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

Optimal Taxation, Marriage, Home Production, and Family Labor Supply

An empirical approach to optimal income taxation design is developed within an equilibrium collective marriage market model with imperfectly transferable utility. Taxes distort labour supply and time allocation decisions, as well as marriage market outcomes, and the within household decision process. Using data from the American Community Survey and American Time Use Survey, we structurally estimate our model and explore empirical design problems. We consider the optimal design problem when the planner is able to condition taxes on marital status, as in the U.S. tax code, but we allow the schedule for married couples to have an arbitrary form of tax jointness. Our results suggest that the optimal tax system for married couples is characterized by negative jointness, although the welfare gains from this jointness are shown to be quite modest.

Network Search: Climbing the Job Ladder Faster

We introduce an irregular network structure into a model of frictional, on-the-job search in which workers find jobs through their network connections or directly from firms. We show that jobs found through network search have wages that stochastically dominate those found through direct contact. In irregular networks, heterogeneity in the worker''s position within the network leads to heterogeneity in wage and employment dynamics: better-connected workers climb the job ladder faster. Despite this rich heterogeneity from the network structure, the mean-field approach allows the problem of our workers to be formulated tractably and recursively. We then calibrate a quantitative version of our mechanism, showing it is consistent with several empirical findings regarding networks and labor markets: jobs found through networks have higher wages and last longer. Finally, we present new evidence consistent with our model that job-to-job switches at higher rungs of the ladder are more likely to use networks.

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.

The Postwar Conquest of the Home Ownership Dream

Post-World War II witnessed the largest housing boom in recent history. This paper develops a quantitative equilibrium model of tenure choice to analyze the key determinants in the co-movement between home-ownership and house prices over the period 1940-1960. The parameterized model matches key features and is capable of accounting for the observed housing boom. The key driver in understanding this boom is an asymmetric productivity change that favors the goods sector relative to the construction sector. Other factors such as demographics, income risk, and government policy are important determinants of the homeownership rate but have small effect on house prices.

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 symmetric micro regions are aggregated into macro regions. We then apply the model to the large literature on border effects in domestic and international trade. Our theory shows that aggregation leads to border effect heterogeneity. Larger regions or countries are systematically associated with smaller border effects. The reason is that due to spatial frictions, aggregation across space increases the cost of trading within borders. The cost of trading across borders therefore appears relatively smaller. We call this mechanism the spatial attenuation effect. Even if no border frictions exist at the micro level, gravity estimation can still produce large border effects. We test our theory with trade flows at the level of U.S. states. Our results confi rm the model's predictions, with quantitatively strong heterogeneity patterns.

Revisiting Gertler-Gilchrist Evidence on the Behavior of Small and Large Firms

Gertler and Gilchrist (1994) provide seminal evidence for the prevailing view that adverse shocks are propagated via credit constraints: small firms are affected more during tight credit periods than large firms. Under this view, the deep recession that followed the 2008 financial crisis is often interpreted as the propagation of the initial “credit shock.” Following Gertler and Gilchrist (1994)’s methodology, we study the behavior of small and large firms during the episodes of credit disruption and extend the analysis to the 2008 financial crisis and NBER-dated recessions. We find that large firms'' short-term debt and sales contracted relatively more than those of small firms during the 2008 financial crisis and during most recessions since 1969. These results, which we show are robust to changes in the business cycle dating procedure, suggest that an alternative view may be needed to understand the prolonged recession following the 2008 financial crisis.

Local and Aggregate Fiscal Policy Multipliers

In this paper, we estimate the effect of defense spending on the U.S. macroeconomy since World War II. First, we construct a new panel dataset of state-level federal defense contracts. Second, we sum observations across states and, using the resulting time series, estimate the aggregate effect of defense spending on national income and employment via instrumental variables. Third, we estimate local multipliers using the state-level data, which measures the relative effect on economic activity due to relative differences in defense spending across states. Comparing the aggregate and local multiplier estimates, we find that the two deliver similar results, providing a case in which local multiplier estimates may be reliable indicators of the aggregate effects of fiscal policy. We also estimate spillovers using interstate commodity flow data and find some evidence of small positive spillovers, which explain part of the (small) difference between the estimated local and aggregate multipliers. Across a wide range of specifications, we estimate income and employment multipliers between zero and 0.5. We reconcile this result with the greater-than-one multipliers found in Nakamura and Steinsson (2014) by analyzing the impact of the Korean War episode in the estimation.

