This paper examines how wealth and income inequality dynamics are related to fluctuations in the functional income distribution over the business cycle. In a panel estimation for OECD countries between 1970 and 2016, although inequality is, on average countercyclical and significantly associated with the capital share, one-third of the countries display a pro- or noncyclical relationship. To analyze the observed pattern, we incorporate distributive shocks into an RBC model, where agents are ex ante heterogeneous with respect to wealth and ability. We find that whether wealth and income inequality behave countercyclically or not depends on the elasticity of intertemporal substitution and the persistence of shocks. We match the model to quarterly US data using Bayesian techniques. The parameter estimates point toward a non-monotonic relationship between productivity and inequality fluctuations. On impact, inequality increases in response to TFP shocks but subsequently declines. Furthermore, TFP shocks explain 17% of inequality fluctuations.

This paper provides an explanation for the supervisory role of the central bank in a monetary general equilibrium model of bank liquidity provision. Under incomplete information on the individual banks' liquidity needs, individual banks find it optimal to invest solely in bank loans holding no cash reserves, and rely on the interbank market for their withdrawal demands. Using the costly state verification approach under uncertainty in aggregate liquidity demands, the supervisory role of the central bank as a large intermediary arises as an incentive-compatible arrangement by which banks hold the correct level of cash reserves. First, it takes up a delegated monitoring role for the banking system. Second, it engages in discount-window lending at a penalty rate, where the discount margin covers exactly the monitoring cost incurred. Finally, under the central banking mechanism, currency premium no longer exists in the sense that currency is worth the same as deposits having an equal face value.

Carbon pricing aims to shift the risk-adjusted returns on investment in favor of green technologies vis-‘a-vis fossil investment, relying on efficient capital markets to redirect investment accordingly. Capital markets with financial frictions can distort this transmission of climate policy. This study analyses the impact of emission taxes on mitigation and low-carbon investment in the presence of financial frictions. We develop a two-sector environmental dynamic stochastic general equilibrium model calibrated to the Euro Area, to simulate an economic transition in line with the EU climate targets. Financial frictions dampen the response of the economy to the carbon tax such that the emissions target will be missed by 11 percentage points. Moreover, the adverse effects of financial frictions increase when climate policy is delayed. We further identify a volume and a risk effect that drive the impact of a financial wealth shock and an uncertainty shock on emission intensity.

Short-selling constraints are common in financial markets, while physical assets such as housing often lack markets for short-selling altogether. As a result, investment decisions are often restricted by such constraints. This paper studies asset prices in behavioral heterogeneous-belief models with short-selling constraints and arbitrarily many belief types. We provide conditions on beliefs such that short-selling constraints bind for different types, along with analytic expressions for price and demands that allow us to construct fast solution algorithms relevant for a wide range of models. An application studies how an alternative uptick rule, as in the United States, affects price dynamics and wealth distribution in a market with many belief types in evolutionary competition. In a numerical example, we highlight a scenario in which a modified version of the alternative uptick rule, triggered by smaller percentage falls in price, reduces both asset mispricing and wealth inequality relative to the current regulation. As extensions, we show how our method applies to multiple asset markets with short-selling constraints, additional heterogeneities, and price setting by a market maker.

Much empirical evidence finds that governments react to fiscal imbalances in a nonlinear way, through an increasing marginal response of primary surpluses to changes in debt. This paper shows that nonlinear fiscal regimes alter equilibria under active and passive monetary–fiscal policies. The Fisher equation combined with nonlinear fiscal policies leads to multiple steady states. Under passive interest rate rules, even if the steady state in which fiscal policy is active is locally saddlepath stable, there exist infinite equilibrium paths originating in the neighborhood of that steady state that converge into a high-debt trap. Under active interest rate rules, even if the steady state at which fiscal policy is active is locally unstable, there exists a saddle connection with the high-debt equilibrium along which inflation is uniquely determined.

We investigate the stability properties of Muth's model of price movements when agents choose a production level using replicator dynamic learning. It turns out that when there is a discrete set of possible production levels, possible stable states and stability conditions differ between adaptive learning and replicator dynamic learning.

