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.

More specifically, section I develops a model for the analysis of the effect of changes in consumer demand on average educational requirements under rather restrictive assumptions. Some quantitative conclusions, based on income elasticities, input-output coefficients and capital-output ratios in the Israeli economy, are presented. Section II deals with the effect of changes in the composition of consumption on the demand for different levels of education, and their effect, in turn, on wage differentials. The discussion is based on the analysis and calculations of section I.

Less extreme cases, however, are even more worrisome, primarily because the distortions in the solutions are less easy to identify. As shown above, (Nim)1 and (N1m) 2 without distortions differ in this illustration by 20 per cent of their mean value. WYhile it is easy to flag this difference for a steady series like labor force, there are many series, e.g., inventory investment, for which a 20 per cent jump is nothing to cause surprise. Further, if the relevant

The use of iterative algorithms, based on the Gauss-Seidel method or a similar approach, to solve systems of nonlinear simultaneous equations may lead to problematical situations which in theory are not surprising, but in practice are unexpected by the user. In particular, such situations may arise in the solution of econometric models for simulation purposes. One source of the problem lies in the failure of these algorithms, which repeatedly solve single equations according to some sequential ordering,1 to deal with the interaction properties of specific higher-order subsystems of closely related equations. One illustration of such a subsystem is the set of equations which determines unemployment and labor force in the Wharton Econometric Forecasting Model [1].

Franklin M. Fisher, Peter Temin, Regional Specialization and the Supply of Wheat in the United States, 1867-1914: A Reply, The Review of Economics and Statistics, Vol. 53, No. 1 (Feb., 1971), pp. 102-103

A UNIQUE feature of the Kennedy Round of the General Agreement on Tariffs and Trade (GATT) Negotiations (1964-1967) was the use of the technique of reducing tariffs. Under a linear approach each participant agrees to make a uniform across-theboard percentage cut in import duties, subject only to a bare minimum of exceptions and to the condition that the country achieves overall reciprocity. This approach was adopted in an effort both to reduce the time and effort involved in traditional item-by-item negotiations and to achieve a deeper average duty-cut for all participants. In prior negotiations under the GATT, the bargaining technique was essentially bilateral. Request and offer lists were exchanged between all pairs of countries and bargaining then proceeded on a two-by-two basis. In order to make this type of negotiation feasible, the so-called principal supplier rule was followed. A country's offer list to another country covered only those items for which the other country was the principal or at least, a very important import supplier.1 This procedure minimized the problem of conducting simultaneous negotiations on the same item by different country teams. At times during the negotiations, however, information concerning concessions tentatively agreed upon in the independent bilateral negotiations was made available to all pair-wise teams so that each might evaluate the indirect effects of the other negotiations on its bilateral balance of concessions. Finally, when each pair of countries had reached a mutually satisfactory balance of concessions, the list of offers by a country to each other country was combined into a single tariff reduction list that applied to all countries. Just what constituted a satisfactory balance of concessions or reciprocity was never openly defined, but it came to mean that a country would achieve an approximately equal increase in exports from the concessions it obtained as the increase in imports from the concessions it granted.2 The main concern of negotiators was to achieve this reciprocity on the total trade of their country with the rest of the world. However, since the negotiations were conducted mainly on a bilateral basis, the notion of reciprocity also tended to dominate the pair-wise negotiations between countries. As became increasingly apparent through successive GATT negotiating rounds, following the principal supplier rule and imposing a condition of approximate bilateral balance for changes in the volume of trade considerably limited the set of feasible total increases in exports and imports. The early hopes of many Kennedy Round negotiators that most of the difficulties connected with the item-by-item, bilateral negotiating technique would be eliminated by following a linear-cut rule proved to be much too optimistic. Some industrial countries, namely Canada and Australia, as well as all the less developed countries did not accept the linear rule. More disappointing, however, was the reluctance of most major countries to cut agricultural duties on a linear basis and the insistence of the European Economic Community (EEC) on a special rule to handle significant disparities in tariff rates of various countries on the same item.3 Lists of exceptions for certain countries also proved to be larger than was hoped for initially. Once it became apparent that reciprocity could not be achieved by bargaining on a