A sufficiency result for constrained economies

This paper presents a general sufficiency result for constrained economies. The result shows that, when an equilibrium allocation satisfies the first order necessary conditions for hybrid efficiency (a new type of constrained efficiency), there exists a marginal cost pricing equilibrium in an associated economy. If this equilibrium is Pareto efficient in the associated economy, then the original equilibrium allocation is hybrid efficient. Hence. the necessary conditions are also sufficient.     

Scarcity, regulation and endogenous technical progress

This paper studies to which extent a firm using a scarce resource input and facing environmental regulation can still manage to have a sustainable growth of output and profits. The firm has a vintage capital technology with two complementary factors, capital and a resource input subject to quota, the latter being increasingly scarce through an exogenously rising price. The firm can scrap obsolete capital and invest in adoptive and/or innovative R&D resource-saving activities. Within this realistic framework, we first characterize long-term growth regimes driven by scarcity (induced-innovation) vs. long-term growth regimes driven by quota regulation (Porter-like innovation). More importantly, we study the interaction between scarcity and quota regulation. In particular, we show that there exists a threshold level for the growth rate of the resource price above which the Porter mechanism is killed while the scarcity-induced growth regime may emerge. Symmetrically, we also find that there must exist a threshold value for the environmental quota under which the growth regime induced by scarcity vanishes while the Porter-like growth regime may survive.     

The elasticity of derived demand, factor substitution, and product demand: Corrections to Hicks' formula and Marshall's Four Rules

The concept of the elasticity of substitution between capital and labor, introduced by John Hicks and Joan Robinson over 75 years ago, has had important implications in labor economics and several areas of economic inquiry. In his The Theory of Wages (1932/1963), Hicks developed a formula that has proven very useful in relating the substitution elasticity to the derived demand for productive factors, the distribution of factor incomes, and Marshall's Four Rules. This short paper shows that the original and subsequent derivations of Hicks' celebrated formula contained a slip (that factor shares are independent of the substitution elasticity and therefore constant), presents a new derivation and a corrected formula, and demonstrates that, with the corrected formula, Marshall's First Rule based on the substitution elasticity is no longer generally valid.     

With a little help from abroad: The effect of low-skilled immigration on the female labour supply

We examine whether and how the inflow of female immigrants who specialize in household production affects the labour supply of Italian women. To identify the causal effect, we exploit the family reunification motives and network effects (i.e., the tendency of newly arriving female immigrants to settle in places where males of the same country already live) which is used as an instrument for the geographical distribution of female foreign workers. We find that when the number of immigrants who provide household services is higher, native Italian women spend more time at work (intensive margin) without affecting their labour force participation (extensive margin). This impact is concentrated on highly skilled women whose time has a higher opportunity cost. These results also hold after a battery of robustness checks. We present some further evidence that is also consistent with the idea that the impact works through substitution in household work rather than complementarities in the production sector. Finally, we show that immigration arises as a substitute to publicly provided welfare services, although this phenomenon raises concerns regarding the fairness and sustainability of this private and informal welfare model.     

Arbitrage, equilibrium, and gains from trade: A counterexample

We present a counterexample to a theorem due to Chichilnisky (Bulletin of the American Mathematical Society, 1993, 29, 189–207; American Economic Review, 1994, 84, 427–434). Chichilnisky's theorem states that her condition of limited arbitrage is necessary and sufficient for the existence of an equilibrium in an economy with unbounded short sales. Our counterexample shows that the condition defined by Chichilnisky is not sufficient for existence of equilibrium. We also discuss difficulties in Chichilnisky (Economic Theory, 1995, 5, 79–107).     

Active intermediation in a monetary overlapping generations economy

This paper establishes that the profit-seeking activities of private intermediaries can ensure Pareto efficiency in the standard pure-exchange monetary overlapping generations economy without the need for government monetary or fiscal policy intervention. Moreover, these profit-seeking activities are shown to rule out all aperiodic and k-periodic cycles for k greater than 2. Contrary to much recent work on intermediation, the profit opportunities that arise for intermediaries in this context are not due to assumed frictions or asymmetric information. Rather, they are due to the dynamic open-ended structure of the economy, which permits debt roll-over.     

Metonymy and cross-section demand

Cross-section consumer expenditure data are frequently used to draw conclusions about consumer demand behavior. Such conclusions, however, are justified only under certain assumptions, which are often left unstated in the empirical demand literature. An assumption of this type, the metonymy hypothesis, was stated rigorously and exploited by Härdle et al. when analyzing the monotonicity of aggregate demand functions. The purpose of the present paper is to examine the metonymy hypothesis in more detail. We prove that the distribution of demand vectors derived from a not necessarily metonymic population is identical with the distribution derived from some metonymic population. This implies, in particular, that the metonymy hypothesis cannot be rejected or confirmed on the basis of data from a single cross-section.     

Housing tenure choice and the dual income household

Housing tenure choice has been the subject of a very large literature. Many treatments have sought to estimate the effect of household income on the likelihood of home ownership. To date, no study has ever disaggregated the household income of married couples into the separate labor income components to see if one partner’s income has a different effect than the other. Using a derived likelihood function to control for censoring in the wife’s income, this paper estimates the effect of separate incomes on housing tenure choice, accounting for possible endogeneity of the wife’s income. To compare the results of this estimation method, the paper also estimates the standard IV models, 2SLS and IV probit. While the results show that there is no endogeneity of the wife’s income, ignoring the censoring of the endogenous variable (when a large fraction of observations are censored) can possibly lead to biased coefficient estimates. Also, this paper confirms the importance of total household income, which has a larger effect than the total disaggregated components.     

Implementation in generalized matching problems

We search for (Nash) implementable solutions on a class of one-to-one matching problems which includes both the housing market (Shapley and Scarf, Journal of Mathematical Economics, 1974, 1, 23–28) and marriage problems (Gale and Shapley, American Mathematical Monthly, 1962, 69, 9–15). We show that the core correspondence is implementable. We show, furthermore, that any solution that is Pareto efficient, individually rational, and implementable is a supersolution of the core correspondence. That is, the core correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable. A corollary of independent interest in the context of the housing market is that the core correspondence is the only single-valued solution that is Pareto efficient, individually rational, and implementable.     

Lattice structure of knowledge and agreeing to disagree

This paper is a contribution to the study of the underlying mathematical structure of common-knowledge, which gives the well-known result of Aumann about the impossibility of ‘agreeing to disagree’. We present the Bayesian subjective probability model with player's belief: i.e. a triple (? %plane1D;4AF;, μ), in which i is a player. ? is a lattice in the field of sets of a state space Ω, %plane1D;4AF;, is a correspondence assigning to each state ω a filter %plane1D;4AF;(ω) in ?, and μ is a common-prior. For this model, we impose none of the important restrictions on the information structure in the Aumann-Bacharach model: axiom of knowledge K₁. axiom of transparency K₂ and axiom of wisdom K₃. We can extend both the disagreement theorem of Aumann and the agreement theorem of Geanacoplos and Polemarchakis under the assumption that each ? is an Artinian lattice.