On Variance Bounds for Asset Price Changes
Forthcoming in Journal of Financial Markets
This paper considers variance bounds for stock price changes in a general setting that allows for ex-dividend stock prices, risk averse investors, and exponentially-growing dividends. I show that providing investors with more information about future dividends can either increase or decrease the variance of stock price changes, depending on key parameters, namely, those governing the properties of dividends and the stochastic discount factor. This finding contrasts with the results of Engel (2005) who shows that news about future dividends will always decrease the variance of stock price changes in a specialized setting with cum-dividend stock prices and risk neutral investors.
Asset Pricing with Concentrated Ownership of Capital and Distribution Shocks
Forthcoming in American Economic Journal – Macroeconomics
This paper develops a production-based asset pricing model with two types of agents and concentrated ownership of physical capital. A temporary but persistent “distribution shock” causes the income share of capital owners to fluctuate in a procyclical manner, consistent with U.S. data. The concentrated ownership model significantly magnifies the equity risk premium relative to a representative-agent model because the capital owners’ consumption is more-strongly linked to volatile dividends from equity. With a steady-state risk aversion coefficient around 4, the model delivers an unlevered equity premium of 3.9 percent relative to short-term bonds and a premium of 1.2 percent relative to long-term bonds.
Discussion of: “Explaining House Price Dynamics: Isolating the Role of Non-Fundamentals”
Journal of Money Credit and Banking 47 (S1), March 2015, 127-132
House Prices, Expectations, and Time-Varying Fundamentals
Journal of Empirical Finance 29, 2014, 3-25 | With Gelain
We investigate the behavior of the equilibrium price-rent ratio for housing in a standard asset pricing model and compare the model predictions to empirical evidence from surveys on the return expectations of real-world housing investors. We allow for time-varying risk aversion (via external habit formation) and time-varying persistence and volatility in the stochastic process for rent growth, consistent with U.S. data for the period 1960 to 2013. Under fully-rational expectations, the model significantly underpredicts the volatility of the U.S. price-rent ratio for reasonable levels of risk aversion. We demonstrate that the model can approximately match the volatility of the price-rent ratio in the data if near-rational agents continually update their estimates for the mean, persistence and volatility of fundamental rent growth using only recent data (i.e., the past 4 years), or if agents employ a simple moving-average forecast rule for the price-rent ratio that places a large weight on the most recent observation. These two versions of the model can be distinguished by their predictions for the correlation between expected future returns on housing and the price-rent ratio. Only the moving-average model predicts a positive correlation such that agents tend to expect higher future returns when prices are high relative to fundamentals—a feature that is consistent with a wide variety of survey evidence from real estate and stock markets.
Risk Aversion, Investor Information, and Stock Market Volatility
European Economic Review 70, August 2014, 88-107 | With LeRoy
This paper employs a standard asset pricing model to derive theoretical volatility measures in a setting that allows for varying degrees of investor information about the dividend process. We show that the volatility of the price-dividend ratio increases monotonically with investor information but the relationship between investor information and equity return volatility (or equity premium volatility) can be non-monotonic, depending on risk aversion and other parameter values. Under some plausible calibrations and information assumptions, we show that the model can match the standard deviations of equity market variables in long-run U.S. data. In the absence of concrete knowledge about investors’ information, it becomes more difficult to conclude that observed volatility in the data is excessive.
Housing Bubbles and Expected Returns to Home Ownership: Lessons and Policy Implications (with M. Jurgilas)
In Property Prices and Real Estate Financing in a Turbulent World, ed. by M. Balling and J. Berg | Société Universitaire Européenne de Recherches Financières (SUERF), 2013. pp. 101-128 | With Jurgilas
House prices in many industrial countries increased dramatically in the years prior to 2007. Countries with the largest increases in household debt relative to income experienced the fastest run-ups in house prices over the same period. During the run-up, many economists and policymakers maintained that U.S. housing market trends could be explained by fundamentals. But in retrospect, studies now mostly attribute events to a classic bubble driven by over-optimistic projections about future house prices which, in turn, led to a collapse in lending standards. A common feature of all bubbles which complicates the job of policymakers is the emergence of seemingly plausible fundamental arguments that seek to justify the dramatic rise in asset prices. A comparison of the U.S. housing market experience with ongoing housing market trends in Norway once again poses the question of whether a bubble can be distinguished from a rational response to fundamentals. Survey evidence on people’s expectations about future house prices can be a useful tool for diagnosing a bubble. In light of the severe economic fallout from the recent financial crisis, central bank views on the use of monetary policy to lean against bubbles appear to be shifting.
