residual,_griliches - journal of Economic Literature Vol....

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Unformatted text preview: journal of Economic Literature Vol. XXXIV (September 1996), pp. 1324—1330 The Discovery of the Residual: A Historical Note ZVI CRILICHES National Bureau of Economic Research and Harvard University HE CONCEPT or total productivity and the notion. that labor is not the only factor of production, that other fac— tors such as capital and land should also be taken into account in a wealth of the nation calculation or a measure of its ' Productivity, were discussed repeatedly in the literature of the 1930s. Two" major strands of research came together, ulti- mately, in what was to become total factor productivity measurement and growth “accounting”: The first developed out of the national income measurement tradition, based largely on the work of NBEB and what was later to become the- ' .BEAJ The second was influenced byr -l Paul Douglas’s work on production func- ' tions. His work had been largely cross- seetional, but as time series data became available it was an obvious generalization to add trend-like terms to the function and allow it to shift over time.2 This re- 1This tradition and the data bases it developed, together with the development of Keynsian eco- nomics, also contributed to the rise of growth the- ory in the works of Roy Harrod, Evsey Domar, and Robert Sblow. But that is a different sto . 2 Douglas had been criticized earlier or not al- lowing for some kind of trend factor in his estima- tion equation, especially by Horst Mendershausen (1938), a criticism that Ian Tinbergen endorsed in his Econometric textbook, published in Dutch in 1941. Given the increasin availability of time se- ries data and the general a vice of that time to use “de-t‘rended" data, it was not long before trend 1324 search tradition had a more econometric background and did not accept, neces- sarily, the various compromises and as- sumptions embedded in the national in- come accounts. It found a fertile soil in agricultural economics, spurred by the presence and teaching of Tip-trier at Iowa State University (Tintner 1944) and the later work of Earl Heady (see Heady and John Dillon 1961, ch. 1, for an early re- view of this literature). The two tradi— tions came together in the work of Solow (1957), in some of my own early papers (Griliches 1960 and 1963), and especially inDale' Jorgenson and Griliches (1967). But they have also kept drifting apart. 9 The first mention of' what-might be called an output-over-input index that I can find appears in Morris Copeland (1937).3 Once one started thinking about “real” national income and worrying how to deflate it, it was a relatively short step to the idea that the two different sides of these accounts (product receipts and fac- variables began to appear in production function estimation. The first one to do so, as far as I can tell, was Victor Smith in 1940, in his Northwestern Ph.D. dissertation on the roductivity of the steel industry, followed by Ger ard Tintner in a num- ber of papers based on data for U3. agriculture (Tintner 1944 and 1946). 3More thorough research may unearth even earlier references. . VDMW “yum.-.” m... more econometric not accept, neces- npromises and as- in the national in- nd a fertile soil in s, spurred by the of Tintner at Iowa I J _ ner 19445.). and” the dy (see Heady and 1, for an early re— r). The two tradi- the work of Solow own early papers 63), and especially 1 Griliches (1967). :drifting apartgg- f 7 3f what ‘might:_.b,e input index that I ' Morris Copeland ted thinking about and worrying how alatively short step J different sides of t receipts and fac— n production function do so, as far as I can 9, in his Northwestern 'oductivity of the steel :rd Tintner in a num- a for U.S. agriculture h may unearth even tor payments) could be deflated sepa- rately, with their own specific deflators, yielding measures of real product and real input, and an associated measure of economic efficiency.4 A year later the idea was much more fleshed out in Copeland and E. M. Martin (1938) who said: construct an index of the physical volume of wealth used in production each year and weight it by the total property income in the period selected for the determination of weights. This weighted ' plant-hour series might then be added to a correspondingly weighted man-hour series to measure physi- cal input for the economic system. (p. 104) . . . divergence is likely to appear between the movements of a series representing the physical volume of input [and output] and . . . this divergence is a rough measure of changes in the efficiency of our economic system. (p. 132) yin commenting on this paper, Milton I ‘39.“ Friedman, iii-one of his earliest appear- ances on the scene, interprets the authors as saying “that a comparison of the two types of indices .[output and in— put] provides a basis for estimating the degree of technical change” (p. 126).5 4 “Income derived from an area may be deflated , r to show changes in the physical volume of services ‘ '.:-’--:of labor and wealth em loyed by the economic r _. system. . . . the deflated 'stributive shares may be compared with the deflated consumed and saved 7 - income to show changes in the efficien of opera- tion of the economic system” (Cope and 1937, . 