The ex-Ante non-optimality of the Dempster-Schafer updating rule for ambiguous beliefs

The most widely used updating rule for non-additive probalities is the Dempster-Schafer rule. Schmeidles and Gilboa have developed a model of decision making under uncertainty based on non-additive probabilities, and in their paper “Updating Ambiguos Beliefs” they justify the Dempster-Schafer rule based on a maximum likelihood procedure. This note shows in the context of Schmeidler-Gilboa preferences under uncertainty, that the Dempster-Schafer rule is in general not ex-ante optimal. This contrasts with Brown’s result that Bayes’ rule is ex-ante optimal for standard Savage preferences with additive probabilities.

Testing the optimality of aggregate consumption decisions: is there rule-of-thumb behavior?

Consumption is an important macroeconomic aggregate, being about 70% of GNP. Finding sub-optimal behavior in consumption decisions casts a serious doubt on whether optimizing behavior is applicable on an economy-wide scale, which, in turn, challenge whether it is applicable at all. This paper has several contributions to the literature on consumption optimality. First, we provide a new result on the basic rule-of-thumb regression, showing that it is observational equivalent to the one obtained in a well known optimizing real-business-cycle model. Second, for rule-of-thumb tests based on the Asset-Pricing Equation, we show that the omission of the higher-order term in the log-linear approximation yields inconsistent estimates when lagged observables are used as instruments. However, these are exactly the instruments that have been traditionally used in this literature. Third, we show that nonlinear estimation of a system of N Asset-Pricing Equations can be done efficiently even if the number of asset returns (N) is high vis-a-vis the number of time-series observations (T). We argue that efficiency can be restored by aggregating returns into a single measure that fully captures intertemporal substitution. Indeed, we show that there is no reason why return aggregation cannot be performed in the nonlinear setting of the Pricing Equation, since the latter is a linear function of individual returns. This forms the basis of a new test of rule-of-thumb behavior, which can be viewed as testing for the importance of rule-of-thumb consumers when the optimizing agent holds an equally-weighted portfolio or a weighted portfolio of traded assets. Using our setup, we find no signs of either rule-of-thumb behavior for U.S. consumers or of habit-formation in consumption decisions in econometric tests. Indeed, we show that the simple representative agent model with a CRRA utility is able to explain the time series data on consumption and aggregate returns. There, the intertemporal discount factor is significant and ranges from 0.956 to 0.969 while the relative risk-aversion coefficient is precisely estimated ranging from 0.829 to 1.126. There is no evidence of rejection in over-identifying-restriction tests.

Testing consumption optimality using aggregate data

The objective of this paper is to test for optimality of consumption decisions at the aggregate level (representative consumer) taking into account popular deviations from the canonical CRRA utility model rule of thumb and habit. First, we show that rule-of-thumb behavior in consumption is observational equivalent to behavior obtained by the optimizing model of King, Plosser and Rebelo (Journal of Monetary Economics, 1988), casting doubt on how reliable standard rule-of-thumb tests are. Second, although Carroll (2001) and Weber (2002) have criticized the linearization and testing of euler equations for consumption, we provide a deeper critique directly applicable to current rule-of-thumb tests. Third, we show that there is no reason why return aggregation cannot be performed in the nonlinear setting of the Asset-Pricing Equation, since the latter is a linear function of individual returns. Fourth, aggregation of the nonlinear euler equation forms the basis of a novel test of deviations from the canonical CRRA model of consumption in the presence of rule-of-thumb and habit behavior. We estimated 48 euler equations using GMM, with encouraging results vis-a-vis the optimality of consumption decisions. At the 5% level, we only rejected optimality twice out of 48 times. Empirical-test results show that we can still rely on the canonical CRRA model so prevalent in macroeconomics: out of 24 regressions, we found the rule-of-thumb parameter to be statistically signi cant at the 5% level only twice, and the habit ƴ parameter to be statistically signi cant on four occasions. The main message of this paper is that proper return aggregation is critical to study intertemporal substitution in a representative-agent framework. In this case, we fi nd little evidence of lack of optimality in consumption decisions, and deviations of the CRRA utility model along the lines of rule-of-thumb behavior and habit in preferences represent the exception, not the rule.

