Todd B. Walker

The Great Recession and worldwide financial crisis have exploded fiscal imbalances and brought fiscal policy and inflation to the forefront of policy concerns. Those concerns will only grow as aging populations increase demands on government expenditures in coming decades. It is widely perceived that fiscal policy is inflationary if and only if it leads the central bank to print new currency to monetize deficits. Monetization can be inflationary. But it is a misperception that this is the only channel for fiscal inflations. Nominal bonds, the predominant form of government debt in advanced economies, derive their value from expected future nominal primary surpluses and money creation; changes in the price level can align the market value of debt to its expected real backing. This introduces a fresh channel, not requiring explicit monetization, through which fiscal deficits directly affect inflation. The paper describes various ways in which fiscal policy can directly affect inflation and explains why these fiscal effects are difficult to detect in time series data.

Policy function iteration methods for solving and analyzing dynamic, stochastic general equilibrium models are powerful from both a theoretical and computational perspective. Despite obvious theoretical appeal, significant startup costs and a reliance on grid-based methods have limited the use of policy function iteration as a solution algorithm. We reduce these costs by providing a user-friendly suite of MATLAB functions that introduce multi-core processing and Fortran via MATLAB’s executable function. Policy function iteration is particularly useful in solving models with regime-dependent parameters and in capturing key expectational effects associated with policy changes. We show how to implement our computational routines and highlight the attractiveness of this algorithm using the canonical real business cycle model and a new Keynesian model that features regime switching in policy parameters. We compare our advocated approach to other more familiar computational methods, highlighting the tradeoffs between accuracy and speed.

We study the dynamics of the neo-classical growth model around the steady state under dispersed information about aggregate productivity. We apply the notion of Information Equilibrium formulated in Rondina and Walker (2011) to solve for the equilibrium dynamics. We assume that, while capital is traded in a centralized market, labor services are traded in decentralized markets. We also assume incomplete markets over the idiosyncratic component of labor income, which ensures that the individual specific productivity is not trivally revealed by the prices of the state-contingent securities. Under these assumptions we show that the endogenous dynamics of aggregate capital introduce an informational friction that keeps the equilibrium variables, such as the rental rate of capital, from revealing the state of aggregate productivity. As a consequence, when the economy is hit by a productivity shock, output undergoes waves of optimism and pessimism.

We generalize the linear rational expectations solution method of Whiteman (1983) to the multivariate case. This permits the use of a generic exogenous driving process that must only satisfy covariance stationarity. We derive the multivariate crossequation restrictions linking the Wold representation of the exogenous process to the endogenous variables of the the model. This mapping is a multivariate version of the celebrated Hansen-Sargent formula, and is shown to provide important insights into equilibrium dynamics of well-known models. We connect our solution methodology to other popular approaches to solving linear rational expectations models (e.g., Sims, 2002). We also provide several motivating examples that highlight the usefulness of our approach.

Bayesian prior predictive analysis of five nested DSGE models suggests that model specifications and prior distributions tightly circumscribe the range of possible government spending multipliers. Multipliers are decomposed into wealth and substitution effects, yielding uniform comparisons across models. By constraining the multiplier to tight ranges, model and prior selections bias results, revealing less about fiscal effects in data than about the lenses through which researchers choose to interpret data. When monetary policy actively targets inflation, output multipliers can exceed one, but investment multipliers are likely to be negative. Passive monetary policy produces consistently strong multipliers for output, consumption, and investment.

News—or foresight—about future economic fundamentals can create rational expectations equilibria with non-fundamental representations that pose substantial challenges to econometric efforts to recover the structural shocks to which economic agents react. Using tax policies as a leading example of foresight, simple theory makes transparent the economic behavior and information structures that generate non-fundamental equilibria. Econometric analyses that fail to model foresight will obtain biased estimates of output multipliers for taxes; biases are quantitatively important when two canonical theoretical models are taken as data generating processes. Both the nature of equilibria and the inferences about the effects of anticipated tax changes hinge critically on hypothesized tax information flows. Differential U.S. federal tax treatment of municipal and treasury bonds embeds news about future taxes in bond yield spreads. Including that measure of tax news in identified VARs produces substantially different inferences about the macroeconomic impacts of anticipated taxes.

