We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on the existing related mathematical literature to derive the Pontryagin conditions. Using explicit representations of the solutions to the PDEs, we first show that the resulting dynamic system gives rise to an ill-posed problem in the sense of Hadamard. We then turn to the spatial Ramsey problem with linear utility. The obtained properties are significantly different from those of the nonspatial linear Ramsey model due to the spatial dynamics induced by capital mobility.

This paper extends the Diamond-Mortensen-Pissarides (DMP) matching model with endogenous job destruction by introducing postmatch labor turnover costs. We consider training and separation costs that create heterogeneity among workers. In particular, there are two types of employed workers: (i) new entrants who need training in order to become fully productive, and (ii) incumbents who are fully productive and whose departure from the firm imposes costs on it. We find that our calibrated model, relative to the standard DMP model, comes closer to the data regarding the volatility of vacancies and unemployment without introducing unrealistic sensitivity to policy changes. Moreover, our extended model nearly reproduces the downward-sloping Beveridge curve, which is unusual when endogenous job destruction exists in this type of model.

In this article we use Bayesian classification and finite mixture models to extract information from the MSI database (maintained by the Federal Reserve Bank of St. Louis) and construct a new set of non-nested monetary aggregates (under the Divisia aggregation procedure) based on statistical similarities and multidimensional structures. We also use recent advances in the fields of applied econometrics, dynamical systems theory, and statistical physics to investigate the relationship between the new money measures and economic activity. The empirical results offer practical evidence in favor of this approach to monetary aggregation.

New technology has been credited with solving environmental problems by mitigating the effects of pollutants. We construct a general equilibrium model in which abatement technology is a real option and pollution's (negative) amenity value alters both risk aversion and the intertemporal elasticity of substitution. We derive the tax scheme such that in a decentralized economy agents adopt the abatement technology at the time that is socially optimal. We show that the higher the greenness of preferences, the earlier the adoption and the higher the optimal tax rate. We also obtain that adoption is fostered by uncertainty if the effective intertemporal elasticity of substitution is large enough, but is not affected by uncertainty if this elasticity is low. Moreover, the optimal tax rate, which only exists if the effective intertemporal elasticity of substitution is high, is an increasing function of uncertainty.

Cross-country studies of economic growth have been hampered by the scarcity of reliable data on productivity at the industry level; see Bernard and Jones [American Economic Review, 91 (4) (2001), 1168–1169] and Rogerson [Journal of Political Economy, 116 (2) (2008), 235–259]. We bring together literature on industry prices, human capital, and capital assets to construct industry-level productivity measures that are well grounded in neoclassical production theory. These theory-based measures differ widely from the crude measures commonly used in the literature. We use these to confirm and strengthen the finding of Bernard and Jones [American Economic Review, 86 (5) (1996), 1216–1238] that for advanced OECD countries, patterns of convergence across sectors have differed since 1970: whereas productivity in market services converged, there is no convergence in manufacturing. More detailed analysis confirms that patterns of convergence are highly industry-specific. There is no dominant convergence trend in sectoral productivity growth across advanced countries.

This paper explores the influence of wage and price staggering on monetary persistence. We show that, for plausible parameter values, wage and price staggering are complementary in generating monetary persistence. We do so by proposing the new measure of “quantitative inertia,” after discussing weaknesses of the “contract multiplier,” a standard measure of monetary persistence. The existence of complementarities means that beyond understanding how wage and price staggering work in isolation, it is important to investigate their interactions. Furthermore, our analysis indicates that the degree of monetary persistence generated by wage vis-à-vis price staggering depends on the relative competitiveness of the labor and product markets. We show that the conventional finding that wage staggering generates more persistence than price staggering holds under homogeneous capital accumulation. Under firm-specific capital, wage staggering generates more persistence only when the labor market is sufficiently competitive relative to the product market.