Testing consumption optimality using aggregate data

This paper tests the optimality of consumption decisions at the aggregate level taking into account popular deviations from the canonical constant-relative-risk-aversion (CRRA) utility function model-rule of thumb and habit. First, based on the critique in Carroll (2001) and Weber (2002) of the linearization and testing strategies using euler equations for consumption, we provide extensive empirical evidence of their inappropriateness - a drawback for standard rule- of-thumb tests. Second, we propose a novel approach to test for consumption optimality in this context: nonlinear estimation coupled with return aggregation, where rule-of-thumb behavior and habit are special cases of an all encompassing model. We estimated 48 euler equations using GMM. At the 5% level, we only rejected optimality twice out of 48 times. Moreover, out of 24 regressions, we found the rule-of-thumb parameter to be statistically significant only twice. Hence, lack of optimality in consumption decisions represent the exception, not the rule. Finally, we found the habit parameter to be statistically significant on four occasions out of 24.

Evidence on the incentive optimality of share contracts

Ever since Adam Smith, economists have argued that share contracts do not provide proper incentives. This paper uses tenancy data from India to assess the existence of missing incentives in this classical example of moral hazard. Sharecroppers are found to be less productive than owners, but as productive as fixed-rent tenants. Also, the productivity gap between owners and both types of tenants is driven by sample-selection issues. An endogenous selection rule matches tenancy contracts with less-skilled farmers and lower-quality lands. Due to complementarity, such a matching affects tenants’ input choices. Controlling for that, the contract form has no effect on the expected output. Next, I explicitly model farmer’s optimal decisions to test the existence of non-contractible inputs being misused. No evidence of missing incentives is found.

On the optimality of the Friedman Rule with heterogeneous agents and non-linear income taxation

We study the optimal “inflation tax” in an environment with heterogeneous agents and non-linear income taxes. We first derive the general conditions needed for the optimality of the Friedman rule in this setup. These general conditions are distinct in nature and more easily interpretable than those obtained in the literature with a representative agent and linear taxation. We then study two standard monetary specifications and derive their implications for the optimality of the Friedman rule. For the shopping-time model the Friedman rule is optimal with essentially no restrictions on preferences or transaction technologies. For the cash-credit model the Friedman rule is optimal if preferences are separable between the consumption goods and leisure, or if leisure shifts consumption towards the credit good. We also study a generalized model which nests both models as special cases.

The optimality of the Friedman rule when some distorting taxes are exogenous

This paper investigates the optimality of the Friedman rule in a two-sector small open economy. That policy prescription is found to be a necessary condition for Pareto efficiency. If a planner can select all conceivable distorting taxes, then, for some initial values of public debt, money balances and foreign assets, it is possible to decentralize a Pareto efficient allocation. If the planner can select only some of these tax rates, then second-best policies may also satisfy the Friedman rule. However, this last result depends on the set of tax instruments the planner can choose from.

Banning information as a redistributive device

In this paper we analyze the optimality of allowing firms to observe signals of workers’ characteristics in an optimal taxation framework. We show that it is always optimal to prohibit signals that disclose information about differences in the intrinsic productivities of workers like mandatory health exams and IQ tests, for example. On the other hand, it is never optimal to forbid signals that reveal information about the comparative advantages of workers like their specialization and profession. When signals are mixed (they disclose both types of information), there is a trade-off between efficiency and equity. It is optimal to prohibit signals with sufficiently low comparative advantage content.

Solving the non-convexity problem in some shopping-time and human-capital models

Several works in the shopping-time and in the human-capital literature, due to the nonconcavity of the underlying Hamiltonian, use Örst-order conditions in dynamic optimization to characterize necessity, but not su¢ ciency, in intertemporal problems. In this work I choose one paper in each one of these two areas and show that optimality can be characterized by means of a simple aplication of Arrowís (1968) su¢ ciency theorem.

On choice of technique in the Robinson-Solow-Srinivasan model

We report results on the optimal \choice of technique" in a model originally formulated by Robinson, Solow and Srinivasan (henceforth, the RSS model) and further discussed by Okishio and Stiglitz. By viewing this vintage-capital model without discounting as a speci c instance of the general theory of intertemporal resource allocation associated with Brock, Gale and McKenzie, we resolve longstanding conjectures in the form of theorems on the existence and price support of optimal paths, and of conditions suÆcient for the optimality of a policy rst identi ed by Stiglitz. We dispose of the necessity of these conditions in surprisingly simple examples of economies in which (i) an optimal path is periodic, (ii) a path following Stiglitz' policy is bad, and (iii) there is optimal investment in di erent vintages at di erent times. (129 words)

Two additions to Lucas's "inflation and welfare"

