nep-dge New Economics Papers
on Dynamic General Equilibrium
Issue of 2013‒10‒05
nineteen papers chosen by
Christian Zimmermann
Federal Reserve Bank of St. Louis

  1. Distribution capital and the short- and long-run import demand elasticity By Scott Davis; Mario Crucini
  2. Uncertainty Shocks Are Aggregate Demand Shocks By Zheng Liu; Sylvain Leduc
  3. The federal funds market, excess reserves, and unconventional monetary policy By Jochen Güntner
  4. Transitional Dynamics and Long-run Optimal Taxation Under Incomplete Markets By Acikgoz, Omer
  5. Labor Market Polarization and International Macroeconomic Dynamics By Federico Mandelman
  6. Envelope condition method versus endogenous grid method for solving dynamic programming problems By Lilia Maliar; Serguei Maliar
  7. Financing Constraints, Firm Dynamics and Innovation By Andrea Caggese
  8. Robust Animal Spirits By Matthew Smith; Rhys Bidder
  9. Optimal Control of Infinite-Horizon Growth Models — A direct approach By Mário Amorim Lopes; Fernando A. C. C. Fontes; Dalila A. C. C. Fontes
  10. Too Old to Work, Too Young to Retire? By Andrea Ichino; Guido Schwerdt; Rudolf Winter-Ebmer; Andrea Ichino
  11. Economic Growth, Health, and the Choice of Polluting Technologies: The Role of Bureaucratic Corruption By Dimitrios Varvarigos
  12. Quantifying the Growth in Services: the Role of Skills, Scale, and Female Labor Supply By Min Qiang (Kent) Zhao; Joseph Kaboski; Francisco Buera
  13. Accounting for the Rise of Health Spending and Longevity By Fonseca, Raquel; Michaud, Pierre-Carl; Kapteyn, Arie; Galama, Titus
  14. Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain By Kenneth Judd; Lilia Maliar; Rafael Valero; Serguei Maliar
  15. Does longevity improvement always raise the length of schooling through the longer-horizon mechanism? By Sau-Him Lau
  16. Uncertainty and Investment Options By Nancy Stokey
  17. Efficient Sovereign Default By Alessandro Dovis
  18. Trade, firm selection, and innovation: the competition channel By Giammario Impullitti; Omar Licandro
  19. Child Labour and Inequality By Simone D\'Alessandro; Tamara Fioroni

  1. By: Scott Davis (Federal Reserve Bank of Dallas); Mario Crucini (Vanderbilt University)
    Abstract: International business-cycle models assume that home and foreign goods are poor substitutes. International trade models assume they are close substitutes. This paper constructs a model where this discrepancy is due to frictions in distribution. Imports need to be combined with a local non-traded input, distribution capital, which is slow to adjust. As a result, imported and domestic goods appear as poor substitutes in the short run. In the long run this non-traded input can be reallocated, and quantities can shift following a change in relative prices. Thus the observed substitutability between home and foreign goods gets larger as time passes.
    Date: 2013
  2. By: Zheng Liu (Federal Reserve Bank of San Francisco); Sylvain Leduc (Federal Reserve Bank of San Francisco)
    Abstract: We present empirical evidence and a theoretical argument that uncertainty shocks act like a negative aggregate demand shock, which raises unemployment and lowers inflation. We measure uncertainty using survey data from the United States and the United Kingdom. We estimate the macroeconomic effects of uncertainty shocks in a vector autoregression (VAR) model, exploiting the relative timing of the surveys and macroeconomic data releases for identification. Our estimation reveals that uncertainty shocks accounted for at least one percentage point increases in unemployment in the Great Recession and recovery, but did not contribute much to the 1981-82 recession. We present a DSGE model to show that, to understand the observed macroeconomic effects of uncertainty shocks, it is essential to have both labor search frictions and nominal rigidities.
