nep-dge New Economics Papers
on Dynamic General Equilibrium
Issue of 2022‒10‒17
eighteen papers chosen by
Christian Zimmermann
Federal Reserve Bank of St. Louis

  1. Introducing an Austrian Backpack in Spain By João Brogueira de Sousa; Julián Díaz-Saavedra; Ramon Marimon
  2. Solving linear DSG models with Newton methods By Meyer-Gohde, Alexander; Saecker, Johanna
  3. Analyzing Linear DSGE models: the Method of Undetermined Markov States By Jordan Roulleau-Pasdeloup
  4. Will the green transition be inflationary? Expectations matter By Ferrari, Alessandro; Landi, Valerio Nispi
  5. Optimal Monetary Policy with r* By Roberto M. Billi; Jordi Galí; Anton Nakov
  6. Redistributive Policy Shocks And Monetary Policy With Heterogeneous Agents By Ojasvita Bahl; Chetan Ghate; Debdulal Mallick
  7. The Risk-Premium Channel of Uncertainty: Implications for Unemployment and Inflation By Freund, L. B.; Lee, H.; Rendahl, P.
  8. Emigration and Fiscal Austerity in a Depression By Guilherme Bandeira; Jordi Caballe; Eugenia Vella
  9. Misallocation and Inequality By Nezih Guner; Alessandro Ruggieri
  10. On the Design of a European Unemployment Insurance System By Árpád Ábrahám; João Brogueira de Sousa; Ramon Marimon; Lukas Mayr
  11. A model of quantitative easing at the zero lower bound By Dürmeier, Stefan
  12. On the Optimal Design of a Financial Stability Fund By Árpád Ábrahám; Eva Cárceles-Poveda; Yan Liu; Ramon Marimon
  13. Making Sovereign Debt Safe with a Financial Stability Fund By Yan Liu; Ramon Marimon; Adrien Wicht
  14. Government Procurement and Access to Credit: Firm Dynamics and Aggregate Implications By Julian di Giovanni; Manuel García-Santana; Priit Jeenas; Enrique Moral-Benito; Josep Pijoan-Mas
  15. The unbearable lightness of equilibria in a low interest rate environment By Guido Ascari; Sophocles Mavroeidis
  16. Environmental sustainability, nonlinear dynamics and chaos reloaded: 0 matters! By Andrea Caravaggio; Mauro Sodini
  17. Patience and Comparative Development By Sunde, Uwe; Dohmen, Thomas; Enke, Benjamin; Falk, Armin; Huffmann, David; Meyerheim, Gerrit
  18. Monetary Policy During Unbalanced Global Recoveries By Luca Fornaro; Federica Romei

  1. By: João Brogueira de Sousa; Julián Díaz-Saavedra; Ramon Marimon
    Abstract: In an overlapping generations economy with incomplete insurance markets, the introduction of an employment fund -akin to the one introduced in Austria in 2003, also known as `Austrian backpack'- can enhance production efficiency and social welfare. It complements the two classical systems of public insurance: pay-as-you-go (PAYG) pensions and unemployment insurance (UI). We show this in a calibrated dynamic general equilibrium model with heterogeneous agents of the Spanish economy in 2018. A `backpack' (BP) employment fund is an individual (across jobs) transferable fund, which earns a market interest rate as a return and is financed with a payroll tax (a BP tax). The worker can use the fund while unemployed or retired. Upon retirement, backpack savings can be converted into an (actuarially fair) retirement pension. To complement the existing PAYG pension and UI systems with a welfare maximising 6% BP tax would raise welfare by 0.96% of average consumption at the new steady state, if we model Spain as an open economy. As a closed economy, there are important general equilibrium effects and, as a result, the social value of introducing the backpack is substantially greater: 16.14%, with a BP tax of 18%. In both economies, the annuity retirement option is an important component of the welfare gains.
