Monte Carlo study. Our estimator performs comparably to the MLE in a finite sample but greatly reduces the computational cost. The paper documents that the quantity-quality trade-offs depend on the household composition and specialization in the household. Using the proposed estimator, we estimate a dynastic model that rationalizes these observed patterns.

What Accounts for the Racial Gap in Time Allocation andIntergenerational Transmission of Human Capital?

This paper analyzes the sources of the racial difference in the intergenerational transmission of human capital by developing and estimating a dynastic model of parental time and monetary inputs in early childhood with endogenous fertility, home hours, labor supply, marriage, and divorce. It finds that the racial differences in the marriage matching patterns lead to racial differences in labor supply and home hours of couples. Although both the black-white labor market earnings and marriage market gaps are important sources of the black-white achievement gap, the assortative mating and divorce probabilities racial gaps accounts for a larger fraction of it.

Was Sarbanes-Oxley Costly? Evidence from Optimal Contracting on CEO Compensation.

This paper investigates the effects of the Sarbanes-Oxley Act (SOX) on CEO compensation, using panel data constructed for the S&P 1500 firms on CEO compensation, financial returns, and reported accounting income. Empirically SOX (i) changes the relationship between a firm’s abnormal returns and CEO compensation, (ii) changes the underlying distribution of abnormal returns, and (iii) significantly raises the expected CEO compensation in the primary sector. We develop and estimate a dynamic principal agent model of hidden information and hidden actions to explain these regularities. We find that SOX (i) increased the administrative burden of compliance in the primary sector, but reduce this burden in the service sector, (ii) increased agency costs in most categories of the firms, and (iii) reduced the off-equilibrium loss from the CEO shirking.

On the Need for a Replication Journal

There is very little replication of research in economics, particularly compared with other sciences. This paper argues that there is a dire need for studies that replicate research, that their scarcity is due to poor or negative rewards for replicators, and that this could be improved with a journal that exclusively publishes replication studies. I then discuss how such a journal could be organized, in particular in the face of some negative rewards some replication studies may elicit.

FRED-MD: A Monthly Database for Macroeconomic Research

This paper describes a large, monthly frequency, macroeconomic database with the goal of establishing a convenient starting point for empirical analysis that requires "big data." The dataset mimics the coverage of those already used in the literature but has three appealing features. First, it is designed to be updated monthly using the FRED database. Second, it will be publicly accessible, facilitating comparison of related research and replication of empirical work. Third, it will relieve researchers from having to manage data changes and revisions. We show that factors extracted from our dataset share the same predictive content as those based on various vintages of the so-called Stock-Watson dataset. In addition, we suggest that diffusion indexes constructed as the partial sum of the factor estimates can potentially be useful for the study of business cycle chronology.

Metro Business Cycles

We construct monthly economic activity indices for the 50 largest U.S. metropolitan statistical areas (MSAs) beginning in 1990. Each index is derived from a dynamic factor model based on twelve underlying variables capturing various aspects of metro area economic activity. To accommodate mixed-frequency data and differences in data-publication lags, we estimate the dynamic factor model using a maximum-likelihood approach that allows for arbitrary patterns of missing data. Our indices highlight important similarities and differences in business cycles across MSAs. While a number of MSAs experience sizable recessions during the national recessions of the early 1990s and early 2000s, other MSAs escape recessions altogether during one or both of these periods. Nearly all MSAs suffer relatively deep recessions near the recent Great Recession, but we still find significant differences in the depth of recent metro recessions. We relate the severity of metro recessions to a variety of MSA characteristics and find that MSAs with less-educated populations and less elastic housing supplies experience significantly more severe recessions. After controlling for national economic activity, we also find significant evidence of dynamic spillover effects in economic activity across MSAs.

The role of jumps in volatility spillovers in foreign exchange markets: meteor showers and heat waves revisited

This paper extends the literature on geographic (heat waves) and intertemporal (meteor showers) foreign exchange volatility transmission to characterize the role of jumps and cross rate propagation. We employ multivariate heterogeneous autoregressive (HAR) models to capture the quasi-long memory properties of volatility and both Shapley-Owen R2s and portfolio optimization exercises to quantify the contributions of information sets. We conclude that meteor showers (MS) are substantially more influential than heat waves (HW), that jumps play a modest but significant role in volatility transmission, that cross market propagation of volatility is important, and that allowing for differential HW and MS effects and differential parameters across intraday market segments is valuable. Finally, we illustrate what types of news weaken or strengthen heat wave, meteor shower, continuous and jump patterns with sensitivity analysis.