We study Rational Expectations equilibria in dynamic models with dispersed information and signal extraction from endogenous variables. An Information Equilibrium is established that delivers existence and uniqueness conditions in a new class of RE equilibria where agents remain dispersedly informed even after observing the entire history of equilibrium prices. A feature of the equilibria belonging to this class is a dynamic response to shocks that displays waves of optimism and pessimism of the market price with respect to the true fundamental. This propagation effect is new to the RE literature and originates from confounding dynamics that remain unraveled in equilibrium. We derive an analytical characterization of the equilibrium that generalizes the celebrated Hansen-Sargent optimal prediction formula, and also allows us to study the higher-order beliefs representation of the equilibria. We show that the higher-order belief dynamics, contrary to what is normally believed, can generate a positive effect on information diffusion: if informed agents were not engaging in formulating expectations about expectations about expectations and so on, information transmission through prices would be reduced.

This paper develops a dynamic asset pricing model with persistent heteroge- neous beliefs. The model features competitive traders who receive idiosyncratic signals about an underlying fundamentals process. We adapt Futia's (1981) frequency domain methods to derive conditions on the fundamentals that guarantee noninvertibility of the mapping between observed market data and the underlying shocks to agents' information sets. When these conditions are satisfied, agents must 'forecast the forecasts of others'. The additional dynamics of the heterogeneous beliefs equilibrium can account for observed violations of variance bounds, predictability of excess returns, and rejections of cross-equation restrictions.

Accommodating asymmetric information in a dynamic asset pricing model is technically challenging due to the problems associated with higher-order expectations. That is, rational investors are forced into a situation where they must forecast the forecasts of other agents. In a dynamic setting, this problem telescopes into the infinite future and the dimension of the relevant state space approaches infinity. By using the frequency domain approach of Whiteman [1983] and Kasa [2000], this paper demonstrates how information structures previously believed to preserve asymmetric information in equilibrium, converge to a symmetric information, rational expectations equilibrium. The revealing aspect of the price process lies in the invertibility of the observed state space, which makes it possible for agents to infer the economically fundamental shocks and thus eliminating the need to forecast the forecasts of others.

Multiple stationary equilibria are often encountered in standard asset pricing models when one assumes negative-exponential utility with Gaussian uncertainty. This paper demonstrates that there are exactly two stationary equilibria, which are due solely to the presence of nonlinearities.

This study generalizes the nonparametric approach to option pricing of Stutzer, M. (1996) by demonstrating that the canonical valuation methodology introduced therein is one member of the Cressie–Read family of divergence measures. Although the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the ability of the alternative divergence measures to price European call options by approximating the risk-neutral, equivalent martingale measure from an empirical distribution of the underlying asset. A simulation study of the finite sample properties of the alternative measure changes reveals that the optimal divergence measure depends upon how accurately the empirical distribution of the underlying asset is estimated. In a simple Black–Scholes model, the optimal measure change is contingent upon the number of outliers observed, whereas the optimal measure change is a function of time to expiration in the stochastic volatility model of Heston, S. L. (1993). Our extension of Stutzer's technique preserves the clean analytic structure of imposing moment restrictions to price options, yet demonstrates that the nonparametric approach is even more general in pricing options than originally believed.

A rational expectations framework is developed to study the consequences of alternative means to resolve the “unfunded liabilities” problem—unsustainable exponential growth in federal Social Security, Medicare, and Medicaid spending with no plan to finance it. Resolution requires specifying a probability distribution for how and when monetary and fiscal policies will change as the economy evolves through the 21st century. Beliefs based on that distribution determine the existence of and the nature of equilibrium. We consider policies that in expectation combine reaching a fiscal limit, some distorting taxation, modest inflation, and some reneging on the government's promised transfers. In the equilibrium, inflation-targeting monetary policy cannot successfully anchor expected inflation. Expectational effects are always present, but need not have a large impacts on inflation and interest rates in the short and medium runs.

