nep-dge New Economics Papers
on Dynamic General Equilibrium
Issue of 2020‒11‒16
23 papers chosen by
Christian Zimmermann
Federal Reserve Bank of St. Louis

  1. Time-Inconsistent Optimal Quantity of Debt By YiLi Chien; Yi Wen
  2. Adverse selection, learning, and competitive search By Mayr-Dorn, Karin
  3. Searching for the Equity Premium By Hang Bai; Lu Zhang
  4. Sectoral Labor Mobility and Optimal Monetary Policy By Alessandro Cantelmo; Giovanni Melina
  5. The public debt multiplier By Alice Albonico; Guido Ascari; Alessandro Gobbi
  6. Higher education funding, welfare and inequality in equilibrium By Gustavo Mellior
  7. Technology adoption and mortality By John P. Hejkal; B. Ravikumar; Guillaume Vandenbroucke
  8. Time consistent equilibria in dynamic models with recursivepayoffs and behavioral discounting By Lukasz Balbus; Kevin Reffett; Lukasz Wozny
  9. How Should Unemployment Insurance Vary over the Business Cycle? By Serdar Birinci; Kurt See
  10. The International Consequences of Bretton Woods Capital Controls and the Value of Geopolitical Stability By Lee E. Ohanian; Paulina Restrepo-Echavarria; Diana Van Patten; Mark L. J. Wright
  11. Unemployment, firm dynamics, and the business cycle By Andrea Colciago; Stefano Fasani; Rossienza Rossi
  12. Recapitalization, Bailout, and Long-run Welfare in a Dynamic Model of Banking By Andrea Modena
  13. Trade Integration, Global Value Chains, and Capital Accumulation By Michael Sposi; Kei-Mu Yi; Jing Zhang
  14. When should retirees tap their home equity? By Hambel, Christoph; Kraft, Holger; Meyer-Wehmann, André
  15. Deep reinforced learning enables solving discrete-choice life cycle models to analyze social security reforms By Antti J. Tanskanen
  16. A simple model of liquidity By Emanuele Franceschi
  17. Hysteresis effects and financial frictions By Abdoulaye Millogo
  18. Wage Setting Under Targeted Search By Anton A. Cheremukhin
  19. Production Networks and the Propagation of Commodity Price Shocks By Shutao Cao; Wei Dong
  20. Financial Development and Trade Liberalization By David Kohn; Fernando Leibovici; Michal Szkup
  21. High-Dimensional DSGE Models: Pointers on Prior, Estimation, Comparison, and Prediction∗ By Siddhartha Chib; Minchul Shin; Fei Tan
  22. Entry Decision, the Option to Delay Entry, and Business Cycles By Ia Vardishvili
  23. Doubts on the Role of Disturbance Variance in New Keynesian Models and Suggested Refinements By Paul J.J. Welfens

  1. By: YiLi Chien; Yi Wen
    Abstract: A key feature of the infinite-horizon heterogeneous-agents incomplete-markets (Inf-HAIM) framework is that the equilibrium interest rate of public debt lies below the time discount rate (regardless of capital). This happens because of a positive liquidity premium on asset returns due to imperfect risk sharing. This fundamental property of standard Inf-HAIM models, however, implies that the Ramsey planner's fiscal policy may be time-inconsistent---because the planner has a dominate incentive to issue plenty of debt such that all households are fully self-insured against idiosyncratic risk whenever the interest rate of government borrowing is lower than the household time discount rate. But such a full self-insurance allocation may be infeasible---because to achieve it the optimal quantity of debt may approach infinity or the optimal labor tax rate may approach 100%. This is puzzling from an intuitive perspective because near the point of full self-insurance the marginal gains of increasing debt should be less than the marginal costs of financing the debt under distortionary taxes. We show that this puzzling behavior originates from the assumption that the planner must commit to future plans at time zero. Under such a full commitment, the Ramsey planner opts to exploit the low interest cost of borrowing to front load consumption by sacrificing future consumption in the long run---because future utilities are heavily discounted compared to the inverse of the interest rate on government bonds. We demonstrate our points analytically using a tractable Inf-HAIM model featuring non-linear preferences and a well-defined distribution of household wealth.