Can risk explain the profitability of technical trading in currency markets?

Academic studies show that technical trading rules would have earned substantial excess returns over long periods in foreign exchange markets. However, the approach to risk adjustment has typically been rather cursory. We examine the ability of a wide range of models: CAPM, quadratic CAPM, downside risk CAPM, C‐CAPM, Carhart’s 4‐factor model, an extended C‐CAPM with durable consumption, Lustig‐Verdelhan (LV) factors, volatility, skewness and liquidity to explain these technical trading returns. No model plausibly accounts for technical profitability in the foreign exchange market.

Tests Of Predictive Ability For Vector Autoregressions Used For Conditional Forecasting

Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments. Even though conditional forecasting is common, there has been little work on methods for evaluating conditional forecasts. This paper provides analytical, Monte Carlo, and empirical evidence on tests of predictive ability for conditional forecasts from estimated models. In the empirical analysis, we consider forecasts of GDP and investment growth as well as inflation from a VAR, based on conditions on the short-term interest rate. Throughout the analysis, we focus on tests of bias, efficiency, and equal accuracy applied to conditional forecasts from VAR models.

Financial Stress Regimes and the Macroeconomy

Some financial stress events lead to macroeconomic downturns, while others appear to be isolated to financial markets. We identify financial stress regimes using a model that explicitly links …financial variables to macroeconomic outcomes. The stress regimes are identified using an unbalanced panel of …financial variables with an embedded method for variable selection. Our identified stress regimes are associated with corporate credit tightening and with NBER recessions. An exogenous deterioration in our …financial condition index has strong negative effects in economic activity, and negative amplification effects on inflation in the stress regime. We employ a novel factor-augmented vector autoregressive model with smooth regime changes (FAST-VAR).

How Has Emprical Monetary Policy Analysis Changed After the Financial Crisis?

In the wake of the Great Recession, the Federal Reserve lowered the federal funds rate (FFR) target essentially to zero and resorted to unconventional monetary policy. With the nominal FFR constrained by the zero lower bound (ZLB) for an extended period, empirical monetary models cannot be estimated as usual. In this paper, we consider whether the standard empirical model of monetary policy can be preserved without breaks. We consider whether alternative policy instruments (e.g., a long-term interest rate) can be considered substitutes for the FFR over the ZLB period. Furthermore, we compare the shadow rates proposed in Krippner [2012] and Wu and Xia [2016] as alternative measures of the stance of monetary policy. We ask whether the shadow rate is a sufficient representation of the policy instrument or if the financial crisis requires other modifications. We find that, when using a dataset that spans both the pre-ZLB and ZLB periods, the shadow rate acts as a fairly good proxy for monetary policy by producing impulse responses of macro indicators similar to what we’d expect based on the post-WWII, non-ZLB benchmark and by displaying stable parameter estimates when compared to this benchmark.

Risk Aversion at the Country Level

In this paper the authors estimate the coefficient of relative risk aversion for 75 countries using data on self-reports of personal well-being from the Gallup World Poll. Their analysis suggests that the coefficient of relative risk aversion varies closely around one, which corresponds to a logarithmic utility function. The authors conclude that their results support the use of the log utility function in numerical simulations.

How Persistent are Monetary Policy Effects at the Zero Lower Bound?

Event studies show that the Federal Reserve’s announcements of forward guidance and large-scale asset purchases had large and desired effects on asset prices but these studies do not tell us how long such effects last. Wright (2012) used a structural vector autoregression (SVAR) to argue that unconventional policies have very transient effects on bond yields, with half-lives of 3 to 6 months. The present paper shows, however, that this inference is unsupported for several reasons. First, accounting for model uncertainty greatly lengthens the estimated persistence. Second, and more seriously, the inference is unreliable because the SVAR is structurally unstable and forecasts very poorly. Finally, the implied in-sample return predictability from the SVAR greatly exceeds a level consistent with rational asset pricing and reasonable risk aversion. Restricted models that respect more plausible asset return predictability are more stable and imply that unconventional monetary policy shocks were fairly persistent. Estimates of the dynamic effects of shocks should respect the limited predictability in asset prices.