    Date: 2013
  3. By: Jochen Güntner
    Abstract: Following the bankruptcy of Lehman Brothers, interbank borrowing and lending dropped, whereas reserve holdings of depository institutions skyrocketed, as the Fed injected liquidity into the U.S. banking sector. This paper introduces bank liquidity risk and limited market participation into a real business cycle model with ex ante identical financial intermediaries and shows, in an analytically tractable way, how interbank trade and excess reserves emerge in general equilibrium. Investigating the role of the federal funds market and unconventional monetary policy for the propagation of aggregate real and financial shocks, I find that federal funds market participation is irrelevant in response to standard supply and demand shocks, whereas it matters for “uncertainty shocks”, i.e. mean-preserving spreads in the cross-section of liquidity risk. Liquidity injections by the central bank can absorb the effects of financial shocks on the real economy, although excess reserves might increase and federal funds might be crowded out, as a side effect.
    Keywords: Excess reserves, Federal funds market, Financial frictions, Liquidity risk, Unconventional monetary policy
    JEL: C61 E32 E51 E52
    Date: 2013–09
  4. By: Acikgoz, Omer
    Abstract: Aiyagari (1995) showed that long-run optimal fiscal policy features a positive tax rate on capital income in Bewley-type economies with heterogeneous agents and incomplete markets. However, determining the magnitude of the optimal capital income tax rate was considered to be prohibitively difficult due to the need to compute the optimal tax rates along the transition path. This paper shows that, in this class of models, long-run optimal fiscal policy and the corresponding allocation can be studied independently of the initial conditions and the transition path. Numerical methods based on this finding are used on a model calibrated to the U.S. economy. I find that the observed average capital income tax rate in the U.S. is too high, the average labor income tax rate and the debt-to-GDP ratio are too low, compared to the long-run optimal levels. The implications of these findings for the existing literature on the optimal quantity of debt and constrained efficiency are also discussed.
    Keywords: Optimal Taxation, Ramsey Problem, Incomplete Markets, Heterogeneous Agents
    JEL: E2 E21 E25 E6 E62 H3 H6
    Date: 2013–09
  5. By: Federico Mandelman (Federal Reserve Bank of Atlanta)
    Abstract: During the last thirty years, labor markets in advanced economies where characterized by their remarkable polarization. As job opportunities in middle-skill occupations disappeared, employment opportunities concentrated in the highest- and lowest wage occupations. I develop a two-country stochastic growth model that incorporates trade in tasks, rather than in goods, and reveal that this setup can replicate the observed polarization in the U.S. This polarization was not an steady process: the relative employment share of each skill group significantly fluctuated over short-to medium horizons. I show that the domestic and international aggregate shocks estimated within this framework can rationalize such employment dynamics, while providing a good fit to the macroeconomic data. The model is estimated with employment data for different skills groups, and trade-weighted macroeconomic indicators.
    Date: 2013
  6. By: Lilia Maliar (Universidad de Alicante); Serguei Maliar (Universidad de Alicante)
    Abstract: We introduce an envelope condition method (ECM) for solving dynamic programming problems. The ECM method is simple to implement, dominates conventional value function iteration and is comparable in accuracy and cost to Carroll’s (2005) endogenous grid method. Codes are available.
    Keywords: Numerical dynamic programming; Value function iteration; Endogenous grid; Envelope condition; Curse of dimensionality; Large scale
    JEL: C6 C61 C63 C68
    Date: 2013–07
  7. By: Andrea Caggese (Pompeu Fabra University)
    Abstract: This paper develops the model of an industry with heterogeneous firms, and studies the effect of financing frictions and bankruptcy risk on innovation and aggregate productivity growth. The model has two main features: i) the technology of firms gradually becomes obsolete. Firms can counter this process by innovating, but the innovation outcome is risky. ii) Financial frictions cause the inefficient default of financially fragile firms, deter entry, and reduce competitive forces in the industry. I calibrate and solve the model and simulate several industries, and show that financing frictions have two distinct effects on innovation: a "direct effect", for firms that cannot innovate because of lack internal funds to invest, and an "indirect effect", where the changes in competition and profitability change also the incentives to innovate. Simulation results first show that, for realistic parameter values, the indirect effect of financing frictions is much more important than the direct effect in determining the innovation decisions. Second, they show that "Safe innovation" (where firms invest to upgrade their technology and are certain to increase their productivity) is increased by the presence of financing frictions, because the reduction in competition increases the return on innovation. Conversely "Risky innovation" (where firms invest to improve their productivity, but with some probability fail to do so and end up reducing their productivity instead), is discouraged by financing frictions. This happens because the reduction in competition implies that firms remain profitable for a longer time and therefore they wait longer before attempting a risky innovation process. I test these predictions and their implications for productivity growth on a sample of Italian manufacturing firms, and I find that the life cycle and innovation decisions of firms are fully consistent with the model with risky innovation.
