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on Dynamic General Equilibrium |
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Issue of 2020‒04‒13
24 papers chosen by |
| By: | Toshiaki Ogawa (Deputy Director and Economist, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: toshiaki.ogawa@boj.or.jp)) |
| Abstract: | This paper studies capital requirements and their welfare implications in a dynamic general equilibrium model of banking. I embed two, less commonly considered but important, mechanisms. Firstly, banks choose entry and exit, which lets the number of banks change endogenously. Strengthening capital requirements reduces banks' franchise value and damages their liquidity providing function through the extensive margin. Secondly, since equity issuance is costly for banks, they precautionarily hold capital buffers against future liquidity shocks. This behavior makes present capital requirements only occasionally binding. My model shows that the optimal capital requirement would be lower than that in the literature because of the expanded negative effects of capital requirements. To maintain financial stability without damaging banks' liquidity provision, strengthening capital requirements needs to be accompanied by reducing the cost of equity issuance for banks. |
| Keywords: | Bank capital requirements, Occasionally binding constraints, Endogenous default, Entry and exit, General equilibrium model |
| JEL: | E00 G21 G28 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:20-e-03&r=all |
| By: | Raquel Fonseca; François Langot; Pierre-Carl Michaud; Thepthida Sopraseuth |
| Abstract: | Using a general equilibrium heterogeneous agent model featuring health production, we quantify the relative contribution of price distortions in the health market, TFP and other health risks in explaining cross-country differences in health expenditure (as a share of GDP) and health status. Estimated parameters reveal a substantial price wedge that explains at most 20% of the difference in health spending (as a share of GDP) and 30% of the difference in health status between Europe and the U.S. We estimate a one percentage point negative impact on the life-time cost-of-living of Americans from higher prices due to inefficiencies. |
| JEL: | E21 H51 I10 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26876&r=all |
| By: | Matthias Meier; Timo Reinelt |
| Abstract: | We document three new empirical facts: (i) monetary policy shocks increase the markup dispersion across firms, (ii) monetary policy shocks increase the relative markup of firms that adjust prices less frequently, and (iii) firms that adjust prices less frequently have higher markups. This is consistent with a New Keynesian model in which price rigidity is heterogeneous across firms. In the model, firms with stickier prices optimally set higher markups and their markups increase by more after monetary policy shocks. The consequent increase in markup dispersion explains why aggregate TFP declines after monetary policy shocks. In the calibrated model, monetary policy shocks explain substantial fluctuations in markup dispersion and aggregate productivity. |
| Keywords: | Monetary policy, markup dispersion, heterogeneous price rigidity, aggregate TFP |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2020_161&r=all |
| By: | Masudul Hasan Adil (Mumbai School of Economics and Public Policy, University of Mumbai); Neeraj R. Hatekar (Mumbai School of Economics and Public Policy, University of Mumbai); Taniya Ghosh (Indira Gandhi Institute of Development Research) |
| Abstract: | In the recent scenario, one of the most pertinent changes in monetary economics has been the virtual disappearance of what was once a dominant focus, the role of money in monetary policy, and in parallel, the disappearance of the LM curve. Economists used to think about issues of monetary policy with the help of the LM curve as being part of the analytical framework which captures the demand for money. However, the workhorse model of modern monetary theory and policy, the New Keynesian Dynamic Stochastic General Equilibrium framework only comprises of, a dynamic aggregate demand (or the dynamic IS) curve, an aggregate supply (or the New Keynesian Phillips) curve, and a monetary policy rule. The monetary policy rule is generally the Taylor rule that relates the nominal interest rate to the output gap and inflation gap, but typically not to either the quantity or the growth rate of money. This change in the modern monetary model reflects how the central banks make monetary policy now. The present study provides a detailed discussion on the role of money in monetary policy formulation, in the context of New Keynesian and New Monetarist perspective. The pros and cons of abandonment of money or the LM curve from monetary policy models have been discussed in detail. |
| Keywords: | Money, DSGE, New Keynesian, new monetarist, LM curve and Monetary policy |
| JEL: | E41 E43 E52 E58 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:ind:igiwpp:2020-005&r=all |
| By: | Christopher Busch (Universitat Autonoma de Barcelona); Dirk Krueger (University of Pennsylvania); Alexander Ludwig (SAFE, University of Mannheim); Irina Popova (Goethe University Frankfurt); Zainab Iftikhar (Goethe University Frankfurt) |
