optimal growth with many consumers abstract a method is described for constructing all pareto optimal allocations for a dynamic economy with many heterogeneous consumers under certainty in which both the technology and consumer preferences are recursive but preferences need not be additively separable over time optimal perfect foresight competitive equilibrium allocations are obtained through the study of a dynamic program for an economy with one consumption good sufficient conditions are given for the existence of a unique interior stationary distribution of consumption and wealth for a two person exchange economy sufficient conditions are given for the global asymptotic stability of the unique interior stationary point

a positive theory of social security based on reputation we construct a general equilibrium model in which a pay as you go social security system can be adopted and sustained as a political and economic equilibrium we alalyze the welfare implictions of this system and compare general equilibrium welfare measure to the commonly used notion of actuarial fairness

a vector autoregressive model for electricity prices subject to long memory and regime switching abstract a regime dependent var model is suggested that allows long memory fractional integration in each of the observed regime states as well as the possibility of fractional cointegration the model is motivated by the dynamics of electricity prices where the transmission of power is subject to occasional congestion periods for a system of bilateral prices non congestion means that electricity prices are identical whereas congestion makes prices depart hence the joint price dynamics implies switching between a univariate price process under non congestion and a bivariate price process under congestion at the same time it is an empirical regularity that electricity prices tend to show a high degree of long memory and thus that prices may be fractionally cointegrated analysis of nord pool data shows that even though the prices are identical under non congestion the prices are not in general fractionally cointegrated in the congestion state hence in most cases price convergence is a property following from regime switching rather than a conventional error correction mechanism finally the suggested model is shown to deliver forecasts that are more precise compared to competing models

public versus private investment in human capital endogenous growth and income inequality in this paper we present an overlapping generations model with heterogeneous agents in which human capital investment through formal schooling is the engine of growth we use simple functional forms for preferences technologies and income distribution to highlight the distinction between economies with public education and those with private education we find that income inequality declines more quickly under public education on the other hand private education yields greater per capita incomes unless the initial income inequality is sufficiently high we also find that societies will choose public education if a majority of agents have incomes below average

evaluating interval forecasts a complete theory for evaluating interval forecasts has not been worked out to date most of the literature implicitly assumes homoskedastic errors even when this is clearly violated and proceed by merely testing for correct unconditional coverage consequently i set out to build a consistent framework for conditional interval forecast evaluation which is crucial when higher order moment dynamics are present the new methodology is demonstrated in an application to the exchange rate forecasting procedures advocated in risk management

an experimental test on retirement decisions i introduction the reform of social security systems is now one of the main issues on the economic policy agenda of most industrialized countries it is widely considered that unless serious changes take place the aging of the population implying a rise in the number of retirees relative to that of workers will threaten the viability of pay as you go public pension systems in the long run this threat is being reinforced by the progressive reduction in the retirement age of the working population the central reforms that are being proposed to neutralize these future financing problems are the raising of the contribution rate the decreasing of pension benefits or and the delay of the retirement age with reference to this latter reform as blondal and scarpetta 1998 state a direct way to encourage people to work longer would be to raise the pensionable age but delaying the retirement age may not be very popular according to recent surveys most workers claim that they are happy with the current retirement age see cremer and pestieau 2003 this may help to explain why reforms on the legal retirement age have currently become a very delicate matter for governments 1 on the other hand pension systems in virtually all organization for economic cooperation and development oecd countries in the mid 1990s made it financially unattractive to work after the age of 55 see gruber and wise 1997 or blondal and scarpetta 1998 indeed the general consensus in the theoretical literature related to social security and retirement decisions is that pension systems create enormous incentives to leave the labor force early 2 therefore increasing the retirement age as a tool to improve the financial problems of public pensions systems faces two sensitive problems the opposition of workers to a delay in the standard retirement age and the disincentives to continuous work being embedded in the pension system the large decline in labor force participation is attributed to the specific fact that to keep on working implies a reduction in the present value of total pension benefits the terms old age pension wealth and implicit tax on postponing retirement have been frequently used to illustrate these disincentives in the pension system the old age pension wealth is the discounted value of expected pension benefits minus the discounted cost of obtaining such benefits after the earliest age at which pensions can be accessed working for an extra year may imply changes in this pension wealth by foregoing 1 yr of pensions paying contributions for an additional year and maybe increasing the pension benefits per year therefore if the costs of postponing retirement are higher than the gains then it is considered that the pension system is implicitly taxing to prolong the working period that is the drop in pension wealth acts as an implicit tax on income from continued work and as such is a clear incentive to retire early actually reforms aiming to increase the effective retirement age to improve the financial problems of public pensions systems have mainly focused on the reduction of this implicit tax on prolonging the working period it is also considered that when the increase in pension benefits is exactly offset by the higher cost in terms of contributions and forgone pensions the pension system is not distorting the retirement decision that is the pension systems that are marginally actuarially fair will not distort individual decisions concerning retirement age and consequently they are defined as neutral systems for this reason the main economic policy measures move in the direction of strengthening the link between lifetime contributions and pension benefits 3 indeed this reform is one of the policy conclusions of maintaining prosperity in an ageing society oecd 2000 the most appropriate reform would be to allow people to retire at the age of their own choice and to adjust pension level so that the pension system is neutral on average