    Keywords: Time Inconsistency; Optimal Debt; Ramsey Problem; Incomplete Markets
    JEL: E13 E62 H21 H30
    Date: 2020–10–29
  2. By: Mayr-Dorn, Karin
    Abstract: I develop a dynamic version of the competitive search model with adverse selection in Guerrieri, Shimer and Wright (2010). My model allows for an analysis of the effects of firm learning on labor market efficiency in the presence of search frictions. I find that firm learning increases relative expected earnings in high-ability jobs and, thereby, enhances imitation incentives of low-ability workers. The net effect on the aggregate expected match surplus and unemployment is indeterminate a priori. Numerical results show that firm learning does not increase labor market efficiency.
    Keywords: job search,on-the-job effort,asymmetric information,learning
    JEL: D82 D83 J64
    Date: 2020
  3. By: Hang Bai; Lu Zhang
    Abstract: Labor market frictions are crucial for the equity premium in production economies. A dynamic stochastic general equilibrium model with recursive utility, search frictions, and capital accumulation yields a high equity premium of 4.26% per annum, a stock market volatility of 11.8%, and a low average interest rate of 1.59%, while simultaneously retaining plausible business cycle dynamics. The equity premium and stock market volatility are strongly countercyclical, while the interest rate and consumption growth are largely unpredictable. Because of wage inertia, dividends are procyclical despite consumption smoothing via capital investment. The welfare cost of business cycles is huge, 29%.
    JEL: E32 E44 G12
    Date: 2020–10
  4. By: Alessandro Cantelmo; Giovanni Melina
    Abstract: How should central banks optimally aggregate sectoral inflation rates in the presence of imperfect labor mobility across sectors? We study this issue in a two-sector New-Keynesian model and show that a lower degree of sectoral labor mobility, ceteris paribus, increases the optimal weight on inflation in a sector that would otherwise receive a lower weight. We analytically and numerically find that, with limited labor mobility, adjustment to asymmetric shocks cannot fully occur through the reallocation of labor, thus putting more pressure on wages, causing inefficient movements in relative prices, and creating scope for central banks intervention. These findings challenge standard central banks practice of computing sectoral inflation weights based solely on sector size, and unveil a significant role for the degree of sectoral labor mobility to play in the optimal computation. In an extended estimated model of the U.S. economy, featuring customary frictions and shocks, the estimated inflation weights imply a decrease in welfare up to 10 percent relative to the case of optimal weights.
    Date: 2020–10
  5. By: Alice Albonico; Guido Ascari; Alessandro Gobbi
    Abstract: We study the effects on economic activity of a pure temporary change in government debt and the relationship between the debt multiplier and the level of debt in an overlapping generations framework. The debt multiplier is positive but quite small during normal times while it is much larger during crises. Moreover, it increases with the steady state level of debt. Hence, the call for fiscal consolidation during recessions seems ill-advised. Finally, a rise in the steady state debt-to-GDP level increases the steady state real interest rate providing more room for manoeuvre to monetary policy to fight deflationary shocks.
    Date: 2020–10
  6. By: Gustavo Mellior
    Abstract: This paper analyses theoretically and quantitatively the effect that different higher education funding policies have on welfare (on aggregate and at the individual level) and wealth inequality. A heterogeneous agent model in continuous time, which has uninsurable income risk and endogenous educational choice is used to evaluate five different higher education financing schemes. Educational investments can be self financed, supported by government guaranteed student loans - that may come with or without income contingent support - or be covered by the public sector. When educational costs are small, differences in outcomes amongst systems are negligible. On the other hand, when these costs rise to realistic levels we see that there can be large gains in welfare and significant drops in inequality by moving to a system with more public sector support. This support can come in the form of tuition subsidies and/or income contingent student loans. However, as the cost of education and the share of debtors in society gets larger, it is preferable to increase public support in the form of tuition subsidies. The reason is that there is a pecuniary externality of debt that gets magnified when student loans become excessive. While I identify large steady state welfare gains from more public sector financing, I show that the transition costs can be large enough to justify the status quo.