| Abstract: | In 2015-2016 Germany experienced a wave of predominantly low-skilled refugee immigration. We evaluate its macroeconomic and distributional effects using a quantitative overlapping generations model calibrated using German micro data to replicate education and productivity differentials between foreign born and native workers. Workers are modelled as imperfect substitutes in aggregate production leading to endogenous wage differentials. We simulate the dynamic effects of this refugee wave, with specific focus on the welfare impact on low skilled natives. Our results indicate that the small losses this group suffers can be compensated by welfare gains of other parts of the native population. |
| Keywords: | immigration, refugees, overlapping generations, demographic change |
| JEL: | F22 E20 H55 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:hka:wpaper:2020-020&r=all |
| By: | Ashima Goyal (Indira Gandhi Institute of Development Research); Akhilesh K. Verma (Indira Gandhi Institute of Development Research) |
| Abstract: | We present a small open economy New Keynesian model with financial intermediation to investigate the interaction between monetary policy and macroprudential regulations. Our model economy attempts to capture the vulnerability of emerging market economies in the face of external and domestic shocks. We build a model that closely captures the dynamics of emerging market economies to show that interest rate policy rules alone may not be an effective instrument to stabilize the economy under negative shocks. Monetary policy implementation through augmented Taylor rule (ATR) is an inadequate tool to absorb negative shocks given its conflict between inflation and exchange rate objectives. We show that the use of macroprudential regulations (MaPs) with simple Taylor rule improves business cycle dynamics relative to ATR under domestic and external shocks. We present two kinds of MaP regulations to show that they effectively mitigate losses during economic downturns and reduce excessive risk-taking behavior during economic booms when used along with a simple monetary policy rule (MP). In addition, we also conduct welfare evaluation that supports complementarity between MP and MaPs under different shocks. |
| Keywords: | DSGE model, cross border flows, monetary policy macroprudential regulation |
| JEL: | E44 E52 E61 F42 G28 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:ind:igiwpp:2020-008&r=all |
| By: | Per Krusell; Toshihiko Mukoyama; Richard Rogerson; Ayşegül Şahin |
| Abstract: | We build a three-state general equilibrium model of the aggregate labor market that features both standard labor supply forces and labor market frictions. Our model matches key features of the cyclical properties of employment, unemployment, and nonparticipation as well as those of gross worker flows across these three labor market states. Our key finding is that shocks to labor market frictions play a dominant role in accounting for labor market fluctuations. This is in contrast to the focus of the traditional RBC literature, which emphasized how employment fluctuations arise as a consequence of labor supply responses to price changes induced by TFP shocks. |
| JEL: | E24 E32 J22 J64 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26878&r=all |
| By: | Coelho, José |
| Abstract: | In the last decades, income inequality has been on the rise in the U.S. The growing skill premium suggests the pivotal role of skill-biased technological change (SBTC) in promoting the observed increase in inequality levels. In this context, labor income tax structures have been central to the policy debate. I develop an overlapping generations model to perform a welfare evaluation of Universal basic income (UBI) tax structures and verify how these interact with SBTC. I find that an UBI system would have improved social welfare in 2010 when compared to the existing tax system and determine that this result is primarily motivated by SBTC. |
| Keywords: | Income Inequality, Skill Premium, Optimal Taxation, Universal Basic Income |
| JEL: | E24 E62 H21 |
| Date: | 2020–01–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:99195&r=all |
| By: | Christopher Busch (Universitat Autonoma de Barcelona); Alexander Ludwig (SAFE, University of Mannheim) |
| Abstract: | We extend the canonical income process with persistent and transitory risk to shock distributions with left-skewness and excess kurtosis, to which we refer as higher-order risk. We estimate our extended income process by GMM for household data from the United States. We find countercyclical variance and procyclical skewness of persistent shocks. All shock distributions are highly leptokurtic. The existing tax and transfer system reduces dispersion and left-skewness of shocks. We then show that in a standard incomplete-markets life-cycle model, first, higher-order risk has sizable welfare implications, which depend crucially on risk attitudes of households; second, higher-order risk matters quantitatively for the welfare costs of cyclical idiosyncratic risk; third, higher-order risk has non-trivial implications for the degree of self-insurance against both transitory and persistent shocks. |
| Keywords: | labor income risk, business cycle, GMM estimation, skewness, persistent and transitory income shocks, risk attitudes, life-cycle model |
| JEL: | D31 E24 E32 H31 J31 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:hka:wpaper:2020-019&r=all |
| By: | Olatunji A. Shobande (Business School, University of Aberdeen, UK); Oladimeji T. Shodipe (Eastern Illinois University, US); Simplice A. Asongu (Yaoundé, Cameroon) |