    Keywords: computable general equilibrium, welfare state, social security reform, Retirement
    JEL: C68 H55 J26
    Date: 2022–03
  2. By: Meyer-Gohde, Alexander; Saecker, Johanna
    Abstract: This paper presents and compares Newton-based methods from the applied mathematics literature for solving the matrix quadratic that underlies the recursive solution of linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and different parameterizations of the monetary policy rule in the medium-scale New Keynesian model of Smets and Wouters (2007) iteratively. We find that Newton-based methods compare favorably in solving DSGE models, providing higher accuracy as measured by the forward error of the solution at a comparable computation burden. The methods, however, suffer from their inability to guarantee convergence to a particular, e.g. unique stable, solution, but their iterative procedures lend themselves to refining solutions either from different methods or parameterizations.
    Keywords: Numerical accuracy,DSGE,Solution methods
    JEL: C61 C63 E17
    Date: 2022
  3. By: Jordan Roulleau-Pasdeloup
    Abstract: I show that a class of Linear DSGE models with one endogenous state variable can be represented as a three-state Markov chain. I develop a new analytical solution method based on this representation, which amounts to solving for a vector of Markov states and one transition probability. These two objects constitute sufficient statistics to compute in closed form objects that have routinely been computed numerically: impulse response function, cumulative sum, present discount value multiplier. I apply the method to a standard New Keynesian model with habit formation.
    Date: 2022–09
  4. By: Ferrari, Alessandro; Landi, Valerio Nispi
    Abstract: We analyse a gradual increase in the tax on emissions in a simple two-period New Keynesian model with an AS-AD representation. We find that the increase in the tax today exerts inflationary pressures, but the expected further increase in the tax tomorrow depresses current demand, putting downward pressure on prices: we show that the second effect is larger. However, if households do not anticipate a future fall in income (because they are not rational or the government is not credible), the overall effect of the transition may be inflationary in the first period. We extend the analysis in a medium-scale DSGE model and we find again that the green transition is deflationary. Also in this larger model, by relaxing the rational expectations assumption, we show the transition may initially be inflationary. JEL Classification: D84, E31, Q58
    Keywords: aggregate prices, AS AD, climate policy, expectations, pollution tax
    Date: 2022–09
  5. By: Roberto M. Billi; Jordi Galí; Anton Nakov
    Abstract: We study the optimal monetary policy problem in a New Keynesian economy with a zero lower bound (ZLB) on the nominal interest rate, and in which the steady state natural rate (r*) is negative. We show that the optimal policy aims to approach gradually a steady state with positive average inflation. Around that steady state, inflation and output fluctuate optimally in response to shocks to the natural rate. The central bank can implement that optimal outcome by means of an appropriate state-contingent rule, even though in equilibrium the nominal rate remains at zero most (or all) of the time. In order to establish that result, we derive sufficient conditions for local determinacy in a more general model with endogenous regime switches.
    Keywords: zero lower bound, New Keynesian model, decline in r*, equilibrium determinacy, regime switching models, secular stagnation
    JEL: E32 E52
    Date: 2022–03
  6. By: Ojasvita Bahl; Chetan Ghate (Institute of Economic Growth, Delhi University, Delhi); Debdulal Mallick
    Abstract: Governments in EMDEs routinely intervene in agriculture markets to stabilize food prices in the wake of adverse shocks. Such interventions usually involve a large increase in the procurement and redistribution of food, which we call a redistributive policy shock. What is the impact of a redistributive policy shock on inflation and the distribution of consumption amongst rich and poor households? We build a tractable two-sector-two-agent NK DSGE model calibrated to the Indian economy. We show that for an inflation targeting central bank, consumer heterogeneity matters for whether monetary policy responses to a variety of shocks raises aggregate welfare or not.
    Keywords: TANK models, Inflation Targeting, Emerging Market and Developing Economies, Procurement and Redistribution, DSGE.
    JEL: E31 E32 E44 E52 E63
    Date: 2022–09–01
  7. By: Freund, L. B.; Lee, H.; Rendahl, P.
    Abstract: This paper studies the role of macroeconomic uncertainty in a search-and-matching framework with risk-averse households. Heightened uncertainty about future productivity reduces current economic activity even in the absence of nominal rigidities. A risk-premium mechanism accounts for this result. As future asset prices become more volatile and covary more positively with aggregate consumption, the risk premium rises in the present. The associated downward pressure on current asset values lowers firm entry, making it harder for workers to find jobs and reduces supply. With nominal rigidities the recession is exacerbated, as a more uncertain future reinforces households’ precautionary behavior, which causes demand to contract. Counterfactual analyses using a calibrated model imply that unemployment would rise by less than half as much absent the risk-premium channel. The presence of this mechanism implies that uncertainty shocks are less deflationary than regular demand shocks, nor can they be fully neutralized by monetary policy.
