The research questions addressed by the literature on learning in macroeconomics can be classified into four categories: First, there are issues related to the convergence and stability under learning in models with unique rational expectations equilibria. Authors here are concerned mainly with the learnability of a rational expectations equilibrium, as a measure of that equilibrium's plausibility as an observed outcome in an actual economy. Second, there are issues related to convergence and stability under learning in models with multiple rational expectations equilibria. In this case, learnability serves as an equilibrium selection device, helping economists decide which equilibria are the more likely to be actually observed among the many that exist under rational expectations. A third set of issues involves the examination of transitional dynamics that accompanies the equilibrium selection process. Following some type of unexpected strcutural change or change in policy regime, for instance, economies necessarily must follow temporary transitional paths to a rational expectations equilibrium associated with the new reality. Learning is sometimes used to help model such transitional dynamics. Finally, there are issues related to the examination of learning dynamics that are intrinsically different, even asymptotically, from the dynamics of the rational expectations versions of the models. In these cases, the learning dynamics do not converge to the rational expectations fixed points, and (unexploitable) expectational errors persist indefinitely. Some authors have tried to make use of this possibility in order to build explanations of otherwise puzzling macroeconomic phenomena based on constantly changing expectations.

This paper investigates how volatile the general price level can be in an equilibrium where all uncertainty is extrinsic. The government operates a lump-sum redistribution policy using fiat money. An approach to modeling asset market segmentation is introduced in which this tax policy determines how volatile the price level can be, which in turn determines the volatility of consumption. The paper characterizes (i) the set of general price levels consistent with the existence of competitive equilibrium and (ii) the resulting set of equilibrium allocations. The results demonstrate how redistribution policies that are fixed in nominal terms can have a destabilizing effect on an economy, and show how to evaluate the amount of volatility that a particular policy may induce.

Inflation and the monetary financing of deficits are analyzed in a model in which the deficit is constrained to be less than a given fraction of a measure of aggregate market activity. Depending on parameter values, the model can have multiple steady states. Under adaptive learning with heterogeneous learning rules, there is convergence to a subset of these steady states. In some cases, a high-inflation constrained steady state will emerge. However, with a sufficiently tight fiscal constraint, the low-inflation steady state is globally stable. We provide experimental evidence in support of our theoretical results.

During the past decade, the popularity of nonlinear models in econometrics has been increasing quite rapidly. Nonlinear models are now widely used for modeling macroeconomic relationships, and they also are used frequently in financial econometrics. The most popular nonlinear models have been univariate. Threshold autoregressive, Markov switching autoregressive, and smooth-transition autoregressive models, just to name a few popular families of models, have been widely applied to modeling of macroeconomic series. Even nonlinear multivariate single-equation models have found application in areas where linear single-equation models traditionally have been used, such as modeling the demand for money, real exchange rates, consumption–income relationship, and house prices. Interest in nonlinearities in the Phillips curve also has grown recently.

This paper examines an intertemporal optimizing consumer or a representative consumer-firm in a deterministic setting subject to a general (either linear or nonlinear) capital accumulation equation. Duality theory is used to recast the Hamilton–Jacobi equation for dynamic optimization in terms of an instantaneous and an intertemporal profit function. An envelope theorem allows derivation of an explicit solution for the value of the costate variable as a function of the state and other variables. The final model form only requires specification of atemporal functions that are linked into a closed-form solution for the optimal dynamic decision variables through a system of contemporaneous simultaneous equations.

This paper provides a historical chronology of economic activity in 16th- and 17th-century France that is based on wheat price series in Paris and Toulouse. A stochastic regime-switching model enables us to benchmark eras and summarize the salient features of a development difficult to appraise in all its complexity. A new class of Markov regime-switching time-series models is introduced to allow for nontrivial interdependencies between different types of cycles that make the economy grow at an unsteady rate. With a predominantly agricultural cycle, we uncover a strongly periodic Markov switching scheme for recorded wheat prices from the grain markets of Paris and Toulouse. Besides the periodic nature of the Markov chain, we also study whether a common factor determined the state of the economy in Paris and Toulouse or whether each series moved independently.

