Raouf Boucekkine

Faculty ,  Aix-Marseille Université , Faculté d'économie et de gestion (FEG)

Development and political economy
Boucekkine
Status
Professor
Research domain(s)
Development economics, Macroeconomics
Thesis
1993, Université Paris I Panthéon-Sorbonne
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CV
Contact
raouf.boucekkine[at]univ-amu.fr
Address

AMU - AMSE
5-9 Boulevard Maurice Bourdet, CS 50498
​13205 Marseille Cedex 1

Abstract We study optimal firm behavior under irreversible pollution risk for a general class of models with irreversible local pollution. Irreversibility comes from the decay rate of pollution dropping to zero above a pollution level featuring non-convexity. In addition, the firm can instantaneously move from a reversible to an irreversible pollution mode, following a Poisson process. First, we prove for the general class of models that for any value of the Poisson probability, the optimal emission policy leads to more pollution with the irreversibility risk than without in a neighborhood of the irreversibility threshold. It’s shown that the extent of uncertainty (as captured by the Poisson arrival rate) is second-order in this neighborhood. Next we study the robustness of the latter result at any pollution level in the case of linear-quadratic objective functions. We find that the general local result does not necessarily hold if actual pollution is far enough from the irreversibility threshold.
Keywords Irreversible pollution, Irreversibility thresholds, Uncertainty, Firm pollution control, Piecewise deterministic problems
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Abstract The modernisation theory of regime change is often perceived to be a murky paradigm, lacking theoretical or empirical foundations. In response, we clarify the links between education and regime change.More specifically, we propose that education contributes indirectly to the collapse of autocratic regimes because educated people engage in non-violent (civil) resistance that reduces the effectiveness of the security apparatus. We empirically test the validity of this 'defanging effect' of education. We indeed find that the combination of high autocracy and high education levels tends to trigger non-violent campaigns, which in turn increases the likelihood of a regime change, likely to be associated with political liberalisation.
Keywords Regime change, Modernisation, Education, Democratisation, Civil resistance, Autocracy
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Abstract A simple model on climate change and the design of international climate agreements
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Abstract We present an overview of selected contributions of the Journal of Mathematical Economics’ authors to growth theory in the last half century. We start with the classical optimal growth theory within a benchmark multisector model and outline the successive developments in the analysis of this model, including the turnpike theory. Different refinements of the benchmark are considered along the way. We then survey the abundant literature on endogenous fluctuations in two-sector models. We conclude with two strong trends in the recent growth literature: green growth and infinite-dimensional growth models.
Keywords Growth theory, Multisector models, Turnpike theory, Green growth, Infinite dimensional growth models, Optimization
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Abstract In this paper, we revisit the theory of spatial externalities. In particular, we depart in several respects from the important literature studying the fundamental pollution free riding problem uncovered in the associated empirical works. First, instead of assuming ad hoc pollution diffusion schemes across space, we consider a realistic spatiotemporal law of motion for air and water pollution (diffusion and advection). Second, we tackle spatiotemporal non-cooperative (and cooperative) differential games. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. Third, we allow for a rich set of geographic heterogeneities across states while the literature assumes identical states. We solve analytically the induced non-cooperative differential game under decentralization and fully characterize the resulting long-term spatial distributions. We further provide with full exploration of the free riding problem, reflected in the so-called border effects. In particular, net pollution flows diffuse at an increasing rate as we approach the borders, with strong asymmetries under advection, and structural breaks show up at the borders. We also build a formal case in which a larger number of states goes with the exacerbation of pollution externalities. Finally, we explore how geographic discrepancies affect the shape of the border effects.
Keywords Transboundary pollution, Environmental federalism, Infinite dimensional optimal control problems, Differential games in continuous time and space, Spatial diffusion, Spatial externalities
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Abstract Since the start of the oil counter-shock in June 2014, Algeria has experienced unprecedented twin deficits. The excessive monetisation of the public deficit coupled with other deep anomalies in the economy of this country acutely calls for reconsideration of its monetary policy. To this end a prior study of the long-run stability of money demand is needed. We estimate the demand for money for monetary aggregates M1 and M2, and cash in Algeria over the period 1979–2019, and study its long-run stability. We show that the transaction motive is significant for all three aggregates, especially for the demand for cash, reflecting the weight of informal economy “practices”. The elasticity of the scale variable is very close to unity for M2 and M1, and even equal to unity for cash demand (1.006). The elasticity of inflation is also significant for all three aggregates, although its level is higher in the case of cash demand (−6.474). Despite the persistence of certain financial repression mechanisms, interest rate elasticity is significant for all three aggregates, but higher for M1 and cash. The same observation is made for elasticity of the exchange rate, reflecting the effect of monetary substitution, especially for M1 and cash. Finally, our study concludes that the demand for money in terms of M1 remains stable, the same observation being confirmed for the M2 aggregate. However, the demand for fiat currency proves not to be stable. The consequences for the optimal design of monetary policy in Algeria are clearly stated.
Keywords Co-integration, Algeria, Resource-rich countries, Long-run stability, Money demand, Monetary policy
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Abstract Elite-biased democracies are those democracies in which former political incumbents and their allies coordinate to impose part of the autocratic institutional rules in the new political regime. We document that this type of democratic transition is much more prevalent than the emergence of pure (popular) democracies in which the majority decides the new institutional rules. We then develop a theoretical model explaining how an elite-biased democracy may arise in an initially autocratic country. To this end, we extend the benchmark political transition model of Acemoglu and Robinson (2005) along two essential directions. First, population is split into majority versus minority groups under the initial autocratic regime. Second, the minority is an insider as it benefits from a more favourable redistribution by the autocrat. We derive conditions under which elite-biased democracies emerge and characterise them, in particular with respect to pure democracies. https://doi.org/10.1016/j.mathsocsci.2021.03.007
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Abstract This paper is an introduction to the special issue of Mathematical Social Sciences on Advances in growth and macroeconomic dynamics in memory of Carine Nourry.
Keywords Inequalities and income distribution, Migration and networks, Existence of equilibria, Macroeconomic stability and fluctuations
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Abstract We study the joint determination of optimal investment and optimal depollution in a spatiotemporal framework where pollution is transboundary. Pollution is controlled at a global level. The regulator internalizes that: (i) production generates pollution, which is bad for the wellbeing of population, and that (ii) pollution flows across space driven by a diffusion process. We solve analytically for the optimal investment and depollution spatiotemporal paths and characterize the optimal long-term spatial distribution when relevant. We finally explore numerically the variety of optimal spatial distributions obtained using a core/periphery model where the core differs from the periphery either in terms of input productivity, depollution efficiency, environmental awareness or self-cleaning capacity of nature. We also compare the distributions with and without diffusion. Key aspects in the optimal policy of the regulator are the role of aversion to inequality, notably leading to smoothing consumption across locations, and the control of diffusive pollution adding another smoothing engine.
Keywords Decision analysis, Pollution control, Geography, Transboundary pollution, Infinite dimensional optimal control problems
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Abstract In this paper, we consider an abstract optimal control problem with state constraint. The methodology relies on the employment of the classical dynamic programming tool considered in the infinite dimensional context. We are able to identify a closed-form solution to the induced Hamilton-Jacobi-Bellman (HJB) equation in infinite dimension and to prove a verification theorem, also providing the optimal control in closed loop form. The abstract problem can be seen an abstract formulation of a PDE optimal control problem and is motivated by an economic application in the context of continuous spatiotemporal growth models with capital diusion, where a social planner chooses the optimal location of economic activity across space by maximization of an utilitarian social welfare function. From the economic point of view, we generalize previous works by considering a continuum of social welfare functions ranging from Benthamite to Millian functions. We prove that the Benthamite case is the unique case for which the optimal stationary detrended consumption spatial distribution is uniform. Interestingly enough, we also find that as the social welfare function gets closer to the Millian case, the optimal spatiotemporal dynamics amplify the typical neoclassical dilution population size effect, even in the long-run.
Keywords PDE, PARTIAL DIFFERENTIAL EQUATION, IMPERFECT ALTRUISM, MILLIAN SOCIAL WELFARE FUNCTION, BENTHAMITE SOCIAL WELFARE FUNCTION, SPATIOTEMPORAL GROWTH MODEL, HAMILTON-JACOBI-BELLMAN EQUATION, INFINITE DIMENSION
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Abstract We study the joint determination of optimal investment and optimal depollution in a spatiotemporal framework where pollution is transboundary. Pollution is controlled at a global level. The regulator internalizes that: (i) production generates pollution, which is bad for the wellbeing of population, and that (ii) pollution flows across space driven by a diffusion process. We solve analytically for the optimal investment and depollution spatiotemporal paths and characterize the optimal long-term spatial distribution when relevant. We finally explore numerically the variety of optimal spatial distributions obtained using a core/periphery model where the core differs from the periphery either in terms of input productivity, depollution efficiency, environmental awareness or self-cleaning capacity of nature. We also compare the distributions with and without diffusion. Key aspects in the optimal policy of the regulator are the role of aversion to inequality, notably leading to smoothing consumption across locations, and the control of diffusive pollution adding another smoothing engine.
Keywords Pollution control, Geography, Infinite dimensional optimal control problems, Decision analysis, Transboundary pollution
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Abstract In this paper, we tackle a generic optimal regime switching problem where the decision-making process is not the same from one regime to another. Precisely, we consider a simple model of optimal switching from competition to cooperation. To this end, we solve a two-stage optimal control problem. In the first stage, two players engage in a dynamic game with a common state variable and one control for each player. We solve for open-loop strategies with a linear state equation and linear-quadratic payoffs. More importantly, the players may also consider the possibility to switch at finite time to a cooperative regime with the associated joint optimization of the sum of the individual payoffs. Using theoretical analysis and numerical exercises, we study the optimal switching strategy from competition to cooperation. We also discuss reverse switching.
Keywords Multi-stage optimal control, Dynamic games, Competition, Cooperation
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Abstract We investigate the link between resource revenues volatility and institutions. We build a stochastic differential game with two players (conservatives vs. liberals) lobbying for changing the institutions in their preferred directions. First, uncertainty surrounds the dynamics of institutions and the resource revenues. Second, the lobbying power is asymmetric, the conservatives’ power being increasing with resource revenues. We show the existence of a unique equilibrium in the set of affine strategies. We then examine to which extent uncertainty leads to more liberal institutions in the long run, compared to the deterministic case. We finally explore the institutional impact of volatility using a database covering 91 countries over the period 1973–2005. Focusing on financial liberalization, we find that as oil revenue volatility increases, liberalization goes down. This result is robust to different specifications and sample distinctions.