    Keywords: inflation, search frictions, Uncertainty, Unemployment
    JEL: J64 E21 E32
    Date: 2022–09–08
  8. By: Guilherme Bandeira (New South Wales Treasury); Jordi Caballe (Universitat Autonoma de Barcelona and Barcelona GSE); Eugenia Vella
    Abstract: What is the role of emigration in a deep recession when the government implements fiscal consolidation? To answer this question, we build a small open economy New Keynesian model with matching frictions and emigration. In simulations for the Greek Depression, fiscal austerity accounts for almost 1/3 of the GDP decline and 12% of emigration. A nomigration scenario under-predicts the bust in output by 1/6 and the rise in the debt-to-GDP ratio by 8 percentage points. The link between emigration and austerity is bi-directional. Emigration increases the labour tax hike and time required to reduce the debt ratio due to endogenous revenue leakage. In turn, tax hikes intensify emigration, while unproductive government spending cuts have a mild, ambiguous impact as they exhibit opposite demand and wealth effects. However, productive spending cuts display a fiscal multiplier above one, which incentivizes emigration. Emigration then amplifies the productive spending multiplier through internal demand. Similarly, the cumulative labour tax multiplier after five years rises from 0.86 without migration to 1.27 when the unemployed emigrate and 1.47 when both the unemployed and the employed emigrate.
    Keywords: fiscal austerity, emigration, on-the-job search, matching frictions, Greek crisis, fiscal multipliers
    JEL: E32 F41
    Date: 2022–08–08
  9. By: Nezih Guner; Alessandro Ruggieri
    Abstract: For a large set of countries, we document how the labor earnings inequality varies with GDP per capita. As countries get richer, the mean-to-median ratio and the Gini coefficient decline. Yet, this decline masks divergent patterns: while inequality at the top of the earnings distribution falls, inequality at the bottom increases. We interpret these facts within a model economy with heterogeneous workers and firms, featuring industry dynamics, search and matching frictions, and skill accumulation of workers through learning-by-doing and on-the-job training. The benchmark economy is calibrated to the UK. We then study how the earnings distribution changes with distortions that penalize high-productivity firms and frictions that reduce match formation. Distortions and frictions reduce employment, average firm size, and GDP per capita. They also affect how much firms are willing to pay workers, how well high-skill workers are matched with high-productivity firms, and how much training workers receive. The model generates the observed cross-country relation between GDP per capita and earnings inequality, as well as a host of cross-country facts on firm size distribution, firms' training decisions, and workers' life-cycle and job tenure earnings profiles.
    Keywords: earnings inequality, Labor market frictions, correlated distortions, human capital, on-the-job training, productivity, firm size, life-cycle earning profiles
    JEL: E23 E24 J24 O11
    Date: 2022–03
  10. By: Árpád Ábrahám; João Brogueira de Sousa; Ramon Marimon; Lukas Mayr
    Abstract: We study the welfare effects of both existing and counter-factual European unemployment insurance policies using a rich multi-country dynamic general equilibrium model with labour market frictions. The model successfully replicates several salient features of European labor markets, in particular the cross-country differences in the flows between employment, unemployment and inactivity. We find that mechanisms like the recently introduced European instrument for temporary support to mitigate unemployment risks in an emergency (SURE), which allows national governments to borrow at low interest rates to cover expenditures on unemployment benefits, yield sizable welfare gains, contradicting the conventional classical view that costs of business cycles are small. Furthermore, we find that a harmonized benefit system that features a one-time payment of around three quarters of income upon separation is welfare improving in all Eurozone countries relative to the status quo.