| Abstract: | The study examines the role of global predictors on national monetary policy formation for Kenya and Ghana within the New Keynesian DSGE framework. We developed and automatically calibrated our DSGE model using the Bayesian estimator, which made our model robust to rigorous stochastic number of subjective choices. Our simulation result indicates that global factors account for the inability of national Central Banks to predict the behaviour of macroeconomic and financial variables among these developing nations. |
| Keywords: | Business Cycle, Macroeconomic policy, Financial crises |
| JEL: | E32 |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:abh:wpaper:19/066&r=all |
| By: | Reiter, Michael (IHS, Vienna and NYU Abu Dhabi); Zessner-Spitzenberg, Leopold (Vienna Graduate School of Economics and IHS, Vienna) |
| Abstract: | Long-term debt contracts transfer aggregate risk from borrowing firms to lending banks. When aggregate shocks increase the future default probability of firms, banks are not compensated for the default risk of existing contracts. If banks are highly leveraged, this can lead to financial instability with severe repercussions in the real economy. To study this mechanism quantitatively, we build a macroeconomic model of financial intermediation with long-term defaultable loan contracts and calibrate it to match aggregate firm and bank exposure to business cycle risks. Our model exhibits banking crises that closely resemble observed crisis episodes. We find that such crises do not arise in an economy with short-term debt. Our results on the role of long-term debt completely reverse if financial regulation is implemented to increase banks' risk bearing capacity. The financial sector is then well equipped to take on the aggregate risk, such that long-term lending stabilizes the business cycle by providing insurance to the corporate sector. |
| Keywords: | Banking, Financial frictions, Maturity transformation |
| JEL: | E32 E43 E44 G01 G21 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihswps:13&r=all |
| By: | Francisco Ilabaca (Department of Economics, University of California-Irvine); Fabio Milani (Department of Economics, University of California-Irvine) |
| Abstract: | This paper estimates a New Keynesian model extended to include heterogeneous expectations, to revisit the evidence that postwar US macroeconomic data can be explained as the outcome of passive monetary policy, indeterminacy, and sunspot-driven fluctuations in the pre-1979 sample, with a switch to active monetary policy and a determinate equilibrium starting in the early 1980s. Different shares of consumers and firms form either rational expectations, or adaptive and extrapolative expectations. The inclusion of heterogeneous expectations alters the determinacy properties of the model compared to the corresponding case under exclusively rational expectations. The Taylor principle is neither necessary nor sufficient, as the details of expectations may matter more for equilibrium stability. The model is estimated with Bayesian techniques, using rolling windows and allowing the parameters to fall both in the determinacy and indeterminacy regions. The estimates reveal large shares of agents who depart from rational expectations; heterogeneous expectations are preferred by the data everywhere in the sample. The results confirm that macroeconomic data in the early windows are better explained by indeterminacy, while determinacy is favored over the latest two decades. We uncover, however, some subsamples that include the 1980s and 1990s in which the Taylor principle is satisfied, but expectations becoming extrapolative raise the probability of indeterminacy to 50% and more. |
| Keywords: | Heterogeneous Expectations in New Keynesian Model; Indeterminacy; Sunspots; Taylor Principle; Deviations from Rational Expectations; Time-Varying Parameters |
| JEL: | E32 E52 E58 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:irv:wpaper:192003&r=all |
| By: | William A. Barnett (University of Kansas); Giovanni Bella (University of Cagliari); Taniya Ghosh (Indira Gandhi Institute of Development Research); Paolo Mattana (University of Cagliari); Beatrice Venturi (University of Cagliari) |
| Abstract: | The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, a la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial loanable funds over-saving theory, which seeks to explain why interest rates and, to a lesser extent inflation rates, have declined to current low levels, such that the real rate of interest is below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Policy options to eliminate or control the chaotic dynamics are developed. |
| Keywords: | Shilnikov chaos criterion, global indeterminacy, long-term un-predictability, liquidity trap |
| JEL: | C61 C62 E12 E52 E63 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:ind:igiwpp:2020-006&r=all |
| By: | Freitas, Bruno |
| Abstract: | We show that the labour share of income is an important factor affecting the mechanisms behind fiscal consolidation programs, thus requiring consideration when evaluating fiscal multipliers across countries. We calibrate a life-cycle, overlapping generations model to match key characteristics of different European economies and evaluate the recessive impacts of fiscal consolidation programs. We find a positive relationship between the labour share and the impact fiscal multipliers generated by our model. This result directly follows from the higher weight of labour on production and the lower opportunity cost of leisure present in economies with a higher labour share. Following the impact period, the relationship between the labour share and the fiscal multipliers is dependent on the type of fiscal instrument employed in the consolidation. |