Keywords Financial liberalization policies, Stochastic dynamic games, Lobbying games, Petropolitics, Institutional dynamics
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Abstract Does drawing economic benefit from nature impinge on conservation? This has been a subject of controversy in the literature. The article presents a management method to overcome this possible dilemma, and reconcile conservation biology with economics. It is based on recent advances in the mathematical theory of dynamic systems under viability constraints. In the case of a one-locus two-allele plant coexisting with a one-locus two-allele parasite, the method provides a rule for deciding when and to what extent the resistant or the susceptible strain should be cultivated, in the uncertain time-varying presence of the parasite. This is useful for preventing the fixation of the susceptible allele - and thereby limiting the plant's vulnerability in the medium term, should the parasite reappear. The method thus provides an aid to decision for economic and ecology-friendly profitability.
Keywords Genetic distance, Genetic diversity, Sustainability, C-viability, Genetic resistance
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Abstract We investigate the link between resource revenues volatility and institutions. We build a stochastic differential game with two players (conservatives vs. liberals) lobbying for changing the institutions in their preferred directions. First, uncertainty surrounds the dynamics of institutions and the resource revenues. Second, the lobbying power is asymmetric, the conservatives’ power being increasing with resource revenues. We show the existence of a unique equilibrium in the set of affine strategies. We then examine to which extent uncertainty leads to more liberal institutions in the long run, compared to the deterministic case. We finally explore the institutional impact of volatility using a database covering 91 countries over the period 1973–2005. Focusing on financial liberalization, we find that as oil revenue volatility increases, liberalization goes down. This result is robust to different specifications and sample distinctions.
Keywords Institutional dynamics, Petropolitics, Lobbying games, Stochastic dynamic games, Financial liberalization policies
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Abstract We provide with an optimal growth spatio-temporal setting with capital accumulation and diffusion across space in order to study the link between economic growth triggered by capital spatio-temporal dynamics and agglomeration across space. We choose the simplest production function generating growth endogenously, the AK technology but in sharp contrast to the related literature which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology (through the productivity parameter A) and population. Beside the mathematical tour de force, we ultimately show that agglomeration may show up in our optimal growth with linear technology, its exact shape depending on the interaction of two main effects, a population dilution effect versus a technology space discrepancy effect.
Keywords Growth, Infinite dimensional optimal control problems, Heterogeneous and continuous space, Agglomeration, Cap- ital mobility
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Abstract The pure risk sharing mechanism implies that financial liberalization is growth enhancing for all countries as the world portfolio shifts from safe low-yield capital to riskier high-yield capital. This result is typically obtained under the assumption that the volatilities for risky assets prevailing under autarky are not altered after liberalization. We relax this assumption within a simple two-country model of intertemporal portfolio choices. By doing so, we put together the risk sharing effect and a well-defined instability effect. We identify the conditions under which liberalization may cause a drop in growth. These conditions combine the typical threshold conditions outlined in the literature, which concern the deep characteristics of the economies, and size conditions on the instability effect induced by liberalization.
Keywords Emerging markets, Volatility, Risk sharing, Financial liberalization, Economic Growth
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Abstract We consider an autocracy where the ruling elite control both the resource wealth and ed- ucation policies. Education prompts economic growth and enriches the budget of the elite. However, education also increases the “awareness of citizens”–capturing their reluctance to accept a dictatorship and their labor market aspirations –and forces the elite to ex- pand redistribution or handover the power. A power handover leads to a more democratic regime, where the elite retains (at least partially) its economic power. This trade-offis the backbone of our Lipsetian theory of voluntary power handover. This theory provides new insights on the positive relationship between economic development, education, and de- mocratization, and on the negative relationship between inequality and democratization. Finally, we revisit the resources-curse hypothesis within our setting
Keywords Resource curse, Institutional change, Human capital, Lipset’s theory
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Abstract We review the most recent advances in distributed optimal control applied to Environmental Economics, covering in particular problems where the state dynamics are governed by partial differential equations (PDEs). This is a quite fresh application area of distributed optimal control, which has already suggested several new mathematical research lines due to the specificities of the Environmental Economics problems involved. We enhance the latter through a survey of the variety of themes and associated mathematical structures beared by this literature. We also provide a quick tour of the existing tools in the theory of distributed optimal control that have been applied so far in Environmental Economics.
Keywords Environmental economics, Distributed systems, Optimal control, Partial differential equations
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Abstract We solve a linear-quadratic model of a spatio-temporal economy using a polluting one-input technology. Space is continuous and heterogenous: locations differ in productivity, nature self-cleaning technology and environmental awareness. The unique link between locations is transboundary pollution which is modelled as a PDE diffusion equation. The spatio-temporal functional is quadratic in local consumption and linear in pollution. Using a dynamic programming method adapted to our infinite dimensional setting, we solve the associated optimal control problem in closed-form and identify the asymptotic (optimal) spatial distribution of pollution. We show that optimal emissions will decrease at given location if and only if local productivity is larger than a threshold which depends both on the local pollution absorption capacity and environmental awareness. Furthermore, we numerically explore the relationship between the spatial optimal distributions of production and (asymptotic) pollution in order to uncover possible (geographic) environmental Kuznets curve cases.
Keywords Transboundary pollution, Infinite dimensional optimal control problems, Geography, Growth
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Abstract This paper revisits the optimal population size problem in a continuous time Ramsey setting with costly child rearing and both intergenerational and intertemporal altruism. The social welfare functions considered range from the Millian to the Benthamite. When population growth is endogenized, the associated optimal control problem involves an endogenous effective discount rate depending on past and current population growth rates, which makes preferences intertemporally dependent. We tackle this problem by using an appropriate maximum principle. Then we study the stationary solutions (balanced growth paths) and show the existence of two admissible solutions except in the Millian case. We prove that only one is optimal. Comparative statics and transitional dynamics are numerically derived in the general case.
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Abstract Under uncertainty, mean growth of, say, wealth is often defined as the growth rate of average wealth, but it can alternatively be defined as the average growth rate of wealth. We argue that stochastic stability points to the latter notion of mean growth as the theoretically relevant one. Our discussion is cast within the class of continuous-time AK-type models subject to geometric Brownian motions. First, stability concepts related to stochastic linear homogeneous differential equations are introduced and applied to the canonical AK model. It is readily shown that exponential balanced-growth paths are not robust to uncertainty. In a second application, we evaluate the quantitative implications of adopting the stochastic-stability-related concept of mean growth for the comparative statics of global diversification in the seminal model due to Obstfeld (1994).
Keywords Mean growth, Global diversification, Stochastic stability, Endogenous stochastic growth, AK model
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Abstract After years of high commodity prices, a new era of lower ones, especially for oil, seems likely to persist. This will be challenging for resource-rich countries, which must cope with the decline in income that accompanies the lower prices and the potential widening of internal and external imbalances. This column presents a new VOXEU eBook in which leading economists from academia and the public and private sector examine the shifting landscape in commodity markets and look at the exchange rate, monetary, and fiscal options policymakers have, as well as the role of finance, including sovereign wealth funds, and diversification.
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Abstract This paper aims at clarifying the analytical conditions under which financial globalization originates welfare gains in a simple endogenous growth setting. We focus on an open-economy AK model in which the capital-deepening effect of financial globalization boosts growth in a in permanent but entails an entry cost in order to access international credit markets. We show that constrained borrowing triggers substantial welfare gains, even at small levels of international financial integration, provided that the autarkic growth rate is larger than the world interest rate. Such conditional welfare benefits boosted by stronger growth—long-run gain—arise in our preferred model without investment commitment and they range, relative to autarky, from about 2% in middle-income countries to about 13% in OECD-type countries under international financial integration. Sizeable benefits emerge despite the fact that consumption initially falls—short-run pain—which is, however, shown not to dwarf positive growth changes.
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Abstract Two countries produce goods and are penalized by the common pollution they generate. Each country maximizes an inter-temporal utility criterion, taking account of the pollution stock to which both contribute. The dynamic is in continuous time with possible sudden switches to less polluting technologies. The set of Nash equilibria, for which solutions also remain in the set of constraints, is the intersection of two manifolds in a certain state space. At the Nash equilibrium, the choices of the two countries are interdependent: different productivity levels after switching lead the more productive country to hasten and the less productive to delay the switch. In the absence of cooperation, efforts by one country to pollute less motivate the other to pollute more, or encourage the country that will be cleaner or less productive country after switching to delay its transition.
Keywords Viability theory, Nash, Dynamic game, Pollution
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Abstract The mechanism stating that longer life implies larger investment in human capital, is premised on the view that individual decision-making governs the relationship between longevity and education. This relationship is revisited here from the perspective of optimal period school life expectancy, obtained from the utility maximization of the whole population characterized by its age structure and its age-specific fertility and mortality. Realistic life tables such as model life tables are mandatory, because the age distribution of mortality matters, notably at infant and juvenile ages. Optimal period school life expectancy varies with life expectancy and fertility. The application to French historical data from 1806 to nowadays shows that the population age structure has indeed modified the relationship between longevity and optimal schooling.
Keywords School life expectancy, Longevity, Age structure, Schooling
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Abstract Measuring direct and indirect effects of extending health insurance coverage in developing countries is a key issue for health system development and for attaining universal health coverage. This paper investigates the role played by health insurance in the relationship between parental morbidity and child work decisions. We use a propensity score matching technique combined with hurdle models, using data from Rwanda. The results show that parental health shocks have a substantial influence on child work when households do not have health insurance. Depending on the gender of the sick parent, there is a substitution effect not only between the parent and the child on the labor market, but also between the time the child spends on different work activities. Altogether, results reveal that health insurance protects children against child work in the presence of parental health shocks.
Keywords Rwanda, Propensity scores, Hurdle model, Health shocks, Health insurance, Child work
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Abstract This note introduces to the literature streams explored in the special section on international financial markets and banking systems crises. All topics tackled are related to the Great Recession. A brief overview of the research questions and related literatures is provided.