Monetary Policy and Asset Prices with Belief Driven Fluctuations
Journal of Economic Dynamics and Control 37, August 2013, 1453-1478 | With Airaudo and Cardani
We present a heterogeneous agents New-Keynesian model subject to a cost channel of monetary policy transmission. Constant turnover between long-time traders and newcomers in market activities, combined with restricted trading opportunities, introduces a feedback from the stock market to real activity, making stock prices non-redundant for the business cycle. We show that strict inflation targeting can lead to equilibrium indeterminacy, even if the policy rule satisfies the Taylor principle. A belief-driven shock to stock price generates relative volatilities of key financial variables which are very close to what is observed in U.S. data. This result hints to the possibility that the financial instability witnessed since the mid-to-late 1990s was the result of waves of (rational) exuberance and pessimism in financial markets. Our analysis suggests that a mild response to stock prices in the central bank’s policy rule can restore equilibrium determinacy and therefore rule out non-fundamental volatility.
House Prices, Credit Growth, and Excess Volatility: Implications for Monetary and Macroprudential Policy
International Journal of Central Banking 9(2), June 2013, 219-276 | With Gelain and Mendicino
Progress on the question of whether policymakers should respond directly to financial variables requires a realistic economic model that captures the links between asset prices, credit expansion, and real economic activity. Standard DSGE models with fully-rational expectations have difficulty producing large swings in house prices and household debt that resemble the patterns observed in many developed countries over the past decade. We introduce excess volatility into an otherwise standard DSGE model by allowing a fraction of households to depart from fully-rational expectations. Specifically, we show that the introduction of simple moving-average forecast rules for a subset of households can significantly magnify the volatility and persistence of house prices and household debt relative to otherwise similar model with fully-rational expectations. We evaluate various policy actions that might be used to dampen the resulting excess volatility, including a direct response to house price growth or credit growth in the central bank’s interest rate rule, the imposition of more restrictive loan-to-value ratios, and the use of a modified collateral constraint that takes into account the borrower’s loan-to-income ratio. Of these, we find that a loan-to-income constraint is the most effective tool for dampening overall excess volatility in the model economy. We find that while an interest-rate response to house price growth or credit growth can stabilize some economic variables, it can significantly magnify the volatility of others, particularly inflation.
Speculative Growth, Overreaction, and the Welfare Cost of Technology-Driven Bubbles
Journal of Economic Behavior and Organization (Special Issue on Financial Crisis) 83, August 2012, 461-483
This paper develops a general equilibrium model to examine the quantitative effects of speculative bubbles on capital accumulation, growth, and welfare. A near-rational bubble component in the model equity price generates excess volatility in response to observed technology shocks. In simulations, intermittent equity price run-ups coincide with positive innovations in technology, investment and consumption booms, and faster trend growth, reminiscent of the U.S. economy during the late 1920s and late 1990s. The welfare cost of speculative bubbles depends crucially on parameter values. Bubbles can improve welfare if risk aversion is low and agents underinvest relative to the socially-optimal level. But for higher levels of risk aversion, the welfare cost of bubbles is large, typically exceeding one percent of annual consumption.
Rational and Near-Rational Bubbles without Drift
Economic Journal 120, December 2010, 1149-1174
This paper derives a general class of intrinsic rational bubble solutions in a Lucas-type asset pricing model. I show that the rational bubble component of the price-dividend ratio can evolve as a geometric random walk without drift, such that the mean of the bubble growth rate is zero. Driftless bubbles are part of a continuum of equilibrium solutions that satisfy a period-by-period no-arbitrage condition. I also derive a near-rational solution in which the agent’s forecast rule is under-parameterized. The near-rational solution generates intermittent bubbles and other behavior that is quantitatively similar to that observed in long-run U.S. stock market data.