In this paper, we explore the consequence of learning to forecast in a very simple environment. Agents have bounded memory and incorrectly believe that there is nonlinear structure underlying the aggregate time series dynamics. Under social learning with finite memory, agents may be unable to learn the true structure of the economy and rather may chase spurious trends, destabilizing the actual aggregate dynamics. We explore the degree to which agents' forecasts are drawn toward a minimal state variable learning equilibrium as well as a weaker long-run consistency condition.

In this paper, we study the stationary and non-stationary equilibria of a deterministic, pure exchange, two-period overlapping generations model with habit persistence. We show that preferences with multiplicative habits can lead to quite different equilibrium outcomes compared to subtractive ones. The two most commonly adopted habit specifications can differ in terms of homotheticity, gross substitutability, and uniqueness of equilibria. We illustrate these differences in terms of steady-state equilibria, as well as local dynamics.

This paper develops a monetary endogenous growth model with capital and skill heterogeneity to analyze the relationship among inflation, growth, and income inequality. In the model inflation, growth, and inequality are jointly determined. We show that an increase in the long-run money growth rate raises inflation and reduces growth, but its effect on income inequality depends on the relative importance of the two types of heterogeneity. Inequality shrinks with the rise of inflation when capital heterogeneity dominates and enlarges when skill heterogeneity dominates. Therefore, our model supports a negative (positive) inflation–inequality relationship and a positive (negative) growth–inequality relationship when capital (skill) heterogeneity dominates. In any event, inflation and growth are negatively related.

The purpose of this note is to analyze the capability of bandpass filters to extract a known periodicity. The specific bandpass filters considered are a conventional discrete Fourier transform (DFT) filter and the filter recently proposed by Iacobucci and Noullez. We employ simulation methods to investigate cycle extraction properties. We also examine the implications arising from the Gibbs effect in practical settings that typically confront applied macroeconomists

This paper analyzes policies by means of which a whole society in an initial state of illiteracy and low productivity can raise itself into a condition of continuous growth. Using an overlapping generations model in which human capital is formed through child rearing and formal education, we show that an escape from a poverty trap, in which children work full time and no human capital accumulation takes place, is possible through compulsory education or programs of taxes and transfers. If school attendance is unenforceable, temporary inequality is unavoidable if the society is to escape in finite time, but long-run inequalities are avoidable provided sufficiently heavy, but temporary, taxes can be imposed on the better off. Programs that aim simply at high attendance rates in the present can be strongly nonoptimal.

Most real business cycle models have a hard time jointly explaining the twin facts of strongly procyclical Solow residuals and extremely low correlations between wages and hours. We present a model that delivers both these results without using exogenous variation in total factor productivity (technology shocks). The key innovation of the paper is to add learning-by-doing to firms' technology. As a result, firms optimally vary their prices to control the amount of learning, which in turn influences future productivity. We show that exogenous variation in labor wedges (preference shocks) measured from aggregate data deliver around 50% of the standard deviation in the efficiency wedge (Solow residual) as well as realistic second moments for key aggregate variables, which is in sharp contrast to the model without learning-by-doing.

The objective of this paper is to develop closed-form formulae for the exact discretization of a third-order system of stochastic differential equations, with fixed initial conditions, driven by observable stochastic trends and white noise innovations. The model provides a realistic alternative to first- and second-order differential equation specifications of the time lag distribution, forming the basis of a testing and estimation procedure. The exact discrete models, derived under two sampling schemes with either stock or flow variables, are put into a system error correction form that preserves the information of the underlying continuous time model regarding the order of integration and the dimension of cointegration space.

This paper introduces a method of optimization in infinite-horizon economies based on the theory of correspondences. The proposed approach allow us to study time-separable and non-time-separable dynamic economic models without resorting to fixed point theorems or transversality conditions. When our technique is applied to the standard time-separable model it provides an alternative and straightforward way to derive the common recursive formulation of these models by means of Bellman equations.

