Measuring information in the market: an application to physician services.

• Author: Gaynor, Martin

1. Introduction

   Background

   Ever since Stigler's |47~ seminal piece on the economics of information, there has been a great deal of research investigating equilibrium in markets with imperfect information. While most of this research has been concerned with theoretically establishing the conditions under which there exists a distribution of prices in equilibrium, the field now contains a small, but growing, body of empirical research.

   This work has followed the suggestion of Stigler and utilized the dispersion of prices (usually the variance) as a measure of incomplete information about price, such as Stigler |47~, Stigler and Kindahl |49~, Pratt, Wise and Zeckhauser |44~, Carlson and Pescatrice |12~, Marvel |34~, Mathewson |35~, Cox, DeSerpa and Canby |13~, Dahlby and West |14~, Van Hoomissen |51~, and Lach and Tsiddon |29~. There are two disadvantages to using the variance (or another measure of dispersion, such as the range) of prices as a measure of incomplete information about price. The first disadvantage, recognized by Stigler and others, is that price can vary for many reasons other than incomplete information. Thus dispersion is not a pure measure of incomplete information about prices. The second disadvantage, which has not been commonly recognized in the empirical literature, is that price dispersion encompasses incomplete information both on the part of buyers and sellers as indicated by Rothschild |45~, Axell |4~, Butters |9~, and Telser |50~, and hence fails to distinguish between these two components.

   In this paper we propose a method for measuring incomplete information about price which builds on Stigler's original suggestion to use dispersion as a measure of incomplete information, but which avoids the pitfalls mentioned above. We apply our approach to the physicians' services market, a market in which incomplete information is widely cited as a source of market failure. After we adjust for physician characteristics and other factors which can influence price we measure incomplete buyer information as the difference between the seller's (adjusted) reservation price (which is the lowest price at which the seller the product) and the (adjusted) price which the consumers pays. This is the money cost to the consumer of not knowing where to obtain the lowest price. Analogously, incomplete seller information is the difference between the (adjusted) buyer's reservation price (i.e., the highest price the buyer will pay) and the (adjusted) price the seller accepts for the product. This is the seller's cost of incomplete information about buyer reservation prices. Thus, these measures provide money metrics for the amount of buyer and seller information in a market. Obviously in a full information competitive market when a unique price evolves both measures are zero.

   The estimation entails a generalized frontier estimation technique developed by Polachek and Yoon |43~ to separate observed price dispersion into purely random variation, variation due to incomplete buyer information, and variation due to incomplete seller information.(1) The application is to the physicians' services market. Measures of incomplete buyer and seller information are computed for eight different physician services(2) and by the proportion of patients a physician receives through referrals as well as by patient income. Hypotheses concerning expected differences in information across these groups correspond to well established hypotheses concerning differences in the costs and benefits of search.

   The estimation results are strikingly consistent with the hypotheses regarding search. Incomplete patient information is approximately 50 percent greater than incompletely physician information. Incomplete patient information is larger than incomplete physician information for smaller ticket items, less frequently purchased items, more heavily insured items, and treatments associated with severe illness. Measured incomplete patient information is also higher relative to incomplete physician information both for high referral practices and those in high income areas.

   In the rest of the paper we provide institutional detail on the market for physician services, describe the model and econometrics (sections II and III, respectively), generate hypotheses (section IV), discuss the data sources and the variables employed (section V) and present the empirical results (section VI). Section VII contains a summary and conclusions.

   The Market For Physician Services

   The health care market in general, but especially the physicians' services market, is often viewed as one in which market forces fail to work effectively, as Arrow |3~, Newhouse |36~, and Pauly |38; 41~ have indicated. Incomplete consumer price information (i.e., lack of consumer information about price) has been viewed as an important reason for this market failure |11; 18~.(3)

   If consumer incomplete information is substantial, policies failing to address this problem could prove ineffective in strengthening the role of market forces |33; 52~.

