Knowledge that Transforms

THIS paper was undertaken for two purposes: (1) to uncover additional quantitative information about the structure of price behavior and (2) to see the extent to which such information could be enlarged as a result of studying price data arrayed by stage-ofprocess. Wholesale price indexes of the Bureau of Labor Statistics (BLS) have long been arranged this way, among others, and components of the Consumer Price Index can be developed that relate to these wholesale indexes. The study of price indexes by stage-of-process can be viewed as an approximation to the type of study that could be conducted in an inputoutput framework, if time-series data were available for I-0 industries. The research consisted of testing theories of price behavior whose determinants could be measured for sectors relevant to the explanation of price behavior by stage-of-process (these are shown in figure 1). This led to the selection of a set of price equations for consumer and producers' goods and their intermediate inputs. Additional equations were estimated for service prices and wages so that a nearly complete price sub-model could be developed. This model was then used to explore the structure of price determination. The stage-of-process approach differs from other studies of price behavior, most of which have sought to explain the deflator for private GNP and its components or the wholesale price index (WPI) for the manufacturing sector and its major subdivisions durable and nondurable goods. Such studies have not used the most relevant price series. The series that should be used are those reflecting the prices at which firms in a sector sell their output to customers outside of the sector. These prices are reflected more closely at high levels of aggregation by using stage-of-processing indexes rather than any other components of the WPI. In a recent review of empirical research on price behavior, Nordhaus (1972) concludes that most specifications and interpretations of price models have proceeded without the benefit of formal theory. While the testing of hypotheses is the focus of the present research, the effort encounters the common difficulties in so doing the lack of precise specification of any but the most simplistic models, poor or missing data, and estimation problems. To preview a conclusion, price behavior is difficult to explain and no one theory can be shown to be superior to all others. At least for the present, it appears that forecasting and policy formulation based on the structure of price determination must combine theory with professional judgments about which reasonable persons may disagree. Given these circumstances, the results of exploring price data by stage-of-process yields some interesting and potentially useful results.

T ESTED with regional data for the United States, the neoclassical growth model has yielded inconsistent results. Borts and Stein (1964, chapter 3) employed a simple growth model relating interregional factor movements to factor price differentials, but found little evidence of responsiveness. In a recent paper Smith (1973) found such a model consistent with the long-run factor mobility experience of states. Since a similar model was employed in both studies, the contrasting results may be ascribed to the use of inappropriate data in the test of the model of Borts and Stein, and/or inadequate model specification. They tested their model on the nonagricultural sector of each state, while Smith's model is tested on aggregate state data. Use of data on the nonagricultural sector of each state embodied the implicit assumption that capital and labor move only between states from one nonagricultural sector to another, and ignored the possibility of intersectoral factor movements. Smith avoided this potential problem by aggregating each state's output to a single sector. Thus, only interstate factor movements were relevant. In this paper, both intersectoral (within states) and interstate factor movements are considered. Factor movements affect the growth rate of a sector's capital-labor ratio, which determines the growth rate of the wage level.

The logarithmic discrepancy of the factor reversal test, to be written DA for (2) and DB for (3), is of the fifth order of smallness (05), but the leading 05 term of DB is closer to zero than that of DA, which is the reason why Sato prefers (3). If the expenditure shares do not change very much, xiyi being close to zero for each i, the discrepancy D is very close to zero for most reasonable choices of f ( ). This applies to the vast majority of annual time series. Tornqvist's choice of the arithmetic average of x and y is then adequate; it has the additional advantage that the sum over i of f(xi, yi) equals 1, which simplifies the index formulas. My own interest in pursuing this topic further was stimulated by C. M. Walsh's proposal to specify f ( ) as the geometric mean of x and y. It can be shown that the leading 03 term of the discrepancy (1) for the geometric mean is equal to minus onehalf of the leading 03 term of that of the arithmetic mean. My immediate reaction was to take the weighted arithmetic mean, with weights equal to 2/3 and 1/3, of the geometric mean and the arithmetic mean so as to eliminate the leading 03 term. This is precisely Sato's choice (3). But I rejected this choice, because D is unbounded under the specification (3) for 0 -O x, y 1. Suppose that x 0, y > 0, so that fB(X, y) 1/6(y) > 0. If this applies to some subscript i, the discrepancy (1) becomes infinitely large. Sato

The insurance industry is populated by some 2867 insurance companies each of which is the object of numerous rules promulgated and enforced by the various State Insurance Commissions.1 Some of the more important rules have to do with new company formations and mergers between existing insurers. If, as seems reasonable, the administration of these rules rests in part on the Commissioner's perceptions concerning the nature and extent of cost economies underlying insurer operations, the recent papers by Hammond, Melander and Shilling (H-M-S) (1971) and Houston and Simon (1970) provide an interesting contrast and deserve more than the usual notation in the files of those concerned with the forces shaping the structure of financial and nonfinancial markets in the American economy. An important concern of these studies has been the identification of insurer size beyond which substantial cost savings cease to accompany increases in insurance output.2 In this regard, the H-M-S study suggests that significant cost savings are realizedby stock property-liability companies up to a size of $300 to $600 million as measured by annual net premium writings.3 This contrasts sharply with the H-S study which finds significant cost savings cease to accrue to life insurers once annual premiums exceed $100 million.4 As there is nothing in the formal organization of life companies vis-a-vis property-liability companies that can account for these differing estimates, and as there is little logic to support the belief that substantial cost savings are dependent on the size of property-liability insurers,5 further research into the behavior of property-liability costs seems appropriate. Accordingly, this paper provides new estimates of the extent of cost economies in the property-liability industry based on a new sample and regression model. The rationale underlying the regression model is set forward in the first section of the paper; the regression results in the second section; and the third section of the paper concludes with summary observations on the results.

Robert Edelstein, The Determinants of Value in the Philadelphia Housing Market: A Case Study of the Main Line 1967-1969, The Review of Economics and Statistics, Vol. 56, No. 3 (Aug., 1974), pp. 319-328

HE method proposed by Almon (1965) has been extensively used in the estimation of distributed lag models. It may be regarded as the least squares method under the linear constraint that the regression coefficients lie on a polynomial of a chosen order. Therefore, the loss or inefficiency of Almon's method (defined as some reasonable function of the mean square error matrix) could be smaller than that of the unconstrained least squares method. Then, an interesting question arises: for what order of polynomial is the loss minimized in a given distributed lag model? The answer depends upon several variables: the true values of the regression coefficients, the number of lags assumed in the model, the sample size, the ratio of the variance of the dependent variable to that of the error term, and the degree of the autocorrelation of the independent variable. In this paper we will evaluate numerically how the optimal order of polynomial is determined by these variables. Because the answer depends on so many variables, it is extremely important to design the study to produce meaningful conclusions. For this purpose we adopt one important simplifying assumption -that the independent variable follows a first-order autoregressive process with a varying correlation coefficient. Such a process is a good approximation of the processes of many economic variables. Given this simplification, we obtain definitive conclusions by judiciously defining the loss function so it depends simply and nicely on the parameters that we allow to change. As a result we can calculate the optimal order of polynomial for a given distributed lag model at a minimal computational cost. The essential part of our definition of the loss function is the trace of the product of the mean square error matrix and the autocovariance matrix of the independent variable. In section II we will offer rationales for this definition, as we believe that this definition has intrinsic merit as well as the advantage of simplifying our computation. Section II defines the model, defines the loss function for Almon's method, and discusses the rationale for and mathematical properties of the loss function. Section III presents and'analyzes the results of the numerical evaluation of the loss function for twelve models. Conclusions are presented in section IV.