Capital-Labor Substitution and Equilibrium Indeterminacy
Journal of Economic Dynamics and Control 33, December 2009, 1991-2000 | With Guo
This paper examines the quantitative relationship between the elasticity of capital-labor substitution in production and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector growth model. With variable capital utilization, the substitution elasticity has little quantitative impact on the minimum degree of increasing returns needed for indeterminacy. However, when capital utilization is constant, a below-unity substitution elasticity sharply raises the minimum degree of increasing returns because it imposes a higher effective adjustment cost on labor hours. Overall, our results show that empirically-plausible departures from the Cobb-Douglas production specification can make indeterminacy more difficult to achieve.
Speculative Bubbles and Overreaction to Technological Innovation
Journal of Financial Transformation 26, September 2009, 51-54
“Nowhere does history indulge in repetitions so often or so uniformly as in Wall Street,” observed legendary speculator Jesse Livermore. History tells us that periods of major technological innovation are typically accompanied by speculative bubbles as economic agents overreact to genuine advancements in productivity. Excessive run-ups in asset prices can have important consequences for the economy as firms and investors respond to the price signals, resulting in capital misallocation. On the one hand, speculation can magnify the volatility of economic and financial variables, thus harming the welfare of those who are averse to uncertainty and fluctuations. But on the other hand, speculation can increase investment in risky ventures, thus yielding benefits to a society that suffers from an underinvestment problem.
Time Varying U.S. Inflation Dynamics and the New Keynesian Phillips Curve
Review of Economic Dynamics 12(2), April 2009, 304-326
This paper introduces a form of boundedly-rational inflation expectations in the New Keynesian Phillips curve. The representative agent is assumed to behave as an econometrician, employing a time series model for inflation that allows for both permanent and temporary shocks. The near-unity coefficient on expected inflation in the Phillips curve causes the agent’s perception of a unit root in inflation to become close to self-fulfilling. In a “consistent expectations equilibrium,” the value of the Kalman gain parameter in the agent’s forecast rule is pinned down using the observed autocorrelation of inflation changes. The forecast errors observed by the agent are close to white noise, making it difficult for the agent to detect a misspecification of the forecast rule. I show that this simple model of inflation expectations can generate time-varying persistence and volatility that is broadly similar to that observed in long-run U.S. data. Model-based values for expected inflation track well with movements in survey-based measures of U.S. expected inflation. In numerical simulations, the model can generate pronounced low-frequency swings in the level of inflation that are driven solely by expectational feedback, not by changes in monetary policy.
Maintenance Expenditures and Indeterminacy under Increasing Returns to Scale
International Journal of Economic Theory 3(2), June 2007, 147-158 | With Guo
This paper develops a one-sector real business cycle model in which competitive firms allocate resources for the production of goods, investment in new capital and maintenance of existing capital. Firms also choose the utilization rate of existing capital. A higher utilization rate leads to faster capital depreciation, and an increase in maintenance activity has the opposite effect. We show that as the equilibrium ratio of maintenance expenditures to GDP rises, the required degree of increasing returns for local indeterminacy declines over a wide range of parameter combinations. When the model is calibrated to match empirical evidence on the relative size of maintenance and repair activity, we find that local indeterminacy (and belief-driven fluctuations) can occur with a mild and empirically-plausible degree of increasing returns: approximately 1.08.
