nep-dge New Economics Papers
on Dynamic General Equilibrium
Issue of 2023‒01‒30
twenty-two papers chosen by
Christian Zimmermann
Federal Reserve Bank of St. Louis

  1. Capital Account Liberalization, Financial Frictions, and Belief-Driven Fluctuations By Takuma Kunieda; Kazuo Nishimura
  2. Fiscal Multipliers with Sovereign Risk and Fragile Banks By Matthieu Darracq Paries; Georg Muller; Niki Papadopoulou
  3. Uncertain Policy Regimes and Government Spending Effects By Ruoyun Mao; Wenyi Shen; Shu-Chun S. Yang
  4. Sectoral Shocks, Reallocation, and Labor Market Policies By Joaquin Garcia-Cabo; Anna Lipinska; Gaston Navarro
  5. Optimal monetary and transfer policy in a liquidity trap By Stefano Maria Corbellini
  6. Heterogeneous Downward Nominal Wage Rigidity: Foundations of a Static Wage Phillips Curve By Stephanie Schmitt-Grohé; Martín Uribe
  7. Learning about labour markets By Jake Bradley; Lukas Mann
  8. The cyclicality of income distribution and innovation induced growth By Uluc Aysun; Sami Alpanda
  9. The Emergence of Procyclical Fertility: The Role of Gender Differences in Employment Risk By Coskun, Sena; Dalgic, Husnu
  10. Optimal Retirement with Disability Pensions By Hans Fehr; Adrian Fröhlich
  11. Sources of Rising Student Debt in the U.S.: College Costs, Wage Inequality, and Delinquency By Heejeong Kim; Jung Hwan Kim
  12. Building on fiscal policy: government consumption and the residential sector. When helping hurts By Javier Ferri; Francisca Herranz-Baez
  13. Optimal Long-run Money Growth Rate in a Cash-in-Advance Economy with Labor-Market Frictions By Been-Lon Chen; Shian-Yu Liao; Dongpeng Liu; Xiangbo Liu
  14. The Dollar’s Imperial Circle By Ozge Akinci; Gianluca Benigno; Serra Pelin; Jonathan Turek
  15. Destabilizing Search Technology By Potter, Tristan
  16. Share Buybacks and Corporate Tax Cuts By Juin-Jen Chang; Chun-Hung Kuo; Hsieh-Yu Lin; Shu-Chun S. Yang
  17. Firm size distribution and informality effects of a revenue-dependent tax policy By Alvarez, Bruna; Pessoa, João Paulo; Souza, André Portela
  18. Debt-Ridden Borrowers and Economic Slowdown By Keiichiro KOBAYASHI; Daichi SHIRAI
  19. The Effects of Monetary Policy: Theory with Measured Expectations By Christopher Roth; Mirko Wiederholt; Johannes Wohlfart
  20. Monetary policy when export revenues drop By Drago Bergholt; Øistein Røisland; Tommy Sveen; Ragnar Torvik
  21. Spillover effects of employment protection By Pierre Cahuc; Pauline Carry; Franck Malherbet; Pedro S. Martins
  22. On the uniqueness of the optimal path in a discrete-time model à la Lucas (1988) By Stefano Bosi; Carmen Camacho; Thai Ha-Huy

  1. By: Takuma Kunieda (School of Economics, Kwansei Gakuin University); Kazuo Nishimura (Kobe University and Research Institute of Economy, Trade and Industry)
    Abstract: To investigate the macroeconomic effects of capital account liberalization, we apply a dynamic general equilibrium model with two production sectors. In contrast to the literature on belief-driven sunspot fluctuations caused by production externalities, our model does not assume any production externalities. In our model, agents face ï¬ nancial constraints and production heterogeneity. The ï¬ nancial constraints and agents’ production heterogeneity are sources of dynamic inefficiency. Although indeterminacy of equilibrium and belief-driven sunspot fluctuations never occur in the closed economy, dynamic inefficiency combined with a negative foreign asset in the steady state produces indeterminacy in the small open economy if ï¬ nancial constraints are fully relaxed under the condition that the investment goods sector is more labor intensive than the consumption goods sector.
    Keywords: Two-sector growth model; small open economy; ï¬ nancial constraints; heterogeneous agents; dynamic inefficiency; indeterminacy.
