EMPIRICAL research in economics has seen the development in recent years of large simultaneous equation econometric models -large both in terms of detail and degree of disaggregation but also in their demands upon a limited of data. In the main these models have been models of macro-economic activity estimated from annual or quarterly data in the postwar period. Statistical methods for estimating simultaneous equation models were first developed by the researchers at Cowles Commission [8]. In recent years, the sheer size of such empirical models has brought a new problem to the fore, as the estimation methods previously developed cannot be used without modification. Most of those estimators -those of the kclass and three-stage-least-squares involve a first of regression or estimation using the predetermined variables of the model as regressors.1 But frequently in large models the is smaller than the number of predetermined variables, so that a meaningful first-stage regression is not possible.2 This is a sample problem of a different sort instead of needing more observations in order that the distribution of the estimates will be satisfactorily approximated by their asymptotic distributions, the is small relative to the size of the large model, to the extent that the standard simultaneous equation estimators either do not exist or are identical to ordinary least squares.3 A variety of solutions have been proposed to cope with the large-model problem, two of which are examined in detail in this paper. Each can be viewed as a modification of twostage-least-squares: 1) 2SPC (Two Stage Principal Components), originally proposed by Kloek and Mennes [11], in which a limited number of principal components of the predetermined variables are used in the first stage. 2) SOIV (Structurally Ordered Instrumental Variables), proposed by Fisher [5, 6], in which a limited number of predetermined variables are selected for the first stage by detailed use of the structure of the model. A complete assessment of the properties of these estimators in a large econometric model requires the knowledge of their small-sample distributions. These are in general unknown, although some progress has recently been made for small models by Amemiya [1], Basmann [2], Kadane [9], Mariano [12], Sawa [15], and Takeuchi [17]. Some information might be obtained by Monte Carlo techniques, except that the computational cost of systematically exploring the parameter space of a large model would be prohibitive. Still, a feasible project would be to employ a miniature model with a very few equations, but having more predetermined variables than observations. It is not clear, however, that the distributions would * This work was supported in part by National Science Foundation Grant GS-2635 and by the Brookings Institution. The initial research was undertaken during the tenure of fellowships from the Danforth Foundation and the National Science Foundation. Computations were done at the Massachusetts Institute of Technology and Stanford University computation centers. I am happy to acknowledge the numerous helpful suggestions of T. Amemiya, T. W. Anderson, P. J. Dhrymes, E. Kuh, F. M. Fisher and a referee. Much of the data was made available by G. Fromm. 1 The limited-information-maximum-likelihood method requires extraction of a characteristic root from a matrix of moments of the predetermined variables; the method can be interpreted as a first-stage regression of a synthetic endogenous variable on the predetermined variables. 2 Full information maximum likelihood estimators fail to exist when the number of parameters to be estimated in the model exceeds the size, another problem which occurs in large models. Because of computational complexity, FIML has not been a feasible estimator for models of even moderate size. 'In other cases the problem may occur in a less acute form -there may be more observations than predetermined variables, but the excess may be small, and in some sense better estimates may be obtained by using fewer variables in the first stage.