Tax Reform with Useful Public Expenditures
Journal of Public Economic Theory 8(4), October 2006, 631-676 | With Cassou
This paper examines the economic effects of tax reform in an endogenous growth model that allows for two types of useful public expenditures; one type contributes to human capital formation while the other provides direct utility to households. We show that the optimal fiscal policy calls for full expensing of private investments, which shifts the tax base to private consumption. The efficient levels of public investment and public consumption relative to output are uniquely pinned down by parameters that govern both technology and preferences. In general, implementing the optimal fiscal policy requires a change in the size of government. If a tax reform holds the size of government fixed to satisfy a revenue-neutrality constraint, then the reform will be suboptimal; theory alone cannot tell us if welfare will be improved. For some calibrations of the model, we find that commonly proposed versions of revenue-neutral tax reforms can result in large welfare gains. For other quite plausible calibrations, the exact same reform can result in tiny or even negative welfare gains as the revenue-neutrality constraint becomes more severely binding. Comparing across calibrations, we find that the welfare rankings of various reforms can change, depending on parameter values. Overall, our results highlight the uncertainty surrounding the potential welfare benefits of fundamental U.S. tax reform.
Lock-in of Extrapolative Expectations in an Asset Pricing Model
Macroeconomic Dynamics 10(3), June 2006, 317-348
This paper examines an agent’s choice of forecast method within a standard asset
pricing model. To make a conditional forecast, a representative agent may choose one
of the following: (1) a rational (or fundamentals-based) forecast that employs knowledge
of the stochastic process governing dividends, (2) a constant forecast based on a simple
long-run average of the forecast variable, or (3) a time-varying forecast that extrapolates
from the last observation of the forecast variable. I show that a representative agent
who is concerned about minimizing forecast errors may inadvertently become “locked in”
to an extrapolative forecast. In particular, the initial use of extrapolation alters the
law of motion of the forecast variable so that the agent perceives no accuracy gain from
switching to one of the alternative forecast methods. Under extrapolative expectations,
the model can generate excess volatility of stock prices, time-varying volatility of returns,
long-horizon predictability of returns, bubbles driven by optimism about the future, and
sharp downward movements in stock prices that resemble market crashes. All of these
features appear to be present in long-run U.S. stock market data.
Inflation-Induced Valuation Errors in the Stock Market
Journal of Financial Transformation 13, April 2005, 124-126
Modigliani and Cohn (1979) put forth a behavioral model that predicted mispricing of stocks in the presence of changing inflation. The comovement of the stock market E/P ratio with the nominal bond yield observed since the mid-1960s (when U.S. inflation started rising) is consistent with the Modigliani-Cohn hypothesis. A regression model that includes a constant term and three nominal variables can account for 70% of the variance in the observed E/P ratio over the past four decades. However, the success of this model in describing investor behavior should not be confused with the model’s ability to forecast what investors should really care about, namely, long-run real returns. Investors of the early 1980s probably did not anticipate the 20-year declining trend of inflation and nominal interest rates that helped produce above-average real returns as stocks moved from a state of undervaluation to one of overvaluation in the manner described by Modigliani and Cohn. Today’s investors may suffer the opposite fate if a secular trend of rising inflation and nominal interest rates causes the stock market to move back towards a state of undervaluation.
Growth Effects of Shifting from a Graduated Rate Tax System to a Flat Tax
Economic Inquiry 42(2), April 2004, 194-213 | With Cassou
We compute the growth effects of adopting a revenue-neutral flat tax for
both a human capital-based endogenous growth model and a standard neoclassical growth model. Long-run growth effects are decomposed into the parts attributable to the flattening of the marginal tax schedule, the full expensing of physical-capital investment, and the elimination of double taxation of business income. The most important element of the reform is the flattening of the marginal tax schedule. Without this element, the combined effects of the other parts of the reform can actually reduce long-run growth. In the years immediately following the reform, the transition dynamics implied by the neoclassical growth model are quite similar to that of the endogenous growth model.
Forward-Looking Behavior and Optimal Discretionary Monetary Policy
Economics Letters 81(2), November 2003, 249-256 | With Trehan
This paper derives a closed-form solution for the optimal discretionary monetary policy in a small macroeconomic model that allows for varying degrees of forward-looking behavior. We show that a more forward-looking
aggregate demand equation serves to attenuate the response to inflation and the output gap in the optimal interest rate rule. In contrast, a more forward-looking real interest rate equation serves to magnify the response to both variables. A more forward-looking Phillips curve serves to attenuate the response to inflation but magnify the response to the output gap. The results have implications for studies that attempt to reconcile estimated versions of the central bank’s policy rule with optimal discretionary monetary policy. In particular, a successful reconciliation is likely to require a different degree of forward-looking behavior in each part of the model economy.
