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=0 ALIGN=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 Curriculum Vita</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 Research Topics</FONT></B><FONT SIZE=4>: Rolling plans; fairness; liquidity; general equilibrium; separability; consumer behavior. </FONT></P> <P ALIGN=CENTER><B><FONT SIZE=4>Current Research Topics</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 Berkeley Campus]</FONT><BR> <IMG SRC="quark.jpg" ALT="[IMAGE]" WIDTH=151 HEIGHT=225 BORDER=0 ALIGN=bottom></P> <P ALIGN=CENTER><FONT SIZE=4><A HREF="101a.htm">Economics 101A</A></FONT></P> <P ALIGN=CENTER><FONT SIZE=4><A HREF="201a.htm">Economics 201A</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 Research in 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 in the following terms: given observations of the independent variables X and the dependent ones Y , there is a presumed functional relationship f so that f(X)+e=Y . What function f best represents this relationship. Clearly, if no restrictions are placed on the set of possible functions, then f(X) should equal Y at every observation. At unobserved values for X nothing can be said and the function is unconstrained. By contrast, if the set of functions were limited to linear relationships alone, then f would be constrained at every possible value of the independent variable. We are concerned with the intermediate case where the set of functions is not so narrowly restricted as to yield a unique best fitting function, but where the set of functions is restricted to, say F. For example, F may be all possible concave functions. There is now, possibly, a set of best fitting functions, a subset D of F. In the case of concavity, f a member of D implies that the best fitting f is determined at each of the observed values for X. That is, there is a single predicted value for the independent variable at each of the realized values for the dependent one. But at unobserved values for the dependent variable, the value of f is not uniquely defined but lies within a bounded range (i.e. f is not simply a selection of any values in this range but must satisfy the concavity restriction and so, the selection at any point may limit those available at another). There is no information regarding a choice among these functions unless further assumptions are made regarding the nature of the theoretical relationship, i.e. F.</FONT></P> <P ALIGN=CENTER><FONT SIZE=4>In </FONT><FONT SIZE=4><A HREF="nonparam.pdf">Nonparametric Multivariate Regression Subject to Constraint (with Paul Ruud)</A></FONT><FONT SIZE=4> we review Hildreth's algorithm for computing the least squares regression subject to inequality constraints and subsequent generalizations, notably Dykstra's. We provide a geometric proof of convergence and a modification to the algorithm which improves computation speed and provides some robustness w.r.t. rounding error.</FONT></P> <P ALIGN=CENTER><FONT SIZE=4><A HREF="demand.pdf">On the Nonconvexity of the Set of Utility-based Demand Functions(with Paul Ruud)</A></FONT><FONT SIZE=4> examines a fundamental question of economic theory: when will a given collection of economics data be consistent with a given theory. For demand analysis, this problem is elegantly solved and elaborated in Afriat (S. Afriat, "On a System of Inequalities in Demand Analysis: An Extension of the Classical Method," 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 query asks what is the ''best'' estimate of economic behavior satisfying some theory with respect to a given collection of observations. This estimation problem is customarily addressed through regression analysis but an alternative procedure involving nonparametric analysis has recently experienced renewed interest. This technique, originates with Hildreth (C. Hildreth, "Point Estimates of Ordinates of Concave Functions," Journal of the American Statistical Association, 49 ,1954, 598-619) and is described in Varian (H. Varian, "Nonparametric Analysis of Optimizing Behavior with Measurement Error, Journal of Econometrics, 30, 1985, 445-458) and Goldman and Ruud ("Nonparametric Multivariate Regression Subject to Constraint," Working Paper No. 93-213, Department of Economics, University of California, revised 1995). We wish to address this question of estimating an individual demand function without imposing any restrictions as to functional form except those directly implied by revealed preference. The problem will be described by the attempt to identify a least squares solution to the distance between the actual observations and those obtained from a demand function derivable from utility maximization. In order for a unique solution to exist to this problem, the allowable set of demand functions in general must be closed and convex. In the note below, we will demonstrate that the set of utility based demand functions fails to be convex and that, consequently, unique estimation is problematic.</FONT></P> <P ALIGN=CENTER><FONT SIZE=4>II. The Economics of the SIS Model of Infectious Disease</FONT></P> <P ALIGN=CENTER><FONT SIZE=4>It has long been known that a person suffering from an infectious disease poses a threat to others. In the language of economics, infectious disease involves an externality. Susceptible people who come into contact with, or in some cases are merely in the vicinity of an infectious individual may involuntarily contract the disease. If the costs of the disease are large enough and if the option existed, some of the susceptible individuals might be willing to pay the sick to quarantine themselves, seek medical treatment more promptly, or take precautions to prevent the infection in the first place. This would decrease the chance of the susceptible contracting the disease. However, there are no markets for trading personal rights to be protected from exposure to the many people in the general population who may have an infectious disease. Therefore the risk of exposure is said to be external to the market forces that could conceivably be used to control the consequences of exposure to these risks. There is no obvious reason to believe that the decentralized decisions made by individuals will provide an economically optimal level of protection against infectious disease for a society. Before any of the biological mechanisms of contagion were understood, this aspect of infectious disease