welfare cost of fluctuations when labor market search interacts with financial frictions we provide a quantitative assessment of welfare costs of fluctuations in a search model with financial frictions the matching process in the labor market leads positive shocks to reduce unemployment less than negative shocks increase it we show that the magnitude of this non linearity is magnified frictions this asymmetric effect of the business cycle leads to sizable welfare costs the model also accounts for the responsiveness of the job finding rate to the business cycle as financial frictions endogenously generate counter cyclical opportunity costs of opening a vacancy and wage sluggishness

social security and retirement decision a positive and normative approach social insurance for the elderly is judged responsible for the widely observed trend towards early retirement in a world of laissez faire or in a first best setting there would be no such trend however when first best instruments are not available because health and productivity are not observable the optimal social insurance policy may imply a distortion on the retirement decision the main point we make is that while there is no doubt that retirement systems induce an excessive bias towards early in many countries a complete elimination of this bias i e a switch to an actuarially fair system is not the right answer this is so and for two reasons first some distortions are secondbest optimal this is the normative argument second and on the positive side the elimination of the bias might be problematic from a political perspective depending on the political process it may either not be feasible or alternatively it may tend to undermine the political support for the pension system itself

a characterization of ramsey equilibrium abstract consider a perfect foresight equilibrium model with a single capital good a borrowing constraint and many infinitely lived households with fixed but different discount factors the steady state capital stock is held by the most patient household quart j econ 95 1980 375 382 econ j 38 1928 543 559 an example shows the total capital can exhibit an equilibrium cycle in contrast to the stability property of the one household case in the example only the most patient household saves and his income deceases in capital we give a condition implying income is increasing in capital and use it to show any equilibrium converges to the steady state

social security retirement age and optimal income taxation it is often argued that implicit taxation on continued activity of elderly workers is responsible for the widely observed trend towards early retirement in a world of laissez faire or of first best efficiency there would be no such implicit taxation the point of this paper is that when first best redistributive instruments are not available because some variables are not observable the optimal policy does imply a distortion of the retirement decision consequently the inducement of early retirement may be part of the optimal tax transfer policy we consider a model in which individuals differ in their productivity and their capacity to work long and choose both their weekly labor supply and their age of retirement we characterize the optimal non linear tax transfer that maximizes a utilitarian welfare function when weekly earnings and the length of active life are observable while individuals productivity and health status are not observable c 2003 elsevier b v all rights reserved

increasing longevity and social security reforms a legislative procedure approach abstract increasing longevity causes an upward trend in the dependency ratio in many countries this raises concerns about the financial sustainability of social security schemes and reform proposals and initiatives abound it is shown that a fundamental policy choice inevitably arises since a given social security system cannot be maintained by simply indexing pension ages to longevity the political reform process is analysed using the so called legislative procedure when longevity increases the retirement age is raised more than proportionally to the increase in longevity but the young also make larger transfers to the old