Globally Stabilizing Fiscal Policy Rules
Studies in Nonlinear Dynamics and Econometrics 7(2), April 2003 | With Guo
This paper demonstrates how fiscal policy rules can be designed to eliminate all forms of endogenous fluctuations in a one-sector growth model with increasing returns-to-scale. When the policy rules are implemented, agents’ optimal decisions depend only on the current state of the economy and not on any expected future states. This property shuts down the mechanism for expectations-driven fluctuations. The proposed policy rules ensure a globally unique and stable equilibrium, regardless of the degree of increasing returns.
Fiscal Policy, Increasing Returns, and Endogenous Fluctuations
Macroeconomic Dynamics 6(5), November 2002, 633-664 | With Guo
This paper examines the quantitative implications of government fiscal
policy in a discrete-time one-sector growth model with a productive externality that generates social increasing returns to scale. Starting from a laissez-faire economy that exhibits local indeterminacy, we show that the introduction of a constant capital tax or subsidy can lead to various forms of endogenous fluctuations, including stable 2-, 4-, 8-, and 10-cycles, quasiperiodic orbits, and chaos. In contrast, a constant labor tax or subsidy has no effect on the qualitative nature of the model’s dynamics. We show that the use of local steady-state analysis to detect the presence of multiple equilibria in this class of models can be misleading. For a plausible range of capital tax rates, the log-linearized dynamical system exhibits saddle-point stability, suggesting a unique equilibrium, whereas the true nonlinear model exhibits global indeterminacy. This result implies that stabilization
policies designed to suppress sunspot fluctuations near the steady state may not prevent sunspots, cycles, or chaos in regions away from the steady state. Overall, our results highlight the importance of using a model’s nonlinear equilibrium conditions to fully investigate global dynamics.
Expectations Credibility and Disinflation in a Small Macroeconomic Model
Journal of Economics and Business 51, January 2000, 51-86 | With Huh
We used a version of the Fuhrer-Moore model to study the effects of expectations and central bank credibility on the economy’s dynamic transition path during a disinflation. Simulations were compared under four different specifications of the model which vary according to the way that expectations are formed (rational versus adaptive) and the degree of central bank credibility (full versus partial). The various specifications exhibited qualitatively similar behavior and were able to reasonably approximate the trend movements in U.S. macro variables during the Volcker disinflation of the early 1980s. However, the specification with adaptive expectations/partial credibility was the only one to capture the temporary rise in long-term nominal interest rates observed in U.S. data at the start of the disinflation. We also found that incremental reductions in the output sacrifice ratio were largest at the low end of the credibility range, suggesting that a central bank may face diminishing returns in its efforts to enhance credibility.
Optimal Redistributive Capital Taxation in a Neoclassical Growth Model
Journal of Public Economics 73, 1999, 423-453
This paper provides a counterexample to the simplest version of the redistribution models considered by Judd (1985) in which the government chooses an optimal distortionary tax on capitalists to finance a lump-sum payment to workers. I show that the steady-state optimal tax on capital income is generally non-zero when the capitalists’ utility is logarithmic and the government faces a balanced-budget constraint. With log utility, agents’ optimal decisions depend solely on the current rate of return, not any future rates of return or tax rates. This feature of the economy effectively deprives the government of a useful policy instrument because promises about future tax rates can no longer influence current allocations. When combined with a lack of other suitable policy instruments (such as government bonds), the result is an inability to decentralize the allocations that are consistent with a zero-limiting capital tax. I show that the standard approach to solving the dynamic optimal tax problem yields the wrong answer in this (knife-edge) case because it fails to properly enforce the constraints associated with the competitive equilibrium. Specifically, the standard approach lets in an additional policy instrument through the back door.
