Steven M. Goldman's Homepage

<BODY><H1><A NAME="top"></A>Steven M. Goldman's HomePage</H1><P><IMG SRC="./images/goldman.gif" ALT="[IMAGE]" WIDTH=60 HEIGHT=70 BORDER=0ALIGN=bottom></P><P ALIGN=CENTER><TABLE BORDER=0 CELLPADDING=1 WIDTH="100%"> <TR> <TH> <P><FONT SIZE=4><A HREF="#vita">Curriculum Vitae</A></FONT> </TH><TH> <P><FONT SIZE=4><A HREF="#research">Research</A></FONT> </TH></TR> <TR> <TH> <P><FONT SIZE=4><A HREF="#notes">Class Notes</A></FONT> </TH><TH> <P><FONT SIZE=4><A HREF="#office">Office hours & mail</A></FONT> </TH></TR> <TR> <TH> <P><FONT SIZE=4><A HREF="#personal">Personal and Family</A></FONT> </TH><TD> <P>  </TD></TR></TABLE></P><P ALIGN=CENTER><BR></P><P ALIGN=CENTER><HR></P><H3 ALIGN=CENTER><A NAME="vita"></A><FONT SIZE=4>Brief CurriculumVita</FONT></H3><H4 ALIGN=CENTER><FONT SIZE=4>Goldman, Steven M. </FONT></H4><P ALIGN=CENTER><FONT SIZE=4>A.B., Harvard University (1962)<BR>Ph.D., Stanford University (1966)<BR>Professor of Economics; Vice Chair </FONT></P><P ALIGN=CENTER><B><FONT SIZE=4>Field</FONT></B><FONT SIZE=4>:Economic theory </FONT></P><P ALIGN=CENTER><B><FONT SIZE=4>Past ResearchTopics</FONT></B><FONT SIZE=4>: Rolling plans; fairness; liquidity;general equilibrium; separability; consumer behavior. </FONT></P><P ALIGN=CENTER><B><FONT SIZE=4>Current ResearchTopics</FONT></B><FONT SIZE=4>: Nonparametric regression analysis;efficiency in exchange equilibria; economics of disease control</FONT></P><P ALIGN=CENTER><FONT SIZE=4><A HREF="#top">return to top</A></FONT></P><P ALIGN=CENTER><HR></P><H3 ALIGN=CENTER><A NAME="notes"></A><FONT SIZE=4>Class Notes</FONT></H3><P ALIGN=CENTER><FONT SIZE=4>[Available to BerkeleyCampus]</FONT><BR><IMG SRC="quark.jpg" ALT="[IMAGE]" WIDTH=151 HEIGHT=225 BORDER=0ALIGN=bottom></P><P ALIGN=CENTER><FONT SIZE=4><A HREF="101a.htm">Economics101A</A></FONT></P><P ALIGN=CENTER><FONT SIZE=4><A HREF="201a.htm">Economics201A</A></FONT></P><P ALIGN=CENTER><FONT SIZE=4><A HREF="#top">return to top</A></FONT></P><P ALIGN=CENTER><HR></P><P ALIGN=CENTER><A NAME="research"></A><FONT SIZE=4>Current Researchin Progress (papers are in postscript format)</FONT></P><P ALIGN=CENTER><FONT SIZE=4>I. Nonparametric Estimation</FONT></P><P ALIGN=CENTER><FONT SIZE=4>The general problem is describable inthe following terms: given observations of the independent variablesX and the dependent ones Y , there is a presumed functionalrelationship f so that f(X)+e=Y . What function f best representsthis relationship. Clearly, if no restrictions are placed on the setof possible functions, then f(X) should equal Y at every observation.At unobserved values for X nothing can be said and the function isunconstrained. By contrast, if the set of functions were limited tolinear relationships alone, then f would be constrained at everypossible value of the independent variable. We are concerned with theintermediate case where the set of functions is not so narrowlyrestricted as to yield a unique best fitting function, but where theset of functions is restricted to, say F. For example, F may be allpossible concave functions. There is now, possibly, a set of bestfitting functions, a subset D of F. In the case of concavity, f amember of D implies that the best fitting f is determined at each ofthe observed values for X. That is, there is a single predicted valuefor the independent variable at each of the realized values for thedependent one. But at unobserved values for the dependent variable,the value of f is not uniquely defined but lies within a boundedrange (i.e. f is not simply a selection of any values in this rangebut must satisfy the concavity restriction and so, the selection atany point may limit those available at another). There is noinformation regarding a choice among these functions unless furtherassumptions are made regarding the nature of the theoreticalrelationship, i.e. F.