Effects of government investment are studied in an estimated neoclassical growth model. The analysis focuses on two dimensions that are critical for understanding government investment as a fiscal stimulus: implementation delays for building public capital and expected fiscal adjustments to deficit-financed spending. Implementation delays can produce small or even negative labor and output responses to increases in government investment in the short run. Anticipated fiscal adjustments matter both quantitatively and qualitatively for long-run growth effects. When public capital is insufficiently productive, distorting financing can make government investment contractionary at longer horizons.

How do information flows influence business cycle dynamics in models with anticipated (news shocks) and unanticipated innovations? To address this question, we show how alternative specifications of news affect the equilibrium by deriving the mapping between news shocks and the endogenous variables in a simple analytical model. News shocks are shown to add moving average (MA) components to endogenous variables. We then show how the additional MA components affect equilibrium dynamics. We generalize two popular forms of news processes to demonstrate how information flows impact equilibrium dynamics. To compare these news processes, we establish conditions under which the two processes have identical information content. We find that allowing news shocks to be correlated across time generates hump-shaped impulse response functions and helps mitigate the comovement problem.
Note: The graphic depicts the anticipation effect due to foresight for different information flows.

We use a rational expectations framework to assess the implications of rising debt in an environment with a ‘‘fiscal limit’’. The fiscal limit is defined as the point where the government no longer has the ability to finance higher debt levels by increasing taxes, so either an adjustment to fiscal spending or monetary policy must occur to stabilize debt. We give households a joint probability distribution over the various policy adjustments that may occur, as well as over the timing of when the fiscal limit is hit. One policy option that stabilizes debt is a passive monetary policy, which generates a burst of inflation that devalues the existing nominal debt stock. The probability of this outcome places upward pressure on inflation expectations and poses a substantial challenge to a central bank pursuing an inflation target. The distribution of outcomes for the path of future inflation has a fat right tail, revealing that only a small set of outcomes imply dire inflationary scenarios. Avoiding these scenarios, however, requires the fiscal authority to renege on some share of future promised transfers.
Note: The graphic depicts the anticipation effect due to foresight plotted against serial

Detecting and quantifying racial discrimination in the labor market is difficult. The sports industry offers a wealth of data and specific hiring practices which mitigates this difficulty. The Rooney Rule requires National Football League teams to interview at least one minority candidate when hiring a head coach. We examine a unique data set of high-level assistant coaches (offensive and defensive coordinators) from the beginning of the 1970 season through the beginning of the 2009 season to determine whether race is a factor in NFL teams' decisions to promote these assistants to head coach. Using logit and hazard models that control for age, experience and performance, we conclude that conditional on a coach reaching coordinator status, there is no evidence that race influences head coach hiring decisions. We also find no evidence that the Rooney Rule has increased the number of minority head coaches.

Ageing populations in advanced economies are placing ever-increasing demands on government spending in the form of old-age benefits, particularly for health care. Economies that have promised substantially more benefits than they have made provision to finance are heading into a prolonged era of fiscal stress. Unresolved fiscal stress raises the possibility that the economies will hit their fiscal limits where taxes and spending no longer adjust to stabilise debt. In such economies, monetary policy may lose its ability to control inflation and influence the economy in the usual ways. The paper discusses models of fiscal limits and their implications and lays out a research agenda to integrate political economy and empirical considerations with general equilibrium models of monetary and fiscal interactions.

We derive a mapping between the shortfall-minimizing portfolio selection based on higherorder entropy measures and expected utility theory. We show that the family of HARA utility functions has a minimum-divergence, shortfall-based representation. This facilitates an interpretation in which the risk aversion parameters and the type of risk aversion arise endogenously. We provide a numerical example illustrating this interpretation.

Changes in fiscal policy typically entail two kinds of lags: the legislative lag—between when legislation is proposed and when it is signed into law—and the implementation lag—from when a new fiscal law is enacted to when it takes effect. These lags imply that substantial time evolves between when news arrives about fiscal changes and when the changes actually take place—time when households and firms can adjust their behavior. We identify two types of fiscal news—government spending and changes in tax policy. We identify news concerning taxes through the municipal bond market, and news concerning government spending through the Survey of Professional Forecasters. The main contribution of the paper is a mapping from reduced-form estimates of news into a DSGE framework. We find that news about fiscal policy is a time-varying process and show that ignoring the time variation can have important consequences in a conventional macroeconomic model.