In this paper we derive a new measure of openness—trade potential index—that quantifies the potential gains from trade as a simple function of data. Using a standard multi-country trade model, we measure openness by a country’s potential welfare gain from moving to a world with frictionless trade. In this model, a country’s trade potential depends on only the trade elasticity and two observable statistics: the country’s home trade share and its income level. Quantitatively, poor countries have greater potential gains from trade relative to rich countries, while their welfare costs of autarky are similar. This leads us to infer that rich countries are more open to trade. Our trade potential index correlates strongly with estimates of trade costs, while both the welfare cost of autarky and the volume of trade correlate weakly with trade costs. Thus, our measure of openness is informative about the underlying trade frictions.

Terrorism, Trade and Welfare: Some Paradoxes and a Policy Conundrum

We present a standard trade model and show that terrorism can be trade inducing, starting from autarky. In addition, terrorism can be shown to be welfare augmenting for a group of nations. Finally, we present some qualitative conditions that identify when a nation’s trade volume may rise (or fall) in response to a greater incidence of terrorism. Our trade and welfare results point to potential difficulties in international coordination of counterterrorism policy because of terrorism’s differential impact across nations.

Trade and Terrorism: A Disaggregated Approach

This paper constructs a model of trade consequences of terrorism, where firms in trading nations face different costs arising from domestic and transnational terrorism. Using dyadic dataset in a gravity model, we test terrorism’s effects on overall trade, exports, and imports, while allowing for disaggregation by primary commodities and manufacturing goods. While terrorism has little or no influence on trade of primary products, terrorism reduces trade of manufactured goods. This novel finding pinpoints the avenue by which terrorism harms trade and suggests why previous studies that looked at all trade found modest impacts. Moreover, the detrimental effect of transnational terrorism on total manufactured trade, exports, and imports as well as on various classes of manufactured trade is substantially larger than that of domestic terrorism. Generally, this adverse impact is more pronounced for imports than for exports.

Incentive Compatibility as a Nonnegative Martingale

This paper considers a dynamic Mirrleesian economy and decomposes agents'''' lifetime incentive compatibility (IC) constraints into a sequence of temporal ones. We encode the frequency and severeness of these temporal IC constraints by their associated Lagrange multipliers,showing that the accumulation of the Lagrange multipliers on the consumption part is a nonnegative martingale. It is emphasized that, distinct from the extant literature, this martingale property is derived directly from the IC constraints and so is independent of the optimization of the social planning problem. We apply our finding to (i) the characterization of constrained efficient intertemporal wedges in the aggregate, and (ii) the extension of the so-called immiseration to an environment more general than the extant literature.

Long-term Unemployment: Attached and Mismatched?

In this paper, I quantify the contribution of occupation-specific shocks and skills to unemployment duration and its cyclical dynamics. I quantify specific skills using microdata on wages, estimating occupational switching cost as a function of the occupations'' difference in skills. The productivity shocks are consistent with job finding rates by occupation. For the period 1995-2013, the model captures 69.5% of long-term unemployment in the data, while a uniform finding rate delivers only 47.2%. In the Great Recession, the model predicts 72.9% of the long-term unemployment that existed in the data whereas a uniform finding rate would predict 57.8%.

International R&D Spillovers and Asset Prices

We provide new empirical evidence of a relationship between asset prices and trade- Induced international R&D spillovers; in particular, we find that pairs of countries that share more research and development exhibit more highly correlated stock market returns and less volatile exchange rates. We develop an endogenous growth model of innovation and international technology diffusion that accounts for these empirical findings. A calibrated version of the model matches several important asset pricing and quantity moments, which helps explain some of the classical quantity–price puzzles highlighted in the literature on international macroeconomics.

Interlocked Excecutives and Insider Board Members: an Empirical Analysis

This paper asked the question of whether the behavior and compensation of interlocked executives and non-independent board of directors are consistent with the hypothesis of governance problem or whether this problem is mitigated by implicit and market incentives. It then analyzes the role of independent board of directors. Empirically, we cannot reject the hypothesis that executives in companies with a large number of non-independent directors on the board receive the same expected compensation as other executives. In our model, every executive has an incentive to work. Placing more of non-independent directors on the board mitigates gross losses to the firm should any one of them shirk because they monitor each other. It also reduces the net benefits from shirking and increases the gross value of the firm from greater coordination (reflected in the firm’s equity value and thus impounded into its financial returns). Therefore having a greater non-independent director representation on the board create a more challenging signaling problem to solve thereby raising the risk premium. However, giving more votes on the board to non-independent executives fosters better executive working conditions, which in turn offsets the higher risk premium in pay by a lower certainty-equivalent wage in equilibrium. Thus, our estimates undergird a plausible explanation of how large shareholders determine the number of insiders on the board to maximize the expected value of their equity. We then conduct counterfactual policy experiment imposing 50% upper bound on the fraction of insiders on the board and another counterfactual imposing 40% quotas for women on the boards.