</FONT></P><P ALIGN=CENTER><FONT SIZE=4>In</FONT><FONT SIZE=4><A HREF="nonparam.pdf">Nonparametric MultivariateRegression Subject to Constraint (with PaulRuud)</A></FONT><FONT SIZE=4> we review Hildreth's algorithm forcomputing the least squares regression subject to inequalityconstraints and subsequent generalizations, notably Dykstra's. Weprovide a geometric proof of convergence and a modification to thealgorithm which improves computation speed and provides somerobustness w.r.t. rounding error.</FONT></P><P ALIGN=CENTER><FONT SIZE=4><A HREF="demand.pdf">On the Nonconvexityof the Set of Utility-based Demand Functions(with PaulRuud)</A></FONT><FONT SIZE=4> examines a fundamental question ofeconomic theory: when will a given collection of economics data beconsistent with a given theory. For demand analysis, this problem iselegantly solved and elaborated in Afriat (S. Afriat, "On a System ofInequalities in Demand Analysis: An Extension of the ClassicalMethod," International Economic Review, 14, 1973, 460-472) and Varian(H. Varian, "The Nonparametric Approach to Demand Analysis,"Econometrica, 50, 1982, 945-973). The empirical version of this queryasks what is the ''best'' estimate of economic behavior satisfyingsome theory with respect to a given collection of observations. Thisestimation problem is customarily addressed through regressionanalysis but an alternative procedure involving nonparametricanalysis has recently experienced renewed interest. This technique,originates with Hildreth (C. Hildreth, "Point Estimates of Ordinatesof Concave Functions," Journal of the American StatisticalAssociation, 49 ,1954, 598-619) and is described in Varian (H.Varian, "Nonparametric Analysis of Optimizing Behavior withMeasurement Error, Journal of Econometrics, 30, 1985, 445-458) andGoldman and Ruud ("Nonparametric Multivariate Regression Subject toConstraint," Working Paper No. 93-213, Department of Economics,University of California, revised 1995). We wish to address thisquestion of estimating an individual demand function without imposingany restrictions as to functional form except those directly impliedby revealed preference. The problem will be described by the attemptto identify a least squares solution to the distance between theactual observations and those obtained from a demand functionderivable from utility maximization. In order for a unique solutionto exist to this problem, the allowable set of demand functions ingeneral must be closed and convex. In the note below, we willdemonstrate that the set of utility based demand functions fails tobe convex and that, consequently, unique estimation isproblematic.</FONT></P><P ALIGN=CENTER><FONT SIZE=4>II. The Economics of the SIS Model ofInfectious Disease</FONT></P><P ALIGN=CENTER><FONT SIZE=4>It has long been known that a personsuffering from an infectious disease poses a threat to others. In thelanguage of economics, infectious disease involves an externality.Susceptible people who come into contact with, or in some cases aremerely in the vicinity of an infectious individual may involuntarilycontract the disease. If the costs of the disease are large enoughand if the option existed, some of the susceptible individuals mightbe willing to pay the sick to quarantine themselves, seek medicaltreatment more promptly, or take precautions to prevent the infectionin the first place. This would decrease the chance of the susceptiblecontracting the disease. However, there are no markets for tradingpersonal rights to be protected from exposure to the many people inthe general population who may have an infectious disease. Thereforethe risk of exposure is said to be external to the market forces thatcould conceivably be used to control the consequences of exposure tothese risks. There is no obvious reason to believe that thedecentralized decisions made by individuals