    Keywords: Incomplete markets; Higher education funding; Human capital
    JEL: D52 D58 E24 I22 I23
    Date: 2020–10
  7. By: John P. Hejkal; B. Ravikumar; Guillaume Vandenbroucke
    Abstract: We develop a quantitative theory of mortality trends and population dynamics. In our theory, individuals incur time and/or goods costs over their life cycle, to adopt a better health technology that increases their age-specific survival probability. Technology adoption is a source of a dynamic externality: As more individuals adopt the better technology, the marginal benefit of future adoption increases. The allocation of time and/or goods also depends on total factor productivity (TFP): As TFP grows, more resources are allocated to technology adoption. Both channels---the dynamic externality and TFP---result in lower mortality. Our theory is consistent with three key facts: (i) The cross-country correlation between mortality and income is negative, (ii) mortality in poor countries has converged to that of rich countries although the income of poor countries has not, and (iii) mortality decline precedes economic take-off. We calibrate the model to match mortality in France from 1816 to 2010. Quantitatively, the model accounts for 54% of the closing of the mortality gap between France and low-income countries over the past 50 years.
    Keywords: Mortality; population dynamics; technology adoption; diffusion
    JEL: E13 I12 I15 J11
    Date: 2020–10
  8. By: Lukasz Balbus; Kevin Reffett; Lukasz Wozny
    Abstract: We prove existence of time consistent equilibria in a wide class of dynamic models with recursive payoffs and generalized discounting involving both behavioral and normative applica-tions. Our generalized Bellman equation method identifies and separates both: recursive andstrategic aspects of the equilibrium problem and allows to precisely determine the sufficientassumptions on preferences and stochastic transition to establish existence. In particular we show existence of minimal state space stationary Markov equilibrium (a time-consistent solution) in a deterministic model of consumption-saving with beta-delta discounting andits generalized versions involving magnitude effects, non-additive payoffs, semi-hyperbolic or hyperbolic discounting (over possibly unbounded state and unbounded above reward space). We also provide an equilibrium approximation method for a hyperbolic discounting model.
    Keywords: Behavioral discounting; Time consistency; Markov equilibrium; Existence; Approximation; Generalized Bellman equation; Hyperbolic discounting; Semi-hyperbolic discounting; Quasi-hyperbolic discounting
    JEL: C61 C73
    Date: 2020–11
  9. By: Serdar Birinci; Kurt See
    Abstract: We study optimal unemployment insurance (UI) policy over the business cycle, using a heterogeneous agent job-search model with aggregate risk and incomplete markets. We validate the model-implied micro and macro labor market elasticities to changes in the generosity of UI benefits against existing estimates and we reconcile divergent empirical findings. We show that generating the observed demographic differences between UI recipients and non-recipients is critical for determining the magnitudes of these elasticities. We find that the optimal UI policy features countercyclical replacement rates with an average generosity that is close to current U.S. policy but that it adopts drastically longer payment durations reminiscent of European policies.
    Keywords: Business fluctuations and cycles; Fiscal policy; Labour markets
    JEL: E32 J65
    Date: 2020–11
  10. By: Lee E. Ohanian; Paulina Restrepo-Echavarria; Diana Van Patten; Mark L. J. Wright
    Abstract: This paper quantifies the positive and normative effects of capital controls on international economic activity under The Bretton Woods international financial system. We develop a three region world economic model consisting of the U.S., Western Europe, and the Rest of the World. The model allows us to quantify the impact of these controls through an open economy general equilibrium capital flows accounting framework. We find these controls had large effects. Counterfactuals show that world output would have been 6% larger had the controls not been implemented. We show that the controls led to much higher welfare for the rest of the world, moderately higher welfare for Europe, but much lower welfare for the U.S. We interpret the large U.S. welfare loss as an estimate of the implicit value to the U.S. of preventing capital flight from other countries and thus promoting economic and political stability in ally and developing countries.