    JEL: E32 F36 F43 O41
    Date: 2023–01
  2. By: Matthieu Darracq Paries (European Central Bank); Georg Muller (European Central Bank); Niki Papadopoulou (Central Bank of Cyprus)
    Abstract: We quantify the size of fiscal multipliers in an economy with sovereign and bank default risk. We build a DSGE model with financial frictions for the euro area in which the interplay of corporate, bank and sovereign solvency risk a?ects the transmission of government spending. Sovereign bonds carry a credit risk premium that depends on government indebtedness. The banking system is fragile through its direct and indirect exposure to sovereign risk and limited loss absorption capacity. Calibrating the model on sovereign and bank riskiness reminiscent of the euro area sovereign debt crisis period, we show that adverse financial channels may signifcantly depress the fiscal multiplier. The trade-o? for the fiscal authority, between the macroeconomic stabilization objective and solvency risks, continues to be relevant in the euro area. We also evaluate the scope for monetary and macro-prudential policy to mitigate the financial setbacks and help restore the e?ectiveness of fiscal stimulus.
    Keywords: DSGE models, fiscal stabilization, sovereign risk, sovereign-bank nexus
    JEL: E44 E52 E62
    Date: 2022–12
  3. By: Ruoyun Mao (Grinnell College); Wenyi Shen (Oklahoma State University); Shu-Chun S. Yang (Institute of Economics, Academia Sinica, Taipei, Taiwan)
    Abstract: Money financing returns to policy debate as governments around the world adopted massive fiscal measures during the pandemic. Using a fully nonlinear New Keynesian model with endogenous policy regime switching, we show thata moderate inflation- driven switching probability to a debt-financing regime reduces money-financed spending multipliers. When interacted with high government debt, money-financed spending multipliers fall below one, similar to the size of debt-financed spending multipliers. This result holds at the zero lower bound, with long-term government debt, and under a wide range of key parameter values. Policy regime uncertainty, on the other hand, has little effect on debt-financed spending multipliers.
    Keywords: government spending effects, fiscal multipliers, regime-switching policy, monetary and fiscal policy interaction, nonlinear New Keynesian models
    JEL: E32 E52 E62 E63 H30
    Date: 2022–09
  4. By: Joaquin Garcia-Cabo; Anna Lipinska; Gaston Navarro
    Abstract: Unemployment insurance and wage subsidies are key tools to support labor markets in recessions. We develop a multi-sector search and matching model with on-the-job human capital accumulation to study labor market policy responses to sector-specific shocks. Our calibration accounts for structural differences in labor markets between the United States and the euro area, including a lower job-finding rate in the latter. We use the model to evaluate unemployment insurance and wage subsidy policies in recessions of different duration. We find that, after a temporary sector-specific shock, unemployment insurance improves both productivity and reallocation toward productive sectors at the cost of initially higher unemployment and, thus, human capital destruction. In the United States, unemployment insurance is preferred to wage subsidies when it does not distort job creation for too long. By contrast, wage subsidies reduce unemployment and preserve human capital, at the cost of limiting reallocation. In the euro area, where the job-finding rate is lower, subsidies are preferred.
    Keywords: labor market policies; reallocation; search and matching
    JEL: E24 J68 J64
    Date: 2022–12
  5. By: Stefano Maria Corbellini
    Abstract: Optimal monetary and fiscal policy are jointly analyzed in a heterogeneous two-agents New Keynesian environment, where fiscal policy is modeled in the form of lump-sum transfers set by the government. The main result is that transfer policy does not serve as a substitute for forward guidance - as it entails consumption dispersion costs - and does not affect its optimal duration. Transfers indeed influence the length of stay at the zero lower bound through two offsetting channels: a shortening channel works through an initial increase in transfers that mitigates the recession (reducing the need for forward guidance), and a lengthening channel works through a later transfer cut that curbs the undesired expansion (making forward guidance desirable for a longer horizon). Imposing a homogeneous transfer policy across agents does not change the stabilization outcome or the effect on the duration of forward guidance, nor does so allowing for cyclical income differences.