will provide aneconomically optimal level of protection against infectious diseasefor a society. Before any of the biological mechanisms of contagionwere understood, this aspect of infectious disease was used tojustify the exercise of social control of individuals suffering frominfectious diseases such as bubonic plague, smallpox, tuberculosis,and leprosy. Therefore even though many of the specific diseasecontrol measures proposed throughout history have been controversial,only the most extreme advocates of a libertarian social order haveadvocated the complete abandonment of public health programs. Theanalysis here focuses on the interaction between the epidemiologicalforces driving the spread of the disease, social control programs,and decentralized individual decision making regarding treatment andprevention. If individual and social control efforts have asignificant impact on the level of disease, then the probability ofinfection will change over time. Assuming that the individuals insociety are rational agents, they will take account of these changesand will modify their behavior accordingly. The question is ''whatwill be the ultimate effect this interaction on the course of thedisease, and the desirability of various public health programs?''However, there are currently no analyses which incorporate both theepidemiological content of infectious disease models and the behaviorof fully rational agents. The approach of biological and medicalscientists uses sophisticated epidemiological models, but theytypically minimize the role of rational individual behavior.Economists' models of individual behavior are more sophisticated inthis regard, but the epidemiological analysis is incomplete. Thispaper reports the results of research that attempts to lay thefoundation for a tractable analysis that includes both explicitmodeling of the individuals' decisions and a complete evaluation ofthe resulting epidemiological effects. The approach taken here aimsto include both the explicit analysis of the interaction of thedecision making of rational agents and the epidemiology of thedisease that will also be simple enough to give some intuitiveinsight into the costs and benefits of alternative policies. Thespecific disease model analyzed here has been the subject of previouswork, but the analysis is extended in significant ways here. Sanders(J. L. Sanders, "Quantitative Guidelines for Communicable DiseaseControl Programs'" Biometrics 27, 1971, 833-893) and Sethi (S. Sethi,"Quantitative Guidelines for Communicable Disease Control Programs: AComplete Synthesis'" Biometrics 30, 1974, 681-691) look at thesocially optimal program under the assumption of linear costs ofmedical treatment. The analysis reported here extends the analysis toinclude a variety of general cost functions, and includes a completeanalysis of the decentralized individually rational solution as wellas the socially optimal one.</FONT></P><P ALIGN=CENTER><FONT SIZE=4>The analysis in</FONT><FONT SIZE=4><A HREF="light1.pdf">The SIS Model of InfectiousDisease with Treatment (with James Lightwood)</A></FONT><FONT SIZE=4>examines the steady state solutions to rational treatment patterns ofSIS diseases. Individual behavior is shown to lead to the possibilityof significant undertreatment through the presence of unrewardedexternal benefits. The main conclusion of the analysis notes that theindividually rational and socially optimal level of disease willusually differ, with the socially optimal level of disease being nolarger than the individually rational level.