This work adds to Lucas (2000) by providing analytical solutions to two problems that are solved only numerically by the author. The first part uses a theorem in control theory (Arrow' s sufficiency theorem) to provide sufficiency conditions to characterize the optimum in a shopping-time problem where the value function need not be concave. In the original paper the optimality of the first-order condition is characterized only by means of a numerical analysis. The second part of the paper provides a closed-form solution to the general-equilibrium expression of the welfare costs of inflation when the money demand is double logarithmic. This closed-form solution allows for the precise calculation of the difference between the general-equilibrium and Bailey's partial-equilibrium estimates of the welfare losses due to inflation. Again, in Lucas's original paper, the solution to the general-equilibrium-case underlying nonlinear differential equation is done only numerically, and the posterior assertion that the general-equilibrium welfare figures cannot be distinguished from those derived using Bailey's formula rely only on numerical simulations as well.

Parcerias público-privadas na presença de seleção adversa: uma análise numérica

Esta dissertação propõe-se a analisar a otimalidade de parcerias público-privadas (PPP) em um ambiente de seleção adversa. Mais especi calmente, analiso se as tarefas de construir e operar uma infraestrutura para serviços públicos deve ser realizada por um consórcio ou se devem ser realizadas por fi rmas contratadas separadamente. Para tal, diferentemente da literatura existente para o problema, focadas nos problemas de contratos incompletos e moral hazard, construo um modelo de seleção adversa multidimensional, onde as firrmas possuem informação privada e podem exercer um esforço não observável em cada atividade, com a existência de externalidade entre as tarefas, em uma extensão do modelo de La¤ont e Tirole (1986). Após defi nir algumas condições sob as quais PPP domina os meios usuais de contratação, utilizo de uma análise numérica para melhor compreender a solução do modelo, que se mostra altamente dependente da correlação entre os parâmetros de informação privada das firmas.

Exact arbitrage, well-diversified portfolios and asset pricing in large markets

: In a model of a nancial market with an atomless continuum of assets, we give a precise and rigorous meaning to the intuitive idea of a \well-diversi ed" portfolio and to a notion of \exact arbitrage". We show this notion to be necessary and su cient for an APT pricing formula to hold, to be strictly weaker than the more conventional notion of \asymptotic arbitrage", and to have novel implications for the continuity of the cost functional as well as for various versions of APT asset pricing. We further justify the idealized measure-theoretic setting in terms of a pricing formula based on \essential" risk, one of the three components of a tri-variate decomposition of an asset's rate of return, and based on a speci c index portfolio constructed from endogenously extracted factors and factor loadings. Our choice of factors is also shown to satisfy an optimality property that the rst m factors always provide the best approximation. We illustrate how the concepts and results translate to markets with a large but nite number of assets, and relate to previous work.

Are one-sided S,s rules useful proxies for optimal pricing rules?

This article is motivated by the prominence of one-sided S,s rules in the literature and by the unrealistic strict conditions necessary for their optimality. It aims to assess whether one-sided pricing rules could be an adequate individual rule for macroeconomic models, despite its suboptimality. It aims to answer two questions. First, since agents are not fully rational, is it plausible that they use such a non-optimal rule? Second, even if the agents adopt optimal rules, is the economist committing a serious mistake by assuming that agents use one-sided Ss rules? Using parameters based on real economy data, we found that since the additional cost involved in adopting the simpler rule is relatively small, it is plausible that one-sided rules are used in practice. We also found that suboptimal one-sided rules and optimal two-sided rules are in practice similar, since one of the bounds is not reached very often. We concluded that the macroeconomic effects when one-sided rules are suboptimal are similar to the results obtained under two-sided optimal rules, when they are close to each other. However, this is true only when one-sided rules are used in the context where they are not optimal.

Private or public? a taxonomy of optimal ownership and management regimes

We develop a theory of public versus private ownership based on value diversion by managers. Government is assumed to face stronger institutional constraints than has been assumed in previous literature. The model which emerges from these assumptions is fexible and has wide application. We provide amapping between the qualitative characteristics of an asset, its main use - including public goods characteristics, and spillovers toother assets values - and the optimal ownership and management regime. The model is applied to single and multiple related assets. We address questions such as; when is it optimal to have one of a pair ofr elated assets public and the other private; when is joint management desirable; and when should a public asset be managed by the owner of a related private asset? We show that while private ownership can be judged optimal in some cases solely on the basis of qualitative information, the optimality of any other ownership and management regimes relies on quantitative analysis. Our results reveal the situations in which policy makers will have difficulty in determining the opimal regime.