    Keywords: Bretton Woods; International Payments; Capital Flows
    JEL: E21 F21 F41 J20
    Date: 2020–10–21
  11. By: Andrea Colciago; Stefano Fasani; Rossienza Rossi
    Abstract: We formulate and estimate a business cycle model which can account for key business cycle properties of labor market variables and other aggregates. Three features distinguish our model from the standard model with Search And Matching (SAM) frictions in the labor market: frictional firm entry, endogenous product variety, and investment in two assets: stocks and physical capital. Our model with firm dynamics displays an endogenous form of wage moderation. Thanks to the latter, it outperforms the SAM framework augmented with exogenous real wage rigidities.
    Keywords: Entry; Unemployment; Bayesian Analysis; Search and Matching
    JEL: C5 E32
    Date: 2020–11
  12. By: Andrea Modena (Institute for Financial Economics and Statistics Department of Economics, University of Bonn)
    Abstract: This paper studies the link between bank recapitalization and welfare in a dynamic production economy. The model features financial frictions because banks benefit of a cost advantage at monitoring firms and face costly equity issuance. The competitive equilibrium outcome is inefficient because agents do not internalize the effects banks’ capitalization over the allocation of capital, its price and, in turn, firms’ investments. It follows, individual recapitalizations are sub-optimal and bailout policies may benefit social welfare in the long run. Bailouts improve capital allocation in states where aggregate banks are poorly capitalized, therefore enhancing their market valuation, fostering investments, and stabilizing the economy recovery path.
    Keywords: Banks, bailout, general equilibrium, financial frictions, recapitalization, welfare
    JEL: D51 G21
    Date: 2020
  13. By: Michael Sposi (Southern Methodist University); Kei-Mu Yi (University of Houston, Federal Reserve Bank of Dallas, and NBER); Jing Zhang (Federal Reserve Bank of Chicago)
    Abstract: Motivated by increasing trade and fragmentation of production across countries since World War II, we build a dynamic two-country model featuring sequential, multi-stage production and capital accumulation. As trade costs decline over time, global-value-chain (GVC) trade expands across countries, particularly more in the faster growing country, consistent with the empirical pattern. The presence of GVC trade boosts capital accumulation and economic growth and magnifies dynamic gains from trade. At the same time, endogenous capital accumulation shapes comparative advantage across countries, impacting the dynamics of GVC trade: a country becoming more capital abundant concentrates more on the capital-intensive stage of the production.
    Keywords: Multistage production; International trade; Capital accumulation
    JEL: F10 F43 E22
    Date: 2020–11
  14. By: Hambel, Christoph; Kraft, Holger; Meyer-Wehmann, André
    Abstract: This paper studies a household's optimal demand for a reverse mortgage. These contracts allow homeowners to tap their home equity to finance consumption needs. In stylized frameworks, we show that the decision to enter a reverse mortgage is mainly driven by the differential between the aggregate appreciation of the house price and principal limiting factor on the one hand and the funding costs of a household on the other hand. We also study a rich life-cycle model that can explain the low demand for reverse mortgages as observed in US data. In this model, we analyze the optimal response of a household that is confronted with a health shock or financial disaster. If an agent suffers from an unexpected health shock, she reduces the risky portfolio share and is more likely to enter a reverse mortgage. On the other hand, if there is a large drop in the stock market, she keeps the risky portfolio share almost constant by buying additional shares of stock. Besides, the probability to take out a reverse mortgage is hardly affected.