| Keywords: | Fiscal Consolidation, Labour Share, Fiscal Multipliers, Public Debt |
| JEL: | D33 E21 E62 H31 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:98973&r=all |
| By: | Glaciel, William |
| Abstract: | As can be seen in Richter and Wong (1999), non-computability of general equilibrium has been recognized in economics. However, despite general non-computability, equilibrium can indeed be computed in specific cases. In this paper, further restriction on computability of equilibrium is provided in contexts of dynamic stochastic general equilibrium (DSGE) models with heterogeneous agents, demonstrating that non-computability concerns apply more generally than often understood. |
| Date: | 2020–03–24 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:23ep9&r=all |
| By: | Chassamboulli, Andri (University of Cyprus); Gomes, Pedro Maia (Birkbeck, University of London) |
| Abstract: | We set up a model with search and matching frictions to understand the effects of employment and wage policies, as well as nepotism in hiring in the public sector, on unemployment and rent seeking. Conditional on inefficiently high public-sector wages, more nepotism in public-sector hiring lowers the unemployment rate because it limits the size of queues for public-sector jobs. Wage and employment policies impose an endogenous constraint on the number of workers the government can hire through connections. |
| Keywords: | public-sector employment, nepotism, public-sector wages, unemployment, queues |
| JEL: | E24 J31 J45 J64 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp13086&r=all |
| By: | José L. Torres (Department of Economics, University of Málaga) |
| Abstract: | This paper studies the macroeconomic implications of the distribution of the social security tax between employees and employers using a general equilibrium framework. We calibrate a Dynamic General Equilibrium model for the average of OECD countries and find that increasing the share of social security contributions paid by employers has a positive effect on economic activity. Whereas raising the employer?s share increases the labor cost for ?firms and reduces the equilibrium gross wage, conversely, workers? net labor income increases, increasing employment and output. The response of the economy to the change in the distribution of social security contributions between employees and employers depends on how the total labor tax wedge changes, which is also affected by the labor income tax and the consumption tax, as distortionary effects from one tax are not independent from the other taxes driving wages? purchasing power. |
| Keywords: | Social Security Contributions; Employees Contributions; Employers Contributions; Dynamic General Equilibrium models |
| JEL: | E20 H20 H22 H55 |
| Date: | 2020–01 |
| URL: | http://d.repec.org/n?u=RePEc:mal:wpaper:2020-1&r=all |
| By: | Bing Tong (Center for Financial Development and Stability at Henan University, and School of Economics at Henan University, Kaifeng, Henan); Guang Yang (School of Economics, Nankai University) |
| Abstract: | Nominal interest rates in China has long been controlled by the government, making their changes lagging behind price changes. We model this in a New Keynesian model with a transiently fixed interest rate, and prove that interest rate fixation can magnify model volatility and lead to economic instability. Under the fixed interest rate, the model enters a vicious spiral until monetary policy switches to a flexible interest rate rule, which represents the shadow rate of the economy, determined by discrete (and insufficient) interest rate adjustments and other policy tools. This explains Chinas large business cycle fluctuations over the past decades. |
| Keywords: | Interest rate peg, Chinese economy,New Keynesian Model, Monetary policy, Business cycle |
| JEL: | E31 E32 E42 E52 E58 |
| Date: | 2020–04 |
| URL: | http://d.repec.org/n?u=RePEc:fds:dpaper:202001&r=all |
| By: | Renato Faccini; Leonardo Melosi |
| Abstract: | We study a model in which firms compete to retain and attract workers searching on the job. A drop in the rate of on-the-job search makes such wage competition less likely, reducing expected labor costs and lowering inflation. This model explains why inflation has remained subdued over the last decade, which is a conundrum for general equilibrium models and Phillips curves. Key to this success is the observed slowdown in the recovery of the employment-to-employment transition rate in the last five years, which is interpreted by the model as a decline in the share of employed workers searching for a job. This fall in the on-the-job search rate is corroborated by the micro data. |
| Keywords: | misallocation; cyclical; labor market slack; Inflation; job ladder; Phillips curve |
| JEL: | C78 E24 E31 |
| Date: | 2020–03–02 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedhwp:87688&r=all |
| By: | Morchio, Iacopo; Moser, Christian |
