We study the small sample properties of the simultaneous equation estimators by a Monte Carlo approach. The four methods of estimation considered are: least squares, two-stage least squares, unbiased and minimumsecond-moment. The last of these four methods possesses the smallest secondorder sampling moments about the true parameter value in a majority of cases, while two-stage least squares shows the smallest bias in all cases. It is also founld that the usual asymptotic standard errors of two-stage least squares give a rather satisfactory picture of the variability of the estimates about the true value. This is not true for the least squares method in all cases considered. Instead, it seems that the classical least squares standard errors measure the variability of the estimates about the biased expectation, not about the true value. In some cases this makes a very large difference. IN A RECENT article Wagner [4] examined certain small-sample properties of limited-information maximum-likelihood, least squares, and instrumentalvariables estimates for two models by a Monte Carlo approach. Although these models are very simple-which is natural enough for a sampling experiment-it seems appropriate for a variety of reasons to consider them somewhat further. First, there are now several alternative estimation procedures available, and it is worth-while to analyse these too. Secondly, by using Wagner's models we can disregard certain methods of estimation for the simple reason that they were already considered by him. Thirdly, it appears that the two equations of both models are in a certain sense of extreme types, so that we may hope that a Monte Carlo approach will shed some light on the particular problems raised by such extremes. Wagner considered only one equation in each model, and one which is over identified. We shall consider also the second equation, which is just-identified. Just-identification implies that the two-stage least squares estimator is identical with the limited information maximum likelihood estimator. Hence we may disregard the latter estimation procedure, the limited

Richard A. Musgrave, Higher Education and the Federal Budget, The Review of Economics and Statistics, Vol. 42, No. 3, Part 2. Higher Education in the United States: The Economic Problems (Aug., 1960), pp. 96-101

accounting is based upon evaluation of the real intersectoral flows of goods and services, far as possible, at market prices, market prices meaning either the prices received by the local seller or the prices paid by the local purchaser.' Apart from other exceptions which are not of immediate interest here, this principle seems to have been abandoned in the case of imports and exports. Apparently in order to preserve consistency with the balance of payments, imports are generally evaluated c.i.f entrance port, and exports f.o.b. leaving port. Any indirect taxes and subsidies incident on imports and exports are recorded, together with indirect taxes and subsidies on domestic flows, as flows between gross domestic product and the governmental accounts.2 This treatment seems to make the national accounts less useful for purposes of dynamic analysis, in the sense of examining the buyers' choice between imports and domestic products, and local producers' choice between domestic and export markets: the purchaser of imports compares their local market prices with the prices of domestic products, and the potential exporter takes into account any taxes and subsidies on exports when deciding what part of his output to export.3 If this treatment seems unsatisfactory for the accounts of any country, this is a fortiori the case for countries with multiple exchange rates. Multiple rates are frequently not explicit but are actually effected by differential taxation or subsidization. But even in those cases where they are made explicit the deviations from the basic rate can be conceived as indirect taxes or subsidies. The treatment of multiple exchange rates in national accounts seems to have been dealt with only from the point of view of how to arrive at constant price estimates.4 But when the accounts are reduced to base-year prices they disappear to the degree that their rates deviate from those of the base year. It follows that for countries with multiple exchange rates, national accounts at current prices are more revealing than at constant prices. Differential exchange rates are established for particular commodities, or groups of commodities, whereas national accounts are built up from sectoral transactions. It is, therefore, necessary to distinguish purchases of imported goods and services within the purchases of each sector, and to compute the weighted average effective exchange rate for the import component of each sector. In the simplified examples shown below the sectors are identical with the three final-product categories of the gross product account: consumption, gross domestic investment, and exports. Thus if intermediate sectors are not represented in the system, the import components must comprise, besides the direct purchases of each sector from abroad, also indirect imports * This article was completed in March 959, so that it does not contain references to papers by William I. Abraham of the United Nations and Graeme S. Dorrance of the International Monetary Fund, which were issued as drafts subsequently and apparently have not been published so far. I would like to acknowledge gratefully valuable comments by Dr. S. J. Prais, now with the International Monetary Fund, and my colleague, Susanne Freund. 1 United Nations, System of Accounts and Supporting Tables (New York, 953), 8. 2Ibid., i8ff. As far as we know the only exception is the United Kingdom Blue Book on Income and Expenditure, issued annually by the Central Statistical Office. See, for example, in the I956 issue, page 9, Table I2. In this document imports include taxes levied on them; and gross product, national and domestic, excludes these taxes. 'A strong case for the inclusion of import duties in import values was made by J. L. Nicholson, National Income at Factor Cost or Market Prices? Economic Journal, LXV (June 1955), 2I6 f. The discussion between Nicholson and Burton (which concerned the consistency of the British official series of GDP at I948 market prices and factor cost with the series at current prices), as well as Nicholson's later discussion with R. L. Sammons, seems to have left unshaken Nicholson's basic argument in regard to the evaluation of imports and exports as affecting the analytical value of national accounts. The statistical side of these disputes is of no interest in our context. Cf. H. Burton, Expenditure Taxes, Imports and Gross Domestic Product at Market Prices, Economlic Journal, LXVII (December 1957), 644-54; J. L. Nicholson, Duties and the Gross Domestic Product at Market Prices, ibid., LXVIII (June I958), 39396; H. Burton, Duties and the Gross Domestic Product at Market Prices: Rejoinder, ibid., LXVIII (September 1958), 585-88; R. L. Sammons, A Note on the Treatment of Import Duties and the Gross Product, ibid., LXVIX (June I959), 384-87, and Nicholson's reply, ibid., 388-go. 'See United Nations, Economic Survey of Latin America, I95I-I952 (New York, I954), 33-35.

In September I958, the Subcommittee on Stabilization of the Joint Committeeof the U.S. Congress distributed an Economic Policy Questionnaire among some I500 college and university economists. The replies on the 65 questionnaires which were returned have been tabulated and appear in a report which has recently become available. It is the purpose of this note to discuss some of the significant aspects of the questionnaire.

The parting of the ways between causal chain (recursive) and interdependent (nonrecursive) systems is reviewed from the point of view of explanatory relations specified in terms of conditional expectations. On the customary assumptions, a causal chain system is designed so that its relations both in the original form and in the reduced form can be specified in terms of conditional expectations, whereas the relations of interdependent systems allow such specification only in the reduced form. A third type of model is discussed, called conditional causal chains, which formally is similar to interdependent systems, with the important difference that the behavioural relations of the original system are specified in terms of conditional expectations.