The government-led transition from barter to fiat money and its possible failure are analyzed in the Kiyotaki-Wright model when prices are determined endogenously by the strategic bargaining process. The transition is shown to be more inflationary as the government becomes less patient and less credible. The possibility of breakdown in fiat money due to uncertainty in the size of government and its patience implies longer transition path and higher expected inflation. An application to the transition from local currencies to currency integration shows that local governments are tempted to issue more currency to extract seigniorage from foreign as well as home agents. As long as the degree of economic integration is sufficiently large, an increasing frequency of trading opportunities implies lower price levels and higher welfare relative to the local currency regime. It is when the two countries are fully integrated that the world economy with the unified currency achieves the highest welfare.

We study a dynamic equilibrium model in which agents have adaptive expectations and monetary authorities pursue an inflation target. We show how alternative monetary stabilization policies become more effective when fiscal constraints on deficits are implemented, although they are not binding at the equilibrium target. In particular, we show that the inflation target equilibrium can be locally, or even globally, stable for a large class of adaptive learning schemes. We also compare alternative stabilization policies in terms of their stability properties. Commonly postulated conditional Taylor-type rules tend to be dominated by other rules, such as an unconditional Friedman type.

Marshallian demand, supply, and entry models are employed for major sectors of an economy that can be combined with factor market models for money, labor, capital, and bonds to provide a Marshallian macroeconomic model (MMM). Sectoral models are used to produce sectoral output forecasts, which are summed to provide forecasts of annual growth rates of U.S. real GDP. These disaggregative forecasts are compared to forecasts derived from models implemented with aggregate data. The empirical evidence indicates that it pays to disaggregate, particularly when employing Bayesian shrinkage forecasting procedures. Further, some considerations bearing on alternative model-building strategies are presented using the MMM as an example and describing its general properties. Last, data requirements for implementing MMMs are discussed.

A survey of nonlinear multivariate macro empirical models is attempted. Although theory may suggest that nonlinearity is to be expected, empirical studies have difficulty in discovering strong consistent effects. Regime switching techniques appear to be the most successful and evidence of nonlinearity is most found for interest rates. Most of the studies emphasize model fitting rather than model evaluation, which limits their usefulness.

Macroeconomic performance in the Economic and Monetary union (EMU) will be impaired if national fiscal policy flexibility and monetary flexibility of the ECB is limited, goods markets adjust sluggishly, labor mobility is low, and automatic stabilization from federal taxes and government spending is low. This paper analyzes the stabilization of output fluctuations induced by symmetric and asymmetric macroeconomic shocks in the EMU. It is shown how national fiscal flexibility and flexibility of the monetary policy of the ECB can stabilize fluctuations of the average EU business cycle that are generated by symmetric shocks. Furthermore, it is demonstrated how, under EMU, national fiscal flexibility and a system of fiscal transfers are able to stabilize differences in national business cycles that are generated by asymmetric shocks.

We develop a test of the null hypothesis that an observed time series is a realization of a strictly stationary random process. Our test is based on the result that the kth value of the discrete Fourier transform of a sample frame has a zero mean under the null hypothesis. The test that we develop will have considerable power against an important form of nonstationarity hitherto not considered in the mainstream econometric time-series literature, that is, where the mean of a time series is periodic with random variation in its periodic structure. The size and power properties of the test are investigated and its applicability to real-world problems is demonstrated by application to three economic data sets.

Karl Shell is without a doubt one of the central players in the development of economic theory and macroeconomics in the latter part of the twentieth century. He has made important contributions on topics ranging from growth theory, to overlapping generations, to extrinsic uncertainty, to monetary economics, to market games, and to technological innovation. His collaborations with Dave Cass are legend, and include the seminal formulation of the concept of sunspot equilibria. His “Notes on the Economics of Infinity,” and his papers with Yves Balasko are overlapping-generations classics. Shell's many coauthors read like a Who's Who in economics, and include (in no particular order) Joe Stiglitz, Franklin Fisher, Miguel Sidrauski, Ned Phelps, Duncan Foley, Walt Heller, Albert Ando, Jim Peck, Rod Garratt, Aditya Goenka, Christian Ghiglino, and Todd Keister. This is also a club to which we are also proud to belong.

Shell's research is first rate and highly innovative, but his full contribution to economic theory must also be judged by his long service as the editor of one of the profession's premier journals, the Journal of Economic Theory. As the founding editor of JET, Shell took a small upstart journal, originally envisioned as a niche outlet for papers on mathematical economics, and turned it into one of the best in the profession. JET has published papers that have had major impacts on the development of economic theory in all its various flavors.