| Abstract: | We assess the sources and consequences of the gender pay gap using a combination of theory and measurement. We start by documenting three empirical facts. First, women are more likely than men to work at low-paying employers. Second, for women as for men, pay is not the sole determinant of workers' revealed-preference rankings of employers. Third, both pay and the revealed-preference rank differ between women and men within the same employer. To interpret these facts, we develop an empirical equilibrium search model featuring endogenous gender differences in pay, amenities, and recruiting intensities across employers. The estimated model suggests that compensating differentials explain one fifth of the gender gap, that there are significant output and welfare gains from eliminating gender differences, and that an equal-pay policy fails to close the gender pay gap. |
| Keywords: | Worker and Firm Heterogeneity, Misallocation, Compensating Differentials, Discrimination, Empirical Equilibrium Search Model, Linked Employer-Employee Data |
| JEL: | E24 E25 J16 J31 |
| Date: | 2018–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:99276&r=all |
| By: | Claire Naiditch (LEM - Lille économie management - LEM - UMR 9221 - Université de Lille - UCL - Université catholique de Lille - CNRS - Centre National de la Recherche Scientifique); Radu Vranceanu (ESSEC Business School - Essec Business School) |
| Abstract: | The important flows of irregular migration could not exist without the emergence of a criminal market for smuggling services. A matching model à la Pissarides (2000) provides a well-suited framework to analyze such a ow market with significant trade frictions. Our analysis considers the competitive segment of this underground market in which small-business smugglers can freely enter. The model allows us to determine the equilibrium number of smugglers, the matching probability, the number of successful irregular migrants and, as an original concept, the equilibrium migrant welfare. Changes in parameters can be related to the various policies implemented by destination countries to cut down irregular migration. |
| Keywords: | Migrant welfare,Smuggling,Irregular migration,Matching model |
| Date: | 2020–01–10 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02463193&r=all |
| By: | Charles Yuji Horioka |
| Abstract: | . In this paper, we first provide a brief exposition of the simplest version of the selfish life cycle model or hypothesis, which is undoubtedly the most widely used theoretical model of household behavior in economics, and then survey the literature on household saving behavior in Japan (with emphasis on the author’s own past research) to shed light on whether or not the selfish life-cycle model applies in the case of Japan. In particular, we survey the literature on the impact of the age structure of the population on the saving rate, the saving behavior of retired households, saving motives, the prevalence of bequests, bequest motives, tests of altruism, and the importance of borrowing (liquidity) constraints and show that almost all of the available evidence suggests that the selfish life-cycle model applies to a greater extent in Japan than it does in other countries. Finally, we discuss the policy implications of our findings. |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1084&r=all |
| By: | Toshiaki Ogawa (Deputy Director and Economist, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: toshiaki.ogawa@boj.or.jp)) |
| Abstract: | I construct a dynamic stochastic general equilibrium model to investigate how the liquidity management of different size banks responds to liquidity and loan demand shocks. My investigation shows the following. Compared with small banks, large banks tend to be net borrowers and thus more exposed to liquidity risk. In response to negative liquidity shocks, large banks decrease their credit supply while small ones increase theirs. In response to negative loan demand shocks, both large and small banks decrease their credit supply. Connecting these implications with the panel data, I argue that negative liquidity shocks served as the main driver of the Great Recession initially, and negative demand shocks did so later, and that demand shocks accounted for two thirds of the greatest fall in aggregate loans during the recession. |
| Keywords: | Great Recession, Bank liquidity management, Occasionally binding constraints, Heterogeneous bank model, General equilibrium model |
| JEL: | E00 G01 G18 G20 G21 |
| Date: | 2020–03 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:20-e-05&r=all |
| By: | Cao, Dan; Evans, Martin; Lua, Wenlan |
| Abstract: | We examine how medium-term movements in real exchange rates and GDP vary with international financial conditions. For this purpose, we study the international transmission of productivity shocks across a variety of IRBC models that incorporate different assumptions about the persistence of productivity shocks, the degree of international risk sharing and access to international asset markets. Using a new global solution method, we demonstrate that the transmission of productivity shocks depends critically on the proximity of a national economy to its international borrowing limit. We then show that this implication of the IRBC model is consistent with the behavior of the US-UK real exchange rate and GDP over the past 200 years. The model also produces a negative correlation between relative consumption growth and real depreciation rate consistent with more recent data, and hence offers a resolution of the Backus-Smith puzzle. |
| Keywords: | Real Exchange Rates, International Real Business Cycles, Global Solution Methods |
| JEL: | C60 F30 F31 F41 F44 G11 |
| Date: | 2020–03–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:99054&r=all |