We discuss the problem known in economics as backward dynamics occurring in models of perfect foresight, intertemporal equilibrium described mathematically by implicit difference equations. In a previously published paper [Journal of Economic Dynamics and Control 31 (2007), 1633–1671], we showed that by means of certain mathematical methods and results known as inverse limits theory it is possible to establish a correspondence between the backward dynamics of a noninvertible map and the forward dynamics of a related invertible map acting on an appropriately defined space of sequences, each of whose elements corresponds to an intertemporal equilibrium. We also proved the existence of different types of topological attractors for one-dimensional models of overlapping generations. In this paper, we provide an extension of those results, constructing a Lebesgue-like probability measure on spaces of infinite sequences that allows us to distinguish typical from exceptional dynamical behaviors in a measure–theoretical sense, thus proving that all the topological attractors considered in MR07 are also metric attractors. We incidentally also prove that the existence of chaos (in the Devaney–Touhey sense) backward in time implies (and is implied by) chaos forward in time.

Typically, contractionary monetary policy shocks increase the nominal and real rate of interest, which reduces both inflation and output . In contrast, the neo-Fisher effect (NFE) suggests that a transitory but persistent increase in the nominal rate of interest increases inflation in the short run. In a New Keynesian model augmented with several frictions, including the cost channel of monetary policy, real wage rigidity, habit formation in consumption, dampened expectations, and anticipated monetary policy shocks, we derive analytical conditions that give rise to (or avert) the NFE. We show that the NFE can arise due to the interplay between these frictions, and not only when the persistence of the policy shock is large, or when agents are forward-looking, as documented by the existing literature.

Many algorithms that provide approximate solutions for dynamic stochastic general equilibrium (DSGE) models employ the QZ factorization because it allows a flexible formulation of the model and exempts the researcher from identifying equations that give raise to infinite eigenvalues. We show, by means of an example, that the policy functions obtained by this approach may differ from both the solution of a properly reduced system and the solution obtained from solving the system of nonlinear equations that arises from applying the implicit function theorem to the model's equilibrium conditions. As a consequence, simulation results may depend on the specific algorithm used and on the numerical values of parameters that are theoretically irrelevant. The sources of this inaccuracy are ill-conditioned matrices as they emerge, e.g., in models with strong habits. Researchers should be aware of those strange effects, and we propose several ways to handle them.

A general equilibrium model with financial frictions in which individuals may encounter unobservable investment opportunities is developed along the lines of Kiyotaki and Moore (2012). I study efficiency properties induced by money and monetary policy when financial frictions prevent optimal equilibrium allocations. By providing closed-form solutions to all prices, allocations, welfare, and, especially, the distribution of individuals with respect to assets, I show that the Friedman rule achieves maximal social welfare, independent of how tight the financial constraints may be. The same level of welfare would be induced by an omniscient central planner able to verify who has an investment opportunity.

For previously identified weakly separable blockings of goods and assets, we construct aggregates using four superlative index numbers, the Fisher, Sato-Vartia, Törnqvist, and Walsh, two non-superlative indexes, the Laspeyres and Paasche, and the atheoretical simple summation. We conduct several tests to examine how well each of these aggregates “fit” the data. These tests are how close the aggregates come to solving the revealed preference conditions for weak separability, how often each aggregate gets the direction of change correct, and how well the aggregates mimic the preference ranking from revealed preference tests. We find that, as the number of goods and assets being aggregated increases, the problems with simple summation manifest.

Wage dispersion is a critical factor in determining the impact of a minimum wage and severance payments on job creation and destruction in a general equilibrium model with search frictions. When wage dispersion is low, the minimum wage and severance payments behave as substitutes. However, as dispersion in wages increases, these policies become complements. The model is estimated using data from Chile and used to perform quantitative welfare analysis.

This note extends the findings of Benhabib and Rusticchini [Journal of Economic Dynamics and Control 18, 807–813 (1994)], who provide a class of dynamic stochastic general equilibrium (DSGE) models whose solution is characterized by a constant savings rate. We show that this class of models may be interpreted as a standard–representative agent DSGE model with costly adjustment of capital.