Why Are Exchange Rates So Smooth? A Household Finance Explanation

Empirical moments of asset prices and exchange rates imply that pricing kernels have to be almost perfectly correlated across countries. If they are not, observed real exchange rates are too smooth to be consistent with high Sharpe ratios in asset markets. However, the cross- country correlation of macro fundamentals is far from perfect. We reconcile these empirical facts in a two-country stochastic growth model with heterogeneous trading technologies for households and a home bias in consumption. In our model, only a small fraction of households actively participate in international risk sharing by frequently trading domestic and foreign equities. These active traders, who induce high cross-country correlation to the pricing kernels, are the marginal investors in foreign exchange markets. In a calibrated version of our model, we show that this mechanism can quantitatively account for the excess smoothness of exchange rates in the presence of highly volatile pricing kernels and weakly correlated macro fundamentals.

The Sufficient Statistic Approach: Predicting the Top of the Laffer Curve

We provide a formula for the tax rate at the top of the Laffer curve as a function of three elasticities. Our formula applies to static models and to steady states of dynamic models. One of the elasticities that enters our formula has been estimated in the elasticity of taxable income literature. We apply standard empirical methods from this literature to data produced by reforming the tax system in a model economy. We find that these standard methods underestimate the relevant elasticity in models with endogenous human capital accumulation.

This paper examines the impact of the Federal Reserve’s founding on seasonal pressures and contagion risk in the interbank system. Deposit flows among classes of banks were highly seasonal before 1914; amplitude and timing varied regionally. Panics interrupted normal flows as banks throughout the country sought funds from the central money markets simultaneously. Seasonal pressures and contagion risk in the system were lower by the 1920s, when the Fed provided seasonal liquidity and reserves. Panics returned in the 1930s, due in part to shocks from nonmember banks and because the Fed’s decentralized structure hampered a vigorous response to national crises.

Natural Resources and Global Misallocation

Are production factors allocated efficiently across countries? To differentiate misallocation from factor intensity differences, we provide a new methodology to estimate output shares of natural resources based solely on current rent flows data. With this methodology, we construct a new dataset of estimates for the output shares of natural resources for a large panel of countries. In sharp contrast with Caselli and Feyrer (2007), we find a significant and persistent degree of misallocation of physical capital. We also find a remarkable movement toward efficiency during last 35 years, associated with the elimination of interventionist policies and driven by domestic accumulation. Interestingly, when both physical and human capital can be reallocated, capital would often flow from poor to rich countries.

Explaining Cross-Cohort Differences in Life Cycle Earnings

College-educated workers entering the labor market in 1940 experienced a 4-fold increase in their labor earnings between the ages of 25 and 55; in contrast, the increase was 2.6-fold for those entering the market in 1980. For workers without a college education these figures are 3.6-fold and 1.5-fold, respectively. Why are earnings profiles flatter for recent cohorts? We build a parsimonious model of schooling and human capital accumulation on the job, and calibrate it to earnings statistics of workers from the 1940 cohort. The model accounts for 99 percent of the flattening of earnings profiles for workers with a college education between the 1940 and the 1980 cohorts (52 percent for workers without a college education). The flattening in our model results from a single exogenous factor: the increasing price of skills. The higher skill price induces (i) higher college enrollment for recent cohorts and thus a change in the educational composition of workers and (ii) higher human capital at the start of work life for college-educated workers in the recent cohorts, which implies lower earnings growth over the life cycle.

Why has the U.S. black/white earnings gap remained around 40 percent for nearly 40 years? This paper''''s answer consists of a model of skill accumulation and neighborhood formation featuring a trap: Initial racial inequality and racial preferences induce racial segregation and asymmetric skill accumulation choices that perpetuate racial inequality. Calibrated to match the U.S. distribution of race, house prices and earnings across neighborhoods, the model produces one-half of the observed racial earnings gap. Moving the economy from the trap to a racially integrated steady state implies a 15.6 percent welfare gain for black households and a 2.7 percent loss for white households.

Mortgages are long-term loans with nominal payments. Consequently, under incomplete asset markets, monetary policy can affect housing investment and the economy through the cost of new mortgage borrowing and real payments on outstanding debt. These channels, distinct from traditional real rate channels, are embedded in a general equilibrium model. The transmission mechanism is found to be stronger under adjustable- than fixed-rate mortgages. Further, monetary policy shocks affecting the level of the nominal yield curve have larger real effects than transitory shocks, affecting its slope. Persistently higher inflation gradually benefits homeowners under FRMs, but hurts them immediately under ARMs.

