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.

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.

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.

Traditional regression models have reported conflicting results on the effectiveness of tax incentives in stimulating business investment. This study investigates the effects of the Bush tax cuts on U.S. investment using intervention analysis in conjunction with regression analysis that controls for relevant variables. Although intervention analysis has the advantage of allowing the behavior of investment to be influenced only by the time path of exogenous shocks such as tax reforms, control variables can test for the robustness of the results. We have found that the two tax reforms enacted in 2001 and 2003 had little impact on marginal investment incentives. The intervention analysis results are further reinforced by the evidence provided by alternative regression models that control for a host of variables. The failure of the tax reforms to stimulate investment spending may be attributable to several factors, such as a global savings glut, cheap global money, inappropriate designs for tax incentives, and budget deficits.

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.

This paper incorporates an education signaling mechanism into a dynamic model of production and asks if “higher education as a signal” helps explain the simultaneous increase in the supply and price of skilled relative to unskilled labor in the United States since 1980. The key mechanism is that if college degrees serve as a signal of unobservable talent and talent is productive at the workplace, then improved access to college will enable a higher fraction of the population to signal talent by completing college, resulting in degrees being a better signal about talent and a widening skill premium. When I assess the contribution of signaling in the model calibrated to the US economy from 1980 to 2003, I find that about 10% of the increase in the skill premium can be attributed to the signaling mechanism, after adjusting for the potential decline in the quality of college graduates.

This paper investigates how responses of US macroeconomic activities to monetary policy shocks depend on the state of broker–dealer leverage. The analysis makes use of leverage data to create an indicator series that distinguishes above and below-trend leverage states for the economy which is then integrated into switching econometric models. Using state-dependent local projection methods, we find that during the below-trend leverage state, monetary policy affects the economy in a traditional fashion. However, during the above-trend leverage state, expansionary monetary policy is problematic for stimulating the economy. Additionally, during the above-trend leverage state, we find that a policy rate cut raises counterparty risks in financial markets, which in part accounts for the weaker effectiveness of the monetary policy. These findings are robust to several alternative modeling specifications and suggest that monetary policy authorities should monitor the leverage cycle when determining their policy stance on macroeconomic stability.

This paper proposes a dynamic model to capture the interaction among the environment, human capital accumulation, and economic growth. We emphasize the mechanism that pollution stock depresses human capital accumulation, which has received increasing support from empirical studies. The model predicts that the development of pollution-intensive industries can help an economy gear up a short-run prosperity, but it impairs the capability for long-run economic growth, trapping the economy at a low development level. The cost for a dirty economy to switch is expensive and even infeasible if the environmental degradation is irreversible. Policy interventions, such as tax on pollution and subsidy on human capital, can help alleviate but cannot eradicate the economic stagnation.

We study the impact of uncertainty shocks using a disaggregated model featuring US state-level unemployment, and uncertainty measured using state-level Google search data. Importantly, the model captures spillovers across states and identifies substantial differences in peak responses and time dynamics. Moreover, the importance of national factors in propagating the effect of uncertainty is also heterogeneous across states, but less relevant than state-level factors. These heterogeneous effects are related to state-specific industry compositions and fiscal positions. In addition, we highlight the usefulness of disaggregated data in models of uncertainty and economic activity for the USA, based on the superior ability of the disaggregate model to predict aggregate uncertainty and unemployment.

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.

This paper estimates an enriched version of the mainstream medium-scale dynamic stochastic general equilibrium model, which features nonseparability between consumption and real money balances in utility and a systematic response of the policy rate to money growth. Estimation results show that money is a significant factor in the monetary policy rule. As a consequence, econometric analysis that omits money from Taylor rules may lead to biased estimates of the model parameters. In contrast to earlier studies that rely on small-scale models, the paper stresses the merits of using a sufficiently rich model. First, it delivers different results, such as the role of nonseparability between consumption and money in utility. Second, the rich dynamics embedded in the model allow us to explore the responses of a larger set of macroeconomic variables, making the model more informative on the effects of shocks and more useful for understanding the sources of business cycles. Third and most importantly, it reveals the possible pitfalls of relying on small-scale models when studying money’s role in business cycles.

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.

A mandate framework is proposed for delegating monetary policy to an instrument-independent, but goal-dependent central bank that emphasizes simplicity in both the objectives entering the welfare criterion and those in the instrument rule. It consists of: (i) a simple quadratic loss function penalizing deviations from target variables; (ii) a welfare-optimized, Taylor-type log-linear nominal interest-rate rule with targets that match those in the loss function; (iii) a zero-lower-bound (ZLB) constraint on the nominal interest rate imposing a low unconditional probability of ZLB episodes; and (iv) a long-run inflation target. In an estimated New Keynesian model with these features, we find that for a quarterly probability of 5%, an optimal annual inflation target is close to 2%, weights for real variables in the loss function are small compared with inflation except for the real wage growth mandate and the optimized rules mimic a price-level rule.

The US Social Security program was created in part as an explicit response to the Great Depression. We evaluate the performance of Social Security as a protective safety net against a rare episode of sudden and significant loss of private wealth such as the Great Depression. We construct a model in which a rare event causes a shock to wealth at an unknown time. How well does Social Security function as a safety net against such risk? The answer depends critically on whether households optimize in the face of this risk. If the household has full information on the distribution of rare event risk and solves a dynamic stochastic problem to hedge this risk, then Social Security is unnecessary along this dimension. Alternatively, if the household does not account for rare event risk in its financial planning, then Social Security can provide very large welfare gains as a safety net.

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.

Recent emphasis has been placed on exploring behavioral aspects of individual agents in explaining macroeconomic phenomena. Of particular interest is augmenting New Keynesian models to produce costly disinflation, as empirics and consensus suggest. We presume a fraction of agents using rule-of-thumb behavior in price setting in an otherwise standard New Keynesian model. Our findings suggest that relatively small amounts of rule-of-thumb behavior are required to offset the net effects of Ball's disinflationary boom. Moderate levels of rule-of-thumb behavior can produce delayed recessions consistent with some VAR evidence. However, high proportions of rule-of-thumb behavior are needed to produce immediate reductions in output following implementation.

This study proposes the unified framework of a three-sector model with structural change where agriculture, manufacturing, and service sectors have different production technologies. All three sectors use the factors of capital, labor, and land as inputs. The constant-growth path (CGP), which is the trajectory along which the rental rate of capital remains constant, is used to reconcile the Kaldor and Kuznets facts, and plays a role in linking the wage rate and land rent in the three-factors model. Because the prices of agricultural goods and services are determined endogenously, the CGP condition is no longer the knife-edge condition. We find that the dynamic system along the CGP in the three-sector, three-factor model corresponds to the standard two-sector optimal growth model.

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.