We calculate the socially optimal level of illiquidity in an economy populated by households with taste shocks and present bias (Amador, Werning, and Angeletos 2006).The government chooses mandatory contributions to respective spending/savings accounts, each with a different preretirement withdrawal penalty.Penalties collected by the government are redistributed through the tax system.When naive households have heterogeneous present bias, the social optimum is well approximated by a three-account system: (i) a completely liquid account, (ii) a completely illiquid account, and (iii) an account with a ~10% early withdrawal penalty.In some ways this resembles the U.S. system, which includes completely liquid accounts, completely illiquid Social Security and 401(k)/IRA accounts with a 10% early withdrawal penalty.The social optimum is also well approximated by an even simpler two-account system-(i) a completely liquid account and (ii) a completely illiquid account-which is the most common retirement system in the world today.

This edition of the biennial Poverty and Shared Prosperity report brings sobering news. The COVID-19 (coronavirus) pandemic and its associated economic crisis, compounded by the effects of armed conflict and climate change, are reversing hard-won gains in poverty reduction and shared prosperity. The fight to end poverty has suffered its worst setback in decades after more than 20 years of progress. The goal of ending extreme poverty by 2030, already at risk before the pandemic, is now beyond reach in the absence of swift, significant, and sustained action, and the objective of advancing shared prosperity—raising the incomes of the poorest 40 percent in each country—will be much more difficult. Poverty and Shared Prosperity 2020: Reversals of Fortune presents new estimates of COVID-19's impacts on global poverty and shared prosperity. Harnessing fresh data from frontline surveys and economic simulations, it shows that pandemicrelated job losses and deprivation worldwide are hitting already poor and vulnerable people hard, while also shifting the profile of global poverty to include millions of 'new poor.' Original analysis included in the report shows that the new poor are more urban, better educated, and less likely to work in agriculture than those living in extreme poverty before COVID-19. It also gives new estimates of the impact of conflict and climate change, and how they overlap. These results are important for targeting policies to safeguard lives and livelihoods. It shows how some countries are acting to reverse the crisis, protect those most vulnerable, and promote a resilient recovery. These findings call for urgent action. If the global response fails the world's poorest and most vulnerable people now, the losses they have experienced to date will be minimal compared with what lies ahead. Success over the long term will require much more than stopping COVID-19. As efforts to curb the disease and its economic fallout intensify, the interrupted development agenda in lowand middle-income countries must be put back on track. Recovering from today's reversals of fortune requires tackling the economic crisis unleashed by COVID-19 with a commitment proportional to the crisis itself. In doing so, countries can also plant the seeds for dealing with the long-term development challenges of promoting inclusive growth, capital accumulation, and risk prevention—particularly the risks of conflict and climate change. The world’s population is now 7.4 billion people, placing ever greater demands on our natural resources. As we stand witness to a possible reversal of modernity’s positive trends, Malthus’s pessimism is worth full reconsideration. This Norton Critical Edition includes: · An introduction and explanatory annotations by Joyce E. Chaplin. · Malthus’s Essay in its first published version (1798) along with selections from the expanded version (1803), which he considered definitive, as well as his Appendix (1806). · An unusually rich

Previous research has shown that some people voluntarily use commitment contracts that restrict their own choice sets. We study how people divide money between two accounts: a liquid account that permits unrestricted withdrawals and a commitment account that is randomly assigned in a between-subject design to have either a 10% early withdrawal penalty, or a 20% early withdrawal penalty, or not to allow early withdrawals at all (i.e., an infinite penalty). When the liquid account and the commitment account pay the same interest rate, higher early-withdrawal penalties attract more commitment account deposits. This pattern is predicted by the hypothesis that some participants are partially- or fully-sophisticated present-biased agents. Such agents perceive that higher penalties generate greater scope for commitment by disincentivizing (penalized) early withdrawals. The experiment also shows that when the commitment account pays a higher interest rate than the liquid account, the positive empirical slope relating penalties and commitment deposits is flattened, suggesting that naïve present-biased agents or agents with standard exponential discounting are also in our sample. Across all of our experimental treatments, higher early withdrawal penalties on the commitment account sometimes increase and never reduce allocations to the commitment account.