The papers collected in this issue are united in a common view that it is rational to recognize that we have a poor perception of the constraints we face when making economic decisions and hence we employ decision rules that are robust. Robustness can be interpreted in different ways but generally it implies that our decision rules should not depend critically on an exact description of these constraints but they should perform well over a prespecified range of potential variations in the assumed economic environment. So, we are interested in deriving optimal and hence rational decisions where our utility or loss function incorporates the need for robustness in the face of a misspecified model. This misspecification can involve placing simple bounds on deviations from the parameters we assume for a nominal model, or misspecified dynamics, neglected nonlinearities, time variation, or quite general arbitrary misspecification in the transfer function between the input uncertainties and the output variables in which we are ultimately interested.

The global financial crisis was characterized by heightened financial risk in the USA, which spread to the rest of the world, including emerging economies. This paper constructs a core–periphery model with a global banking network and financial frictions. Due to a common-lender effect, when global banks lend to an emerging economy, heightened financial risk in the center depresses cross-border lending to the emerging economy, reducing real activities, and exacerbating monetary policy trade-offs. As financial markets become more integrated, exchange rate flexibility becomes less welfare enhancing and active capital account policy becomes more welfare enhancing.

The deleterious effect of debt restructuring on banks’ balance sheets and, consequently, on the economy as a whole has been a key policy issue. This paper studies how post-default fiscal policy interacts with this sovereign-bank loop and shape the response of a model economy. Calibration of the model matches characteristics of the Greek economy at the time of the bond exchange. Debt restructuring in place of higher lump-sum taxation or lower nonproductive government spending harms the economy even if no other cost of default is considered. However, the sovereign-debt loop is less costly to the economy than increases in labor or capital taxes to service debt. Even so, if fiscal policy is too responsive, a crowding-out effect inhibits the recovery of capital markets, hence a more conservative fiscal stance is desirable. Thus, how diabolic the post-default sovereign-bank loop is depends to a large extent on the way fiscal policy responds.

This paper investigates the effects of estate taxation when firms cannot directly observe worker skill levels. Imperfect labor market signaling gives rise to an information externality that causes workers to free-ride off of others’ human capital acquisition. Inherited wealth exacerbates the information externality because risk averse workers with larger inheritances exert less effort to acquire skills. By reducing these inheritances, an estate tax induces greater skill acquisition effort and increases the number of skilled workers. In a quantitative model with employer learning and capital accumulation, the optimal estate tax is significantly above zero, increases wages and output, and benefits a large majority of households.

Money and credit are ubiquitous in actual economies, but there is an active theoretical debate on whether they are both necessary if they can both be used in all transactions. Recently, Gu et al. (2016) have shown that money and credit cannot be simultaneously essential and debt limits do not matter for the determination of real allocations in a class of monetary economies. In this paper, we revisit their irrelevance result in a monetary economy based on Lagos and Wright (2005), which exhibits a misallocation of liquidity that is common in search models of money. We show that monetary loans, which naturally require the use of both money and credit, implement Pareto superior allocations in which the size of debt limits matters.

Understanding the causes of the Industrial Revolution, namely the process of transition from a Malthusian equilibrium to modern economic growth, has been the subject of passionate debate. This paper contributes to insights into the process of industrialization and the demographic transition that followed. We present a model that proposes a mechanism behind the claim that landed elites had strong incentives to block education reforms. By applying the theory of interest groups to landownership, landowners could delay education. However, they could not prevent its introduction indefinitely since gains for the landed elites derived from education would at some moment surpass the costs associated with them. We also sustain that improvements in agricultural productivity prior to the Industrial Revolution may have induced a positive impact on the landowners’ decision to educate the population, which led to an earlier introduction of education reforms. The conclusions fit the patterns of the late boom of industrialization and demographic transition and help explain why some countries (e.g., Britain and The Netherlands) had accelerated education reforms and a faster process of industrialization than most continental countries. A theoretical model is presented, and numerical simulations are exhibited to illustrate our claims.