    Keywords: heterogeneity, inequality, liquidity trap, optimal monetary policy, optimal fiscal policy, forward guidance
    JEL: E52 E62 E63
    Date: 2022–12
  6. By: Stephanie Schmitt-Grohé; Martín Uribe
    Abstract: We introduce a form of downward nominal wage rigidity that can vary in intensity across a continuum of labor varieties. The model delivers a static wage Phillips curve linking current wage inflation to current unemployment. For standard parameterizations, the dynamics of the model are qualitatively and quantitatively similar to those of the new-Keynesian model with wage stickiness, which features a forward-looking wage Phillips curve, linking current wage inflation to future expected wage inflation and current unemployment. This result puts in perspective the role played by the forward-looking component of the new-Keynesian wage Phillips curve. A convenient property of the proposed model is that it is amenable to perturbation analysis because although it features occasionally binding constraints at the level of individual labor types it does not have such constraints at the aggregate level.
    JEL: E24 E31 E32
    Date: 2022–12
  7. By: Jake Bradley; Lukas Mann
    Abstract: We study a general equilibrium model of the labor market in which agents slowly learn about their suitability for jobs. Our model reproduces desirable features of the data, many of which standard models fail to replicate. We explore how, in such an environment, asymmetric information can lead to substantial misallocation. We calibrate our model to US data and quantify the welfare loss arising from misallocation due to informational frictions. The tractability of the model allows us to explore the responsiveness of wages and employment to an aggregate shock. We find that wage rigidity arises endogenously because of protracted learning, and in line with the data, the model is able to generate a larger and more persistent employment response.
    Keywords: Learning, misallocation, labor markets, wage rigidity
    Date: 2023
  8. By: Uluc Aysun (University of Central Florida, Orlando, FL); Sami Alpanda (University of Central Florida, Orlando, FL)
    Abstract: This paper demonstrates the countercyclicality of income inequality. Inferences are drawn from a unique model that combines a new Keynesian framework with an endogenous growth mechanism that features a labor-augmenting technology. The income disparity is between high-skill workers who service firms’ R&D activities and low-skill workers who contribute to output via a standard neoclassical function. Successful R&D activities increase firms’ knowledge stock that in turn augments low-skill workers’ efficiency and the trend growth rate of the economy. Both a reasonable calibration of the model and a Bayesian estimation exercise demonstrate that the share of high-skill workers’ income is countercyclical and that demand and price shocks are the drivers of this cyclicality. The reason is that the marginal product of high-skill workers is larger in magnitude and this renders the demand for their services less sensitive to shocks. In particular, firms require relatively smaller adjustments in this type of labor to match the changes in the demand for their goods. The disparity in demand for the two types of labor then implies that the high-skill/low-skill wage gap increases during recessions and decreases during expansions.
    Keywords: R&D, endogenous growth, DSGE, income distribution, Bayesian estimation.
    JEL: E24 E32 O30 O33
    Date: 2023–01
  9. By: Coskun, Sena (Institute for Employment Research (IAB), Nuremberg, Germany ; FAU); Dalgic, Husnu (Univ. Mannheim)
    Abstract: "Fertility in the US exhibits an increasingly more procyclical pattern. We argue that women’s breadwinner status is behind procyclical fertility: (i) women’s relative income in the family has increased over time; and (ii) women are more likely to work in relatively stable and countercyclical industries whereas men tend to work in volatile and procyclical industries. This creates a countercyclical gender income gap as women become breadwinners in recessions, producing an insurance effect of women’s income. Our quantitative framework features a general equilibrium OLG model with endogenous fertility and human capital choice. We show that the change in gender employment cyclicality can explain 38 to 44 percent of the emergence of procyclical fertility. Our counterfactual analysis shows that in a world in which men become nurses and women become construction workers, we would observe “countercyclical fertility” but at the expense of lower human capital accumulation as families lean in more towards quantity in the quality-quantity trade-off." (Author's abstract, IAB-Doku) ((en))
    Keywords: USA ; IAB-Open-Access-Publikation ; Auswirkungen ; Erwerbsbeteiligung ; erwerbstätige Frauen ; Familieneinkommen ; Frauen ; Fruchtbarkeit ; generatives Verhalten ; geschlechtsspezifische Faktoren ; geschlechtsspezifischer Arbeitsmarkt ; Konjunkturabhängigkeit ; Arbeitsmarktrisiko ; Arbeitsplatzgefährdung ; Wirtschaftszweige ; 1964-2018
    JEL: E24 E32 J11 J13 J16 J21 J24
    Date: 2022–12–21
  10. By: Hans Fehr; Adrian Fröhlich
    Abstract: This paper develops a general equilibrium life-cycle model with endogenous retirement and disability risk, in order to quantify the impact of recent pension reforms in Germany. At certain ages households may either apply for disability pensions (DP) or old-age pensions (OAP), de-pending on eligibility rules and the generosity of the two programs. Our policy analysis focus on the increase in the normal retirement age (NRA) from age 65 to 67 (Reform 2007) and the recent increase in the maximum assessment age (MAA) for DP benefits (Reform 2018). In contrast to the first reform, the second reform received hardly any attention in the public pension debate in Germany. Our simulation results indicate that with current eligibility and benefit rules, the second reform will almost neutralize the financial and economic benefits of the first reform. Consequently, securing the financial stability of the system will require a tightening of eligibility rules and/or a reduction of early retirement benefits in the future.
