Equilibrium analysis and envelope theory

Qualitative comparative statics amounts to a study of the qualitative properties of the Debreu mapping, i.e., the restriction of the projection (p,ω)?ω to the equilibrium manifold. We show that a natural framework for such a study is Thom's envelope theory which generalizes the theory of planar curve envelopes.     

When worlds collide: Different comparative static predictions of continuous and discrete agent models with land

This paper presents a difference in the comparative statics of general equilibrium models with land when there are finitely many agents, and when there is a continuum of agents. Restricting attention to quasi-linear and Cobb–Douglas utility, it is shown that with finitely many agents, an increase in the (marginal) commuting cost increases land rent per unit (that is, land rent averaged over the consumer's equilibrium parcel) paid by the consumer located at each fixed distance from the central business district. In contrast, with a continuum of agents, average land rent goes up for consumers at each fixed distance close to the central business district, is constant at some intermediate distance, and decreases for locations farther away. Therefore, there is a qualitative difference between the two types of models, and this difference is potentially testable.     

Debt and Development

This paper examines incentive and valuation effects of debt financing on land investment. When land is debt financed, the landowner holds both a development option on the land and a default option on the debt. Because development typically devalues the default option, investment may be delayed past the point at which efficient investment would otherwise proceed. The incentive to underinvest is shown to be more pronounced as debt level increases, i.e., as the debt becomes riskier. This agency problem provides an explanation as to why land is generally difficult to debt finance and may also explain why debt levels are relatively low for “land-intensive” real estate firms. Novel comparative statics show that debt value may increase for a given increase in asset volatility as well as for a given increase in interest rate. Renegotiation and restrictive contract provisions are considered as mechanisms to promote efficient investment policy in the presence of debt financing.     

On the upper and lower semicontinuity of the Aumann integral

Let (T,τ,μ) be a finite measure space, X be a Banach space, P be a metric space and let L₁(μ,X) denote the space of equivalence classes of X-valued Bochner integrable functions on (T,τ,μ). We show that if φ:T×P→2^X is a set-valued function such that for each fixed pεP, φ(·,p) has a measurable graph and for each fixed tεT, φ(t,·) is either upper or lower semicontinuous then the Aumann integral of φ, i.e.,∫_Tφ(t,p)dμ(t)= {∫_Tx(t)dμ(t):xεS_φ(p)}, where S_φ(p)= {yεL₁(μ,X):y(t)εφ(t,p)μ−a.e.}, is either upper or lower semicontinuous in the variable p as well. Our results generalize those of Aumann (1965, 1976) who has considered the above problem for X=Rⁿ, and they have useful applications in general equilibrium and game theory.     

Commodity chain systems and the housing market

A system of gross substitutes, referred to here as a chain system, is analyzed and the results applied to the housing market. The stability conditions and comparative statics properties of the system are examined in detail. One of the results is that a specific numerical magnitude is of special importance to the system's stability and comparative statics behavior. Implications of the analysis for the housing market and for government policy are discussed.     

Income taxes and urban spatial structure

This paper examines the impact of an income tax in a monocentric city where households equilibriate their allocation of time between work, commuting, and leisure. An increase in the income tax rate lowers the implicit value of time, and hence transportation costs. “Compensated equilibrium” comparative statics analysis shows that under certain conditions, this results in a larger, more dispersed urban area, with lower land rents at the city center and less population within any given distance from the center. The welfare effect of an income tax rate change is also studied, and an expression for the marginal excess burden is derived. The income tax produces welfare losses both because it induces substitution in favor of leisure and in favor of travel—the latter accompanied by excessive spatial dispersion and consumption of space. The marginal excess burden depends not only on the compensated demand elasticity for leisure, but also on that for space. Finally, the problem of benefit measurement for transportation projects in this tax-distorted spatial economy is examined. Benefit measures should be deflated to adjust for the fact that further transportation improvements lead to reduction of land use intensity, exacerbating the problem of spatial resource misallocation in an already excessively dispersed urban area.     