This paper investigates the effects of a binding minimum wage in an economy which exhibits multiple unemployment equilibria. For this purpose, we develop a theoretical model based on the simple imperfectly competitive model of Manning [In Conference Papers, Economic Journal 100, 151–162 (1990)], in which we introduce labor heterogeneity and knowledge spillovers in the individual production technology. Then, using numerical simulations, we show that a binding minimum wage rules out the occurrence of an inefficient equilibrium. Last, we analyze the effects of a minimum wage increase on the labor market's outcomes.

Edward C. Prescott has argued that mandatory saving is socially desirable because it solves the problem of people intentionally free riding and becoming a welfare burden. Inspired by Prescott's argument, we develop a model in which rational individuals choose between saving and free riding. We find that free riding is a robust outcome for a significant share of the population and that everyone, including the free riders, benefits from the elimination of free riding through mandatory saving. Our results strengthen Prescott's position that free riding is a serious problem and that mandatory saving is socially desirable.

This paper presents a theoretical and empirical investigation of the relationship between human capital composition and economic growth. In the theoretical analysis, we allow for nonconstant returns to scale in technological activities. Differently from previous literature, our results show that, under broad and plausible model parameterizations, the marginal growth effect of skilled workers is increasing with the distance to the frontier for sufficiently poor countries while it is decreasing (in agreement with the existing literature) only for countries close to the technological frontier. Our empirical analysis provides robust evidence for this theoretical prediction by using a 10-year panel of 85 countries for the years in between 1960 and 2000, as well as by using the System Generalized Methods of Moments (GMM) technique to address the problem of endogeneity. Results are robust to different proxies of human capital and different specifications.

We revisit the Friedman rule in a labor search model and extend Heer (2003), Cooley and Quadrini (2004), and Wang and Xie (2013) to one that allows for endogenous growth. We show that, even without a liquidity effect or a CIA constraint on firms’ wage payment, our model offers a different channel for moderate money growth to increase welfare. Intuitively, in a one-sector endogenous growth economy, the technology is of constant returns with respect to capital. When the labor market is frictional, a moderate increase in money growth induces an expansion in vacancy and employment. Labor and capital are complements in production. With an increase in employment, when the technology is neoclassical, the decreasing return in capital leads to a lower marginal product of labor. However, in an endogenous growth framework wherein the technology exhibits socially constant returns in capital, the marginal product of labor is constant. Due to a constant marginal product of labor, modest inflation raises employment, enlarges economic growth, and increases welfare. Moreover, the optimal long-run inflation rate departs from the Friedman rule, even when the Hosios rule holds. Finally, we find that our model with sustainable growth fits the data better than that without sustainable growth.

We study a New Keynesian model with bounded rationality, where agents choose their expectations heterogeneously from a discrete choice set. The range of their set of possible expectation values can be interpreted as the anchoring of expectations. In the model, multiple locally stable steady states can arise that reflect coordination on particular expectation values. Moreover, bad shocks to the economy can trigger a self-reinforcing wave of pessimism, where the zero lower bound on the nominal interest rate becomes binding, and agents coordinate on a locally stable liquidity trap steady state. When we let the anchoring of expectations evolve endogenously, it turns out that the anchoring of expectations at the time the bad shocks hit the economy is crucial in determining whether the economy can recover from the liquidity trap. Finally, we find that a higher inflation target makes it less likely that self-reinforcing liquidity traps arise.

When the returns to scale of a production process vary with the intensity it is operated at, an AK model with constant returns to scale in production arises endogenously due to replication driven by profit maximization. If replication occurs at the efficiency-maximizing scale, as with perfect competition, the result applies also when the number of production processes must be discrete, thus, overcoming the so-called integer problem. When competition is imperfect, there is only convergence toward the AK model for large enough input use, so an economy is more prone to stalling in a steady state without growth, the smaller and less competitive it is.