    Date: 2013
  8. By: Matthew Smith (Federal Reserve Board of Governors); Rhys Bidder (Federal Reserve Bank of San Francisco)
    Abstract: In a real business cycle model, an agent's fear of model misspecification interacts with stochastic volatility to induce time varying worst case scenarios. These time varying worst case scenarios capture a notion of animal spirits where the probability distributions used to evaluate decision rules and price assets do not necessarily reflect the fundamental characteristics of the economy. Households entertain a pessimistic view of the world and their pessimism varies with the overall level of volatility in the economy, implying an amplification of the effects of volatility shocks. By using perturbation methods and Monte Carlo techniques we extend the class of models analyzed with robust control methods to include the sort of nonlinear production-based DSGE models that are popular in academic research and policymaking practice.
    Date: 2013
  9. By: Mário Amorim Lopes (FEP); Fernando A. C. C. Fontes (FEUP); Dalila A. C. C. Fontes (FEP)
    Abstract: We propose a framework to solve dynamic nonlinear infinite-horizon models like those found in the standard economic growth literature. We employ a direct method to solve the underlying optimal control problem, something novel in the economic literature. Instead of deriving the necessary optimality conditions and solving the originated ordinary differential equations, this method first discretizes and then optimizes, in effect transforming the prob- lem into a nonlinear programming problem to be optimized at each sampling instant. We incorporate the work of Fontes (2001) in order to transform the infinite-horizon problem into an equivalent finite-horizon representation of the model. This framework presents several advantages in comparison to the available alternatives that use indirect methods. First, no linearization is required, which sometimes can be erroneous. The problem can be studied in its nonlinear form. Secondly, it enables the simulation of a shock when the economy is not at its steady state, a broad assumption required by all available numerical methods. Thirdly, it allows for the easy study of anticipated shocks. It also allows for the analysis of multiple, sequential shocks. Finally, it is extremely robust and easy to use. We illustrate the application of the framework by solving the standard Ramsey-Cass-Koopsman exogenous growth model and the Uzawa-Lucas endogenous two-sector growth model.
    Keywords: optimal control, direct methods, transitional dynamics, economic growth, non-steady state shocks, sequential shocks.
    JEL: C61 C63 O40
    Date: 2013–10
  10. By: Andrea Ichino; Guido Schwerdt; Rudolf Winter-Ebmer; Andrea Ichino
    Abstract: We study whether employment prospects of old and young workers differ after a plant closure. Using Austrian administrative data, we show that old and young workers face similar displacement costs in terms of employment in the long-run, but old workers lose considerably more initially and gain later. We interpret these findings using a search model with retirement as an absorbing state, that we calibrate to match the observed patterns. Our finding is that the dynamics of relative employment losses of old versus young workers after a displacement are mainly explained by different opportunities of transition into retirement. In contrast, differences in layoff rates and job offer arrival rates cannot explain these patterns. Our results support the idea that retirement incentives, more than weak labor demand, are responsible for the low employment rates of older workers.
    Keywords: Aging, Employability, Plant Closures, Matching
    JEL: J14 J65
    Date: 2013–08
  11. By: Dimitrios Varvarigos
    Abstract: I model an economy where the adverse health effects of pollution impede labour productivity and capital accumulation is the source of economic growth. Pollution is generated by firms that choose whether to employ a dirty technology and pay an environmental tax, or employ a clean technology and incur the cost of its adoption. The task of inspecting the environmental impact of each firm’s production technology is delegated to bureaucrats who are corruptible since they receive bribes in order to mislead authorities on the firms’ actual technology choice. The model can generate multiple steady state equilibria. In this context, the multiplicity of equilibria is associated with indeterminacy, due to the self-fulfilling nature of corruption incentives and the relevant implications for pollution, productivity and economic growth.