equilibrium cycling with small discounting abstract a misinterpretation of turnpike theorems suggests that persistent cyclic behavior in optimal growth models is only possible with large discount rates this paper shows that for any positive discount rate there exists a large family of standard cobb douglas technologies with three sectors which have optimal growth paths of persistent cycles

the effects of the raising the official pension age policy in an overlapping generations economy this paper studies how economic variables are affected by raising the official pension age although it is said that such a policy increases output this paper shows that such a statement is not necessarily true moreover the paper finds that the social security benefit can decrease which implies that it might be impossible to sustain the same level of benefit only by such a policy

comparison of extended mean reversion and time series models for electricity spot price simulation considering negative prices abstract this paper evaluates different financial price and time series models such as mean reversion autoregressive moving average arma integrated arma arima and general autoregressive conditional heteroscedasticity garch process usually applied for electricity price simulations however as these models are developed to describe the stochastic behaviour of electricity prices they are extended by a separate data treatment for the deterministic components trend daily weekly and annual cycles of electricity spot prices furthermore price jumps are considered and implemented within a regime switching model since 2008 market design allows for negative prices at the european energy exchange which also occurred for several hours in the last years up to now only a few financial and time series approaches exist which are able to capture negative prices this paper presents a new approach incorporating negative prices the evaluation of the different approaches presented points out that the mean reversion and the arma models deliver the lowest mean root square error between simulated and historical electricity spot prices gained from the european energy exchange these models posses also lower mean average errors than garch models hence they are more suitable to simulate well fitting price paths furthermore it is shown that the daily structure of historical price curves is better captured applying arma or arima processes instead of mean reversion or garch models another important outcome of the paper is that the regime switching approach and the consideration of negative prices via the new proposed approach lead to a significant improvement of the electricity price simulation

equilibrium models displaying endogenous fluctuations and chaos abstract this paper surveys current developments in dynamic general equilibrium theory concerned with conditions under which endogenous fluctuations are possible existing contributions are divided into two classes the larger one consists of models with a unique perfect foresight equilibrium while the second includes models where equilibrium is indeterminate and the set of equilibria involving endogenous fluctuations includes sunspots equilibria while the two classes of models involve oscillations of different natures and with different policy implications we show that both are consistent with optimizing behavior and competitive equilibrium

a regime switching copula approach to modeling day ahead prices in coupled electricity markets abstract the recent price coupling of many european electricity markets has triggered a fundamental change in the interaction of day ahead prices challenging additionally the modeling of the joint behavior of prices in interconnected markets in this paper we propose a regime switching ar garch copula to model pairs of day ahead electricity prices in coupled european markets while capturing key stylized facts empirically substantiated in the literature this model easily allows us to 1 deviate from the assumption of normal margins and 2 include a more detailed description of the dependence between prices we base our empirical study on four pairs of prices namely germany france germany netherlands netherlands belgium and germany western denmark we find that the marginal dynamics are better described by the flexible skew t distribution than the benchmark normal distribution also we find significant evidence of tail dependence in all pairs of interconnected areas we consider as a first application of the proposed model we consider the pricing of financial transmission rights and highlight how the choice of marginal distributions and copula impacts prices as a second application we consider the forecasting of tail quantiles and evaluate the out of sample performance of competing models

ageing government budgets retirement and growth we analyze the short and long run effects of demographic ageing increased longevity and reduced fertility on per capita growth the olg model captures direct effects working through adjustments in the savings rate labor supply and capital deepening and indirect effects working through changes of taxes government spending components and the retirement age in politico economic equilibrium growth is driven by capital accumulation and productivity increases fueled by public investment the closed form solutions of the model predict taxation and the retirement age in oecd economies to increase in response to demographic ageing and per capita growth to accelerate if the retirement age were held constant the growth rate in politico economic equilibrium would essentially remain unchanged due to a surge of social security transfers and crowding out of public investment