   Despite universal agreement that information deficiencies are important causes of failure in the physician services market, there are no direct estimates of the extent of consumer incomplete information in this market. This is not surprising, given that information is difficult to observe and quantify. Pauly |38; 41~ points out that, while consumer information is perhaps the most important feature of the health services marketplace, nearly absolutely incomplete consumer information has been accepted as fact with very little empirical evidence.

   A considerable number of studies have documented the large dispersion in physician fees.(4) This is commonly interpreted as indicative of the extensive lack of information in this market, a la Stigler's suggestion, despite the fact that there are product differences among physicians and these product differences are reflected in price. As Phelps |42, 193-95~ contends, although quality and price are undoubtedly connected, "The dispersion of prices seems far too large to correspond to quality differences." Some evidence on this can be gleaned from data on the price distributions from several cities. The mean price for a standard office visit in Dayton, Ohio differed by only $1.50 between general practitioners and internists, while within each specialty the highest price was more than twice as high as the lowest price |42~. Presumably internists are perceived as being of higher quality. It is hard to believe that quality alone is responsible for such wide specialty price variations, when the variation across these specialties is so small. Newhouse and Sloan |37~ report coefficients of variation for selected physician fees in New York and Chicago. The coefficient of variation for all these services is higher by an order of magnitude than for the asking price of a Chevrolet in Chicago or for bids on federal contracts for delivery of anthracite coal. As both Phelps and Newhouse and Sloan indicate, it is difficult to believe that quality differences can account for these wide variations in price, after controlling for specialty, market area, and service performed.

   Another body of empirical work examines the link between information and the price level.(5) These studies attribute higher prices to incomplete consumer information, using advertising or other variables as proxies for information. As Pauly |38; 41~ indicates, incomplete consumer information alone is not sufficient to reduce consumer welfare relative to the full information equilibrium. An informational asymmetry favoring the seller must also be present for incomplete information to present a problem. This study devises a way to measure incomplete price information as well as disentangle incomplete buyer and seller information.

2. The Model

   The approach taken here is based on results from the extensive literature on search theory. Price dispersion is possible in an otherwise competitive market if informational imperfections are present. For instance, buyers are motivated to purchase the product for the lowest possible price. They know the distribution of prices in the market, but not the price charged by any given seller. Buyers choose an optimal amount of search based on a weighing of the expected savings from search versus its associated costs. Let a buyer's reservation price, i.e., the highest price a patient will pay, be a function of factors which affect the patient's search cost and benefits such as the extent of insurance coverage, the patient's education and income, the severity of the patient's illness, and the frequency with which the physician's services are needed. For transaction i this reservation price (|P.sub.b~) can be expressed as

   |P.sub.bi~ = |X.sub.bi~||Beta~.sub.b~ + |u.sub.bi,~ (1)

   where |X.sub.b~ are the exogenous factors just noted, |u.sub.b~ is a random error term and subscript i denotes transaction i.

   Similarly, sellers seek to sell at the highest price possible. For physicians the reservation price is a function of factors that affect the lowest price a physician can charge, e.g., input prices, technology, age of equipment, and factors affecting efficiency. For transaction i this reservation price (|P.sub.s~) is

   |P.sub.si~ = |X.sub.si~||Beta~.sub.s~ + |u.sub.si~, (2)

   where |X.sub.s~ are the exogenous factors affecting the physician's reservation price, |u.sub.s~ is a random error term and i denotes transaction i.

   In a market with imperfect information buyers on average pay more than the seller's reservation price and sellers will sell at a price lower than some consumers are willing to pay.(6) For a given transaction we define the gap between the seller's reservation price and the price the consumer actually pays as incomplete consumer information,

   |W.sub.i~ |approximately equal to~ |P.sub.ci~ - |P.sub.si~, (3)

   where |W.sub.i~ is consumer ignorance, |P.sub.ci~ is the price paid by the consumer, and |P.sub.si~ is...