    Keywords: overlapping generations, stochastic general equilibrium, endogenous retirement, disability pensions
    JEL: C68 D91 H55 J24
    Date: 2022
  11. By: Heejeong Kim (Concordia University); Jung Hwan Kim (Concordia University)
    Abstract: This paper examines the quantitative effects of rising college costs, wage inequality, and delinquencies on growing student debt balances in the U.S. We build an incompletemarkets overlapping-generation (OLG) model with choices for a college education, student loans, and delinquency. We solve transitional dynamics with the estimated timevarying changes in college costs and wage inequality, in addition to a stronger preference for college education, that affect the repayment decision of borrowers. We find that these sources increase aggregate student debt balances by $480 billion between 1979 and 2015. Rising college costs increase borrowing by recent college students. The declining average ability of college students and increasing volatility of wage shocks lead to a higher delinquency rate among borrowers over time. Importantly, we find that when borrowers are not delinquent on their payments, the aggregate student debt only increases by 50% of the increase in the benchmark economy, despite all the time-varying sources. This suggests that although the rising college costs largely affect the borrowing behavior of college students, the increasing delinquency rate over time significantly contributes to the rapid growth of U.S. student debt.
    Keywords: Student Debt, College Cost, College Choice, Wage Inequality, Delinquency
  12. By: Javier Ferri; Francisca Herranz-Baez
    Abstract: Increased public spending to combat an economic recession caused by a housing demand shock can significantly harm investment and employment in the housing sector, despite its positive effect on GDP. In terms of the extent of this decoupling between output at the aggregate level and in the housing sector, we find that the easier it is to reallocate employment between production sectors, the lower the reaction of hours worked to wages, and the higher the level of household indebtedness, the more pronounced the decoupling is. Using a Dynamic General Equilibrium model that incorporates a housing construction sector, we find that fiscal stimulus causes an increase in the production of tradable goods that incentivizes the demand for labor and capital, leading to higher wages, which pulls workers out of the construction sector and negatively affects residential investment and total credit. The result is a widespread welfare loss that especially hurts borrowers. Our study offers different possible explanations for the lack of consensus in the empirical evidence on the effects of fiscal policy on the construction sector.
    Date: 2023–01
  13. By: Been-Lon Chen (Institute of Economics, Academia Sinica, Taipei, Taiwan); Shian-Yu Liao (Fu Jen Catholic University); Dongpeng Liu (Nanjing University); Xiangbo Liu (Renmin University of China)
    Abstract: We revisit the Friedman rule in a labor search model and extend Heer (2003), Cooley and Quadrini (2004), and Wang and Xie (2013) to one that allows for endogenous growth. We show that, even without a liquidity effect or a CIA constraint on firms’wage payment, our model offers a different channel for moderate money growth to increase welfare. Intuitively, in a one-sector endogenous growth economy, the technology is of constant returns with respect to capital. When the labor market is frictional, a moderate increase in money growth induces an expansion in vacancy and employment. Labor and capital are complements in production. With an increase in employment, when the technology is neoclassical, the decreasing return in capital leads to a lower marginal product of labor. However, in an endogenous growth framework wherein the technology exhibits socially constant returns in capital, the marginal product of labor is constant. Due to a constant marginal product of labor, modest inflation raises employment, enlarges economic growth, and increases welfare. Moreover, the optimallong-run inflation rate departs from the Friedman rule, even when the Hosios rule holds. Fi-nally, wefind that our model with sustainable growthfits the data better than that withoutsustainable growth.
