A competitive equilibrium for a warm-glow economy

The warm-glow model (Andreoni in J Political Econ 97:1447–1458, 1989; Econ J 100:464–477, 1990) of public goods provision has received widespread interest, yet surprisingly most attention has focused on the voluntary contribution equilibrium of the model, and only very little attention has been devoted to the competitive equilibrium. In this paper, we introduce the concept of competitive equilibrium for a warm-glow economy (henceforth, warm-glow equilibrium) and establish both existence and welfare properties. The warm-glow equilibrium concept may prove to be very useful to the normative and positive theory of public goods provision. First, it is a price-based mechanism achieving efficient outcomes. Second, not only could the warm-glow equilibria outcomes serve as a point of reference to measure free-riding and welfare loss but also, as suggested by Bernheim and Rangel (Behavioral Economics and Its Applications, 2007), in large economies they may be approximated by Walrasian equilibria outcomes.     

Welfare and excess volatility of exchange rates

We study the properties of a GEI model with nominal assets, outside money (injected into the economy as in Magill and Quinzii (J Math Econ 21:301–342, 1992)), and multiple currencies. We analyze the existence of monetary equilibria and the structure of the equilibrium set under two different assumptions on the determination of the exchange rates. If currencies are perfect substitutes, equilibrium allocations are indeterminate and, generically, sunspot equilibria exist. Generically, given a nonsunspot equilibrium, there are Pareto improving (and Pareto worsening) sunspot equilibria associated with an increase in the volatility of the future exchange rates. We interpret this property as showing that, in general, there is no clear-cut effect on welfare of the excess volatility of exchange rates, even when due to purely extrinsic phenomena.     

Bargaining over productivity and wages when technical change is induced: implications for growth, distribution, and employment

I study a model of growth and income distribution in which workers and firms bargain à la Nash (Econometrica 18(2):155–162, 1950) over wages and productivity gains, taking into account the trade-offs faced by firms in choosing factor-augmenting technologies. The aggregate environment resulting from self-interested, objective function-maximizing decision rules on wages, productivity gains, savings and investment, is described by a two-dimensional dynamical system in the employment rate and output/capital ratio. The economy converges cyclically to a long-run equilibrium involving a Harrod-neutral profile of technical change, a constant rate of employment of labor, and constant input shares. The type of oscillations predicted by the model is qualitatively consistent with the available data on the United States (1963–2003), replicates the dynamics found in earlier models of growth cycles such as Goodwin (A growth cycle, in C.H. Feinstein (ed). Socialism, Capitalism and Economic Growth. Cambridge University Press, Cambridge 1967. Cambridge University Press, Cambridge, 1967); Shah and Desai (Econ J 91:1006–1010, 1981); van der Ploeg (J Macroecon 9:1–12, 1987); Flaschel (J Econ: Zeitschrift für Nationalökonomie 44:63–69, 1984) and Sportelli (J Econ: Zeitschrift für Nationalökonomie 61(1):35–64, 1995), and can be verified numerically in simulations. Institutional change, as captured by variations in workers’ bargaining power, has a positive effect on the long-run rate of growth of output per worker but a negative effect on long-run employment. Economic policy can also affect the growth and distribution pattern through changes in the unemployment compensation, which also have a positive long-run impact on labor productivity growth but a negative long-run impact on employment. In both cases, employment can overshoot its new equilibrium value along the transitional dynamics.     

Multiple equilibrium under CES preferences

Under the simplifying assumptions that (1) there are two commodities and two agents, (2) production (endowment) of each commodity per period is fixed, (3) preferences of the two agents are of CES type, and (4) both the endowments and the CES preferences are mirror images of each other (called “supersymmetry”), it is shown that (a) there always exists a symmetric equilibrium with a unit price ratio, (b) a sufficient condition for the stability (hence uniqueness) of this symmetric equilibrium is that the elasticity of substitution satisfy ${\sigma\geqq 1/2}$ , and (c) multiple (triple) equilibrium is possible if and only if each agent has a relative preference for the good that is sold (“exported”) to the other agent. Further conditions for multiple equilibrium are derived.     