financial openness financial frictions and optimal monetary policy increasing financial integration challenges the optimality of inward looking strategies for optimal monetary policy those issues are analyzed in an open economy where foreign net lending and the current account are determined by a collateral constraint durables represent collateral the current account features persistent imbalances but can deliver a long run stationary equilibrium the comparison between floating and managed exchange rate regimes shows that the impossible trinity is reversed higher financial integration increases the persistence and volatility of the current account and calls for exchange rate stabilization in this context the ramsey plan too prescribes stabilization of the exchange rate alongside with domestic inflation

spatial dependence in wind and optimal wind power allocation a copula based analysis abstract the investment decision on the placement of wind turbines is neglecting legal formalities mainly driven by the aim to maximize the expected annual energy production of single turbines the result is a concentration of wind farms at locations with high average wind speed while this strategy may be optimal for single investors maximizing their own return on investment the resulting overall allocation of wind turbines may be unfavorable for energy suppliers and the economy because of large fluctuations in the overall wind power output this paper investigates to what extent optimal allocation of wind farms in germany can reduce these fluctuations we analyze stochastic dependencies of wind speed for a large data set of german on and offshore weather stations and find that these dependencies turn out to be highly nonlinear but constant over time using copula theory we determine the value at risk of energy production for given allocation sets of wind farms and derive optimal allocation plans we find that the optimized allocation of wind farms may substantially stabilize the overall wind energy supply on daily as well as hourly frequency

introduction to a general equilibrium approach to economic growth abstract endogenous growth theory has had some success in explaining the observed data related to the process of economic growth however the results of the models in this literature are typically very sensitive to their micro economic structure it is therefore important to understand how the growth process behaves under more general specifications of such features as the number of commodities the number and preferences of consumers the factors of production and the financial and information structures in other words valuable insights can be gained by integrating growth theory into the framework of general equilibrium theory the summary of the papers in this volume focuses on seven issues that are crucial to this integration and highlights the contributions of the papers to the resolution of these issues journal of economic literature classification numbers c61 d50 d90 f43 o30 o41

on ramsey s conjecture efficient allocations in the neoclassical growth model with private information abstract in his seminal paper of 1928 ramsey conjectured that if agents discounted the future differently in the long run all agents except the most patient would live at the subsistence level the validity of this conjecture was investigated in different environments in particular it has been confirmed in the neoclassical growth model with dynamically complete markets this paper studies this conjecture in a version of this model that includes private information and heterogeneous agents a version of bayesian implementation is introduced and a recursive formulation of the original allocation problem is established efficient allocations are renegotiation proof and the expected utility of any agent cannot go to zero with positive probability if the economy does not collapse if the economy collapses all agents will get zero consumption forever thus including any degree of private information in the neoclassical growth model will deny ramsey s conjecture if efficient allocations are considered

reforming our pension system is it a demographic financial or political problem we argue that economic and demographic factors play a relatively small role in the old age crisis political factors are far more important a benevolent social planner can address the problems raised by population ageing and declining productivity growth however in reality social security systems are established and reformed through the political process majority voting and lobbying consequently the outcome is likely not to be socially optimal majority voting typically results in overspending on social security but also in rapidly phasing it out in case of unexpected shocks then the entrenched interests of retirees that oppose drastic cuts in benefits can be socially desirable

distributional dynamics in a neoclassical growth model the role of elastic labor supply we examine the evolution of the distributions of wealth and income in a ramsey model in which agents differ in their initial capital endowment and where the labor supply is endogenous the assumption that the utility function is homogeneous implies that the macroeconomic equilibrium is independent of the distribution of wealth and allows us to characterize fully income and wealth dynamics we find that although the dynamics of the distribution of wealth are similar under fixed and flexible labor those of the income distribution are not in response to a structural change income inequality may move in opposite ways depending on whether or not the labor supply is fixed