    Keywords: Endogenous Growth, Money Supply, Labor Search, Unemployment, Welfare
    JEL: E41 J64 O42
    Date: 2022–08
  14. By: Ozge Akinci; Gianluca Benigno; Serra Pelin; Jonathan Turek
    Abstract: In this paper we highlight a new channel through which dollar fluctuations can become a self-fulfilling pro-cyclical force. We call this mechanism “Imperial Circle” as it makes the dollar the dominant macroeconomic variable in the context of the current international monetary system. At the core of it, there is a fundamental asymmetry between the shrinking exposure of the “real” U.S. economy to global developments versus the growing global role of the U.S. dollar. Dollar appreciation leads to a decline in global economic activity, which in turn benefits, in relative terms, the dollar itself, reinforcing the initial appreciation and its effects.
    Keywords: Dynamic Stochastic General Equilibrium (DSGE) models; global supply chains; dollar currency pricing; trade; spillover
    JEL: E32 E44 F41
    Date: 2022–12–01
  15. By: Potter, Tristan (Drexel University)
    Abstract: Modern search technologies enable workers to monitor - and thus quickly apply to - newly posted jobs. I conceptualize search as a monitoring decision and study the implications for labor market dynamics. The central insight is that monitoring leads to a novel source of strategic complementarities in search decisions, which results in multiple equilibria that can exert a destabilizing force on the labor market. Strategic complementarities arise because workers who actively monitor new job postings are able to apply before those who do not. This leads to a rat race for jobs in which the belief that others are monitoring new postings necessitates doing the same in order to avoid falling to the back of the queue. I show that this mechanism leads to multiple equilibria in a stylized monitoring game and then embed the game in a quantitative macroeconomic model of the labor market. With a plausibly elastic job creation process (i.e., away from the free-entry limit), multiplicity arises in the quantitative model. The model provides (i) a theory of belief-driven fluctuations in labor supply that can permanently alter the path of the economy, (ii) a mechanism through which transitory demand shocks can permanently affect labor supply, and (iii) an account of the recovery from the Great Recession, during which a historically tight labor market coexisted with weak wage growth---observations difficult to reconcile with traditional models. I document two facts that are supportive of the model and its implications.
    Keywords: Search and matching; online job search; hysteresis
    JEL: E24 E71 J64 O33
    Date: 2023–01–05
  16. By: Juin-Jen Chang (Institute of Economics, Academia Sinica, Taipei, Taiwan); Chun-Hung Kuo (Department of Economics, National Tsing Hua University); Hsieh-Yu Lin (Department of Economics, Tunghai University); Shu-Chun S. Yang (Institute of Economics, Academia Sinica, Taipei, Taiwan)
    Abstract: Since the mid-1980s, U.S. corporate tax cuts have become less expansionary and increasingly associated with rising share buybacks. Using dynamic general equilibrium models with corporate financial allocations, we show that buybacks render a corporate tax cut less expansionary. Simulations based on the Tax Cuts and Jobs Act have the optimal buyback response much smaller than that observed. This implies that restricting buybacks is likely to enhance the expansionary effects of a corporate tax cut. Both shareholders and non-shareholders enjoy higher income from a corporate tax cut, but most of the income increases accrue to shareholders. Whether non-shareholders enjoy higher consumption de- pends on the fiscal adjustment mechanism.
    Keywords: corporate tax cuts, share buybacks, tax policy effects, fiscal policy effects, SVAR estimation
    JEL: E62 H25 H30 C32 D53
    Date: 2022–11
  17. By: Alvarez, Bruna; Pessoa, João Paulo; Souza, André Portela
    Abstract: We study how revenue-dependent tax policies affect wages, productivity, and welfare in an economy where formal and informal firms co-exist. We use a dynamic entrepreneurial choice model and bring it to the data to assess the effects of the Brazilian Simples, a simplified tax scheme that reduces the tax burden of small- and medium-sized firms. We find that the Simples increases firm formalization, raising the demand for labor and benefiting workers. Meanwhile, tax collection falls as some formal firms withhold production to pay lower taxes. Overall, productivity (weighted by firm size), per capita production, and welfare fall. Alternative policies that reduce the tax gap between small and large firms perform better in welfare and tax collection terms.
    Date: 2022–12–19
  18. By: Keiichiro KOBAYASHI; Daichi SHIRAI
    Abstract: Economic growth slows for an extended period after a financial crisis. We construct a model in which a one-time buildup of debt can depress the economy persistently, even when there is no financial technology shock. We consider the debt dynamics of firms under endogenous borrowing constraints, with lenders having an option to forgive defaulting borrowers. A firm is referred to as debt-ridden when it owes maximum debt and pays all income in each period as an interest payment. In the deterministic case, a debt-ridden firm continues inefficient production permanently. Further, if the initial debt exceeds a certain threshold, the firm intentionally chooses to increase borrowing and, thus, to become debt-ridden. The emergence of a substantial number of debt-ridden firms lowers economic growth persistently. A debt restructuring policy or the relief of debt-ridden borrowers from excessive debt may be able to restore their efficiency and economic growth.