    Keywords: reverse mortgage,consumption-portfolio decisions,optimal stopping,biometric risks,financial disasters
    JEL: D14 E21 G11 G21 J14 R21
    Date: 2020
  15. By: Antti J. Tanskanen
    Abstract: Discrete-choice life cycle models can be used to, e.g., estimate how social security reforms change employment rate. Optimal employment choices during the life course of an individual can be solved in the framework of life cycle models. This enables estimating how a social security reform influences employment rate. Mostly, life cycle models have been solved with dynamic programming, which is not feasible when the state space is large, as often is the case in a realistic life cycle model. Solving such life cycle models requires the use of approximate methods, such as reinforced learning algorithms. We compare how well a deep reinforced learning algorithm ACKTR and dynamic programming solve a relatively simple life cycle model. We find that the average utility is almost the same in both algorithms, however, the details of the best policies found with different algorithms differ to a degree. In the baseline model representing the current Finnish social security scheme, we find that reinforced learning yields essentially as good results as dynamics programming. We then analyze a straight-forward social security reform and find that the employment changes due to the reform are almost the same. Our results suggest that reinforced learning algorithms are of significant value in analyzing complex life cycle models.
    Date: 2020–10
  16. By: Emanuele Franceschi (PSE - Paris School of Economics, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)
    Abstract: We introduce liquidity motives in an otherwise standard monetary model. The Central Bank's policy rule is adapted to target the interest rate on liquid bonds. These deviations are sufficient to relax the requirement for active monetary policy and warrant determi-nacy in both passive and active policy regimes. We compare this model of liquidity with workhorse models and find that it can substantially replicate usual dynamics. By means of stochastic simulations, we also study how monetary policy stance affect inflation dynamics and find evidence of increased persistence for passive monetary policy.
    Date: 2020–10–26
  17. By: Abdoulaye Millogo (Université de Sherbrooke)
    Abstract: In the aftermath of the 2008 financial crisis, production and employment in advanced economies fell significantly, and remained below their pre-crisis potential level for almost a decade. A recent literature argues that market forces seem to have maintained or amplified this downward trend through hysteresis effects. Particularly intuitive arguments about the emergence of hysteresis effects through financial friction are provided by this literature. However, based on the current state of our knowledge, the theoretical models on hysteresis disregard this important dimension to the understanding of hysteresis. This article contributes to the literature by developing a New-Keynesian model where financial frictions amplify the lingering effects of economic shocks. By calibrating the model on the euro area, the results show that a deterioration of bank capital following a capital quality shock similar to the crisis of high-risk loans generates both persistence and more severity in the fall of production and in the rise of unemployment— more so than the classical models of hysteresis. The impact of shocks is magnified due to the reduction of physical capital in response to a weakening of the financing capacity of investment projects by the banking sector.
    Keywords: Production, unemployment, financial frictions, hysteresis, insider-outsider model
    JEL: E23 E24 E32 G01
    Date: 2020–11
  18. By: Anton A. Cheremukhin
    Abstract: When setting initial compensation some firms set a fixed non-negotiable wage while others bargain. In this paper we propose a parsimonious search and matching model with two sided heterogeneity, where search intensity and the degree of randomness in matching are endogenous, and firms decide whether to bargain or post wages. We study the implications of heterogeneous search costs and market tightness on the choice of the wage setting mechanism, as well as the relationship between bargaining prevalence and wage level, residual wage dispersion, and labor market tightness. We find that bargaining prevalence is positively correlated with wages, residual wage dispersion, and labor market tightness, both in the model and in the data.