political complements in the welfare state health care and social security abstract all oecd countries target a large majority of their welfare spending to the elderly through public pensions and health care programs spending in both programs has largely increased in the past decades often more than the share of elderly in the population we suggest that these phenomena may be due to political complementarities between these two transfer programs we show that these two programs may coexist because public health care may increase the political constituency in favor of social security and vice versa specifically public health decreases the absolute longevity differential between low and high income individuals therefore rising the retirement period and the total pension benefits of the former relatively to the latter this effect increases the political support for social security among the low income young we show that in a political equilibrium of a two dimensional majoritarian election a voting majority of low income young and retirees supports a large welfare state the composition between public health and social security is determined by intermediate median income types who favor the contemporaneous existence of these two programs since public health increases their longevity enough to make social security more attractive technological improvements in health care strengthens this complementarity and lead to more welfare spending

utility over time the homothetic case the purpose of this paper is to show how the economics of choice over time can be strengthened by introduction of restrictive assumptions namely additivity and homotheticity of utility we consider applications to labor supply 2 savings behavior and long run distribution and welfare measurement labor supply is mainly a function of the ratio of non labor income to the wage rate savings generally increase with increases in the rate of interest in the long run distribution is not much dependent upon initial wealth and instead is mainly determined by attitudes towards time in the long run the as if social utility function is often well measured by consumer surplus the applications appear to be strong therefore it is appropriate to begin with a general argument for the main assumptions to be imposed two early contributions to the economics of time are by becker 1 and koopmans 111 the former presents a general framework without any specific assumptions about utility over time at most there is a homogeneous technology to produce consumption from goods and time pollak and wachter 131 koopmans 1 l adds highly intuitive assumptions to show utility additive and discounted over time koopmans analysis could be extended to cases where utility is additive merely between remote time periods see rader 15 pp 161 1851 this would correspond to the realistic case where the influence of distant consumption on preferences is negligible additivity must be reinterpreted in terms of a shifting environment of current consumption plus consumption sufficiently contiguous in time the analysis following could be adapted to this most compelling case merely adding utility over time does have implications for demand for example if complementaries occur between two goods they must occur between many others e g 15 pp 228 2331 however the results are meager and insufficient for the kind of analysis economists generally want to apply therefore we are led to add the assumption of homotheticity namely 219 0022 0531 81 050219 18 02 00 o

lessons for an aging society the political sustainability of social security systems what is the future of social systems in oecd countries in our view the answer belongs to the realm of politics we evaluate how political constraints shape the social security system in six countries france germany italy spain the uk and the us under population aging two main aspects of the aging process are relevant to the analysis first the increase in the dependency ratio the ratio of retirees of workers reduces the average profitability of the unfunded social security system thereby inducing the agents to reduce the size of the system by substituting their claims towards future pensions with more private savings second an aging electorate leads to larger systems since it increases the relevance of pension spending on the policy makers agenda the overall assessment from our simulations is that the political aspect dominates in all countries albeit with some differences spain the fastest aging country faces the largest increase in the social security contribution rate when labor market considerations are introduced the political effect still dominates but it is less sizeable country specific characteristics not accounted for in our simulations such as the degree of redistribution in the pension system and the existence of family ties in the society may also matter our simulations deliver a strong policy implication an increase in the effective retirement age always decreases the size of the system chosen by the voters while often increasing its generosity finally delegation of pension policy to the ec may reduce political accountability and hence help to reform the systems

the survival of the welfare state this paper provides an analytical characterization of markov perfect equilibria in a model with repeated voting where agents vote over distortionary income redistribution a key result is that the future constituency for redistributive policies depends positively on current redistribution since this affects both private investments and the future distribution of voters the model features multiple equilibria in some equilibria positive redistribution persists forever in other equilibria even a majority of beneficiaries of redistribution vote strategically so as to induce the end of the welfare state next period skill biased technical change makes the survival of the welfare state less likely

the macroeconomics of early retirement early retirement was introduced after the appearance of redundant middle aged workers not entitled to pensions this distortionary policy reduces human capital accumulation and economic growth but shifts part of the tax burden on future generations why was it adopted alternative policies which do not introduce long term distortions but impose a larger cost on the current generation of workers were blocked by a coalition of high income workers who did not plan to retire early but sought to reduce the current tax burden and low income workers who expected to retire early and to benefit from the early retirement pension