In this paper I consider the relation between gross output– and value added–based total factor productivity (TFP) measures. It appears that, without any (micro-)economic theory being required, a conditional relationship between TFP indices can be derived, in which the Domar factor plays an important role. At the same time it turns out that gross output– and value added–based TFP indicators (difference-type measures) always coincide. In the Divisia index framework and maintaining the classical assumptions (profit maximization and a production technology that exhibits globally constant returns to scale), it appears that both TFP indices measure technological change, albeit in a dual way. In establishing this result, no separability assumptions are involved. Both indices are in general path-dependent. Path independence of the gross output–based TFP index requires that the technology exhibit Hicks input neutrality, whereas path independence of the value added–based TFP index requires Hicks value-added neutrality. These two concepts of neutrality are, however, not dual.

It has been shown that the Ramsey growth model with agents that differ in their initial wealth endowments is compatible with a wide range of distributional outcomes, yet it is difficult to characterize under which circumstances the distribution of wealth becomes more or less unequal. In this note, we characterize the steady state distribution of wealth and compare it to the initial distribution, obtaining analytical conditions for one to be more skewed than the other. We show that whether wealth inequality increases or decreases during the transition to the steady state depends on simple and intuitive conditions on parameter values. Standard values for these parameters indicate that it is more likely that wealth inequality decreases as the economy accumulates capital.

We generalize existing fair wage models to allow effort to vary over the business cycle. When effort is variable, wage fluctuations are partially compensated for by endogenous effort fluctuations, so that the sensitivity of marginal cost to output and employment variations is decreased. This new mechanism decreases the need for sluggishness to explain the observed high inflation persistence.

We study the impact that financial intermediation can have on productivity through the alleviation of credit constraints in occupation choice and/or an improved allocation of risk, using both static and dynamic structural models as well as reduced-form OLS and IV regressions. Our goal in this paper is to bring these two strands of the literature together. Even though, under certain assumptions, IV regressions can accurately recover the true model-generated local average treatment effect, this is quantitatively different, in order of magnitude and even sign, from other policy impact parameters (e.g., ATE and TT). We also show that laying out clearly alternative models can guide the search for instruments. On the other hand, adding more margins of decision, that is, occupation choice and intermediation jointly, or adding more periods with promised utilities as key state variables, as in optimal multiperiod contracts, can cause the misinterpretation of IV as the causal effect of interest.

The banking literature following Diamond and Dybvig [Journal of Political Economy 85, 191–206 (1983)] has assumed that all depositors are ex ante identical. This paper relaxes this assumption by introducing two types of agents. Whereas some agents are uncertain about their liquidity needs at the time they deposit in banks, other agents know exactly at what time they will want to withdraw their funds. Agents who know ex ante that they will want to withdraw in the short term will tend to disrupt the ability of a bank to serve customers who are uncertain about their timing of withdrawal. An adverse selection problem arises, where short-term deposits have the incentive to join the financial system and limit, or completely do away with, banks' liquidity provision service. On the other hand, potentially beneficial long-term funds will not be deposited in banks. Further, when unpredicted short-term withdrawal needs are sufficiently high, bank reserves are exhausted, and long-term investments need to be disrupted, causing a banking crisis.

Hirofumi Uzawa is one of the giants of modern economic theory. Hiro is probably best known to the readers of Macroeconomic Dynamics (MD) for his seminal articles on two-sector economic growth. The two-sector technology is more general than the one-sector technology: it allows a production possibility frontier that is strictly concave to the origin as opposed to being necessarily flat. This generality allows richer and more complex dynamics. This makes it especially useful for the analysis of economic fluctuations. The two-sector model is perfect for dynamic international trade.

Hiro is also well known to macroeconomists for his seminal contribution to endogenous growth. In his article in the 1965 IER, productivity permanently increases as the result of permanent accumulation of human capital. Uzawa was thus a first mover in the new growth theory. The symbol H (for Human Capital, or for Hiro?) is today everywhere in models of economic dynamics.

On his own and through his many students and mentees, Hiro has been the major inspiration for the modern theory of optimal economic growth. He taught a generation of pure and applied economists how to apply Pontryagin's maximum principle in economic dynamics. It seems that Uzawa introduced—or at least pushed the use of—phase diagrams in economic dynamics. Where would we be without this essential tool?