This paper investigates the market provision of firm-specific training, and identifies the inefficiencies associated with it. Within a general stochastic learning-by-doing model, there is a potential inefficiency in the market provision of firm-specific training. In order to determine whether this inefficiency is in fact present, we analyze two special cases of the model: the accelerated productivity-enhancement model and the accelerated learning model. In both models, the inefficiency is indeed present. However, the nature of the inefficiency depends on the balance between the two key components of training, namely productivity enhancement and employee evaluation. In the accelerated productivity-enhancement model, training results in an increase in productivity enhancement but no change in employee evaluation, and training is overprovided by the market. In the accelerated learning model, training results in a proportionate increase in both productivity enhancement and employee evaluation, and training is underprovided by the market. In both cases, turnover is inefficiently low.

If individuals have self-control problems, they may take up commitment contracts that restrict their spending. We experimentally investigate how contract design affects the demand for commitment contracts. Each participant divides money between a liquid account, which permits unrestricted withdrawals, and a commitment account with withdrawal restrictions that are randomized across participants. When the two accounts pay the same interest rate, the most illiquid commitment account attracts more money than any of the other commitment accounts. We show theoretically that this pattern is consistent with the presence of sophisticated present-biased agents, who prefer more illiquid commitment accounts even if they are subject to uninsurable marginal utility shocks drawn from a broad class of distributions. When the commitment account pays a higher interest rate than the liquid account, the relationship between illiquidity and deposits is flat, suggesting that agents without present bias and/or naive present-biased agents are also present in our sample.

Extending Barro (1999) and Luttmer and Mariotti (2003), we introduce a new model of time preferences: the instantaneous-gratification model. This model applies tractably to a much wider range of settings than existing models. It applies to both complete- and incomplete-market settings and it works with generic utility functions. It works in settings with linear policy rules and in settings in which equilibrium cannot be supported by linear rules. The instantaneous-gratification model also generates a unique equilibrium, even in infinite-horizon applications, thereby resolving the multiplicity problem hitherto associated with dynamically inconsistent models. Finally, it simultaneously features a single welfare criterion and a behavioral tendency towards overconsumption.

We study N-player continuous-time Cournot games in an oligopoly where firms choose production quantities. These are nonzero-sum differential games, whose value functions may be characterized by systems of nonlinear Hamilton-Jacobi partial differential equations. When resources are in finite supply, such as oil, exhaustibility enters as boundary conditions for the PDEs. We analyze the problem when there is an alternative, but expensive, technology (for example solar power for energy production), and give an asymptotic approximation in the limit of small exhaustibility. We illustrate the two-player problem by numerical solutions, and discuss the impact of limited oil reserves on production and oil prices in the duopoly case.

We study a dynamic-contracting problem involving risk sharing between two parties -- the Proposer and the Responder -- who invest in a risky asset until an exogenous but random termination time. In any time period they must invest all their wealth in the risky asset, but they can share the underlying investment and termination risk. When the project ends they consume their final accumulated wealth. The Proposer and the Responder have constant relative risk aversion R and r respectively, with R>r>0. We show that the optimal contract has three components: a non-contingent flow payment, a share in investment risk and a termination payment. We derive approximations for the optimal share in investment risk and the optimal termination payment, and we use numerical simulations to show that these approximations offer a close fit to the exact rules. The approximations take the form of a myopic benchmark plus a dynamic correction. In the case of the approximation for the optimal share in investment risk, the myopic benchmark is simply the classical formula for optimal risk sharing. This benchmark is endogenous because it depends on the wealths of the two parties. The dynamic correction is driven by counterparty risk. If both parties are fairly risk tolerant, in the sense that 2>R>r, then the Proposer takes on more risk than she would under the myopic benchmark. If both parties are fairly risk averse, in the sense that R>r>2, then the Proposer takes on less risk than she would under the myopic benchmark. In the mixed case, in which R>2>r, the Proposer takes on more risk when the Responder's share in total wealth is low and less risk when the Responder's share in total wealth is high. In the case of the approximation for the optimal termination payment, the myopic benchmark is zero. The dynamic correction tells us, among other things, that: (i) if the asset has a high return then, following termination, the Responder compensates the Proposer for the loss of a valuable investment opportunity; and (ii) if the asset has a low return then, prior to termination, the Responder compensates the Proposer for the low returns obtained. Finally, we exploit our representation of the optimal contract to derive simple and easily interpretable sufficient conditions for the existence of an optimal contract.