Interest Rate Dynamics, Variable-Rate Loan Contracts, and the Business Cycle

The interest rate at which US firms borrow funds has two features: (i) it moves in a countercyclical fashion and (ii) it is an inverted leading indicator of real economic activity: low interest rates forecast booms in GDP, consumption, investment, and employment. We show that a Kiyotaki-Moore model accounts for both properties when business-cycle movements are driven, in a significant way, by animal spirit shocks to credit-financed investment demand. The credit-based nature of such self-fulfilling equilibria is shown to be essential: the dynamic correlation between current loanable funds rate and future aggregate economic activity depends critically on the property that the loan has a variable-rate component. In addition, Bayesian estimation of our benchmark DSGE model on US data 1975-2010 shows that movements in investment driven by animal spirits are quantitatively important and result in a better fit to the data than both standard RBC models and Kiyotaki-Moore type models with unique equilibrium.

We compare methods to measure comovement in business cycle data using multi-level dynamic factor models. To do so, we employ a Monte Carlo procedure to evaluate model performance for different specifications of factor models across three different estimation procedures. We consider three general factor model specifications used in applied work. The first is a single- factor model, the second a two-level factor model, and the third a three-level factor model. Our estimation procedures are the Bayesian approach of Otrok and Whiteman (1998), the Bayesian state space approach of Kim and Nelson (1998) and a frequentist principal components approach. The latter serves as a benchmark to measure any potential gains from the more computationally intensive Bayesian procedures. We then apply the three methods to a novel new dataset on house prices in advanced and emerging markets from Cesa-Bianchi, Cespedes, and Rebucci (2015) and interpret the empirical results in light of the Monte Carlo results.

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.

Nominal Exchange Rate Determinacy under the Threat of Currency Counterfeiting

We study the endogenous choice to accept fiat objects as media of exchange and their implications for nominal exchange rate determination. We consider a two-country environment with two currencies which can be used to settle any transactions. However, currencies can be counterfeited at a fixed cost and the decision to counterfeit is private information. This induces equilibrium liquidity constraints on the currencies in circulation. We show that the threat of counterfeiting can pin down the nominal exchange rate even when the currencies are perfect substitutes, thus breaking the Kareken-Wallace indeterminacy result. When the two currencies are not perfect substitutes, an international currency can exist whereby one country has two currencies circulating while the other country uses only one. We also find that with appropriate fiscal policies we can enlarge the set of monetary equilibria with determinate nominal exchange rates. Finally, we show that the threat of counterfeiting can also help determine nominal exchange rates in a variety of different trading environments.

Stabilization Policy at the Zero Lower Bound

We construct a monetary economy in which agents face aggregate demand shocks and hetero- generous idiosyncratic preference shocks. We show that, even when the Friedman rule is the best interest rate policy, not all agents are satiated at the zero lower bound. Thus, quantitative easing can be welfare improving since it temporarily relaxes the liquidity constraint of some agents, without harming others. Moreover, due to a pricing externality, quantitative easing may also have beneficial general equilibrium effects for the unconstrained agents. Lastly, our model suggests that it can be optimal for the central bank to buy private debt claims instead of government debt.

Local Fiscal Multipliers, Negative Spillovers and the Macroeconomy

This paper analyzes the impact of within-state military spending and national military spending on a state''s employment. I estimate that, while within-state spending increases that state''s employment (i.e., a positive local effect), an increase in national military spending ceteris paribus decreases employment in the state (i.e., a negative spillover effect). The combined local and spillover effects imply an aggregate employment effect that is close to zero. The estimates are consistent with a resource reallocation explanation: Persons take jobs in or move to a state with increased military spending, but they leave when increased out-of-state military spending creates opportunities elsewhere. I find support for this interpretation based on estimates of population changes by demographic groups in response to spending shocks.

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.

Interest on Reserves, Interbank Lending, and Monetary Policy

A two-sector general equilibrium banking model is constructed to study the functioning of a floor system of central bank intervention. Only retail banks can hold reserves, and these banks are also subject to a capital requirement, which creates “balance sheet costs” of holding reserves. An increase in the interest rate on reserves has very different qualitative effects from a reduction in the central bank’s balance sheet. Increases in the central bank’s balance sheet can have redistributive effects, and can reduce welfare. A reverse repo facility at the central bank puts a floor un- der the interbank interest rate, and is always welfare improving. However, an increase in reverse repos outstanding can increase the margin between the interbank interest rate and the interest rate on government debt.