The LeChatelier principle for changes in risk

In this paper, we analyze the comparative statics of changes in risk in the context of problems with multiple decision variables. We demonstrate, in particular, that the Samuelson–LeChatelier principle extends naturally to the comparative statics of changes in risk: in the presence of positive feedbacks between the decision variables, the unrestricted response to an increase in risk is in the same direction and stronger in magnitude than the restricted response (i.e. the choice when other decision variables are fixed). We define the concepts of Nth-degree risk complements and Nth-degree risk substitutes and we show that it is in any one of these two cases (and only in these cases) that we will observe positive feedbacks between the decision variables. We also analyze the extent to which the same principle can be applied to strategic settings under uncertainty.     

Labour adjustment costs: Estimation of a dynamic discrete choice model using panel data for Greek manufacturing firms

In this paper we estimate a dynamic structural model of employment at firm level. Our dataset consists of a balanced panel of 2790 Greek manufacturing firms. The empirical evidence of this dataset stresses three important stylized facts: (a) there are periods in which firms decide not to change their labour input, (b) there are periods of large employment changes (lumpy nature of labour adjustment) and (c) the commonality is employment spikes to be followed by smooth and low employment growth periods. Following Cooper and Haltiwanger [Cooper, R.W. and Haltiwanger, J. “On the Nature of Capital Adjustment Costs”, Review of Economic Studies, 2006; 73(3); 611–633], we consider a dynamic discrete choice model of a general specification of adjustment costs including convex, non-convex and “disruption of production” components. We use a method of simulated moments procedure to estimate the structural parameters. Our results indicate considerable fixed costs in the Greek employment adjustment.     

Comparative statics in markets for indivisible goods

This paper builds upon Caplin and Leahy (2014), which introduced a new mathematical apparatus for understanding allocation markets with nontransferable utility, as such covering the housing market and other markets for large indivisible goods. In the current paper we complete the study of comparative statics initiated therein. We introduce homotopy methods to characterize how equilibrium changes in response to arbitrary parameter changes. Generically, we show that there can be five and only five qualitatively distinct forms of market transition: Graft; Prune and Plant; Prune and Graft; Cycle and Reverse; and Shift and Replant. Our path-following methods identify new algorithms for computing market equilibria.     

Tests for location-scale families based on the empirical characteristic function

A class of procedures is presented for using random samples to test the fit of location-scale families—distributions F(·;θ₁,θ₂) such that Z=(X−θ₁)/θ₂ has distribution Working with empirically standardized data, the test statistic is a measure of distance between the empirical characteristic function, and the c.f. of Z under the null hypothesis, ϕ₀(t). The closed-form test statistic is derived by integrating over the product of a weight function times Using as weight function for each location-scale family the squared modulus of ϕ₀ itself presents a unified test procedure. Included as special cases are well-known tests for normal and Cauchy laws. Small-sample powers are compared with those of Anderson-Darling tests for each of seven univariate location-scale families.     

The dominant firm with convex technology

The paper analyses a dominant firm model in which firms have convex production sets. The model is shown to be determinate, and to be expressible by a set of (n+1) equilibrium conditions. A previous attempt to obtain comparative statics results is criticized as being invalid, and a new framework for comparative statics is developed.     

Conjunctural causation in comparative case-oriented research

This article highlights one of the major benefits of qualitative comparative methodology as applied within a “small-N” research design, namely its potential use for specifying the scope conditions of (theoretically competing) causal mechanisms. It is argued that the identification of set-theoretic relationships, multiple paths, and analytic efforts in typological mapping can make valuable contributions to the elaboration and further development of middle-range theory.     

A remark on economic response to technological innovation

In this article differential techniques are applied to a two-sector equilibrium model of economic response to technological innovation. These techniques allow a parametric comparative statics interpretation of the model, and qualitative results on the directions of parameter shifts are obtained.     

Solving the income fluctuation problem with unbounded rewards

This paper studies the income fluctuation problem without imposing bounds on utility, assets, income or consumption. We prove that the Coleman operator is a contraction mapping over the natural class of candidate consumption policies when endowed with a metric that evaluates consumption differences in terms of marginal utility. We show that this metric is complete, and that the fixed point of the operator coincides with the unique optimal policy. As a consequence, even in this unbounded setting, policy function iteration always converges to the optimal policy at a geometric rate.     