Keywords International transmission, Financial instability, Financial frictions, Credit crunch, Banking and sovereign debt crisis
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Abstract no abstract
Keywords Sector-specific externalities, Sunspots, O41, Infinite-horizon two-sector model, Indeterminacy, Income and substitution effects, Social and Behav Sciences, Economics, Game Theory, Economic Theory/Quantitative Economics/Mathematical Methods, Economic Growth, E32, C62
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Abstract This paper introduces variable markups in a horizontal-differentiation growth model by considering a larger class of preferences that nests the classic “CES” specification usually present in the workhorse love-for-variety models. Our first result is to obtain a generalized characterization of the Euler condition for this broader class of utility functions: in our model, the Euler rule features a supplementary term aiming at compensating the consumer for variations in the preference for variety along the consumption level. We are then also able to demonstrate that in our generalized framework, the economy’s balanced growth path displays both endogenous markups and a strictly positive growth rate of the number of available varieties (being the engine of growth). Finally, we show that under endogenous markups, the economy’s growth rate and firms’ market power can display a negative correlation, as opposed to the standard result obtained in the CES framework.
Keywords Indirectly additive preferences, Variable markups, Endogenous growth
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Abstract We present a set of theoretical and empirical papers and briefly describe the specific contributions to the Macroeconomic Dynamics special issue on technology aspects in the process of development.
Keywords Technology, Social and Human Capital, Environment and Natural Resources, Public Investment, Innovation and Productivity, Structural Changes
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Abstract We propose an endogenous growth model incorporating social capital. Social capital serves only as an input in the production of human capital and it involves a cost in terms of the final good. In contrast to alternative specifications, this model ensures that social capital enhances productivity gains by playing the role of a timing belt that drives the transmission and propagation of all productivity shocks. We find that, depending on the measure of social capital, the elasticity of human capital with respect to social capital varies from 6% to 10%. Finally, we investigate the short-term dynamics and imbalance effect properties of the model, depending on the value of this elasticity. In particular, we show that when the substitutability of social capital for human capital increases, the economy is better equipped to surmount initial imbalances, as individuals may allocate more working time to the final good sector without impeding economic growth.
Keywords Human capital, Economic Growth, Imbalance Effects, Social capital
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Abstract No abstract is available for this item.
Keywords Economie quantitative
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Abstract We consider a resource-dependent economy initially ruled by the elite. The transition from the autocratic to a more democratic regime takes place only if the citizens decide to revolt against the elite. The occurrence of a revolution primarily depends on the autocratic regime vulnerability and the level of inequalities, both being driven by the elite׳s redistribution and repression policies. First, we show that when a political transition is inevitable, the elite choose the maximum rate of redistribution to lengthen their period in office. Second, we find that the duration of the autocratic regime is linked to resource abundance, and how it relates to the elite׳s policies. More resources lead to a shorter reign of a redistributive regime, which may not be the case of a repressive regime. Finally, we interpret the Arab spring sequence in light of our findings.
Keywords Arab sprin, Arab spring, Duration of autocracies, Natural resources, Political transitions, Timing of revolutions
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Abstract We build an economico-epidemiological Solow-Swan model. Mortality and morbidity effects on effective labor are taken into account. A Ben-Porath-like mechanism affects the dynamics of the saving rate and reduces labor productivity. Based on optimal projections of the demographic and economic South African series on the period 2000-2050, we identify a delayed effect of HIV/AIDS on economic growth: the growth rate gap between the AIDS and no-AIDS scenarios is rather stable between 2010 and 2020, but then it increases sharply between 2020 and 2030, keeps increasing at a much lower pace between 2030 and 2040, and finally stabilizes after 2040. The fall in active population is the main factor behind AIDS impact on economic growth during the decade 2020-2030 while the Ben-Porath mechanism on labor productivity is more relevant in the last decade. Physical capital accumulation plays a minor role.
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Abstract We study an optimal AK-like model of capital accumulation and growth in the presence of a negative environmental externality in the tradition of Stokey (Int Econ Rev 39(1):1–31, 1998). Both production and consumption activities generate polluting waste. The economy exerts a recycling effort to reduce the stock of waste. Recycling also generates income, which is fully devoted to capital accumulation. The whole problem amounts to choosing the optimal control paths for consumption and recycling to maximize a social welfare function that notably includes the waste stock and disutility from the recycling effort. We provide a mathematical analysis of both the asymptotic behavior of the optimal trajectories and the shape of transition dynamics. Numerical exercises are performed to illustrate the analysis and to highlight some of the economic implications of the model. The results suggest that when recycling acts as an income generator, (1) a contraction of both the consumption and capital stock is observed in the long run after an expansion phase; (2) whether polluting waste is predominantly due to production or consumption, greater consumption and lower capital stock are obtained in the long run compared with the situation when recycling does not create additional income; (3) greater recycling effort and lower stock of waste are resulted in the long run.
Keywords Calculus of Variations and Optimal Control, Optimization, Economic Theory/Quantitative Economics/Mathematical Methods, Operation Research/Decision Theory, Operations Management
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Abstract When cheap fossil energy is polluting and pollutant no longer absorbed beyond a certain concentration, there is a moment when the introduction of a cleaner renewable energy, although onerous, is optimal with respect to inter-temporal utility. The cleaner technology is adopted either instantaneously or gradually at a controlled rate. The problem of optimum under viability constraints is 6-dimensional under a continuous-discrete dynamic controlled by energy consumption and investment into production of renewable energy. Viable optima are obtained either with gradual or with instantaneous adoption. A longer time horizon increases the probability of adoption of renewable energy and the time for starting this adoption. It also increases maximal utility and the probability to cross the threshold of irreversible pollution. Exploiting a renewable energy starts sooner when adoption is gradual rather than instantaneous. The shorter the period remaining after adoption until the time horizon, the higher the investment into renewable energy.
Keywords Viability, Threshold effects, Non-renewable Resources, Multi-stage optimal control, Irreversibility
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Abstract This is an introduction to the special section on financial frictions and debt constraints.
Keywords Public debt constraints, Incomplete markets, Credit and borrowing constraints, Constrained efficie
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Abstract The paper addresses the role of education policies for institutional change. Our paradigmatic model consists of an autocratic elite and a mass of handto- mouth workers. The elite has full political and economic control. First, it anticipates and can avoid revolutionary threats through income redistribution. Second, it sets the education policy: a higher level of human capital results in a larger productivity of the national industry, but also in higher consumption aspirations of citizens (and thus more costly redistribution). Finally and in contrast to the recent literature on democratization games, the elite can stop the autocracy and initiate an institutional change. We show that perspective economic returns on education and resources play a crucial role: if sufficiently high, these may prompt high investment in education, human capital accumulation, and, eventually, an institutional change. Our theory of institutional change captures three essential dimensions of Lipset’s view: the positive relationship between education and institutional change, the positive relationship between income and institutional change and, in a more stylized fashion, the negative relationship between inequality and institutional change.
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Abstract We study the compatibility of the optimal population size concepts produced by different social welfare functions and egalitarianism meant as "equal consumption for all individuals of all generations". Social welfare functions are parameterized by an altruism parameter generating the Benthamite and Millian criteria as polar cases. The economy considered is in continuous time and is populated by homogeneous cohorts with a given life span. Production functions are linear in labor, (costly) procreation is the unique way to transfer resources forward in time. First, we show that egalitarianism is optimal whatever the degree of altruism in "perpetual youth" model, that is when lifetime span is finite but age structure does not matter: in this case egalitarianism does not discriminate between the social welfare functions considered. Then we show that, when life span is finite but age structure matters, egalitarianism does not arise systematically as an optimal outcome. In particular, in a growing economy, that is when population growth is optimal in the long-run, this egalitarian rule can only hold when the welfare function is Benthamite. When altruism is impure, egalitarianism is impossible in the context of a growing economy. Either in the Benthamite or impure altruism cases, procreation is never optimal for small enough life spans, leading to finite time extinction and maximal consumption for all existing individuals.
Keywords Total utilitarianism, Impure altruism, Endogenous growth, Egalitarianism, Age structure
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Abstract Abstract We develop a dynamic game to provide with a comprehensive theory of Arab spring-type events. We consider two interacting groups, the elite vs. the citizens, two political regimes, dictatorship vs. a freer regime, the possibility to switch from the first to the second regime as a conse- quence of a revolution by the citizens and finally the opportunity, for the elite, to affect the citizens’ decision through concession and/or repression strategies. In this framework, we provide a full characterization of the equilibrium of the political regime switching game. First, we emphasize the role of the direct switching cost of a revolution (for the citizens) and of the elite’s self-preservation options. Under the concession strategy, when the switching cost is low, the elite can’t avoid the political regime change. She optimally adapts to the overthrow of their political power by setting the rate of redistribution to the highest possible level, thereby extending the period during which she has full control on resources. This surprising result actually illustrates the role of the timing of events in these situa- tions of interaction between the ruling elite and the people. When the direct switching is high, the elite can ultimately select the equilibrium outcome and adopts the opposite strategy, i.e. she chooses the lowest level of redistribution that allows her to stay in power forever. The same kind of results are obtained when the elite relies on repression to keep the citizens under control. Next, the equilibrium properties under a mix of repression and redistribution are analyzed. It is shown that in situations where neither repression (only) nor redistribution (only) protect the elite against the uprising of citizens, a subtle mixture of the two instruments is sufficient to make the dictatorship permanent. Based on our theoretical results, we finally examine the reason for such a large variety of decisions and outcomes during the Arab Spring events.
Keywords Revolution, Regime switching, Political transitions, Optimal timing, Natural resources, Dynamic game
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Abstract We consider a small-open, collateral-constrained AK economy. We show that the combination of CARA preferences and uncertainty on capital inflows generates long-term growth while the deterministic counterpart does not: long-term growth is entirely driven by precautionary savings, and the asymptotic growth rate of the expected capital stock is increasing in both the risk magnitude and the Arrow–Pratt absolute risk aversion parameters.