Geography, institutions, and the making of comparative development

While the direct impact of geographic endowments on prosperity is present in all countries, in former colonies, geography has also affected colonization policies and, therefore, institutional outcomes. Using non-colonized countries as a control group, I re-examine the theories put forward by La Porta et al. (J Law Econ Org 15(1):222–279, 1999 and Acemoglu et al. (Am Econ Rev 91(5), 1369–1401, 2001. I find strong support for both theories, but also evidence that the authors’ estimates of the impact of colonization on institutions and growth are biased, since they confound the effect of the historical determinants of institutions with the direct impact of geographic endowments on development. In a baseline estimation, I find that the approach of Acemoglu et al. (2001) overestimates the importance of institutions for economic growth by 28 %, as a country’s natural disease environment affected settler mortality during colonization and also has a direct impact on prosperity. The approach of La Porta et al. (1999) underestimates the importance of colonization-imposed legal origin for institutional development by 63 %, as Britain tended to colonize countries that are remote from Europe and thus suffer from low access to international markets.     

Outsourcing versus technology transfer: Hotelling meets Stackelberg

We consider a Hotelling duopoly with two firms $A$ and $B$ in the final good market. Both can produce the required intermediate good, firm $B$ having a lower cost due to a superior technology. We compare two contracts: outsourcing ( $A$ orders the intermediate good from $B$ ) and technology transfer ( $B$ transfers its technology to $A$ ). An outsourcing order is equivalent to building an endogenous capacity and it generates a Stackelberg leadership effect for firm $A,$ which is absent in technology transfer. We show that compared to the situation of no contracts there are always Pareto improving outsourcing contracts (making both firms better off and all consumers at least weakly better off), but no Pareto improving technology transfer contracts. It is also shown that if firm $B$ has a relatively large bargaining power in its negotiations with $A,$ then both firms prefer technology transfer while all consumers prefer outsourcing.     

Further results on essential Nash equilibria in normal-form games

A Nash equilibrium \(x\) of a normal-form game \(G\) is essential if any perturbation of \(G\) has an equilibrium close to \(x\). Using payoff perturbations, we identify a new collection of games containing a dense, residual subset of games whose Nash equilibria are all essential. This collection covers economic examples that cannot be handled by extant results and subsumes the sets of games considered in the literature.     

Underground Economy,Evasion and Inequality

Economic theory is paying increasing attention to a non-observed economy (NOE) and its causes. Recently, a couple of works (Rosser et al., 2000 Rosser, J. B., Rosser, M. V. and Ahmed, E. 2000. Income inequality and the informal economy in transitions economies. Journal of Comparative Economics, 28(1): 156–171.  [Google Scholar], 2003 Rosser, J. B., Rosser, M. V. and Ahmed, E. 2003. Multiple unofficial economy equilibria and income distribution dynamics in systemic transition. Journal of Post Keynesian Economics, 25(3): 425–447. [Web of Science ®] , [Google Scholar]) have claimed that there is a positive relationship between income inequality and the size of NOE. This supposed relationship is not so clear and deserves in-depth analysis. There is a crucial aspect that has been completely avoided in these studies: income inequality is mainly measured using ‘regular’ incomes and this fact could lead to some bias. The existence of a certain size of NOE implies some income evasion that can affect the inequality indexes used in the study of the relationship between NOE and inequality. Including the regional share of NOE in a wage equation, I find that, in the specific case of the Italian private sector employees, the income evasion attached to NOE tends to reduce inequality measured by regular wages statistics.     