was used to justify the exercise of social control of individuals suffering from infectious diseases such as bubonic plague, smallpox, tuberculosis, and leprosy. Therefore even though many of the specific disease control measures proposed throughout history have been controversial, only the most extreme advocates of a libertarian social order have advocated the complete abandonment of public health programs. The analysis here focuses on the interaction between the epidemiological forces driving the spread of the disease, social control programs, and decentralized individual decision making regarding treatment and prevention. If individual and social control efforts have a significant impact on the level of disease, then the probability of infection will change over time. Assuming that the individuals in society are rational agents, they will take account of these changes and will modify their behavior accordingly. The question is ''what will be the ultimate effect this interaction on the course of the disease, and the desirability of various public health programs?'' However, there are currently no analyses which incorporate both the epidemiological content of infectious disease models and the behavior of fully rational agents. The approach of biological and medical scientists uses sophisticated epidemiological models, but they typically minimize the role of rational individual behavior. Economists' models of individual behavior are more sophisticated in this regard, but the epidemiological analysis is incomplete. This paper reports the results of research that attempts to lay the foundation for a tractable analysis that includes both explicit modeling of the individuals' decisions and a complete evaluation of the resulting epidemiological effects. The approach taken here aims to include both the explicit analysis of the interaction of the decision making of rational agents and the epidemiology of the disease that will also be simple enough to give some intuitive insight into the costs and benefits of alternative policies. The specific disease model analyzed here has been the subject of previous work, but the analysis is extended in significant ways here. Sanders (J. L. Sanders, "Quantitative Guidelines for Communicable Disease Control Programs'" Biometrics 27, 1971, 833-893) and Sethi (S. Sethi, "Quantitative Guidelines for Communicable Disease Control Programs: A Complete Synthesis'" Biometrics 30, 1974, 681-691) look at the socially optimal program under the assumption of linear costs of medical treatment. The analysis reported here extends the analysis to include a variety of general cost functions, and includes a complete analysis of the decentralized individually rational solution as well as the socially optimal one.</FONT></P> <P ALIGN=CENTER><FONT SIZE=4>The analysis in </FONT><FONT SIZE=4><A HREF="light1.ps">The SIS Model of Infectious Disease with Treatment (with James Lightwood)</A></FONT><FONT SIZE=4> examines the steady state solutions to rational treatment patterns of SIS diseases. Individual behavior is shown to lead to the possibility of significant undertreatment through the presence of unrewarded external benefits. The main conclusion of the analysis notes that the individually rational and socially optimal level of disease will usually differ, with the socially optimal level of disease being no larger 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 the SIS Model of Disease with Treatment (with James Lightwood)</A></FONT><FONT SIZE=4> we consider the intertemporal social optimization problem of minimizing the present value of the costs incurred from both disease and treatment Our analysis allows for a robust collection of treatment cost functions and so extends the previous analysis by Sanders who examines only the case of constant marginal treatment cost. Though this extension of the analysis is substantially complicated by the resulting failure of concavity , we are able to characterize both the long run equilibria and the adjustment paths. Sanders results generalize is the following manner: The "bang-bang" treatment pattern discerned by Sanders where, below some level of infection, the entire population of infecteds is treated while, above that level, treatment is completely discontinued is here replaced by a montonically decreasing level of treatment with respect to the level of disease incidence. The socially optimal program is then compared to individually rational behavior and the inefficiencies in private behavior from the infection externality are shown to cause potentially large increases in the equilibrium rate of infection. The negative monotonic relationship (described above) is shown to hold in both the individual and social cases and is a direct consequence of the increased likelihood of reinfection at higher levels of disease incidence which renders the benefits less worthwhile.</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 Pareto Efficiency</A></FONT><FONT SIZE=4> generalizes the corner efficiency conditions of the Edgeworth Box to consider trades among multiple agents in many goods. The familiar inequality conditions on the MRS's are replaced by ones on "chained MRS's" over possible cyclic trades. The set of Pareto improving trades can then be characterized as a linear space spanned by a relative low dimensional set of cyclic trades. Thus, an equilibrium w.r.t. such a basis, implies efficiency. This paper extends Goldman and Starr, ''Pairwise, t-Wise and Pareto Optimalities,'' Econometrica, 50, 1982, 593-606. In general a symmetry is shown to exist between the role played by markets (here characterized as the opportunity to exchange one good for another) and media of exchange (taken as a specific commodity which may be used to exchange for a wide variety of others). The analysis is relevant to a wide variety of applied problems in which limitations are placed on the allowable trades between agents. For example, there may be relatively free trade within subsets of agents but only limited trades between those subsets as in the case of trading blocks. Or, licensing arrangements may permit only some agents to engage 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>Office Hours</FONT></B><FONT SIZE=5> Thursday 11:00 A.M. - 12:00 P.M., 509 Evans Hall</FONT></P> <P ALIGN=CENTER><B><FONT SIZE=5>U.S. mail may be sent to:</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>