Keywords Precautionary savings, Growth, Financial liberalization, Collateral constraints, CARA preferences, CARA preferences
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Abstract Contract theory qualifies legal origins theory by focusing on codified default rules, which ease the conclusion of enforceable contracts. We have selected 10 economically important codified contract types containing default rules and 8 countries particularly relevant as mother countries of legal origins, financial centers or newly industrialized economies (France, Germany, Japan, South Korea, Switzerland, Taiwan, the UK and the US). We exclude countries having received their laws as colonial “transplants” and countries in legal transformation. The economic impact of default rules is detectable by econometric analysis based on panel data inference over prolonged periods (1870-2008). Codified default rules favor economic performance, the higher their number the better. The results are controlled for time and country fixed effects, confirmed by counterfactual simulations and robust. We also test whether the presence of all ten contract types can compensate the absence of financial center advantage, and find that they do so in the civil law mother countries and the two newly industrialized countries of our sample. The Swiss case shows that the cumulation of default rule advantage and financial center advantage results in superior economic performance. While qualifying legal origins theory, our results strongly confirm institutional economics in its core of contract theory.
Keywords Economie quantitative
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Abstract Work significantly affects human life and health. Overworking may decrease the quality of life and cause direct economic losses. Technological innovations encourage modernization of firms' capital and improve labor productivity in the workplace. The paper investigates the optimal individual choice of work intensity under improving technology embodied in new equipment leading to shorter lifetime of capital goods (obsolescence). The balanced growth trajectories are analyzed in this context to find out, in particular, how the optimal choice of work intensity is tied to the rate of embodied technological change. The impact of embodied technological advances on the work/life balance problem is discussed and their macroeconomic consequences are highlighted.
Keywords Economie quantitative
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Abstract We study optimal sustainable policies in a benchmark logistic world (where both population and technological progress follow logistic laws of motion) subject to a pollution ceiling. The main policy in the hands of the benevolent planner is pollution abatement, ultimately leading to the control of a dirtiness index as in the early literature of the limits to growth literature. Besides inclusion of demographic dynamics, we also hypothesize that population size affects negatively the natural regeneration or assimilation rate, as a side product of human activities (like increasing pollution, deforestation, ...). We first characterize optimal sustainable policies. Under certain conditions, the planner goes to the pollution ceiling value and stays on, involving a more stringent environmental policy and a sacrifice in terms of consumption per capita. Second, we study how the sustainable problem is altered when we depart from the logistic world by considering exponential technical progress (keeping population growth logistic). It's shown that, as expected, introducing such an asymmetry widens the margins of optimal policies as sustainable environmental policies are clearly less stringent under exponential technical progress. Third we connect our model to the data, using in particular UN population projections.
Keywords Sustainable policy, Pollution ceiling, Optimal Growth, Limits to growth, Demographic dynamics
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Abstract We consider the optimal control of nonlinear integral equations with endogenous delay and state constraints, which describe a developing economy subjected to resource constraints. The economy invests in new resource-efficient technologies, invests in new capital, and scraps obsolete capital. We derive the optimality condition and determine long-term asymptotically exponential trajectories that optimally combine scrapping the dirtiest capital and developing new clean technologies. Next, we study the short-term dynamics of the model and show that it leads to a sustainable growth with active resource constraint.
Keywords Economie quantitative
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Abstract We consider a framework à la Wirl (1994) where political liberalization is the outcome of a lobbying differential game between a conservative elite and a reformist group, the former player pushing against political liberalization in opposition to the latter. In contrast to the benchmark model, we introduce uncertainty. We consider the typical case of an Arab oil exporter country where oil rents are fiercely controlled by the conservative elite. We assume that the higher the oil rents, the more reluctant to political liberalization the elite is. Two states of nature are considered (high vs low resource rents). We then compute the Market-perfect equilibria of the corresponding piecewise deterministic differential game. It is shown that introducing uncertainty in this manner increases the set of strategies compared to Wirl's original setting. In particular, it is shown that the cost of lobbying might be significantly increased under uncertainty with respect to the benchmark. This ultimately highlights some specificities of the political liberalization at stake in Arab countries and the associated risks.
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Abstract We consider a framework à la Wirl (1994) where political liberalization is the outcome of a lobbying differential game between a conservative elite and a reformist group, the former player pushing against political liberalization in opposition to the latter. In contrast to the benchmark model, we introduce uncertainty. We consider the typical case of an Arab oil exporter country where oil rents are fiercely controlled by the conservative elite. We assume that the higher the oil rents, the more reluctant to political liberalization the elite is. Two states of nature are considered (high vs low resource rents). We then compute the Market-perfect equilibria of the corresponding piecewise deterministic differential game. It is shown that introducing uncertainty in this manner increases the set of strategies compared to Wirl's original setting. In particular, it is shown that the cost of lobbying might be significantly increased under uncertainty with respect to the benchmark. This ultimately highlights some specificities of the political liberalization at stake in Arab countries and the associated risks.
Keywords Economie quantitative
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Abstract The Ramsey model of economic growth is revisited from the perspective of viability theory. The Ramsey model, augmented with minimal consumption and sustainability criteria, becomes a viability problem. The framework allows for a clear picture of optimal viable, optimal nonviable, and viable nonoptimal paths. The drastic sacrifices in terms of present consumption required by the implementation of Brundtland sustainability are visualized, the rich countries bearing the major part of the burden. The econometric analysis of viability sets enhances the role of technological progress in ensuring Brundtland sustainability. Preference parameters such as the pure time preference rate are statistically nonsignificant.
Keywords Economie quantitative
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Abstract We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Spatio-temporal capital dynamics are described by a parabolic partial differential equation. The application of the maximum principle leads to necessary but non-sufficient first-order conditions. Thanks to the linearity of the production technology and the special spatial setting considered, the value function of the problem is found explicitly, and the (unique) optimal control is identified in feedback form. Despite constant returns to capital, we prove that the spatio-temporal dynamics, induced by the willingness of the planner to give the same (detrended) consumption over space and time, lead to convergence in the level of capital across locations in the long-run.
Keywords Economic Growth, Partial differential equations, Optimal control, Spatial dynamics
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Abstract We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Spatio-temporal capital dynamics are described by a parabolic partial differential equation. The application of the maximum principle leads to necessary but non-sufficient first-order conditions. Thanks to the linearity of the production technology and the special spatial setting considered, the value-fonction of the problem is found explicitly, and the (unique) optimal control is identified in feedback form. Despite constant returns to capital, we prove that the spatio-temporal dynamics, induced by the willingness of the planner to give the same (detrended) consumption over space and time, lead to convergence in the level of capital across locations in the long-run.
Keywords Spatial dynamics, Economic Growth, Partial-differential equations, Optimal control, Équations aux dérivées partielles, Contrôle optimal, Croissance économique, Dynamique spatiale
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Abstract Parfit’s Repugnant Conclusion stipulates that under total utilitarianism, it might be optimal to choose increasing population size while consumption per capita goes to zero. We evaluate this claim within a canonical AK model with endogenous population size and a reduced form relationship between demographic and economic growth. First we characterize the optimal solution paths for any capital dilution function. Second, we prove that while the Repugnant Conclusion can never occur for realistic values of intertemporal substitution in the traditional linear dilution model, it does occur when population growth is linked to economic growth via an inverted U-shaped relationship. Copyright Springer-Verlag 2013
Keywords Parfit’s Repugnant conclusion, O41, J10, Intertemporal altruism, I20, Endogenous population size
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Abstract This paper studies the different mechanisms and the dynamics through which demography is channeled to the economy. We analyze the role of demographic changes in the economic development process by studying the transitional and the long-run impact of both the rate of population growth and the initial population size on the levels of per capita human capital and income. We do that in an enlarged Lucas–Uzawa model with intergenerational altruism. In contrast to the existing theoretical literature, the long-run level effects of demographic changes, i.e. their impact on the levels of the variables along the balanced growth path, are deeply characterized in addition to the more standard long-run growth effects. We prove that the level effect of the population rate of growth is non-negative (positive in the empirically most relevant case) for the average level of human capital, but a priori ambiguous for the level of per capita income due to the interaction of three transmission mechanisms of demographic shocks, a standard one (dilution) and two non-standard (altruism and human capital accumulation). Overall, the sign of the level effects of population growth depends on preference and technology parameters, but numerically we show that the joint negative effect of dilution and altruism is always stronger than the induced positive human capital effect. The growth effect of population growth depends basically on the attitude to intergenerational altruism and intertemporal substitution. Moreover, we also prove that the long-run level effects of population size on per capita human capital and income may be negative, nil, or positive, depending on the relationship between preferences and technology, while its growth effect is zero. Finally, we show that the model is able to replicate complicated time relationships between economic and demographic changes. In particular, it entails a negative effect of population growth on per capita income, which dominates in the initial periods, and a positive effect which restores a positive correlation between population growth and economic performance in the long term.
Keywords Population size, Population growth, Level effect, Human capital, Growth effect, Endogenous growth
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Abstract In this paper, we apply two optimization methods to solve an optimal control problem of a linear neutral differential equation (NDE) arising in economics. The first one is a variational method, the second follows a dynamic programming approach. Due to the infinite dimensionality of the NDE, the second method requires the reformulation of the latter as an ordinary differential equation in an appropriate abstract space. It is shown that the resulting HJB equation admits a closed-form solution, allowing for a much finer characterization of the optimal dynamics compared to the alternative variational method. The latter is clearly limited by the nontrivial nature of asymptotic analysis of NDEs.
Keywords INFINITE DIMENSION, Dynamic programming, Calculus of variations, Optimal control, Economic dynamics, Neutral differential equations
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Abstract We review an emerging application field to parabolic partial differential equations (PDEs), that's economic growth theory. After a short presentation of concrete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular, the heuristic application of the maximum principle to the latter leads to single out a serious ill-posedness problem, which is, in our view, a barrier to the use of parabolic PDEs in economic growth studies as the latter are interested in long-run asymptotic solutions, thus requiring the solution to infinite time horizon optimal control problems. Adapted dynamic programming methods are used to dig deeper into the identified ill-posedness issue.
Keywords Dynamic programming, Ill-posedness, Infinite time horizons, Infinite dimensional problems, Optimal control, Parabolic partial differential equations
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Abstract We prove that the introduction of endogenous indivisible labor supply into the vintage capital growth model does not rule out the turnpike and optimal permanent regime properties, notably the non-monotonicity properties of optimal paths, inherent in this model.
Keywords Vintage capital, Optimal control, Integral equations with delays and advances, Endogenous labor supp
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Abstract This paper solves a second-best problem where a government has to choose whether to tax financial inflows (capital controls) or not, and when. A multi-stage optimal control technique is used to this end. First, it is shown that it is optimal to switch in finite time from capital controls to full financial liberalization whenever a measure of total wealth is above a certain threshold. In particular, a too large initial debt makes financial liberalization sub-optimal. Second, capital controls should be used countercyclically. Third, financial liberalization is not unaffordable only for poor countries, even wealthy countries might find it optimal to implement capital controls if they aim to keep a large amount of public expenditure.