    Keywords: Corruption; Economic Growth; Health; Pollution; Productivity
    JEL: D73 O44 Q58
    Date: 2013–09
  12. By: Min Qiang (Kent) Zhao (Xiamen University); Joseph Kaboski (University of Notre Dame); Francisco Buera (University of California at Los Angeles)
    Abstract: This paper quanties the role that increases in the demand for skill intensive goods and services, the ecient scale of production of services, and female labor supply have in explaining the growth of services. We extend the model in Buera and Kaboski (2012a,b) to a two-person household model, incorporating a joint household decision on home and market production into the model, and allow for skill and sectoral biased technology progress. The calibrated analysis shows that the channels emphasized in the theory are quantitatively important. The rising scale of services, the rising demand for skill-intensive output stemming from rising incomes, skill-biased technical change, and rising female labor supply all play important quantitative roles and together account for the majority of the growth of services. The extended model provides a direct link between female labor supply and the growth of service economy, which is shown to be important in the data.
    Date: 2013
  13. By: Fonseca, Raquel (University of Québec at Montréal); Michaud, Pierre-Carl (University of Québec at Montréal); Kapteyn, Arie (University of Southern California); Galama, Titus (University of Southern California)
    Abstract: We estimate a stochastic life-cycle model of endogenous health spending, asset accumulation and retirement to investigate the causes behind the increase in health spending and longevity in the U.S. over the period 1965-2005. We estimate that technological change and the increase in the generosity of health insurance on their own may explain 36% of the rise in health spending (technology 30% and insurance 6%), while income explains only 4% and other health trends 0.5%. By simultaneously occurring over this period, these changes may have led to complementarity effects which we find to explain an additional 57% increase in health spending. The estimates suggest that the elasticity of health spending with respect to changes in both income and insurance is larger with co-occurring improvements in technology. Technological change, taking the form of increased health care productivity at an annual rate of 1.3%, explains almost all of the rise in life expectancy at age 25 over this period, while changes in insurance and income together explain less than 10%. Welfare gains are substantial and most of the gain appears to be due to technological change.
    Keywords: health spending, longevity, life-cycle models, technological change
    JEL: I10 I38 J26
    Date: 2013–09
  14. By: Kenneth Judd (Hoover Institution); Lilia Maliar (Universidad de Alicante); Rafael Valero (Dpto. Fundamentos del Análisis Económico); Serguei Maliar (Universidad de Alicante)
    Abstract: First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to target higher quality of approximation in some dimensions than in others. Third, we show how to effectively adapt the Smolyak hypercube to a solution domain of a given economic model. Finally, we advocate the use of low-cost fixed-point iteration, instead of conventional time iteration. In the context of one- and multi-agent growth models, we find that the proposed techniques lead to substantial increases in accuracy and speed of a Smolyak-based projection method for solving dynamic economic models.
    Keywords: Smolyak method; sparse grid; adaptive domain; projection; anisotropic grid; collocation; high-dimensional problem
    JEL: C63 C68
    Date: 2013–09
  15. By: Sau-Him Lau (University of Hong Kong)
    Abstract: Hazan (2009) performs empirical analysis based on the conjecture that a necessary condition for higher life expectancy to cause longer schooling years is that it also increases lifetime labor supply, and reaches controversial conclusions. We aim to examine the theoretical validity of Hazan's (2009) conjecture, and more generally, to understand the relation between these two conditions in a standard life-cycle model. We find that the relation between the effects on optimal schooling years and expected lifetime labor supply differs systematically with respect to mortality reductions at different stages of the life cycle. Based on these systematic differences, we find that longer lifetime labor supply is not sufficient for increased schooling years for mortality reductions during the schooling years, and not necessary for increased schooling years for some mortality reductions during the working years. We provide explanations regarding why Ben-Porath’s (1967) longer-horizon mechanism in the analysis of the timing of human capital investment is not always applicable to the question regarding the impact of mortality decline on human capital investment.