Countercyclical Policy and the Speed of Recovery After Recessions

We consider the effect of some policies intended to shorten recessions and accelerate recoveries. Our innovation is to analyze the duration of the recoveries of various U.S. states, which gives us a cross-section of both state- and national-level policies. Because we study multiple recessions for the same state and multiple states for the same recession, we can control for differences in the economic conditions preceding recessions and the causes of the recessions when evaluating various policies. We find that expansionary monetary policy at the national level helps to stimulate the exit of individual states from recession. We …find that exogenous measures of decreases in taxes or targeted increases in federal spending reduce recovery times for state-recessions. We also …find ambient economic conditions can extend expected recovery times: other states in the same region suffering from recession around the same time, the length of the preceding recession, and increases in oil prices.

Which Continuous-time Model Is Most Appropriate For Exchange Rates?

This paper evaluates the most appropriate ways to model diffusion and jump features of high-frequency exchange rates in the presence of intraday periodicity in volatility. We show that periodic volatility distorts the size and power of conventional tests of Brownian motion, jumps and (in)finite activity. We propose a correction for periodicity that restores the properties of the test statistics. Empirically, the most plausible model for 1-minute exchange rate data features Brownian motion and both finite activity and infinite activity jumps. Test rejection rates vary over time, however, indicating time variation in the data generating process. We discuss the implications of results for market microstructure and currency option pricing.

Conflict, Evolution, Hegemony, and the Power of the State

In a model of evolution driven by conflict between societies more powerful states have an advantage. When the influence of outsiders is small we show that this results in a tendency to hegemony. In a simple example in which institutions differ in their “exclusiveness” we find that these hegemonies will be inefficiently “extractive” in the sense of having inefficiently high taxes, high compensation for state officials, and low welfare.

Frictionless Technology Diffusion: The Case of Tractors

Many new technologies display long adoption lags, and this is often interpreted as evidence of frictions inconsistent with the standard neoclassical model. In this paper we study the diffusion of the tractor in American agriculture between 1910 and 1960 ─ a well known case of slow diffusion ─ and show that the speed of adoption was consistent with the predictions of a simple neoclassical growth model. The reason for the slow rate was that tractor quality kept improving over this period and, more importantly, that only when wages increased did it become relatively unprofitable to operate the alternative, labor-intensive, horse technology.

Clustered Housing Cycles

Using a panel of U.S. city-level building permits data, we estimate a Markov-switching model of housing cycles that allows cities to systematically deviate from the national housing cycle. These deviations occur for clusters of cities that experience simultaneous housing contractions. We find that cities do not form housing regions in the traditional geographic sense. Instead, similarities in factors affecting the demand for housing (such as population growth or availability of credit) appear to be more important determinants of cyclical co-movements than similarities in factors affecting the supply for land (such as the availability of developable land or the elasticity of land supply).

Nonlinear Relationships Between Permanent and Transitory Components of Monetary Aggregates and the Economy

This paper uses several methods to study the interrelationship among Divisia monetary aggregates, prices, and income, allowing for nonstationary, nonlinearities, asymmetries, and time-varying relationships among the series. We propose a multivariate regime switching unobserved components model to obtain transitory and permanent components for each series, allowing for potential recurrent and structural changes in their dynamics. Each component follows distinct two-state Markov processes representing low or high phases. Since the lead-lag relationship between the phases can vary over time, rather than preimposing a structure to their linkages, the proposed flexible framework enables us to study their specific lead-lag relationship over each one of their cycles and over each U.S. recession in the last 40 years. The decomposition of the series into permanent and transitory components reveals striking results. First, we find a strong nonlinear association between the components of money and prices – all low phases of the transitory component of prices were preceded by tight transitory and permanent money phases. We also find that most recessions were preceded by tight money phases (its cyclical and permanent components) and high transitory price phases (with the exception of the 2001 and 2009-2010 recessions). In addition, all recessions were associated with a decrease in transitory and permanent income.


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