Abstract Lipton (1983) defined an individual to be ‘ultrapoor’ if and only if: (i) his calorie intake falls below 0.8 of the intake appropriate for his age, sex, and activity group; and (ii) his foodshare exceeds 0.8. of the appropriate foodshare. This chapter evaluates Lipton's concept of ultrapoverty. This is done by relating it to the well-established welfare indicator ‘total expenditure’, on the one hand, and to a wide range of housing and other non-monetary indicators on the other. The chapter agues that: (i) while calorie intake does contain important poverty information, it contains less poverty information than total expenditure; and (ii) foodshare contains very little poverty information. Hence, neither of the components of Lipton's double criterion is, on its own, a good criterion for poverty. It further argues that while the double 0.8 (or ‘double-eighty’) criterion may have some merits over each of its components, it is nonetheless inferior to a poverty criterion based simply on total expenditure. A particular feature of the analysis is the chapter's use of non-parametric methods to assess the local strength of the association between calorie intake and foodshare, respectively, against total expenditure.

In the 1960s Shapley provided an example of a two-player fictitious game with periodic behaviour. In this game, player A aims to copy B's behaviour and player B aims to play one ahead of player A. In this paper we generalise Shapley's example by introducing an external parameter. We show that the periodic behaviour in Shapley's example at some critical parameter value disintegrates into unpredictable (chaotic) behaviour, with players dithering a huge number of times between different strategies. At a further critical parameter the dynamics becomes periodic again, but now both players aim to play one ahead of the other. In this paper we adopt a geometric (dynamical systems) approach. Here we prove rigorous results on continuity of the dynamics and on the periodic behaviour, while in the sequel to this paper we shall describe the chaotic behaviour.

Normal form games are nearly compact and continuous (NCC) if they can be understood as games played on strategy spaces that are dense subsets of the strategy spaces of larger compact games with jointly continuous payoffs. There are intrinsic algebraic, measure theoretic, functional analysis, and finite approximability characterizations of NCC games. NCC games have finitely additive equilibria, and all their finitely additive equilibria are equivalent to countably additive equilibria on metric compactifications. The equilibrium set of an NCC game depends upper hemicontinuously on the specification of the game and contains only the limits of approximate equilibria of approximate games.

