Solving heterogeneous-agent models by projection and perturbation

The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solutionof the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible.Matlab programs to solve the model can be downloaded.

Entrepreneurial risk, investment and innovation

In this paper I develop a general equilibrium model with risk averse entrepreneurialfirms and with public firms. The model predicts that an increase in uncertainty reducesthe propensity of entrepreneurial firms to innovate, while it does not affect thepropensity of public firms to innovate. Furthermore, it predicts that the negativeeffect of uncertainty on innovation is stronger for the less diversified entrepreneurialfirms, and is stronger in the absence of financing frictions in the economy. In thesecond part of the paper I test these predictions on a dataset of small and mediumItalian manufacturing firms.

On the quantitative importance of wage bargaining models

Four general equilibrium search models are compared quantitatively. Thebaseline framework is a calibrated macroeconomic model of the US economydesigned for a welfare analysis of unemployment insurance policy. Theother models make three simple and natural specification changes,regarding tax incidence, monopsony power in wage determination, and therelevant threat point. These specification changes have a major impacton the equilibrium and on the welfare implications of unemploymentinsurance, partly because search externalities magnify the effects ofwage changes. The optimal level of unemployment insurance dependsstrongly on whether raising benefits has a larger impact on searcheffort or on hiring expenditure.

Increasing returns, imperfect competition and factor prices

We show how, in general equilibrium models featuring increasing returns, imperfectcompetition and endogenous markups, changes in the scale of economic activity affectincome distribution across factors. Whenever final goods are gross-substitutes (gross-complements), a scale expansion raises (lowers) the relative reward of the scarce factoror the factor used intensively in the sector characterized by a higher degree of product differentiation and higher fixed costs. Under very reasonable hypothesis, our theory suggests that scale is skill-biased. This result provides a microfoundation for the secular increase in the relative demand for skilled labor. Moreover, it constitutes an important link among major explanations for the rise in wage inequality: skill-biased technical change, capital-skill complementarities and international trade. We provide new evidence on the mechanism underlying the skill bias of scale.

The variability of money velocity in a generalized cash-in-advance model

This paper presents a general equilibrium model of money demand wherethe velocity of money changes in response to endogenous fluctuations in the interest rate. The parameter space can be divided into two subsets: one where velocity is constant and equal to one as in cash-in-advance models, and another one where velocity fluctuates as in Baumol (1952). Despite its simplicity, in terms of paramaters to calibrate, the model performs surprisingly well. In particular, it approximates the variability of money velocity observed in the U.S. for the post-war period. The model is then used to analyze the welfare costs of inflation under uncertainty. This application calculates the errors derived from computing the costs of inflation with deterministic models. It turns out that the size of this difference is small, at least for the levels of uncertainty estimated for the U.S. economy.

Educational attainment and timing of fertility decisions

This paper focuses on timing of fertility decisions, conditional on the level of educational attainment of parents. Timing of fertility and educational attainment of parents rationalize the negative relationship observed in the data between hourly wages and childbearing. It is shown how the recent evolution in total fertility rates observed in developed countries could be in part the result of a transition from an early childbearing regime to a late childbearing regime. I develop a general equilibrium overlapping generations model in order to understand the joint determination of timing of childbearing decisions together with other household economic decisions in a life cycle framework. I show how idiosyncratic uncertainty might have asymmetric efects on completed fertility depending on timing of childbearing, generating the diferences in completed fertility observed between households that difer in their level of educational attainment.

Educational attainment and timing of fertility decisions

This paper focuses on timing of fertility decisions, conditional on the level of educational attainment of parents. Timing of fertility and educational attainment of parents rationalize the negative relationship observed in the data between hourly wages and childbearing. It is shown how the recent evolution in total fertility rates observed in developed countries could be in part the result of a transition from an early childbearing regime to a late childbearing regime. I develop a general equilibrium overlapping generations model in order to understand the joint determination of timing of childbearing decisions together with other household economic decisions in a life cycle framework. I show how idiosyncratic uncertainty might have asymmetric efects on completed fertility depending on timing of childbearing, generating the diferences in completed fertility observed between households that difer in their level of educational attainment.