Keywords Economie quantitative
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Abstract We consider a general control problem with two types of optimal regime switch. The first one concerns technological and/or institutional regimes indexed by a finite number of discrete parameter values, and the second features ecological-like regimes relying on given threshold values for given state variables. We propose a general optimal control framework allowing to derive the first-order optimality conditions and in particular to characterize the geometry of the shadow prices at optimal switching times (if any). We apply this new optimal control material to address the problem of the optimal management of natural resources under ecological irreversibility, and with the possibility to switch to a backstop technology.
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Abstract We consider a general control problem with two types of optimal regime switch. The first one concerns technological and/or institutional regimes indexed by a finite number of discrete parameter values, and the second features regimes relying on given threshold values for given state variables. We propose a general optimal control framework allowing to derive the first-order optimality conditions and in particular to characterize the geometry of the shadow prices at optimal switching times (if any). We apply this new optimal control material to address the problem of the optimal management of natural resources under ecological irreversibility, and with the possibility to switch to a backstop technology.
Keywords Backstop technology, Irreversibility, Multi-stage optimal control, Non-renewable Resources, Threshold effects
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Abstract We consider an optimal technology adoption AK model in line with Boucekkine Krawczyk and Vallée (2011): an economy, caring about consumption and pollution as well, starts with a given technological regime and may decide to switch at any moment to a cleaner technology at a given permanent or transitory output cost. At the same time, we posit that there exists a pollution threshold above which the assimilation capacity of Nature goes down, featuring a kind of irreversible ecological regime. We study how ecological irreversibility interacts with the ingredients of the latter optimal technological switch problem, with a special attention to induced capital-pollution relationship. We find that if a single technological switch is optimal, one recovers the Environmental Kuznets Curve provided initial pollution is high enough. If exceeding the ecological threshold is optimal, then the latter configuration is far from being the rule.
Keywords Multi-stage optimal control, Environmental Kuznets Curve, Ecological irreversibility, Courbes de Kuznets, Technology adoption
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Abstract We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on the existing related mathematical literature to derive the Pontryagin conditions. Using explicit representations of the solutions to the PDEs, we first show that the resulting dynamic system gives rise to an ill-posed problem in the sense of Hadamard. We then turn to the spatial Ramsey problem with linear utility. The obtained properties are significantly different from those of the nonspatial linear Ramsey model due to the spatial dynamics induced by capital mobility.
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Abstract We study the relationship between economic growth and longevity in a model with a realistic demographic structure and with endogenous growth. In contrast to the early contributions in the field, the engine of growth is physical capital accumulation. The results extracted from the analysis of steady state growth paths, tend to show that despite the decreasing pattern of savings over lifetime, a larger life expectancy is always associated with a rising economic growth. This is disappointing regarding the related empirical literature. Nonetheless, we have also shown that though the growth rate is a monotonic function of life expectancy, its first-order derivative is non-monotonic, reflecting the growth enhancing effect of longevity at low levels of development and longevity.
Keywords Economic development, Longevity, Capital accumulation, Overlapping generations
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Abstract This special issue of Louvain Economic Review is devoted to the 'New Economy'.Indeed, a few months after the rapid decline in the stock market for new technologies in most places in the world, it was time to try to draw a balanced synthesis of the economic implications of the so-called New Economy. A few figures are needed to realize why the last decade was indeed an exceptional period, according to historical standards.First of all, the increasing role of information technologies is simply overwhelming.Ov er the last decade, the real value of business investment in the USA has been multiplied by 22 for computers and peripherals, 3 for communication equipment, and 6 for software (...).
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Abstract In order to investigate strategic interactions between a "global north" and a "global south" we introduce a two-country extension of the model in Golosov et al. (2014). We consider different transfers between the two regions, including transfers that can improve the abatement technology. Our model can accommodate several kinds of heterogeneity, including in preferences, time discount rates, and damages resulting from the stock of accumulated GHG. We solve for both planner's solutions and non-cooperative equilibria. We then calibrate our model in order to study quantitative differences between these solutions and to quantitatively explore the role of heterogeneity and Knightian uncertainty. We characterize emissions, damages, consumption, transfers, and welfare by computing the Nash equilibria of the associated dynamic game. We then compare these to efficiency benchmarks. Further, we investigate how (deep) uncertainty affects climate outcomes. We develop a general model for the study of optimal control and differential games that are linear-in-state, which we term the Integral Transformation Method (ITM), which encompasses several existing models as special cases.
Keywords Integral Transformation Method, Analytical integrated assessment model, Differential game, Climate policy, Robust control
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Abstract The dynamics of capital distribution across space are an important topic in economic geography and, more recently, in growth theory. In particular, the spatial AK model has been intensively studied in the latter stream. It turns out that the positivity of optimal capital stocks over time and space for any initial capital spatial distribution has not been entirely settled even in the simple linear AK case. We use Ekeland’s variational principle together with Pontrya-gin’s maximum principle to solve an optimal spatiotemporal AK model with a state constraint (non-negative capital stock), where the capital law of motion follows a diffusion equation. We derive the necessary optimality conditions to ensure the solution satisfies the state constraints for all times and locations. The maximum principle enables the reduction of the infinite-horizon optimal control problem to a finite-horizon problem, ultimately proving the uniqueness of the optimal solution with positive capital and the non-existence of such a solution when the time discount rate is either too large or too small.
Keywords Diffusion and growth, Optimal control, State constraint, Ekeland&#039, s variational principle, Convergence
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Abstract We propose a mean-field game (MFG) set-up to study the dynamics of spatial agglomeration in a continuous space-time framework where trade across locations may follow a broad class of static gravity models. Forward-looking intertemporal utility-maximizing agents work and migrate in a twodimensional geography and face idiosyncratic shocks. Equilibrium wages and prices depend on their common distribution and adjust statically according to the underlying trade model. We first prove existence and uniqueness of the static trade equilibrium. We then prove existence of dynamic equilibria. In the case of Krugman (1996)'s racetrack economy, we obtain closed-form solutions for small sinusoidal perturbations around the steady state, and we identify the sets of parameters that lead to agglomeration or dispersion. We exploit the MFG structure of the model to explicitly quantify how uncertainty and forward-looking expectations contribute to agglomeration and dispersion. In particular, we show that, regardless of the static trade model, forward-looking expectations always promote agglomeration, but cannot reverse the dominant pattern that would arise under myopic behavior.
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Abstract The modernisation theory of regime change is often perceived to be a murky paradigm, lacking theoretical or empirical foundations. In response, we clarify the links between education and regime change. More specifically, we propose that education contributes indirectly to the collapse of autocratic regimes because educated people engage in non-violent (civil) resistance that reduces the effectiveness of the security apparatus. We empirically test the validity of this ‘defanging effect’ of education. We indeed find that the combination of high autocracy and high education levels tends to trigger non-violent campaigns, which in turn increases the likelihood of a regime change, often associated with political liberalisation and, to a lesser degree, democratisation.
Keywords Autocracy, Civil resistance, Democratisation, Education, Modernisation, Regime change
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Abstract We present an overview of selected contributions of the Journal of Mathematical Economics' authors in the last half century. We start with the classical optimal growth theory within a benchmark multisector model and outline the successive developments in the analysis of this model, including the turnpike theory. Different refinements of the benchmark are considered along the way. We after survey the abundant literature on endogenous fluctuations in two-sector models. We conclude with two strong trends in the recent growth literature: green growth and infinite-dimensional growth models.
Keywords Infinite-dimensional growth models, Optimization, Green growth, Turnpike theory, Multisector models, Growth theory
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Abstract Revolutions are often perceived as the key event triggering the fall of an autocratic regime. They are believed to be driven by the people with the purpose of establishing a democratic regime for the people. However, the historical record does not agree with this picture: revolutions are rare, elite-driven, and often non-democratising. We first develop a new set of stylised facts summarising and deepening the latter features. Second, to explain these facts, we develop a theory of elite-driven non-democratising institutional changes triggered by popular uprisings. Our model includes four key ingredients: (i) a minority/majority split in the population; (ii) the persistence of fiscal particularism post-revolution; (iii) the presence of windfall resources; (iv) a distinction between labour income and resource windfalls as well as endogeneity of the labour supply. We show that revolutions are initiated by the elite and only when fractionalisation is moderate. Resource windfalls and labour market repression can also play a role in triggering this 'alliance' between the majority and the elite. If a revolution happens, redistribution in the subsequent regime still favours the elite, although the masses are better off.
Keywords Dominant minorities, Elite-led revolutions, Social structures, Particularism, Resources
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Abstract In this paper, we revisit the theory of spatial externalities. In particular, we depart in several respects from the important literature studying the fundamental pollution free riding problem uncovered in the associated empirical works. First, instead of assuming ad hoc pollution diffusion schemes across space, we consider a realistic spatiotemporal law of motion for air and water pollution (diffusion and advection). Second, we tackle spatiotemporal non-cooperative (and cooperative) differential games. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. Third, we allow for a rich set of geographic heterogeneities across states while the literature assumes identical states. We solve analytically the induced non-cooperative differential game under decentralization and fully characterize the resulting long-term spatial distributions. We further provide with full exploration of the free riding problem, reflected in the so-called border effects. In particular, net pollution flows diffuse at an increasing rate as we approach the borders, with strong asymmetries under advection, and structural breaks show up at the borders. We also build a formal case in which a larger number of states goes with the exacerbation of pollution externalities. Finally, we explore how geographic discrepancies affect the shape of the border effects.
Keywords Transboundary pollution, Environmental federalism, Infinite dimensional optimal control problems, Differential games in continuous time and space, Spatial diffusion, Spatial externalities
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Abstract We estimate the demand for money for monetary aggregates M1 and M2, and cash in Algeria over the period 1979-2019, and study its long-run stability. We show that the transaction motive is significant for all three aggregates, especially for the demand for cash, reflecting the weight of informal economy “practices”. The elasticity of the scale variable is very close to unity for M2 and M1, and even equal to unity for cash demand (1.006). The elasticity of inflation is also significant for all three aggregates, although its level is higher in the case of cash demand (-6.474). Despite the persistence of certain financial repression mechanisms, interest rate elasticity is significant for all three aggregates, but higher for M1 and cash. The same observation is made for elasticity of the exchange rate, reflecting the effect of monetary substitution, especially for M1 and cash. Finally, our study concludes that the demand for money in terms of M1 remains stable, the same observation being confirmed for the M2 aggregate. However, the demand for fiat currency proves not to be stable. The consequences for the optimal design of monetary policy in Algeria are clearly stated.