Estimation of the parameters in the gravity model for trip distribution : A new method and solution algorithm

For the unique determination of the parameters in the doubly constrained gravity model with exponential friction function two approaches are common: (1) entropy maximization and (2) application of a travel cost budget. This paper shows by making use of geometric programming that both of these approaches are equivalent with another natural criterion: the minimization of the deviation between the observed [t_1j] and the estimated [x_1j] table for a base year. By means of calculating the derivative of total cost as a function of σ the construction of an efficient algorithm for estimation of σ is made possible.     

Continua of stochastic dominance relations for bounded probability distributions

Let P={F,G,…} be the set of probability distribution functions on [0,b]. For each αε[1, ∞), F_αG means that ∫^x_o(x−y^α−1dF(y)∫^x_o(x−y)^α−1dG(y) for all xε[0, b], and F>_αG means that F_αG and F≠G. Each _α is reflexive and transitive and each>_α is asymmetric and transitive. Both _α and>_α increase as α increases but their limits are not complete. A class U_α of utility functions is defined to give F>_αG iff ∫udF>∫udG for all uεU_α. These classes decrease as α increases, and their limit is empty. Similar decreasing classes are defined for each _α, and their limit is essentially the constant functions on (0, b].     

The theta model: a decomposition approach to forecasting

This paper presents a new univariate forecasting method. The method is based on the concept of modifying the local curvature of the time-series through a coefficient ‘Theta’ (the Greek letter θ), that is applied directly to the second differences of the data. The resulting series that are created maintain the mean and the slope of the original data but not their curvatures. These new time series are named Theta-lines. Their primary qualitative characteristic is the improvement of the approximation of the long-term behavior of the data or the augmentation of the short-term features, depending on the value of the Theta coefficient. The proposed method decomposes the original time series into two or more different Theta-lines. These are extrapolated separately and the subsequent forecasts are combined. The simple combination of two Theta-lines, the Theta=0 (straight line) and Theta=2 (double local curves) was adopted in order to produce forecasts for the 3003 series of the M3 competition. The method performed well, particularly for monthly series and for microeconomic data.     

Optimal reinsurance with multiple tranches

Motivated by common practices in the reinsurance industry and in insurance markets such as Lloyd’s, we study the general problem of optimal insurance contracts design in the presence of multiple insurance providers. We show that the optimal risk allocation rule is characterized by a hierarchical structure of risk sharing where all agents take on risks only above the endogenously determined thresholds, or agent-specific deductibles. Linear risk sharing between two adjacent thresholds is shown to be optimal when all agents have CARA utilities. Furthermore, we show that the optimal thresholds can be efficiently calculated through the fixed point of a contraction mapping.     

The case for heterogeneity of cities

The general similarity of the results of comparative statics in a semiclosed and in a fully closed city have been demonstrated by Pines and Sadka (Journal of Urban Economics 20, 1–20, 1986). The objective of this paper is to determine if the consequences of different forms of public regulation of the urban land market are also invariant with respect to the type of city. The conclusion is that while there are well-defined consequences of such controls on metropolitan area and land values in a semiclosed city, the impacts in a fully closed city are generally ambiguous. Therefore, proposals for the introduction of zoning and density regulation have to be city-specific and take into consideration the pattern of land ownership and the extent of leakage of urban land rent income.     

Semiparametric tests of conditional moment restrictions under weak or partial identification

We propose two new semiparametric specification tests which test whether a vector of conditional moment conditions is satisfied for any vector of parameter values θ₀. Unlike most existing tests, our tests are asymptotically valid under weak and/or partial identification and can accommodate discontinuities in the conditional moment functions. Our tests are moreover consistent provided that identification is not too weak. We do not require the availability of a consistent first step estimator. Like Robinson [Robinson, Peter M., 1987. Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55, 875–891] and many others in similar problems subsequently, we use k-nearest neighbor (knn) weights instead of kernel weights. The advantage of using knn weights is that local power is invariant to transformations of the instruments and that under strong point identification computation of the test statistic yields an efficient estimator of θ₀ as a byproduct.