Liquidity and the marginal value of information

We revisit Kyle’s (Econometrica 53:1315–1335, 1985) model of price formation in the presence of private information. We begin by using Back’s (Rev Financ Stud 5(3):387–409, 1992) approach, demonstrating that if standard assumptions are imposed, the model has a unique equilibrium solution and that the insider’s trading strategy has a martingale property. That in turn implies that the insider’s strategies are linear in total order flow. We also show that for arbitrary prior distributions, the insider’s trading strategy is uniquely determined by a Doob $h$ -transform that expresses the insider’s informational advantage. This allows us to reformulate the model so that Kyle’s liquidity parameter $\lambda $ is characterized by a Lagrange multiplier that is the marginal value or shadow price of information. Based on these findings, we can then interpret liquidity as the marginal value of information.     

Removing biases in forecasts of fishery status

A recent highly cited paper from this journal develops a model predicting maximum sustainable yield ( \(MSY\) ) of a fishery using the historical maximum catch ( \(MaxCatch\) ). The model is parameterized with a small sample of fisheries from the United States, and is subsequently applied globally to estimate the benefits of fishery recovery. That empirical relationship has been adopted for many subsequent high-profile analyses. Unfortunately, the analysis suffers from two important oversights: (1) because the model is non-linear, it suffers from “retransformation bias” and therefore the results significantly understate \(MSY\) and (2) the analysis is parameterized from of a very limited data set and so generalizability of the fitted empirical relationship between \(MSY\) and \(MaxCatch\) to global fisheries is questionable. Here, we rectify both oversights and provide an updated estimate of the relationship between \(MSY\) and \(MaxCatch\) .     

Estimated non-linearities and multiple equilibria in a model of distributive-demand cycles

We introduce the results of a non-parametric estimate of the US wage-Phillips Curve into a simplified version of the model of the wage-price spiral by Flaschel and Krolzig (2008). Making use of Okun’s law, the non-linearity in the wage inflation-employment relation translates into a non-linearity in the so-called ‘distributive curve’ of the economy. Exploiting the observed non-linearity in extending an otherwise standard demand-distribution model (Taylor 2004 Taylor, Lance. 2004. Reconstructing macroeconomics. structuralist proposals and critique of the mainstream, Cambridge, MA: Harvard University Press.  [Google Scholar]), we provide a dynamical analysis both in wage-led and profit-led effective demand regimes. In a profit-led scenario, shown to be the empirically relevant case for the US economy, there are two stable equilibria of Goodwin (1967 Goodwin, R.M. 1967. “A growth cycle”. In Socialism, capitalism and economic growth, Edited by: Feinstein, C.H. Cambridge, , UK: Cambridge University Press.  [Google Scholar]) growth cycle type, identified as a stable depression and a stable boom, and a saddle-path stable equilibrium in between them. Both stable steady states are surrounded by trajectories that cycle counterclockwise around their basins of attraction. The obtained type of growth fluctuations can be verified by a long phase cycle estimation for the US economy using a method developed by Kauermann, Teuber and Flaschel (2008 Kauermann, G., Teuber, T. and Flaschel, P. 2008. “Estimating loops and cycles using penalized splines”. Bielefeld: CEM working paper.  [Google Scholar]).     

Walras’ theory of capital formation: an intertemporal equilibrium reformulation

We develop a mainstream reformulation of the original Walras?? model of capital accumulation. We overcome the shortcomings of the original model. First, we prove the existence of intertemporal competitive equilibria. Our proof combines a well known theorem due to Yannelis and Prabhakar (J Math Econ 12:233?C245, 1983) with a lemma due to Geanakoplos (Econ Theory 21:585?C603, 2003). Secondly, we remedy the indeterminacy of allocation of savings across multiple types of capital goods by introducing a storage technology. Finally, we show that, for stored capital goods, the equality of rates of returns emerges endogenously in equilibrium, while it was imposed by Walras from the outset in his original contribution.     

Household behavior and individual autonomy: an extended Lindahl mechanism

We present a comprehensive model of household economic decision covering both full cooperation and noncooperation as well as semi-cooperative cases, varying with income distribution and a parameter vector $\theta $ representing degrees of individual autonomy with respect to the public goods. In this model, the concept of “household $\theta $ -equilibrium” is introduced through the reformulation of the Lindahl equilibrium for Nash implementation and its extension to semi-cooperation. Existence is proved and some generic properties derived. An example is given to illustrate. An important benefit of this approach is to allow for a compact and unified investigation of the testable (local) restrictions of household demand. A particular decomposition of the pseudo-Slutsky matrix is derived and the testability of the various models discussed.     