This is the second part of a two-part survey of the modern theory of nonlinear dynamical systems. We focus on the study of statistical properties of orbits generated by maps, a field of research known as ergodic theory. After introducing some basic concepts of measure theory, we discuss the notions of invariant and ergodic measures and provide examples of economic applications. The question of attractiveness and observability, already considered in Part I, is revisited and the concept of natural, or physical, measure is explained. This theoretical apparatus then is applied to the question of predictability of dynamical systems, and the notion of metric entropy is discussed. Finally, we consider the class of Bernoulli dynamical systems and discuss the possibility of distinguishing orbits of deterministic chaotic systems and realizations of stochastic processes.

We analyze the implications of trend growth for optimal monetary policy in the presence of search and matching unemployment. We show that trend growth interacts importantly with the inefficiencies stemming from the labor market. Higher trend growth exacerbates the inefficiencies of the labor market and therefore calls for larger deviations from price stability. Our analysis implies that lower trend growth reduces not only the level but also the optimal volatility of the nominal interest rate.

This paper examines optimal policy in a macroeconomic model with collateral constraints. Binding collateral constraints yield inefficient competitive equilibrium allocations because they distort the optimal utilization of real resources. I identify the set of policy instruments that can be used by a Ramsey planner to achieve the first-best and the second-best (i.e., constrained planner's) allocations. A system of distortionary taxes on capital and labor income, along with direct lump-sum transfers among borrowers and lenders replicates the first-best outcome. The tax rates correct for the marginal distortions, whereas the direct lump-sum transfers perform income redistributions among the agents. In absence of direct lump-sum transfers, the distortionary taxes have an additional role, i.e., to perform implicit income transfers, and only second-best outcomes are attainable. I also derive the optimal policy in response to real and financial shocks, and show how the policy recommendations differ depending on the set of policy instruments available.

This paper shows how fiscal policy affects unemployment in a New Keynesian model with search and matching frictions and distortionary taxation. The model is estimated using US data that includes labor market flows and distinct fiscal instruments. Several findings stand out. First, unemployment multipliers for spending and consumption tax cuts are substantial, even though output multipliers turn out to be less than one. Second, multipliers for labor tax cuts are small. Third, fiscal rules enhance the positive effects of discretionary fiscal policy. However, these expansionary effects on the multipliers are modest compared to earlier studies.

This paper studies how search externalities and wage bargaining distort vacancy creation and the allocation of workers to jobs in markets with two-sided heterogeneity. To do so, I propose a model of a frictional labor market where heterogeneous workers decide which job to look for and firms decide which technology to adopt. At equilibrium, there is perfect segmentation across sectors, which is determined by a unique threshold of workers' productivity. This threshold is inefficient because of participation and composition externalities. The Pigouvian tax scheme that decentralizes optimal sorting shows that these externalities have opposite signs. Furthermore, their relative strength depends on the distribution of workers' skills, so that when there are many (few) skilled workers, too many (few) high-technology jobs are created.

This paper analyzes whether the Fed had the ability through its conventional monetary policy to affect key economic and financial variables, and, in particular, the term structure of interest rates, during the recent financial crisis. This departs from the empirical literature that focuses mainly on the effectiveness of unconventional monetary policies during this episode, although these policies are appropriate only to the extent that the conventional policy was ineffective in the first place. Our identification strategy based on the conditional heteroskedasticity of the structural innovations allows us to specify a flexible structural vector auto-regressive process that relaxes the identifying assumptions commonly used in earlier studies. Comparing our results obtained from samples excluding and including the financial crisis, we find that the conventional monetary policy has lost its effectiveness shortly after the beginning of the financial turmoil. This result suggests that the Fed's use of unconventional policies was appropriate, at least, with the objective of changing the term structure of interest rates.

Growth in total factor productivity (TFP) in the USA has slowed down significantly since the mid-2000s, reminiscent of the productivity slowdown of the 1970s. This paper investigates the implications of a productivity slowdown on macroeconomic variables using a standard real business cycle (RBC) model, extended with regime-switching in trend productivity growth and Bayesian learning regarding the growth regime. I estimate the Markov-switching parameters using US data and maximum-likelihood methods, and compute the model solution using global projection methods. Simulations reveal that, while adding a regime-switching component to the standard RBC setup increases the volatility in the system, further incorporating incomplete information and learning significantly dampens this effect. The dampening is mainly due to the responses of investment and labor in response to a switch in the trend component of TFP growth, which are weaker in the incomplete information case as agents mistakenly place some probability that the observed decline in TFP growth is due to the transient component and not due to a regime switch. The model offers an objective way to infer slowdowns in trend productivity, and suggests that macroeconomic aggregates in the USA are currently close to their potential levels given observed productivity, while counterfactual simulations indicate that the cost of the productivity slowdown to US welfare has been significant.