    Keywords: Wage bargaining; wage posting; wage dispersion
    JEL: E24 J3 J41
    Date: 2020–10
  19. By: Shutao Cao; Wei Dong
    Abstract: Fluctuations of commodity prices are frequently associated with the volatility of aggregate output and prices. As commodity prices rise and fall, adjustments take place in the economy, ranging from shifts in investment, employment and output to changes in interest rates and exchange rates. While these adjustments are already quite complex, one important channel often overlooked in the literature is the input-output linkages. In this paper, we examine the macro implications of commodity price shocks in a structural model with input-output linkages for a commodity-exporting small open economy. Calibrated to the Canadian economy, our model can explain a large part of the decline in real gross domestic product (GDP) that we saw in 2015 and 2016 following the sharp drop in commodity prices. We find that as the model economy adjusts to commodity price shocks, domestic downstream linkages and the export connection with the rest of the world play an important role.
    Keywords: Business fluctuations and cycles; International topics
    JEL: D57 F41
    Date: 2020–11
  20. By: David Kohn; Fernando Leibovici; Michal Szkup
    Abstract: We study the role of financial development on the aggregate effects and welfare implications of reducing international trade barriers on production inputs such as physical capital and intermediates. We document that financially underdeveloped economies feature a slower response of real GDP, consumption, and investment following trade liberalization episodes that improve access to imported production inputs. We set up a quantitative general equilibrium model with heterogeneous firms subject to financial constraints and estimate it to match salient features from Colombian plant-level data. We find that the adjustment to a decline of import tariffs on physical capital and intermediate inputs is significantly slower in financially underdeveloped economies in line with the empirical evidence. Moreover, we find that financial development increases the welfare gains from trade liberalization; low-income agents benefit from higher wages while exporters benefit from a depreciated real exchange rate and lower capital costs.
    Keywords: financial development; trade liberalization; welfare
    JEL: F1 F4
    Date: 2020–10
  21. By: Siddhartha Chib; Minchul Shin; Fei Tan
    Keywords: Bayesian inference; MCMC; Metropolis-Hastings; Marginal likelihood; Tailored
    JEL: C11 C15 C32 E37 E63
    Date: 2020–09–15
  22. By: Ia Vardishvili
    Abstract: I show that firms' ability to delay entry generates a countercyclical opportunity cost of entry and significantly amplifies the effect of the initial aggregate conditions on the selection of entrants. This mechanism enables existing firm dynamics models to reconcile the documented business cycle dynamics of US entrant establishments without leading to an excessive variation in economic aggregates. I find the observed variation of firms at entry is responsible for around three-fourths of the business cycle fluctuations. Finally, I argue that not accounting for the option to delay entry may result in misleading predictions about entrants' responses to different shocks or policies.
    Keywords: Option value, entry, firm dynamics, business cycles, propagation, Great Recession
    JEL: E22 E23 E32 E37 L25
    Date: 2020–10
  23. By: Paul J.J. Welfens (Europäisches Institut für Internationale Wirtschaftsbeziehungen (EIIW))
    Abstract: Models with rational expectation have become quite popular in macroeconomics, particularly in the context of New Keynesian Models and DSGE models, respectively. These models are useful in many respects; however, they suffer from a serious problem which is discussed here in a very basic version: These models have equations with white-noise disturbance terms with finite variance where the size of this variance is assumed to have no impact on the behavior of economic agents and the equilibrium solution or the steady state values, respectively. This, however, is totally implausible Ð from a theoretical perspective, a disturbance term with a very large variance, for example, should have a crucial impact on consumption, investment and output, respectively. In the context of the Great Recession and the Transatlantic Banking Crisis as well as in the Euro Crisis Ð during which one could observe very high volatility of bonds prices pointing to a high variance of disturbance terms - one may therefore raise critical questions with respect to validity of policy recommendations derived from DSGE models. Hence these models should be refined adequately; institutions and regulations have an influence on the variance of white noise disturbance terms and thus various institutional regimes with differences in the variances of these disturbance terms should be discussed. Selected digital expansion and innovation aspects Ð e.g. related to the Corona shock - also are highlighted.
    Keywords: New Keynesian Models, DSGE, Rational behavior, Risk, Digital Economics, Macroeconomics
    JEL: E31 E44 E47 E52
    Date: 2020–03

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