Keywords Resource-rich countries, Algeria, Co-integration, Long-run stability, Money demand, Monetary policy
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Abstract Elite-biased democracies are those democracies in which former political incumbents and their allies coordinate to impose part of the autocratic institutional rules in the new political regime. We document that this type of democratic transition is much more prevalent than the emergence of pure (popular) democracies in which the majority decides the new political rules. We then develop a theoretical model explaining how an elitebiased democracy may arise in an initially autocratic country. To this end, we extend the benchmark political transition model of Acemoglu and Robinson (2006) along two essential directions. First, population is split into majority versus minority groups under the initial autocratic regime. Second, the minority is an insider as it benefits from a more favourable redistribution by the autocrat. We derive conditions under which elite-biased democracies emerge and characterise them, in particular with respect to pure democracies.
Keywords Elite-biased democracy, Institutional change, Minority/majority, Economic favouritism, Inequality, Revolution
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Abstract The occurrence of some revolutionary episodes seems initially puzzling. For example, before the 'Arab Spring', macroeconomic conditions were improving, the political leaders had been in power for a long time, and the autocrats had shown an apparent interest in the welfare of their population by investing in human capital. We argue that such a paradox can be solved by considering that high education levels are incompatible with the features characterising strong neopatrimonial states. We develop this intuition in a simple theoretical model and we test our prediction in a sequential empirical study of regime changes and regime breakdowns in a large panel of countries. We indeed find that a regime change is more likely in countries combining high neopatrimonialism and high education levels. Moreover, when a regime change happens under these circumstances, a revolution is the most likely type of regime breakdown. These results help to understand the 'Arab Spring' but are not specific to the Arab world.
Keywords Education, Neopatrimonialism, Regime breakdown, Regime change, Revolution
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Abstract In this paper, we consider a spatiotemporal growth model where a social planner chooses the optimal location of economic activity across space by maximization of a spatiotemporal utilitarian social welfare function. Space and time are continuous, and capital law of motion is a parabolic partial differential diffusion equation. The production function is AK. We generalize previous work by considering a continuum of social welfare functions ranging from Benthamite to Millian functions. Using a dynamic programming method in infinite dimension, we can identify a closed-form solution to the induced HJB equation in infinite dimension and recover the optimal control for the original spatiotemporal optimal control problem. Optimal stationary spatial distributions are also obtained analytically. We prove that the Benthamite case is the unique case for which the optimal stationary detrended consumption spatial distribution is uniform. Interestingly enough, we also find that as the social welfare function gets closer to the Millian case, the optimal spatiotemporal dynamics amplify the typical neoclassical dilution population size effect, even in the long-run.
Keywords Spatiotemporal growth models, Benthamite vs Millian social welfare functions, IMPERFECT ALTRUISM, Diffusion, Dynamic programming in infinite dimension
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Abstract We construct a spatiotemporal frame for the study of optimal growth under transboundary pollution. Space is continuous and polluting emissions originate in the intensity of use of the production input. Pollution flows across locations following a diffusion process. The objective functional of the economy is to set the optimal production policy over time and space to maximize welfare from consumption, taking into account a negative local pollution externality and the diffusive nature of pollution. Our framework allows for space and time dependent preferences and productivity, and does not restrict diffusion speed to be space-independent. This provides a comprehensive setting to analyze pollution diffusion with a close account of geographic heterogeneity. The involved optimization problem is infinite-dimensional. We propose an alternative method for an analytical characterization of the optimal paths and the asymptotic spatial distributions. The method builds on a deep economic concept of pollution spatiotemporal welfare effect, which makes it definitely useful for economic analysis.
Keywords Infinite dimensional optimal control, Optimal Growth, Spatiotemporal modelling, Transboundary pollution
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Abstract We develop a theory of institutional transition from dictatorship to minority dominant-based regimes. We depart from the standard political transition framework à la Acemoglu-Robinson in four essential ways: (i) population is heterogeneous, there is a minority/majority split, heterogeneity being generic, simply reflecting subgroup size; (ii) there is no median voter in the post-dictatorship period, political and economic competition is favorable to the minority (fiscal particularism); (iii) (windfall) resources are introduced, and (iv) we distinguish between labor income and resources, and labor supply is endogenous. We first document empirically fiscal particularism, its connection with resource endowment, and the impact of both on revolutionary bursts. Second, we construct a full-fledged model incorporating the four characteristics outlined above. We show, among others, that polarization is a sufficient condition for revolutions, while resource rents are not: they do matter though when polarization is low. In agreement with our empirical facts, countries engaging in revolutions tend to be slightly less resource-rich than other countries. We also outline the interplay between resource rents, polarization and labor market conditions at the dawn of institutional change. Our theory is appropriate to understand the institutional dynamics in highly homogeneous resource-rich countries, which after post-independence autocratic regimes, turn to be dominated by minorities, Algeria being the paradigmatic case.
Keywords Political transition, Minority/majority, Fiscal particularism, Dominant minority, Resources, Labor Market
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Abstract Somehow paradoxically, it is common for research on the determinants of civil wars to conclude that social factors matter much less, if at all, than economic factors. We contribute to this debate by conducting an original empirical analysis in which we investigate whether the deliberate unequal treatment of groups of people by a government can give rise to movements opposing the current political system. In doing so, we significantly innovate on the existing literature exploring the links between grievances and civil war. We look at all forms of social conflict, violent and non-violent, high and low intensity. Our index of social divisiveness captures multiple dimensions of observed unequal group treatments and is not restricted to latent ethnic divisions. We control for time-invariant factors in a large sample of countries over a long period of time. We take into account measurement uncertainty, dynamics, cross-region heterogeneity, localised spatial effects, non-linearity of effects, and a potential endogeneity bias. Our results show that social divisiveness has a large, positive, and statistically significant robust effect on anti-system opposition. It also appears to be the main channel through which long-lasting ethnic polarisation influences the onset of civil wars.
Keywords Civil resistance, Civil war, Grievances, Social conflict, Social divisiveness
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Abstract We review the most recent advances in distributed optimal control applied to environmental economics, covering in particular problems where the state dynamics are governed by partial differential equations (PDEs). This is a quite fresh application area of distributed optimal control, which has already suggested several new mathematical research lines due to the specificities of the environmental economics problems involved. We enhance the latter through a survey of the variety of themes and associated mathematical structures beared by this literature. We also provide a quick tour of the existing tools in the theory of distributed optimal control that have been applied so far in environmental economics.
Keywords Environmental economics, Distributed systems, Optimal control, Partial differential equations
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Abstract We solve a linear-quadratic model of a spatio-temporal economy using a polluting one-input technology. Space is continuous and heterogenous: locations differ in productivity, nature self-cleaning technology and environmental awareness. The unique link between locations is transboundary pollution which is modelled as a PDE diffusion equation. The spatio-temporal functional is quadratic in local consumption and linear in pollution. Using a dynamic programming method adapted to our infinite dimensional setting, we solve the associated optimal control problem in closed-form and identify the asymptotic (optimal) spatial distribution of pollution. We show that optimal emissions will decrease at given location if and only if local productivity is larger than a threshold which depends both on the local pollution absorption capacity and environmental awareness. Furthermore, we numerically explore the relationship between the spatial optimal distributions of production and (asymptotic) pollution in order to uncover possible (geographic) Environmental Kuznets Curve cases.
Keywords Growth, Geography, Transboundary pollution, Infinite dimensional optimal control problems
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Abstract We provide an analysis of institutional dynamics under uncertainty by means of a stochastic differential game of lobbying with two players (conservatives vs liberals) and three main ingredients. The first one is uncertainty inherent in the institutional process itself. The second considers resource windfalls volatility impact on economic and institutional outcomes. Last but not least, the resource windfall level matters in the relative bargaining power of the players. We compute a unique closed-loop equilibrium with linear feedbacks. We show that the legislative state converges to an invariant distribution. Even more importantly, we demonstrate that the most likely asymptotic legislative state is favorable to the liberals. However, the more volatile resource windfalls, the less liberal is the most likely asymptotic state. Finally, we assess the latter prediction on a database covering 91 countries over the period 1973-2005. We focus on financial liberalization policies. We find that as the resources revenues volatility increases, the financial liberalization index goes down. We also find that this property remains robust across different specifications and sample distinctions.
Keywords Revenue-dependent lobbying power, Lobbying games, Petropolitics, Stochastic dynamic games, Stochastic stability, Institutional dynamics
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Abstract Under uncertainty, mean growth of, say, wealth is often defined as the growth rate of average wealth, but it can alternatively be defined as the average growth rate of wealth. We argue that stochastic stability points to the latter notion of mean growth as the theoretically relevant one. Our discussion is cast within the class of continuous-time AK-type models subject to geometric Brownian motions. First, stability concepts related to stochastic linear homogenous differential equations are introduced and applied to the canonical AK model. It is readily shown that exponential balanced-growth paths are not robust to uncertainty. In a second application, we evaluate the quantitative implications of adopting the stochastic-stability-related concept of mean growth for the comparative statics of global diversification in the seminal model due to Obstfeld (1994).
Keywords Stochastic stability, AK model, Global diversification, Endogenous stochastic growth, Mean growth
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Abstract We study a 2-players stochastic dynamic symmetric lobbying differential game. Players have opposite interests; at any date, each player invests in lobbying activities to alter the legislation in her own benefit. The payoffs are quadratic and uncertainty is driven by a Wiener process. We prove that while a symmetric Markov Perfect Equilibrium (MPE) always exists, an asymmetric MPE only emerges when uncertainty is large enough. In the latter case, the legislative state converges to a stationary invariant distribution. Interestingly enough, the implications for the rent dissipation problem are much more involved than in the deterministic counterpart: the symmetric MPE still yields a limited social cost while the asymmetric may yield significant losses. We also characterize the most likely asymptotic state, in particular regarding the level of uncertainty.