Optimal Taxation of Capital Income with Imperfectly Competitive Product Markets
Journal of Economic Dynamics and Control 23, 1999, 967-995 | With Guo
We show that the steady-state optimal tax on capital income can be negative, positive, or zero in a neoclassical growth model that allows for imperfectly competitive product markets. The sign of the optimal tax rate depends crucially on (1) the degree of monopoly power, (2) the extent to which monopoly profits can be taxed, (3) the size of the depreciation allowance, and (4) the magnitude of government expenditures. For an empirically plausible set of parameters, we find that the steady-state optimal capital tax can range between -10 and 22%.
Fiscal Policy and Productivity Growth in the OECD
Canadian Journal of Economics 32, 1999, 1215-1226 | With Cassou
We use a simple endogenous growth model with productive public capital to investigate the degree to which observed fiscal policies in eight OECD countries can account for slowdowns in the growth rates of aggregate labor productivity since 1970. In model simulations, we find that none of the observed public capital policies can generate slowdowns of sufficient magnitude to match those in the data. For most countries in our sample, a simulation that combines the observed public capital policy with the observed tax policy does a better job of accounting for the slowdown than either policy in isolation.
Indeterminacy and Stabilization Policy
Journal of Economic Theory 82, 1998, 481-490 | With Guo
It has been shown that a one-sector real business cycle model with sufficient increasing returns in production may possess an indeterminate steady state that can be exploited to generate business cycles driven by “animal spirits” of agents. This paper shows how an income tax schedule that exhibits a progressivity feature can ensure saddle path stability in such a framework and thereby stabilize the economy against sunspot fluctuations. Conversely, an economy with a flat or regressive tax schedule is more susceptible to indeterminacy.
Optimal Fiscal Policy, Public Capital, and the Productivity Slowdown
Journal of Economic Dynamics and Control 22, 1998, 911-935 | With Cassou
This paper develops a quantitative theoretical model for the optimal provision of public capital. We show that the ratio of public to private capital in the U.S. economy since 1925 evolves in a manner that is broadly consistent with an optimal transition path derived from a simple growth model. The model is used to quantify the conditions under which an increase in the stock of public capital is desirable and to investigate the degree to which nonoptimal fiscal policies can account for the U.S. productivity slowdown.
Optimal Fiscal Policy in a Business Cycle Model with Public Capital
Canadian Journal of Economics 31, 1998, 337-364
This paper analyzes a real business cycle model with optimal tax rates, government borrowing, and productive public capital. A specification that allows for multiple stochastic shocks (to technology and preferences) can reproduce some key features describing the cyclical behavior of postwar U.S. fiscal policy. The optimally chosen policy variables fluctuate substantially over the business cycle, but do not operate like automatic stabilizers.
Welfare, Stabilization, or Growth: A Comparison of Different Fiscal Objectives
In Business Cycles and Macroeconomic Stability, ed. by Hairault, Henin, and Portier | New York: Kluwer Academic Publishers, 1997. 55-78 | With Cassou
This paper investigates a variety of objectives that are commonly used to motivate government fiscal action. These include welfare maximization, stabilization, and growth maximization. The policies are compared on the basis of their implications for welfare, volatility, and growth. We show that stabilization policies can produce welfare levels that are nearly identical to those of welfare maximization policies and that both welfare maximization and stabilization policies yield large welfare gains and modest growth losses relative to growth maximization policies. We also show that there are side issues to stabilization policies. In particular: (1) It is not possible to stabilize all macroeconomic variables simultaneously, even when the number of policy instruments is equal to the number of shocks; (2) stabilizing a particular variable requires increased volatility of some other variable; (3) stabilization requires some flexibility regarding the government’s budget constraint; and, (4) stabilization requires the government to respond in a precise and immediate way to exogenous shocks which hit the economy.
Computable General Equilibrium Models and Monetary Policy Advice
Journal of Money Credit and Banking 27, 1995, 1472-1493 | With Altig and Carlstrom
We develop a computable general equilibrium monetary model to show that models of this type can be used for real-time macroeconomic forecasting. Specifically, we show that the forecast errors that result from our model are comparable to those of the Greenbook projections over the 1984 to 1990 period.