Because of Shell's long stewardship of JET, the story of his professional life—which we hope we have captured in this interview—is also a history of the evolution of economic theory over the past quarter century. We spoke with Karl in his office at Cornell University and over lunch at the faculty club in the Statler, and the interview tapes we made were very much a three-way conversation between Karl and the two of us. In editing the transcripts of these tapes for publication, we wished to keep the focus of the conversation on Shell, and have therefore adopted the same anonymous “MD” moniker we used in our interview of Dave Cass to mask the identity of the questioner. We hope you enjoy the conversation as much as we did.

Price fluctuations under adaptive learning in renewable resource markets such as fisheries are examined. Optimal fishery management with logistic fish population growth implies a backward-bending, discounted supply curve for bioeconomic equilibrium sustained yield. Higher discount rates bend supply backward more to generate multiple steady-state rational expectations equilibria. Under bounded rationality, adaptive learning of a linear forecasting rule generates steady-state, two-cycle as well as chaotic consistent expectations equilibria, which are self-fulfilling in sample average and autocorrelations. The possibility of “learning to believe in chaos” is robust and even enhanced by dynamic noise.

We develop nonlinear leading-indicator models for GDP growth, with the interest-rate spread and growth in M2 as leading indicators. Since policy makers typically are interested in whether a recession is imminent, we evaluate these models according to their ability to predict the probability of a recession. Using data for the United States, we find that conditional on the spread, the marginal contribution of M2 growth in predicting recessions is negligible.

We develop a theory of financial development based on the costs associated with the provision of external finance. These costs arise through informational asymmetries between borrowers and lenders that are costly to resolve. When borrowing is limited, producers with access to financial intermediary loans obtain higher returns to investment than other producers. This creates incentives for others to undertake the technology adoption necessary to access investment loans. Over time, as increasing numbers of producers gain access to external finance, borrowers' net worth rises relative to debt. This reduces the costs of financial intermediation and raises the overall return on investment. The theory is consistent with recent evidence that financial development reduces the costs associated with the provision of external finance and increases the rate of economic growth. Furthermore, the theory predicts that financial development will raise the return on loans and reduce the spread between borrowing and lending rates.

This paper investigates the potential for nonlinear Granger causality from money to output. Using a standard four-variable linear (subset) vector error-correction model (VECM), we first show that the null hypothesis of linearity can be rejected against the alternative of smooth-transition autoregressive nonlinearity. An interesting result from this stage of the analysis is that the yearly growth rate of money is identified as one of the variables that may govern the switching between regimes. Smooth-transition VECM's (STVECM's) are then used to examine whether there is nonlinear Granger causality in the money–output relationship in the sense that lagged values of money enter the model's output equation as regressors. We evaluate this type of nonlinear Granger causality with both in-sample and out-of-sample analyses. For the in-sample analysis, we compare alternative models using the Akaike information criteria, which can be interpreted as a predictive accuracy test. The results show that allowing for both nonlinearity and for money–output causality leads to considerable improvement in model's in-sample performance. By contrast, the out-of-sample forecasting results do not suggest that money is nonlinearly Granger causal for output. They also show that, according to several criteria, the linear VECM's dominate the STVECM's. However, these forecast improvements seldomly are statistically significant at conventional levels.

It is argued that standard impulse response analysis based on vector autoregressive models has a number of shortcomings. Although the impulse responses are estimated quantities, measures for sampling variability such as confidence intervals sometimes are not provided. If confidence intervals are given, they often are based on bootstrap methods with dubious theoretical properties. These problems are illustrated using two German monetary systems. Proposals are made for improving current practice. Special emphasis is placed on systems with cointegrated variables.

We analyze the role of intrafirm bargaining in the large-firm matching model and underline the conditions under which the Pissarides equivalence between this model and the “single-worker” firm's model holds.

The model is a two-country overlapping generations economy with boundedly rational agents who update their decision rules using a version of the stochastic replicator dynamic. The results show that stationary rational expectations equilibria of this model are unstable under this type of evolutionary adaptation. The paper also derives a two-period-ahead forecast of the values of average fractions of savings placed in each of the two currencies. This forecast is used in decisionmaking of a rational agent who has a full knowledge of the evolutionary economy. The performance of the rational agent is compared to the performance of boundedly rational agents, based on the average utility received over time. Results show that the difference between utilities earned by rational and boundedly rational agents is small. In addition, the average utility of the best-performing boundedly rational agents is higher than the average utility of the rational agents.