Keywords Political lobbying, Symmetric versus asymmetric equilibrium, Stochastic differential games, Stochastic stability, Social cost of lobbying
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Abstract This paper proposes a theoretical model of forecasts formation which implies that in presence of information observation and forecasts communication costs, rational professional forecasters might find it optimal not to revise their forecasts continuously, or at any time. The threshold time- and state-dependence of the observation review and forecasts revisions implied by this model are then tested using inflation forecast updates of professional forecasters from recent Consensus Economics panel data for France and Germany. Our empirical results support the presence of both kinds of dependence, as well as their threshold-type shape. They also imply an upper bound of the optimal time between two information observations of about six months and the co-existence of both types of costs, the observation cost being about 1.5 times larger than the communication cost.
Keywords Information and communication costs, Forecast revision, Binary choice models
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Abstract International risk sharing is one of the main arguments in favor of financial liberalization. The pure risk sharing mechanism highlighted by Obstfeld (1994) implies that liberalization is growth enhancing for all countries as it allows the world portfolio to shift from safe low-yield capital to riskier high yield capital. This result is obtained under the assumption that the volatility figures for risky assets prevailing under autarky are not altered after liberalization. This note relaxes this assumption within the standard two-country model with intertemporal portfolio choices, formally incorporating the instability effect invoked by Stiglitz (2000). We show that putting together the pure risk sharing and instability effects in the latter set-up enriches the analysis and delivers predictions more consistent with the contrasted related empirical literature.
Keywords Financial liberalization, Optimal Growth, Risk sharing, Volatility
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Abstract This paper revisits the optimal population size problem in a continuous time Ramsey setting with costly child rearing and both intergenerational and intertemporal altruism. The social welfare functions considered range from the Millian to the Benthamite. When population growth is endogenized, the associated optimal control problem involves an endogenous effective discount rate depending on past and current population growth rates, which makes preferences intertemporally dependent. We tackle this problem by using an appropriate maximum principle. Then we study the stationary solutions (balanced growth paths) and show the existence of two admissible solutions except in the Millian case. We prove that only one is optimal. Comparative statics and transitional dynamics are numerically derived in the general case.
Keywords Optimal population size, Optimal Growth, Population ethics, Endogenous discounting, Optimal demographic transitions
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Abstract We provide with an optimal growth spatio-temporal setting with capital accumulation and diffusion across space in order to study the link between economic growth triggered by capital spatio-temporal dynamics and agglomeration across space. We choose the simplest production function generating growth endogenously, the AK technology but in sharp contrast to the related literature which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology (through the productivity parameter A) and population. Beside the mathematical tour de force, we ultimately show that agglomeration may show up in our optimal growth with linear technology, its exact shape depending on the interaction of two main effects, a population dilution effect versus a technology space discrepancy effect.
Keywords Agglomeration, Growth, Heterogeneous and continuous space, Capital mobility, Infinite dimensional optimal control problems
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Abstract The mechanism stating that longer life implies larger investment in human capital, is premised on the view that individual decision-making governs the relationship between longevity and education. This relationship is revisited here from the perspective of optimal period school life expectancy, obtained from the utility maximization of the whole population characterized by its age structure and its age-specific fertility and mortality. Realistic life tables such as model life tables are mandatory, because the age distribution of mortality matters, notably at infant and juvenile ages. Optimal period school life expectancy varies with life expectancy and mortality. The application to French historical data from 1806 to nowadays shows that the population age structure has indeed modified the relationship between longevity and optimal schooling.
Keywords Age structure, School life expectancy, Schooling, Longevity
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Abstract This paper aims at clarifying the analytical conditions under which financial globalization originates welfare gains in a simple endogenous growth setting. We focus on an open-economy AK model in which the capital-deepening effect of financial globalization boosts growth in a in permanent but entails an entry cost in order to access international credit markets. We show that constrained borrowing triggers substantial welfare gains, even at small levels of international financial integration, provided that the autarkic growth rate is larger than the world interest rate. Such conditional welfare benefits boosted by stronger growth - long-run gain - arise in our preferred model without investment commitment and they range, relative to autarky, from about 2% in middle-income countries to about 13% in OECD-type countries under international financial integration. Sizeable benefits emerge despite the fact that consumption initially falls - short-run pain - which is however shown not to dwarf positive growth changes.
Keywords Growth Breaks, Collateral-Constrained Borrowing, International financial integration, Endogenous growth, Welfare Gains
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Abstract Two countries produce goods and are penalized by the common pollution they generate. Each country maximizes an inter-temporal utility criterion, taking account of the pollution stock to which both contribute. The dynamic is in continuous time with possible sudden switches to less polluting technologies. The set of Nash equilibria, for which solutions also remain in the set of constraints, is the intersection of two manifolds in a certain state space. At the Nash equilibrium, the choices of the two countries are interdependent: different productivity levels after switching lead the more productive country to hasten and the less productive to delay the switch. In the absence of cooperation, efforts by one country to pollute less motivate the other to pollute more, or encourage the country that will be cleaner or less productive country after switching to delay its transition.
Keywords Pollution, Dynamic game, Nash, Viability theory
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Abstract This paper introduces variable mark-ups in a horizontal-differentiation growth model by considering a larger class of preferences that nests the classic “CES” specification usually present in the workhorse love-for-variety models. Our first result is to obtain a generalized characterization of the Euler condition for this broader class of utility functions: in our model, the Euler rule features a supplementary term aiming at compensating the consumer for variations in the preference for variety along the consumption level. We are then also able to demonstrate that in our generalized framework, the economy’s balanced growth path displays both endogenous markups and a strictly positive growth rate of the number of available varieties (being the engine of growth). Finally, we show that under endogenous markups, the economy’s growth rate and firms’ market power can display a negative correlation, as opposed to the standard result obtained in the CES framework.
Keywords Endogenous growth, Variable markups, Indirectly additive preferences
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Abstract We study the impact of technological progress on the level of employment in a vintage capital model where: i) capital and labor are gross complementary; ii) labor supply is endogenous and indivisible; iii) there is full employment, and iv) the rate of labor-saving technological progress is endogenous. We characterize the stationary distributions of vintage capital goods and the corresponding equilibrium values for employment and capital lifetime. It is shown that both variables are non-monotonic functions of technological progress indicators. Technological accelerations are found to increase employment provided innovations are not too radical.
Keywords Vintage capital, Technological progress, Employment, Compensation theory
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Abstract The paper addresses the role of education policies for institutional change. We focus on two contrasting effects of education and human capital accumulation. On the one side, education prompts economic growth and increases the wealth managed by an autocratic elite. On the other side, education increases the awareness of citizens (capturing their reluctance to accept a dictatorship and their labor-market aspirations) and requires the elite to devote more resources to income redistribution. Along the lines of this trade-off, our theory provides a Lipsetian explanation of the positive relationship between education and institutional change, the positive relationship between development and institutional change, and the negative relationship between inequality and institutional change. Furthermore, we obtain new insights on the natural resources curse hypothesis and on the design of development aid programs.
Keywords Lipset’s theory, Natural resource curse, Democratization, Human capital
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Abstract In this paper, we revisit the question of how domestic and foreign risks affect growth through the lens of an AK small-open economy model with risky borrowing/lending and global diversification. Wealth is allocated between domestic and foreign assets and the optimal allocation depends on both the difference in deterministic returns and the relative magnitude and correlation of domestic and foreign risks. Depending on parameters, the small-open economy may choose to either borrow from abroad, despite the fact that this is risky, or lend. In contrast to standard N-country models, whether growth is faster or slower (and whether growth is more or less volatile) compared to autarky is not entirely driven by relative risk aversion but also depends on the return and risk characteristics of domestic and foreign assets. We also show that growth volatility and mean growth have typically nonmonotonic relationships with the the levels and correlation of domestic and foreign risks. We argue that these results are in line with, and lay down some theoretical foundations for explaining the conflicting empirical results regarding the impact of international financial integration on growth and in particular threshold effects.
Keywords International financial integration, Endogenous growth, Small open economy, Domestic and foreign risks
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Abstract We examine the issue of stability of stochastic endogenous growth. First, stochastic stability concepts are introduced and applied to stochastic linear homogenous differential equations to which several stochastic endogenous growth models reduce. Second, we apply the mathematical theory to two models, starting with the stochastic AK model. It's shown that in this case exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncertainty: the economy may almost surely collapse at exponential speed even though productivity is initially arbitrarily high. Finally, we revisit the seminal global diversification endogenous growth model (Obstfeld, 1994): taking into account stochastic stability calls for a redefinition of the mean growth concept, which leads to revisit the established wisdom on the growth effect of global diversification.
Keywords Endogenous growth, Stochastic growth, Stochastic stability, AK model, Global diversification
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Abstract This paper presents a non-technical overview of the recent investment literature with a special emphasis on the connection between technological progress and the investment decision. First of all, we acknowledge that some dramatic advances have been made in the 1990s in understanding and modelling non-convex capital adjustment schemes and irreversibility. Nonetheless, this new literature has not always satisfactorily accounted for the investment-specific (or embodied) nature of technical progress. We argue that the recent technological trends towards more embodiment have had a heavy impact on the way the investment decision is taken and is to be taken. This is turn should imply the reconsideration of many empirical results, and a more careful modelling strategy taking into account the price variables and scrupulously choosing the most appropriate level of (dis)aggregation.
Keywords Investment, Technological progress, Non-convex adjustment, Irreversibility, Embodiment
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Abstract We study an optimal AK-like model of capital accumulation and growth in the presence of a negative environmental externality in the tradition of Stokey (1998). Both production and consumption activities generate polluting waste. The economy exerts a recycling effort to reduce the stock of waste. Recycling also generates income, which is fully devoted to capital accumulation. The whole problem amounts to choosing the optimal control paths for consumption and recycling to maximize a social welfare function that notably includes the waste stock and disutility from the recycling effort. We provide a mathematical analysis of both the asymptotic behavior of the optimal trajectories and the shape of transition dynamics. Numerical exercises are performed to illustrate the analysis and to highlight some of the economic implications of the model.
Keywords Sustainability, Recycling, Capital accumulation, Waste
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Abstract This note studies the stochastic stability of the standard AK growth model under uncertain output technology. Capital accumulation follows a stochastic linear homogenous differential equation. It's shown that exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncertainty. Precisely, it's demonstrated that the economy almost surely collapses at exponential speed even though productivity is initially arbitrarily high.