Although payment for nearly all other goods and services, including toll (long distance) telephone calls, increases with greater consumption, nearly 90 percent of the residential telephone subscribers and more than half the business subscribers in the United States now pay a flat monthly rate for local calls (see Larry Garfinkel). Recently, however, the telephone companies and regulatory commissions have been moving cautiously toward imposing usage charges for local telephone calls. There is renewed interest in what is currently termed pricingt (USP). It is due to the combined forces of inflation, increased local usage, and competition from independent firms that sell telephone terminal equipment and supply private toll lines to business customers. Under USP, the of such services as telephone installation, directory assistance, and minutes of calling is based on incremental rather than average costs. Since World War II, technological advances have benefited long distance far more than local telephone calling. Development in microwave communications, coaxial cable, satellites, and waveguides have dramatically lowered the costs of long distance transmission. In contrast, the costs of local service have moved upward since the late 1960's at a rate not far below the general price index (see AT&T, 1975). Faced with a continuing stream of requests for local telephone rate increases, state regulatory commissions are finding the concept of tying prices to usage increasingly attractive. AT&T and some of the independent telephone carriers are beginning to test USP plans in several cities. With flat rate tariffs, increases in local calling add to carrier costs but not to their revenues. The local calling rate per subscriber has increased by an average of 2 percent for the past seven years. AT&T's chairman has stated, We are moving more and more in the direction of usage-sensitive pricing (see Washington Star News, p. A12), and according to newspaper accounts of AT&T management documents, the Bell System plans to phase out flat rate telephone service and begin charging for each local call in major metropolitan areas in 1978-80 (see Seattle PostIntelligencer, pp. 1, 10). Still, regulatory commissions, consumer groups, and the carriers themselves remain cautious about requiring usage-sensitive tariffs for all subscribers. The prospective gains from prices more closely related to costs are at least partially offset by the added costs of metering equipment and billing. Most telephone subscribers prefer flat rates, according to Bell System marketing surveys (see Garfinkel, p. 28). And it is by no means clear which groups of subscribers will be helped and which harmed by such revisions in local tariff structures. Will the poor end up paying more because they use their phones more? Should different prices be charged for calls at different times of day? On what bases should the monthly and per call rates be determined? The purpose of this paper is to sort out some of the questions of economic efficiency and equity that arise when changes are considered in the methods of local telephone services. In Section I, I construct a * Department of economics, The Rand Corporation, and the International Institute of Management, Berlin. This study was supported under a grant from the John and Mary R.. Markle Foundation. I am indebted to Walter S. Baer for numerous contributions to this paper, to S. C. Littlechild and Patricia Munch, and to the managing editor and a referee of this Review for critical and constructive review of a draft. I have benefited as well from the comments and suggestions of James H. Alleman, Stanley M. Besen, William S. Comanor, John M. Drew, Leland L. Johnson, John A. Kay, Edward D. Lowry, Carl Pavarini, John Rolph, Ralph Turvey, and Chris Witze. Bryant Mori assisted with the computer programming. See my 1976 paper for a more extensive version of this paper, which also discusses optimal flat rate and optimal peak load tariffs.

This paper assesses some economic consequences of financing national health insurance by mandating that employers provide insurance for their employees and dependents. Effects in 1975 are simulated using data from a 1970 health care survey. The findings are as follows: (1) Employer premiums would rise between 5 and 21 billion for plans under congressional consideration. (2) Without offsetting subsidies, these premium increases will cause a transitory increase in unemployment of 0.4-1.4 percentage points. (3) As employer premium payments are shifted to employees, taxable income will fall, leading to additional tax expenditures of 1.3-5.9 billion. (4) Tax expenditure on existing subsidies to health insurance is $6.4 billion.

Price elasticities are estimated for telephone calls and minutes of conversation using data from a experiment in central Illinois conducted by General Telephone and Electronics. The experiment charges separately for calls and for minutes. Using a model that is consistent with the theory of telephone demand, the authors estimate the effects of both prices. The nonlinear generalized least squares estimates of the elasticities are fairly small-about 0.1 or less in absolute value at experimental price levels-but they are estimated with high precision. The report briefly considers the application of these results to predict the effects of introducing measured service telephone rates in other cities. RESIDENTIAL TELEPHONE SUBSCRIBERS in the United States typically pay a flat monthly rate for with no extra charge for calls within the area. The alternative of explicitly charging for calls, commonly referred to as usage-sensitive pricing or local measured service, is of increasing interest to U.S. telephone companies and regulatory commissions (Cosgrove and Linhart [5]; Garfinkel and Linhart [8]; Baude, ed. [2]).3 Charging for calls that are now free clearly holds promise of increasing economic efficiency (Alleman [1]; Mitch

I. Nature and significance of the problem, 227. — II. The audience-revenue relation, 231. — III. The determinants of station audience: the form of the model, 232. — IV. The variables, 234. — V. Off-the-air potential audience and the measurement of overlap, 238. — VI. The results and their interpretation, 242. — VII. Effect of CATV duplication on study station audience, 245. — VIII. Conclusions: the economic impact of CATV, 247.

This paper assesses some economic consequences of financing national health insurance by mandating that employers provide insurance for their employees and dependents. Effects in 1975 are simulated using data from a 1970 health care survey. The findings are as follows: (1) Employer premiums would rise between 5 and 21 billion for plans under congressional consideration. (2) Without offsetting subsidies, these premium increases will cause a transitory increase in unemployment of 0.4-1.4 percentage points. (3) As employer premium payments are shifted to employees, taxable income will fall, leading to additional tax expenditures of 1.3-5.9 billion. (4) Tax expenditure on existing subsidies to health insurance is $6.4 billion.

Advances in Routing Technologies and Internet Peering Agreements by Stanley Besen, Paul Milgrom, Bridger Mitchell and Padmanabhan Srinagesh. Published in volume 91, issue 2, pages 292-296 of American Economic Review, May 2001