    Keywords: labour markets, Unemployment Insurance, job creation, job destruction, risk-sharing, Economic Monetary Union
    JEL: J6 E2
    Date: 2022–03
  11. By: Dürmeier, Stefan
    Abstract: The research question relates to the quantitative impact of government bond purchases of the European Central Bank on inflation and other economic variables at the zero lower bound. At the core is a standard New Keynesian Dynamic Stochastic General Equilibrium model with several financial frictions. The model replicates the intended effect of Quantitative Easing regarding the drop in the government bond yield at the expense of a rise in public debt, and displays the crowding out effect on the balance sheet of the bank which spurs credit and output. Amid lower levels of wages and consumption, the overall quantitative effect is nevertheless not inflationary but deflationary. After a shock to the credit supply, Quantitative Easing is activated more if the zero lower bound on the policy rate is in place. Output after the first period, consumption as well as wages and inflation drop more in the case of the zero lower bound and Quantitative Easing does not make up for the loss. The same findings for the economic performance marked by these four variables are obtained for the analysis at the zero lower bound when a shock hits the exposure of financial intermediaries to public debt.
    Keywords: Quantitative Easing,Taylor Rule,Zero Lower Bound,Moral Hazard
    Date: 2022
  12. By: Árpád Ábrahám; Eva Cárceles-Poveda; Yan Liu; Ramon Marimon
    Abstract: We develop a model of a Financial Stability Fund (Fund) for a union of sovereign countries. By contract design, the Fund never has expected undesired losses while, being default-free, a participant country has greater ability to borrow and share risks than using sovereign debt financing. The Fund contract also provides better incentives for the country to reduce endogenous risks. These efficiency gains arise from the ability of the Fund to offer long-term contingent financial contracts, subject to limited enforcement (LE) and moral hazard (MH) constraints as part of the contingencies. We develop the theory (welfare theorems, with a new price decentralization) and quantitatively compare the constrained-efficient Fund economy with an incomplete markets economy with default. In particular, we characterize how prices and allocations differ, when the two economies are subject to exogenous productivity and endogenous government expenditure shocks. In our economies, calibrated to the euro area ‘stressed countries’, substantial welfare gains are achieved, particularly in times of crisis. The Fund is, in fact, a risk-sharing, crisis prevention and resolution mechanism, which transforms participant countries’ defaultable sovereign debts into union’s safe assets. In sum, our theory can help to improve current official lending practices and, eventually, to design an European Fiscal Fund.
    Keywords: fiscal unions, recursive contracts, Debt Contracts, partnerships, limited enforcement, moral hazard, debt restructuring, Debt Overhang, sovereign fund
    JEL: E43 E44 E47 E63 F34 F36
    Date: 2022–03
  13. By: Yan Liu; Ramon Marimon; Adrien Wicht
    Abstract: We develop an optimal design of a Financial Stability Fund that coexists with the international debt market. The sovereign can borrow long-term defaultable bonds on the private international market, while having with the Fund a long-term contingent contracts subject to limited enforcement constraints. There is a contract that minimizes the debt absorbed by the Fund, guaranteeing full debt stabilization. In equilibrium, the seniority of the Fund contract, with respect to the privately held debt, is irrelevant. We calibrate our model to the Italian economy and show it would have been a more efficient path of debt accumulation with the Fund.
    Keywords: recursive contracts, limited enforcement, debt stabilisation, Debt Overhang, safe assets, seniority structure
    JEL: E43 E44 E47 E62 F34 F36 F37
    Date: 2022–03
  14. By: Julian di Giovanni; Manuel García-Santana; Priit Jeenas; Enrique Moral-Benito; Josep Pijoan-Mas
    Abstract: We provide a framework to study how different allocation systems of public procurement contracts affect firm dynamics and long-run macroeconomic outcomes. We start by using a newly created panel dataset of administrative data that merges Spanish credit register loan data, quasi-census firm-level data, and public procurement projects to study firm selection into procurement and the effects of procurement on credit growth and firm growth. We show evidence consistent with the hypotheses that there is selection of large firms into procurement, that procurement contracts provide useful collateral for firms -more so than sales to the private sector- and that procurement contracts facilitate firm growth beyond the contract duration. We next build a model of firm dynamics with both asset-based and earnings-based borrowing constraints and a government that buys goods and services from private sector firms. We use the calibrated model to quantify the long-run macroeconomic consequences of alternative procurement allocation systems. We find that granting procurement contracts to small firms, either by directly targeting them or by slicing large contracts into smaller ones, helps these firms grow and overcome financial constraints in the long run. However, we also find that reducing the average size of contracts |or making it less likely for large firms to access them| removes saving incentives for large firms, whose negative effects on capital accumulation can overcome the expansionary consequences for small firms and hence generate a drop in aggregate output.