Keywords Optimal Growth, AK model, Ito stochastic differential equation, Balanced growth paths, Stochastic stability
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Abstract When cheap fossil energy is polluting and pollutant no longer absorbed beyond a certain concentration, there is a moment when the introduction of a cleaner renewable energy, although onerous, is optimal with respect to inter-temporal utility. The cleaner technology is adopted either instantaneously or gradually at a controlled rate. The problem of optimum under viability constraints is 6-dimensional under a continuous-discrete dynamic controlled by energy consumption and investment into production of renewable energy. Viable optima are obtained either with gradual or with instantaneous adoption. A longer time horizon increases the probability of adoption of renewable energy and the time for starting this adoption. It also increases maximal utility and the probability to cross the threshold of irreversible pollution. Exploiting a renewable energy starts sooner when adoption is gradual rather than instantaneous. The shorter the period remaining after adoption until the time horizon, the higher the investment into renewable energy.
Keywords Multi-stage optimal control, Threshold effects, Irreversibility, Non-renewable Resources, Viability
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Abstract We develop a dynamic game to provide with a theory of Arab spring-type events. We consider two interacting groups, the elite vs the citizens, two political regimes, dictatorship vs a freer regime, the possibility to switch from the first to the second regime as a consequence of a revolution, and finally the opportunity, for the elite, to affect the citizens' decision through concession and/or repression strategies. In this framework, we provide a full characterization of the equilibrium of the political regime switching game. First, we emphasize the role of the direct switching cost of a revolution (for the citizens) and of the elite's self-preservation options. Under the concession strategy, when the switching cost is low, the elite can't avoid the political regime change. She optimally adapts to the overthrow of their political power by setting the rate of redistribution to the highest possible level, thereby extending the period during which she has full control on resources. This surprising result actually illustrates the role of the timing of events in these situations of interaction between the ruling elite and the people. When the direct switching is high, the elite can ultimately select the equilibrium outcome and adopts the opposite strategy, i.e. she chooses the lowest level of redistribution that allows her to stay in power forever. The same kind of results are obtained when the elite relies on repression to keep the citizens under control. Next, the equilibrium properties under a mix of repression and redistribution are analyzed. It is shown that in situations where neither repression (only) nor redistribution (only) protect the elite against the uprising of citizens, a subtle mixture of the two instruments is sufficient to make the dictatorship permanent. Based on our theoretical results, we finally examine the reason for such a large variety of decisions and outcomes during the Arab Spring events.
Keywords Political transitions, Revolution, Natural resources, Optimal timing, Regime switching, Dynamic game
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Abstract We study optimal sustainable policies in a benchmark logistic world (where both population and technological progress follow logistic laws of motion) subject to a pollution ceiling. The main policy in the hands of the benevolent planner is pollution abatement, ultimately leading to the control of a dirtiness index as in the early literature of the limits to growth literature. Besides inclusion of demographic dynamics, we also hypothesize that population size affects negatively the natural regeneration or assimilation rate, as a side product of human activities (like increasing pollution, deforestation,...). We first characterize optimal sustainable policies. Under certain conditions, the planner goes to the pollution ceiling value and stays on, involving a more stringent environmental policy and a sacrifice in terms of consumption per capita. Second, we study how the sustainable problem is altered when we depart from the logistic world by considering exponential technical progress (keeping population growth logistic). It's shown that, as expected, introducing such an asymmetry widens the margins of optimal policies as sustainable environmental policies are clearly less stringent under exponential technical progress. Third we connect our model to the data, using in particular UN population projections.
Keywords Limits to growth, Optimal Growth, Sustainable policy, Demographic dynamics, Pollution ceiling
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Abstract We consider a small-open, collateral-constrained AK economy. We show that the combination of CARA preferences and uncertainty on capital inflows in such an economy generates long-term (expected) growth while the deterministic counterpart does not. In this framework, long-term growth is entirely driven by precautionary savings. In particular, we show that the asymptotic growth rate of the expected capital stock is an increasing function of both the risk parameter and the Arrow-Prat absolute risk aversion parameter. The model also predicts that economies that are more financially integrated through international borrowing experience lower consumption growth volatility relative to output growth volatility.
Keywords CARA preferences, Growth, Financial liberalization, Collateral constraints, Precautionary savings
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Abstract We review an emerging application field to parabolic partial differential equations (PDEs), that's economic growth theory. After a short presentation of concrete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular, the heuristic application of the maximum principle to the latter leads to single out a serious ill-posedness problem, which is, in our view, a barrier to the use of parabolic PDEs in economic growth studies as the latter are interested in long-run asymptotic solutions, thus requiring the solution to infinite time horizon optimal control problems. Adapted dynamic programming methods are used to dig deeper into the identified ill-posedness issue.
Keywords Parabolic partial differential equations, Optimal control, Infinite dimensional problems, Infinite time horizons, Ill-posedness, Dynamic programming
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Abstract Work significantly affects human life and health. Overworking may decrease the quality of life and cause direct economic losses. Technological innovations encourage modernization of firms' capital and improve labor productivity in the workplace. The paper investigates the optimal individual choice of work intensity under improving technology embodied in new equipment leading to shorter lifetime of capital goods (obsolescence). The balanced growth trajectories are analyzed in this context to find out, in particular, how the optimal choice of work intensity is tied to the rate of embodied technological change. The impact of embodied technological advances on the work/life balance problem is discussed and their macroeconomic consequences are highlighted.
Keywords Vintage capital, Technological development, Work-life balance, Rational individual choice
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Abstract We consider a framework à la Wirl (1994) where political liberalization is the outcome of a lobbying differential game between a conservative elite and a reformist group, the former player pushing against political liberalization in opposition to the latter. In contrast to the benchmark model, we introduce uncertainty. We consider the typical case of an Arab oil exporter country where oil rents are fiercely controlled by the conservative elite. We assume that the higher the oil rents, the more reluctant to political liberalization the elite is. Two states of nature are considered (high vs low resource rents). We then compute the Market-perfect equilibria of the corresponding piecewise deterministic differential game. It is shown that introducing uncertainty in this manner increases the set of strategies compared to Wirl's original setting. In particular, it is shown that the cost of lobbying might be significantly increased under uncertainty with respect to the benchmark. This ultimately highlights some specificities of the political liberalization at stake in Arab countries and the associated risks.
Keywords Rent-seeking, Lobbying, Natural resources, Arab countries, Piecewise deterministic differential games
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Abstract We prove that the introduction of endogenous indivisible labor supply into the vintage capital growth model does not rule out the turnpike and optimal permanent regime properties, notably the non- monotonicity properties of optimal paths, inherent in this model.
Keywords Vintage capital, Optimal control, Integral equations with delays and advances, Endogenous labor supply
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Abstract We consider a general control problem with two types of optimal regime switch. The first one concerns technological and/or institutional regimes indexed by a finite number of discrete parameter values, and the second features ecological-like regimes relying on given threshold values for given state variables. We propose a general optimal control framework allowing to derive the first-order optimality conditions and in particular to characterize the geometry of the shadow prices at optimal switching times (if any). We apply this new optimal control material to address the problem of the optimal management of natural resources under ecological irreversibility, and with the possibility to switch to a backstop technology.
Keywords Multi-stage optimal control, Threshold effects, Irreversibility, Non-renewable Resources, Backstop technology
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Abstract We study the compatibility of the optimal population size concepts produced by different social welfare functions and egalitarism meant as "equal consumption for all individuals of all generations". Social welfare functions are parameterized by an altruism parameter generating the Benthamite and Millian criteria as polar cases. The economy considered is in continuous time and is populated by homogenous cohorts with a given life span. Production functions are linear in labor, (costly) procreation is the unique way to transfer resources forward in time. First, we show that egalitarism is optimal whatever the degree of altruism when life spans are infinite. That is egalitarism does not discriminate between the social welfare functions considered. However, when life spans are finite, egalitarism does not arise systematically as an optimal outcome. In particular, it depends on the degree of altruism, and also on the magnitude of the life span. In particular, to be enforced in a growing economy, that is when population growth is optimal in the long-run, this egalitarian rule can only hold when (i) the welfare function is Benthamite, (ii) and for a large enough life span. When altruism is impure, egalitarism is impossible in the context of a growing economy. Either in the Millian case, whatever the life span, or in the Benthamite/impure altruism cases, for small enough life spans, procreation is never optimal, leading to finite time extinction and maximal consumption for all existing individuals.
Keywords Egalitarism, Population change, Optimal population size, Benthamite Vs Millian criterion, Finite lives, Growth
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Abstract This paper solves a second-best problem where a government has in particular to choose whether to tax financial inflows (capital controls) or not, and when. A multi-stage optimal control technique is used to this end. First, it is shown that it is optimal to switch in finite time from capital controls to full financial liberalization (zero tax on capital inflows) whenever a measure of total wealth is above a certain threshold. In particular, a too large initial debt makes financial liberalization sub-optimal. Second, our analysis suggests that capital controls should be used countercyclically: booms should be responded by more financial liberalization while recessions should rather lead to more stringent capital controls. Third, when public expenditure is chosen in order to maximize social welfare, financial liberalization is not unaffordable only for poor countries, even wealthy countries might find it optimal to implement capital controls if they aim to keep a large amount of public expenditure. In short, the preservation of the welfare states might require a more frequent use of capital controls.
Keywords Capital controls, Second-best, Debt, Public expenditures, Multi-stage optimal control
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Abstract We propose a multisector endogenous growth model incorporating social capital. Social capital only serves as input in the production of human capital and it involves a cost in terms of the final good. We show that in contrast to existing alternative specifications, this setting assures that social capital enhances productivity gains by playing the role of a timing belt driving the transmission and propagation of all productivity shocks throughout society whatever the sectoral origin of the shocks. Further econometric work is conducted in order to estimate the contribution of social capital to human capital formation. We find that depending on the measure of social capital considered, the elasticity of human capital to social capital varies from 6% to 10%. Finally we investigate the short-term dynamics and imbalance effects properties of the models depending on the value of this elasticity (taking the Lucas-Uzawa model as a limit case). In particular, it's shown that when the substitutability of social capital to human capital increases, the economy is better equipped to surmount initial imbalances as individuals may allocate more working time in the final goods sector without impeding economic growth.
Keywords Social capital, Human capital, Economic Growth, Imbalance Effects
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