</FONT></P><P ALIGN=CENTER><FONT SIZE=4>In</FONT><FONT SIZE=4><A HREF="lightwo5.pdf">Cost Optimization in theSIS Model of Disease with Treatment (with JamesLightwood)</A></FONT><FONT SIZE=4> we consider the intertemporalsocial optimization problem of minimizing the present value of thecosts incurred from both disease and treatment Our analysis allowsfor a robust collection of treatment cost functions and so extendsthe previous analysis by Sanders who examines only the case ofconstant marginal treatment cost. Though this extension of theanalysis is substantially complicated by the resulting failure ofconcavity , we are able to characterize both the long run equilibriaand the adjustment paths. Sanders results generalize is the followingmanner: The "bang-bang" treatment pattern discerned by Sanders where,below some level of infection, the entire population of infecteds istreated while, above that level, treatment is completely discontinuedis here replaced by a montonically decreasing level of treatment withrespect to the level of disease incidence. The socially optimalprogram is then compared to individually rational behavior and theinefficiencies in private behavior from the infection externality areshown to cause potentially large increases in the equilibrium rate ofinfection. The negative monotonic relationship (described above) isshown to hold in both the individual and social cases and is a directconsequence of the increased likelihood of reinfection at higherlevels of disease incidence which renders the benefits lessworthwhile.</FONT></P><P ALIGN=CENTER><FONT SIZE=4>III. Welfare Economics</FONT></P><P ALIGN=CENTER><FONT SIZE=4>The paper entitled</FONT><FONT SIZE=4><A HREF="cycle.pdf">Cyclic Trades and ParetoEfficiency</A></FONT><FONT SIZE=4> generalizes the corner efficiencyconditions of the Edgeworth Box to consider trades among multipleagents in many goods. The familiar inequality conditions on the MRS'sare replaced by ones on "chained MRS's" over possible cyclic trades.The set of Pareto improving trades can then be characterized as alinear space spanned by a relative low dimensional set of cyclictrades. Thus, an equilibrium w.r.t. such a basis, implies efficiency.This paper extends Goldman and Starr, ''Pairwise, t-Wise and ParetoOptimalities,'' Econometrica, 50, 1982, 593-606. In general asymmetry is shown to exist between the role played by markets (herecharacterized as the opportunity to exchange one good for another)and media of exchange (taken as a specific commodity which may beused to exchange for a wide variety of others). The analysis isrelevant to a wide variety of applied problems in which limitationsare placed on the allowable trades between agents. For example, theremay be relatively free trade within subsets of agents but onlylimited trades between those subsets as in the case of tradingblocks. Or, licensing arrangements may permit only some agents toengage in the exchange of specific commodities.<BR></FONT></P><P ALIGN=CENTER><FONT SIZE=5><A HREF="#top">return to top</A></FONT></P><P ALIGN=CENTER><FONT SIZE=4><HR></FONT></P><H3 ALIGN=CENTER><FONT SIZE=4><A NAME="personal"></A></FONT><FONT SIZE=5>Personal& Family</FONT></H3><P ALIGN=CENTER><FONT SIZE=5><A HREF="JGOLDMAN.HTM">Jules</A></FONT></P><P ALIGN=CENTER><FONT SIZE=5><A HREF="AGOLDMAN.HTM">Aaron</A></FONT></P><P ALIGN=CENTER><FONT SIZE=5><A HREF="#top">return to top</A></FONT></P><P ALIGN=CENTER><FONT SIZE=4><HR></FONT></P><P ALIGN=CENTER><FONT SIZE=4><A NAME="office"></A></FONT><B><FONT SIZE=5>OfficeHours</FONT></B><FONT SIZE=5> Thursday 11:00 A.M. - 12:00 P.M., 509Evans Hall</FONT></P><P ALIGN=CENTER><B><FONT SIZE=5>U.S. mail may be sentto:</FONT></B><FONT SIZE=5> Professor Steven Marc Goldman<BR>University of California<BR>Department of Economics<BR>549 Evans Hall # 3880<BR>Berkeley, CA 94720-3880</FONT></P><P ALIGN=CENTER><B><FONT SIZE=5>Telephone:</FONT></B><FONT SIZE=5>510-642-2787, </FONT><B><FONT SIZE=5>e-mail:</FONT><FONT SIZE=5><A HREF="mailto: goldman@econ.berkeley.edu">goldman@econ.berkeley.edu</A></FONT><FONT SIZE=5></FONT></B></P><P ALIGN=CENTER><FONT SIZE=5><A HREF="#top">return to top</A></FONT></P></BODY>