Most readers of MD are likely to think first of Uzawa's contributions to macro, but Hiro is equally well known for his superb works on mathematical economics, general equilibrium, and demand theory. Hiro's mathematics is elegant and often very deep. Like the quality mathematician that he is, he does not apply technique for technique's sake.

Hiro has made fundamental contributions to nonlinear programming. For the convex (but not necessarily smooth) case, he employed Slater's condition to obtain Kuhn–Tucker multipliers that satisfy the saddlepoint property necessary for an optimum. For the smooth (but not necessarily convex) case, Arrow, Hurwicz, and Uzawa introduced the current version of the constraint qualification, which ensures that optimality implies the existence of Kuhn–Tucker multipliers satisfying the saddlepoint property.

Hiro's paper “Walras's Existence Theorem and Brouwer's Fixed Point Theorem” in the Economic Studies Quarterly (1962) is a hidden gem on general equilibrium. This paper can be seen as foreshadowing Sonnenschein's result on excess demand functions. Hiro clarified old, important questions about recovering preference maps from demand functions. Hiro was probably the first to convincingly show—in the context of tatonnement adjustment—the important distinction between local stability and global stability in economic dynamics.

We have given here only a glimpse into the very large body of beautiful, influential Uzawa papers. Hiro's splendid bibliography is given at the end of the interview. Some of the work that Hiro has pursued energetically has yet to be widely recognized. One thinks, for example, of the Penrose Effect, Hiro's modeling of the organizational costs incurred in adding capital or making other changes in the way a firm does business.

Hiro has had many successful students and mentees. Your MD interviewers are lucky to have been among those whom Hiro has influenced profoundly. A very incomplete list of the others would also include Dave Cass, Steve Goldman, Harl Ryder, Hajime Oniki, Bob Lucas, George Akerlof, Joe Stiglitz, Miguel Sidrauski, Morris Teubal, Assaf Razin, Guillermo Calvo, Bill Ethier, and Lenny Mirman.

Hiro is widely recognized and even revered in Japan. He was elected to the very selective Japan Academy in 1989 at a remarkably young age. He was named “A Person of Cultural Merit” in 1983 and elected to the Order of Culture in 1997. Hiro has received significant international recognition. He was President of the Econometric Society. He is a Fellow of the Econometric Society, Member of the American Academy of Arts and Sciences, Foreign Honorary Member of the American Economic Association, and Foreign Associate of the U.S. National Academy of Sciences.

This interview took place nearly 10 years ago. We apologize to the readers and to Professor Uzawa for the delay in getting the transcript to the editor. The interview was held at the Research Center on Global Warming of the Development Bank of Japan, at which Hiro plays an important role. Four of us—Uzawa, the two interviewers, and Yumiko Baba, who was then a post-doc in economics at the University of Tokyo, there to operate the tape recorder—were collected at the Meiji Gakuin University in central Tokyo and whisked away in a large black automobile to Hiro's home court at the Bank. Hiro is an imposing figure: tall and erect with a very long, pointed white beard. His eyes are very active. He strokes his beard in a soothing manner. It is not difficult to be in awe of him. The interview took an even more formal tack because there were two in the room with the nickname “Hiro.” It was hence efficient to use last names at times.

The interviewers had agreed to try to steer Uzawa toward a discussion of his well-known basic technical contributions and away from his less well-known and more political contributions. In the end, we failed to steer Hiro onto any course other than his own. This is mostly as it should be. In this interview, you will hear about some of the technical contributions for which Hiro is widely known. You will also hear about what motivated him to enter economics, his strong social concerns and strong political views, the turbulence of the war years and the postwar years, and his recent work and interests. A few of the paragraphs at the end of the interview were added to bring the record up to date. What comes through is a picture of Hirofumi Uzawa, a truly distinguished scholar and a person dedicated to human betterment.

Hiro talked in his usual warm, friendly voice. He peppered the interview with his strong opinions about other major economists, often with lively anecdotes. Of course, Hiro's opinions are his own, not those of the interviewers or the editors. We hope that the readers will get as much out of this conversation with Hiro as we did.