Inferior factor in Cournot oligopoly revisited

We reconsider the recent work by Okuguchi (J Econ 101:125–131, 2010) on (possibly asymmetric) Cournotian firms with two production factors, one being inferior for each firm. It is shown there that an increase in the price of the inferior factor does raise the equilibrium industry output. In addition of providing a simpler and more rigorous proof of that result, we generalize it to the case of technologies with $s\ge 2$ factors and also allow some firms not to use the inferior one.     

Restrictions and identification in a multidimensional risk-sharing problem

We consider $H$ expected utility maximizers that have to share a risky aggregate multivariate endowment $X\in {\mathbb {R}}^{N}$ and address the following two questions: does efficient risk-sharing imply restrictions on the form of individual consumptions as a function of $X$ ? Can one identify the individual utility functions from the observation of the risk-sharing? We show that when $H\ge \frac{2N}{N-1}$ efficient risk sharings have to satisfy a system of nonlinear PDEs. Under an additional rank condition, we prove an identification theorem.     

Forecasting spatially dependent origin and destination commodity flows

We explore origin–destination forecasting of commodity flows between 15 Spanish regions, using data covering the period from 1995 to 2004. The 1-year-ahead forecasts are based on a recently introduced spatial autoregressive variant of the traditional gravity model. Gravity (or spatial interaction models) attempt to explain variation in \(N = n^2\) flows between \(n\) origin and destination regions that reflect a vector arising from an \(n\) by \(n\) flow matrix. The spatial autoregressive variant of the gravity model used here takes into account spatial dependence between flows from regions neighboring both the origin and destinations during estimation and forecasting. One-year-ahead forecast accuracy of non-spatial and spatial models are compared.     

Definitions of ambiguous events and the smooth ambiguity model

We examine a variety of preference-based definitions of ambiguous events in the context of the smooth ambiguity model. We first consider the definition proposed in Klibanoff et?al. (Econometrica 73(6):1849?C1892, 2005) based on the classic Ellsberg two-urn paradox (Ellsberg Q J Econ 75:643?C669, 1961) and show that it satisfies several desirable properties. We then compare this definition with those of Nehring (Math Soc Sci 38(2):197?C213, 1999), Epstein and Zhang (Econometrica 69:265?C306, 2001), Zhang (Econ Theory 20:159?C181, 2002), and Ghirardato and Marinacci (J Econ Theory 102:251?C289, 2002). Within the smooth ambiguity model, we show that Ghirardato and Marinacci (J Econ Theory 102:251?C289, 2002) would identify the same set of ambiguous and unambiguous events as our definition while Epstein and Zhang (Econometrica 69:265?C306, 2001) and Zhang (Econ Theory 20:159?C181, 2002) would yield a different classification. Moreover, we discuss and formally identify two key sources of the differences compared to Epstein and Zhang (Econometrica 69:265?C306, 2001) and Zhang (Econ Theory 20:159?C181, 2002). The more interesting source is that these two definitions can confound non-constant ambiguity attitude and the ambiguity of an event.     

Is there really a gap between aggregate productivity and technology?

The important contribution by Basu and Fernald (2002 Basu, S and Fernald, JG. 2002. Aggregate productivity and aggregate technology. European Economic Review, 46: 963–91.  [Google Scholar]) shows that, in practice, there is a statistically significant gap between aggregate productivity and technology that can be attributed to inefficient product and labour markets. This is important, as it implies that the Solow residual is an imperfect index for aggregate technology change. We take a related approach and find that when we control for capacity utilization, time varying markup and account for externalities between industries, by employing a superior system estimator, the gap between the aggregate productivity and technology is shown to narrow considerably.