Is the matching function Cobb-Douglas?

[cat] Estudiem les propietats teòriques que una funció d.emparellament ha de satisfer per tal de representar un mercat laboral amb friccions dins d'un model d'equilibri general amb emparellament aleatori. Analitzem el cas Cobb-Douglas, CES i altres formes funcionals per a la funció d.emparellament. Els nostres resultats estableixen restriccions sobre els paràmetres d'aquests formes funcionals per assegurar que l.equilibri és interior. Aquestes restriccions aporten raons teòriques per escollir entre diverses formes funcionals i permeten dissenyar tests d'error d'especificació de model en els treballs empírics.

Is the matching function Cobb-Douglas?

[cat] Estudiem les propietats teòriques que una funció d.emparellament ha de satisfer per tal de representar un mercat laboral amb friccions dins d'un model d'equilibri general amb emparellament aleatori. Analitzem el cas Cobb-Douglas, CES i altres formes funcionals per a la funció d.emparellament. Els nostres resultats estableixen restriccions sobre els paràmetres d'aquests formes funcionals per assegurar que l.equilibri és interior. Aquestes restriccions aporten raons teòriques per escollir entre diverses formes funcionals i permeten dissenyar tests d'error d'especificació de model en els treballs empírics.

Habit Formation and the Persistence of Monetary Shocks

This paper studies the persistent effects of monetary shocks on output. Previous empirical literature documents this persistence, but standard general equilibrium models with sticky prices fail to generate output responses beyond the duration of nominal contracts. This paper constructs and estimates a general equilibrium model with price rigidities, habit formation, and costly capital adjustment. The model is estimated via Maximum Likelihood using US data on output, the real money stock, and the nominal interest rate. Econometric results suggest that habit formation and adjustment costs to capital play an important role in explaining the output effects of monetary policy. In particular, impulse response analysis indicates that the model generates persistent, hump-shaped output responses to monetary shocks.

Industrial Adjustment: Context, Causes, Impacts and Methods for Analysis

Adjustement is an ongoing process by which factors of reallocated to equalize their returns in different uses. Adjustment occurs though market mechanisms or intrafirm reallocation of resources as a result of changes in terms of trade, government policies, resource availability, technological change, etc. These changes alter production opportunities and production, transaction and information costs, and consequently modify production functions, organizational design, etc. In this paper we define adjustment (section 2); review empirical estimates of the extent of adjustment in Canada and abroad (section 3); review selected features of the trade policy and adjustment context of relevance for policy formulation among which: slow growth, a shift to services, a shift to the Pacific Rim, the internationalization of production, investment distribution communications the growing use of NTB's, changes in foreign direct investment patterns, intrafirm and intraindustry trade, interregional trade flows, differences in micro economic adjustment processes of adjustment as between subsidiaries and Canadian companies (section 4); examine methodologies and results of studies of the impact of trade liberalization on jobs (section 5); and review the R. Harris general equilibrium model (section 6). Our conclusion emphasizes the importance of harmonizing commercial and domestic policies dealing with adjustment (section 7). We close with a bibliography of relevant publications.

Macroclosures in Open Economy Cge Models: a Numerical Reappraisal

It Has Been Argued That in the Construction and Simulation Process of Computable General Equilibrium (Cge) Models, the Choice of the Proper Macroclosure Remains a Fundamental Problem. in This Study, with a Standard Cge Model, We Simulate Disturbances Stemming From the Supply Or Demand Side of the Economy, Under Alternative Macroclosures. According to Our Results, the Choice of a Particular Closure Rule, for a Given Disturbance, May Have Different Quantitative and Qualitative Impacts. This Seems to Confirm the Imiportance of Simulating Cge Models Under Alternative Closure Rules and Eventually Choosing the Closure Which Best Applies to the Economy Under Study.

The Transformation Problem : an Aleternative Solution with an Identical Aggregate Profit Rate in the Labor value and the Monetary Space.

The aim of this paper is to demonstrate that, even if Marx's solution to the transformation problem can be modified, his basic conclusions remain valid. the proposed alternative solution which is presented hare is based on the constraint of a common general profit rate in both spaces and a money wage level which will be determined simultaneously with prices.