The objective of this book is to provide “a systematic theory of endogenous business fluctuations and growth with a hierarchical structure of integrated macro-dynamical models” (p. 372). The starting point is Tobin's neoclassical model of monetary growth, and successive chapters show how Tobin's model can be extended in various “realistic” directions while preserving the relevant adding-up and balance-sheet constraints of a macro model. The work reported here is squarely in an ongoing European theoretical tradition that eschews the stochastic, representative-agent, approach to macroeconomic modeling. Absent stochastic disturbances, the authors provide a qualitative analysis of dynamic behavior for a variety of closed-economy models—a variety that, as the authors themselves point out, is closely related to three prototype models studied in Part I of Sargent's 1977 book, Macroeconomic Theory.

We study production functions with capital and labor as arguments that exhibit positive, yet diminishing marginal products and constant returns to scale. We show that such functions satisfy the Inada conditions if (i) both inputs are essential and (ii) an unbounded quantity of either input leads to unbounded output. This allows for an alternative characterization of the neoclassical production function that altogether dispenses with the Inada conditions. Although this proposition generalizes to the case of n > 2 factors of production, its converse does not hold: 2n Inada conditions do not imply that each factor is essential.

In this paper, we study the positive and normative implications of financial shocks in a standard New Keynesian model that includes banks and frictions in the market for bank capital. We show how such frictions influence materially the effects of bank liquidity shocks and the properties of optimal policy. In particular, they limit the scope for countercyclical monetary policy in the face of these shocks. A fiscal policy instrument can complement monetary policy by offsetting the balance-sheet effects of these shocks, and jointly optimal policies attain the same equilibrium that monetary policy (alone) could attain in the absence of equity-market frictions.

We develop a model with financial frictions and sovereign default risk wherein the maturity of public debt is allowed to be larger than one period. When the debt portfolio has longer average maturities, public debt increases less in the event of a crisis, reducing the size of the subsequent fiscal consolidation through distorsionary taxes or public spending, with positive effects on welfare. In addition, we provide some results suggesting that optimized fiscal responses to a crisis depend on the average maturity of the debt portfolio.

This paper develops a theory of human capital to investigate the role of early childhood health in explaining the large and persistent schooling gaps observed within and across countries. Quantitative analysis using the theory and data from 98 countries shows that early health inequalities within developingcountries strongly amplify later schooling gaps— counterfactually eliminating inequalities reduces schooling Ginis by an average of 18% in developing economies but has only mild effects in richer countries. Moreover, early health inequalities are found to be an important source of schooling variation across countries— universally equating early health to the average US level reduces the cross-country standard deviation of average schooling attainment by over 40%. Additional policy experiments reveal that the gains from early health interventions tend to be amplified by later educational investments in developing economies, while those targeting school-aged children may be limited if early health conditions are ignored.

One usually identifies bubble solutions to linear rational expectations models by extra components (irrelevant lags) arising in addition to market fundamentals. Although there are still many solutions relying on a minimal set of state variables, i.e., relating in equilibrium the current state of the economic system to as many lags as initial conditions, there is a conventional wisdom that the bubble-free (fundamentals) solution should be unique. This paper examines the existence of endogenous stochastic sunspot fluctuations close to solutions relying on a minimal set of state variables, which provides a natural test for identifying bubble and bubble-free solutions. It turns out that only one solution is locally immune to sunspots, independently of the stability properties of the perfect-foresight dynamics. In the standard saddle-point configuration for these dynamics, this solution corresponds to the so-called saddle stable path.

By studying complete and incomplete dynamic financial markets, I show that if some agents are money-illusioned and neglect inflation, the rational agents who are aware of inflation are driven out of the market in the long run, in the sense that the money-illusioned agents consume the economy's entire endowment. The reason for this finding is that with inflation, the money-illusioned agents always believe that the return on their savings is higher than it actually is. Because these agents trade financial assets in markets with the rational agents, the rational agents end up being borrowers and the money-illusioned agents lenders. Because the rational agents' debt accumulates over time, they become so indebted that the money-illusioned agents eventually consume the economy's entire endowment. If there is deflation, the opposite is true, and the rational agents evolutionarily dominate.