postponing retirement the political effect of aging abstract conventional economic wisdom suggests that because of the aging process social security systems will have to be retrenched in particular retirement age will have to be largely increased yet is this policy measure feasible in oecd countries since the answer belongs mainly to the realm of politics i evaluate the political feasibility of postponing retirement under aging in france italy the uk and the us simulations for the year 2050 steady state demographic economic and political scenario suggest that retirement age will be postponed in all countries while the social security contribution rate will rise in all countries but italy the political support for increasing the retirement age stems mainly from the negative income effect induced by aging which reduces the profitability of the existing social security system and thus the individuals net social security wealth

spatial dependencies of wind power and interrelations with spot price dynamics abstract wind power has seen strong growth over the last decade and increasingly affects electricity spot prices in particular prices are more volatile due to the stochastic nature of wind such that more generation of wind energy yields lower prices therefore it is important to assess the value of wind power at different locations not only for an investor but for the electricity system as a whole in this paper we develop a stochastic simulation model that captures the full spatial dependence structure of wind power by using copulas incorporated into a supply and demand based model for the electricity spot price this model is calibrated with german data we find that the specific location of a turbine i e its spatial dependence with respect to the aggregated wind power in the system is of high relevance for its value many of the locations analyzed show an upper tail dependence that adversely impacts the market value therefore a model that assumes a linear dependence structure would systematically overestimate the market value of wind power in many cases this effect becomes more important for increasing levels of wind power penetration and may render the large scale integration into markets more difficult

are benefits from oil stocks diversification gone new evidence from a dynamic copula and high frequency data abstract oil is perceived as a good diversification tool for stock markets to fully understand this potential we propose a new empirical methodology that combines generalized autoregressive score copula functions with high frequency data and allows us to capture and forecast the conditional time varying joint distribution of the oil stocks pair accurately our realized garch with time varying copula yields statistically better forecasts of the dependence and quantiles of the distribution relative to competing models employing a recently proposed conditional diversification benefits measure that considers higher order moments and nonlinear dependence from tail events we document decreasing benefits from diversification over the past ten years the diversification benefits implied by our empirical model are moreover strongly varied over time these findings have important implications for asset allocation as the benefits of including oil in stock portfolios may not be as large as perceived

intertemporal transfer institutions abstract we consider a single commodity overlapping generations model where at a cost institutions can be created or transformed to carry out intergenerational transfers we analyze the game with both strategic and cooperative methods characterizing the unique stationary equilibrium as well as the set of transfer institutions that belong to the core which we show to coincide with the consistent core we conclude that as long as the creation of an institution is costly it is possible to sustain positive transfers though those will be below the optimal level moreover the lower the costs the more efficient the transfer will be journal of economic literature classification numbers c71 c72 d23 e21 h55

a positive theory of social security in many countries social security accounts for a large fraction of the government budget why is this so given that at any point in time the number of recipients of social security benefits is smaller than the number of contributors in the overlapping generations model studied in this paper all individuals currently alive vote on social security in every period in equilibrium the size of social security is larger the greater is the proportion of elderly people in the population and the greater is the inequality of pre tax income within each generation both predictions of the theory are supported by the empirical evidence in cross country data

the timing of redistribution we investigate whether late redistribution programs that can be targeted toward low income families but that may distort savings decisions can dominate early redistribution programs that cannot be targeted as a result of information constraints we use simple two period overlapping generations models with heterogeneous agents under six policy regimes a model calibrated to the u s economy benchmark two early redistribution lump sum regimes two targeted late redistribution regimes and finally a model without taxes and redistribution redistribution programs are financed by a labor tax on the young generation and a capital tax on the old generation we argue that if the programs are small in size late redistribution can dominate early redistribution in terms of welfare but not in terms of real output better targeting of low income households cannot completely offset savings distortions in addition we find that the optimal transfer and tax policy implies a capital tax of 100 and transfers exclusively to the young generation