Roger E. A. Farmer

Indeterminacy and sector-specific externalities

We introduce mild increasing returns to scale into a version of the Real Business Cycle model. These increasing returns to scale occur as a consequence of sector-specific externalities, that is, externalities where the output of the consumption and investment sectors have external effects on the output of firms within their own sector. Keeping the production technologies for both sectors identical, for expositional simplicity, we show that indeterminacy can easily occur for parameter values typically used in the real business cycle literature, and in contrast to some earlier literature on indeterminacies, for externalities mild enough so that labour demand curves are downward sloping.

Confidence, Crashes and Animal Spirits

This paper presents a model of the macroeconomy that reformulates what I take to be two important ideas from Keynes General Theory. The first is that there may be a continuum of steady state unemployment rates. The second is that beliefs select an equilibrium. I argue that search and matching costs in the labor market lead to the existence of a continuum of equilibria and I resolve the resulting indeterminacy by assuming that the beliefs of stock market participants are self-fulfilling. The paper reconciles Keynesian economics with general equilibrium theory without invoking the assumption of frictions that prevent wages and prices from reaching their equilibrium levels.

Understanding Markov-switching rational expectations models

We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models and we develop an algorithm to check these conditions in practice. We use three examples, based on the new-Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov-switching with forward looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region.

The econometrics of indeterminacy: an applied study

Abstract This paper presents evidence from the US economy on the propagation mechanism and on the impulses that have been responsible for business cycles in the United States over the period from 1929 through 1988. Our results support the view, advanced in earlier work, that a general equilibrium model with an indeterminate steady state does a good job of accounting for the propagation mechanism in US data. In addition to suggesting a novel explanation for the propagation mechanism of business fluctuations, the method by which we estimate our model is able to measure the relative importance of different sources of fluctuations by identifying different shocks with the residuals to our estimated equations. We divide the impulses to the business cycle into supply shocks (shocks that affect productivity) and demand shocks (unexplained fluctuations in private and government consumption). We find that demand shocks are roughly twice as important as supply shocks in the US data over the period from 1929 through 1988; in the postwar period, however, supply shocks and demand shocks have both been of roughly equal magnitude and the variances of both kinds of disturbances have been five times lower than in the prewar period.

Chapter 6 Indeterminacy and sunspots in macroeconomics

Abstract This chapter gives an overview of the recent literature on indeterminacy and sunspots in macroeconomics. It discusses of some of the conceptual and the technical aspects of this literature, and provides a simple framework for illustrating the mechanisms of various dynamic equilibrium models that give rise to indeterminate equilibria. The role of external effects, monopolistic competition, and increasing returns in generating indeterminacy is explored for one-sector and multi-sector models of real business cycles and of economic growth. Indeterminacy is also studied in monetary models, as well as in models where monetary and fiscal policy are endogenous and determined by feedback rules. Particular attention is paid to the empirical plausibility of these models and their parametrizations in generating indeterminate equilibria. An overview of calibrated macroeconomic models with sunspot equilibria is given, and their successes and shortcomings in matching properties of data are assessed. Finally some issues regarding the selection of equilibria, the observable implications, and difficulties of forecasting that arise in such models are briefly addressed.

Deficits and cycles

Abstract This paper shows that periodic equilibria may arise in a simple overlapping generations model with capital. If the government follows a policy of fixing the value of the deficit, rather than fixing the value of government debt, then the difference equation that describes competitive equilibria may posses complex roots in the neighborhood of the golden rule stationary state. One may show that if there exist parametric families of economies for which these roots change stability then, locally, there exists an invariant closed curve. The paper provides two simple examples that generate such equilibria, and it solves these examples numerically.

Implicit Contracts with Asymmetric Information and Bankruptcy: The Effect of Interest Rates on Layoffs

This paper develops a model in which a firm writes labour contracts with workers and debt contracts with creditors. Firms have more information than do the owners of the factors of production and they are also subject to limited liability. We show that if the limited liability constraint is binding then the employment level is inefficient relative to a situation of symmetric information. The firm is then embedded into a partial equilibrium model in which the real rate of interest is exogenously determined. We show that increases in the real rate of interest increase the inefficiency of the optimal employment contract and lead to layoffs in more states of nature than would occur at lower real interest rates.

SELF-FULFILLING PROPHECIES AND THE BUSINESS CYCLE

We demonstrate that multiple stationary rational-expectations equilibria exist in a version of Lucas’s island economy. The existence of these equilibria follows from the fact that there is an indeterminate set of monetary equilibria in the two-period overlappinggenerations model. We show how to construct stationary rational-expectations equilibria by randomizing over the set of nonstationary monetary equilibria. In some of our equilibria, a positively sloped Phillips curve exists even though our economy contains no signal-extraction problem as in the original Lucas paper. Our equilibria are indexed by beliefs and are examples of the existence of sunspot equilibria in which allocations may differ across states of nature for which preferences, technology, and endowments are identical. Our technique for constructing stationary sunspot equilibria should prove useful in a wide class of models in which an indeterminate stationary equilibrium exists.

Money In A Real Business Cycle Model

This paper constructs a real business cycle model in which real money balances yield utility. We calibrate the model to fit the first moments of US data and simulate a set of impulse response functions that are generated by the model for GDP, the rate of interest, money growth and real balances. These theoretical impulse responses are compared with actual impulse responses from US data. The model does a reasonably good job of capturing the dynamic interactions of money and real variables in US data. It differs from most existing approaches by choosing a parameterization of utility for which the model admits the existence of indeterminate equilibria. It is argued that this fact is critical in explaining the monetary propagation mechanism.

Generalizing the Taylor Principle: Comment

Davig and Leeper (2007) have proposed a condition they call the generalized Taylor principle to rule out indeterminate equilibria in a version of the New Keynesian model, where the parameters of the policy rule follow a Markov-switching process. We show that although their condition rules out a subset of indeterminate equilibria, it does not establish uniqueness of the fundamental equilibrium. We discuss the differences between indeterminate fundamental equilibria included by Davig and Leepers condition and fundamental equilibria that their condition misses.