The vital essence of invention is creativity. Yet creative people and teamwork are potentially uneasy bedfellows. By their very nature, creative people are different – different in their expectations, temperaments, even their beliefs and values. And it is these very distinctions in disposition that can lead to difficulties in team performance development. This chapter looks at the many obstacles and points of discussion here, and reveals insights into how it is possible to have the best of both worlds: creativity and teamwork.KeywordsCreative IndividualEventual InnovationCreative PeopleThought FunctionCreative TypeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Innovation is a competitive necessity today. Yet this competitive must-do is unlike any business activity I have come to know. It is an enigmatic endeavour that few have mastered. And those who claim to be masters of the dynamics of innovation secretly tell that they are still subject to the same peculiarities of innovation as any novice. Innovation can be, and often is, a cruel venture. It can put out the flame of a budding business in an instant, it can send a giant corporation reeling down the stock market and off the chart (permanently) and of course it can cause confusion and utter distress in already overburdened public services. For it is easier for an innovation to flounder, than to fall off a log. And believe me, my colleagues and I have the wounds to prove it.KeywordsUnique NatureCore TechnologySuccessful InnovationInternet BankingBrand ExtensionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We study the dynamics of a two player continuous time bi-matrix fictitious play. In particular, we investigate the dynamics of a one-parameter family of 3 x 3 games that includes a well-known example of Shapley's as a special case. We adopt a geometric (dynamical systems) approach and study the dynamics and bifurcations both on the strategy simplex, and projected onto S3. For the more interesting parameter values we show that the flow is essentially continuous and uniquely defined everywhere except at the interior equilibrium. We prove the existence and stability properties of three periodic orbits of the flow analytically, and study in some detail the dynamics near a co-dimension two indifference set that is crucial to understanding the global dynamics. We prove that for a range of parameter values the flow has infinitely many periodic orbits. For one parameter value we find that all trajectories tend to a neighborhood of the interior equilibrium, though this is not asymptotically stable. We illustrate the properties of the flow with numerical simulations. We note that many of the phenomena we observe and results we obtain are new, and where possible we state and prove general theorems that apply to more general games. Finally, we describe some areas where further study is warranted.

Is more intense product market competition and imitation good or bad for growth? This question is addressed in the context of an endogenous growth model with "step-by-step" innovations, in which technological laggards must first catch up with the leading-edge technology before battling for technological leadership in the future. In contrast to earlier Schumpeterian models in which innovations are always made by outsider firms who earn no rents if they fail to innovate and become monopolies if they do innovate, here we find: first, that the usual Schumpeterian effect of more intense product market competition (PMC) is almost always outweighed by the increased incentive for firms to innovate in order to escape competition, so that PMC has a positive effect on growth; second, that a little imitation is almost always growth-enhancing, as it promotes more frequent neck-and-neck competition, but too much imitation is unambiguously growth-reducing. The model thus points to complementary roles for competition (anti-trust) policy and patent policy.

Laboratory and field studies of time preference find that discount rates are much greater in the short-run than in the long-run, Hyperbolic discount functions capture this property. This paper solves the decision problem of a hyperbolic consumer who faces stochastic income and a burrowing constraint. The paper uses the bounded variation calculus to derive the Hyperbolic Euler Relation, a natural generalization of the standard Exponential Euler Relation. The Hyperbolic Euler Relation implies that consumers act as if they have endogenous rates of time preference that rise and fall with the future marginal propensity to consume (e.g., discount rates that endogenously range from 5% to 41% for the example discussed in the paper).

Abstract Bolton and Harris (1999) consider a game of strategic experimentation. In this game, each player divides her time in any given period between a ‘safe’ action and a ‘risky’ action. The underlying pay-off of the safe action is known. The underlying pay-off of the risky action is unknown, and can be higher or lower than that of the safe action. The actual pay-off received by any player from an action is the underlying pay-off plus noise. Once players’ actions have been chosen and pay-offs realized all players observe all choices and pay-offs. Through these observations they are able to learn about the underlying pay-off of the risky action and thus revise their common beliefs and optimal choice of action. In other words, players can learn from others’ current experimentation as well as their own.

This paper extends the classic two-armed bandit problem to a many-agent setting in which N players each face the same experimentation problem. The main change from the single-agent problem is that an agent can now learn from the current experimentation of other agents. Information is therefore a public good, and a free-rider problem in experimentation naturally arises. More interestingly, the prospect of future experimentation by others encourages agents to increase current experimentation, in order to bring forward the time at which the extra information generated by such experimentation becomes available. The paper provides an analysis of the set of stationary Markov equilibria in terms of the free-rider effect and the encouragement effect.

This paper develops a simple example to analyse the relationship between product market competition and growth in a model with step-by-step innovations, where laggards can never leapfrog the current industry leaders, but instead must first catch up with the leaders before battling for technological leadership in the future. Unlike in existing Schumpeterian models of growth, more intense product market competition and/or imitations may be growth-enhancing.