    Keywords: Government procurement, financial frictions, capital accumulation, aggregate productivity
    JEL: E22 E23 E62 G32
    Date: 2022–02
  15. By: Guido Ascari; Sophocles Mavroeidis
    Abstract: Structural models with no solution are incoherent, and those with multiple solutions are incomplete. We show that models with occasionally binding constraints are not generically coherent. Coherency requires restrictions on the parameters or on the support of the distribution of the shocks. In presence of multiple shocks, the support restrictions cannot be independent from each other, so the assumption of orthogonality of structural shocks is incompatible with coherency. Models whose coherency is based on support restrictions are generically incomplete, admitting a very large number of minimum state variable solutions.
    Keywords: incompleteness; incoherency; rational expectations; zero lower bound; DSGE
    JEL: C62 E4 E52
    Date: 2021–12
  16. By: Andrea Caravaggio; Mauro Sodini
    Abstract: In this paper, we reconsider the overlapping generations (OLG) environmental model introduced in John and Pecchenino (1994) and Zhang (1999) by adopting the specification of the environmental dynamics proposed by Naimzada and Sodini (2010). The model two different regimes that may alternate: one in which the economy and the environment co-evolve in the same direction; the other in which the environmental problem is not internalized by the agents, that is, the agents do not devolve any private resource to the environmental good, leading to a possible trade-off between environment and economic growth. The analysis of the equilibrium dynamics, described by a two dimensional piecewise smooth map, shows that starting from a parametric configuration in which the dynamics are definitely driven by a unique regime, the increase of the negative effect of the agents' consumption activity ends up in scenarios where the two regimes alternate, determining the arise of stable cycles or the occurrence of chaotic regimes. It is interesting to notice that because of the nonsmoothness of the map, the rise in environmental harm produced by economic activity may induce a sudden transition to chaotic regime.
    Keywords: Bifurcations, Complex Dynamics, Overlapping Generations, Sustainability
    JEL: O13 O41 C62
    Date: 2022–09–01
  17. By: Sunde, Uwe (LMU Munich); Dohmen, Thomas (University of Bonn); Enke, Benjamin (Harvard University); Falk, Armin (briq and University of Bonn); Huffmann, David (University of Pittsburgh); Meyerheim, Gerrit (LMU Munich)
    Abstract: This paper studies the relationship between patience and comparative development through a combination of reduced-form analyses and model estimations. Based on a globally representative dataset on time preference in 76 countries, we document two sets of stylized facts. First, patience is strongly correlated with per capita income and the accumulation of physical capital, human capital and productivity. These correlations hold across countries, subnational regions, and individuals. Second, the magnitude of the patience elasticity strongly increases in the level of aggregation. To provide an interpretive lens for these patterns, we analyze an OLG model in which savings and education decisions are endogenous to patience, aggregate production is characterized by capital-skill complementarities, and productivity implicitly depends on patience through a human capital externality. In our model estimations, general equilibrium effects alone account for a non-trivial share of the observed amplification effects, and an extension to human capital externalities can quantitatively match the empirical evidence.
    Keywords: time preference; comparative development; factor accumulation;
    JEL: D03 D90 O10 O30 O40
    Date: 2021–11–11
  18. By: Luca Fornaro; Federica Romei
    Abstract: We study optimal monetary policy during times of exceptionally high global demand for tradable goods, relative to non-tradable services. The optimal monetary response entails a rise in inflation, which helps rebalance production toward the tradable sector. While the inflation costs are fully beared domestically, however, part of the gains in terms of higher supply of tradable goods spill over to the rest of the world. National central banks may thus fall into a coordination trap, and implement an excessively tight monetary policy during tradable goods-driven recoveries.
    Keywords: asymmetric shocks, reallocation, monetary policy, international monetary cooperation, inflation, global supply shortages
    JEL: E32 E44 E52 F41 F42
    Date: 2022–01

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