    Date: 2022–12
  19. By: Christopher Roth (University of Cologne, ECONtribute); Mirko Wiederholt (LMU Munich and Sciences Po, CESifo, CEPR); Johannes Wohlfart (Department of Economics and CEBI, University of Copenhagen, CESifo, Danish Finance Institute)
    Abstract: We study the effects of monetary policy on aggregate consumption combining a heterogeneous agent model with measured expectations under different policy counterfactuals. We express the consumption of non-hand-to-mouth households as a function of expectations only and elicit all expectations appearing in the consumption functions for alternative policy scenarios with tailored surveys. Feeding these individual-level expectations into the model illustrates that a modest forward guidance statement in March 2021 would have reduced aggregate consumption by 0.14 percent on impact and an interest rate hike of 40 basis points in March 2022 would have reduced aggregate consumption by 0.30 percent on impact.
    Keywords: Monetary Policy, Expectation Formation, Aggregate Consumption
    JEL: D12 D14 D83 D84 E32 G11
    Date: 2023–01
  20. By: Drago Bergholt; Øistein Røisland; Tommy Sveen; Ragnar Torvik
    Abstract: We study how monetary policy should respond to shocks which permanently alter the steady state structure of the economy. In such a case monetary policy affects not only the short run misallocations due to nominal rigidities, but also relative prices which stimulate reallocation of capital. We consider a permanent and negative shock to export revenues that requires a larger traded sector and a smaller non-traded sector in the new steady state. This reallocation calls for a change in relative prices during the transition, but may also lead to a period of high unemployment. We show how an appropriate monetary policy could mitigate the welfare costs of the transition by allowing the exchange rate to depreciate, and thereby allowing inflation to increase in the short run. Traditional monetary policy regimes, such as inflation targeting or a fixed exchange rate, would imply high unemployment and inefficiently slow transition. Stabilizing nominal wage growth, in contrast, would be close to the welfare-optimal monetary policy.
    Keywords: Structural Change, Dutch Disease, Monetary Policy
    JEL: E52 F41 O14
    Date: 2022–11
  21. By: Pierre Cahuc; Pauline Carry; Franck Malherbet; Pedro S. Martins
    Abstract: Estimates of the impact of employment protection heavily rely on reduced-form methods, assuming that there are no indirect effects between firms. This paper exploits a labor law reform implemented in Portugal in 2009 which restricted the use of fixed-term contracts for large firms above a specific size threshold, to investigate and quantify spillover effects. Standardreduced-form estimates based on the hypothesis of the absence of spillover towards firms for which the reform does not apply yield a negative impact on employment of about 1.5%. However, we find evidence of significant spillovers. The estimation of the macroeconomic effects of the reform with a search and matching model accounting for spillovers yields an almost negligible employment impact of the reform, more than ten times smaller than that obtained with the reduced form estimates. This result underlines that the numerous reduced-form estimates of the impact of employment protection that rely on firm size thresholds must be interpreted with caution.
    Keywords: Employmentprotection legislation, Spillover effects, Directed search and matching
    JEL: J23 J41 J63
    Date: 2023
  22. By: Stefano Bosi (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay, Université Paris-Saclay, UEVE - Université d'Évry-Val-d'Essonne); Carmen Camacho (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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); Thai Ha-Huy (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay, Université Paris-Saclay, UEVE - Université d'Évry-Val-d'Essonne)
    Abstract: In a simple discrete-time version of the Lucas (1988) model, we prove, first, that the Balanced Growth Path (BGP) is optimal and, second, that the optimal solution is unique. After briefly discussing the results obtained in some of the continuous-time versions of the Lucas model, we address the issues of existence and uniqueness of the optimal solution in discrete time. Making use of the supermodularity of the value function, we prove that the optimal solution must be monotonically increasing. This feature does indeed suit the BGP, although nothing can ensure yet its optimality. After providing the exact expression of the BGP, we do prove both its optimality and its uniqueness.
    Keywords: Human capital, Balanced growth path
    Date: 2023–01

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