    Date: 2013
  16. By: Nancy Stokey (University of Chicago)
    Abstract: This paper develops a simple model in which uncertainty about future tax policy leads to a temporary reduction in investment. The basic idea is that policy uncertainty creates uncertainty about the profitability of investment. If the uncertainty is likely to be resolved in the not-too-distant future, firms rationally delay committing resources to irreversible projects, reducing current investment. When the uncertainty is resolved, investment recovers, generating a temporary boom. The size of the boom depends on the realization of the fiscal uncertainty, with lower realizations of the tax rate producing larger booms.
    Date: 2013
  17. By: Alessandro Dovis (University of Minnesota)
    Abstract: Sovereign debt crises are associated with severe output and consumption losses for the debtor country and with reductions in payments for the creditors. Moreover, such crises are accompanied by trade disruptions that lead to a sharp fall in the imports of intermediate inputs. Here I study the efficient risk-sharing arrangement between a sovereign borrower and foreign lenders in a production economy where the sovereign government cannot commit and has some private information. I show that the ex-ante efficient arrangement involves outcomes that resemble sovereign default episodes in the data. These outcomes are ex-post inefficient, in the sense that if the borrower and the lenders could renegotiate the terms of their agreement, committing not to do it again in the future, then both could be made better off. The resulting efficient allocations can be implemented with non-contingent defaultable bonds and active maturity management. Defaults and periods of temporary exclusion from international credit markets happen along the equilibrium path and are essential to supporting the efficient allocation. Furthermore, as in the data, interest rate spreads increase and the maturity composition of debt shifts toward short-term debt as the indebtedness of the sovereign borrower increases.
    Date: 2013
  18. By: Giammario Impullitti; Omar Licandro
    Abstract: The availability of rich ?rm-level data has led researchers to uncover new evidence on the effects of trade liberalization. First, trade openness forces the least productive fi?rms to exit the market; secondly, it induces surviving fi?rms to increase their innovation efforts; thirdly, it increases the degree of product market competition. In this paper, we propose a model aimed at providing a coherent interpretation of these ?ndings, and use it to asses the role of fi?rm selection in shaping the aggregate welfare gains from trade. We introduce ?firm heterogeneity into an innovation-driven growth model where incumbent fi?rms operating in oligopolistic industries perform cost-reducing innovation. In this environment, trade liberalization leads to lower markups level and dispersion, tougher fi?rm selection, and more innovation. Calibrated to match US aggregate and fi?rm-level statistics, the model predicts that moving from a 13% variable trade costs to free trade increases the stationary annual rate of productivity growth from 1:19 to 1:29% and increases welfare by about 3% of steady state consumption. Selection accounts for about 1/4th of the overall growth increase and 2/5th of the welfare gains from trade.
    Keywords: International Trade, Heterogeneous Firms, Oligopoly, Innovation, Endogenous Markups, Welfare, Competition. JEL codes: F12, F13, O31, O41
    Date: 2013–04
  19. By: Simone D\'Alessandro (University of Pisa); Tamara Fioroni (Department of Economics (University of Verona))
    Abstract: This paper focuses on the evolution of child labour, fertility and human capital in an economy characterized by two types of workers, low- and high-skilled. This heterogeneity allows an endogenous analysis of inequality generated by child labour. More specifically, according to empirical evidence, we offer an explanation for the emergence of a vicious cycle between child labour and inequality. The basic intuition behind this result arises from the interdependence between child labour and fertility decisions. Furthermore, we investigate how child labour regulation policies can influence the welfare of the two groups in the short run, and the income distribution in the long run. We find that conflicts of interest may arise between the two groups
    Keywords: Child Labour, Fertility, Human capital, Inequality
    JEL: J13 J24 J82 K31
    Date: 2013–10

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