31). P 5 Friedman also raised a series of doubts about the empirical feasibility of this approach. After discussing the substitution bias that is implicit in any fixed wei ht index construction, he oes on to say: “Add to [the substitution bias] t e neces- sity of assuming 'coustant tastes,’ if the com ari- son is to be meaningful, and the difficulty 0 ob- tainirzig an adequate measure of the quantity of capit , . . . as well as the lesser difficulties with the other factors of production, and the possibility of actual] emplo 'ng the procedure suggested is . . . Co e and an Martin seems exceedingly smal . The erivation of a measure of ‘real input’ that would provide an ade uate basis for measuring changes in economic ef ‘cien is even more com- plicated and difficult than Elie measurement of ‘real output’; for the former involves the latter and Griliches: The Residual ' 1325 John Hicks, while considering a similar approach to “efficiency” measurement in 1940, added an explicit discussion of in— dex number biases, noting that the prob- lem “is much worse when we allow for increasing returns and imperfect compe- tition” (p. 12.1). He also asked whether taxes should be included in the weights (yes for output indexes, no for input). Actual measurement was initiated by several people, working independently but subject to the same intellectual mi- lieu. Whether they measured it as a shifter of the production function (Tin- bergen 1942; Tintner 1944; D. Gale Johnson 1950; Solow 1957) or as an output-over-total-input index (George Stigler 1947; Glen Barton and Martin Cooper 1948; Jacob Schmookler 1952; other difficulties as well. . . . We can . . . ask the question—to whatextentis the-change in output over somerspecifiedf‘l elriodga-resp-lt-ro 3 Chan e in the quantity of a" isle raiseurce's', ". . . [or the way these resources are employed. [This se ara- tion is to a considerable extent artificial: tedlino— logical change affects not only the way in which resources are em loyed but also the uantity and the character of t e resources themsdlvesj In or- der to answer this question it would be necessary to determine the volume of ‘real output' that would have been produced had techniques re- mained..unchanged.- .A-comparison of this series with the:,actual-Freiil.'output’fthenyptovides a mea- sure of the changel.iri,_.efficiericy’7_,(. Ap;..126—:27). Copeland and Martinres. .onde 1.‘_1The meaSure- ment difficultieshabout w ich‘ Mr.‘ Friedman is concerned do not seem to have deterred others to the same extent. Dr. Kuznets has already provided measures of deflated national income in an output sense. Dr. Kuznets’- measures of ca ital formation necessaril involve measurements 0 the quantities of all kin of capital . . . Moreover, . . . estimates of total man-years of employment have been de- veloped. Thus . . . the two main elements for mea- surements of chan es in social input (except . . . for non-reproducible wealth . . .) are admittedly at hand. . . . It must . . . be conceded that [such] measure- ments . . . are certain to be rough under present conditions. However, those who insist on a high degree of recision had best choose some field of activity otlihr than estimating nafional wealth and income" ( . 134). Remem er, this discussion is taking place in 1937! 1326 Solomon Fabricant 1954; Vernon Ruttan 1954 and 1956; john Kendrick 1955 and 1956; Moses Abramovitz 1956), they did not claim any particular originality for it. They were making illuminating calcula— tions for a concept that was obviously already there. Credit for the earliest explicit calculation clearly belongs to Tinb'ergen, who in a 1942 paper, publish- ed in German, generalizes the Cobb- Douglas production function by adding an exponential trend to it, intended to represent various “technical develop- ments.”6 He computed the average value of this trend component, calling it a measure of “efficiency,” for four coun- tries: Germany, Great Britain, France, and the U.S., using the formula 1.“ = y— 21’311 - 1181:, where yrn, andsk are the av- - erage growthfiiat’es 'of output, labor, and capital respectively and the weights are taken explicitly from Douglas. Note how close this is to Solow who will let these weights change, shifting the index num- ber formula from a fixed-weight geomet- ric to an approximate Divisia form. Nobody seems to have-.heen. aware of Tinbergen’s paper in the US. until much later.7 . 7 ‘- v . w - - The developments 'in the U.S. origi- nated primarily at the NBEB where a program of constructing national income 5 The fact that an occupied Dutchman was pub- lishing in Germany in 1942 caused some comment after the war. This was an example of trying to keep “science” going despite the circumstances. A position that was tenable in 1942 when much of what was hap ening was not yet widely known. 7 Stefan Vsllavanis-Vail (1955) mentions Tinher- gen but, it is obvious from the context, not this paper. Following a suggestion attributed to Arnold Herberger, he uses average factor shares to com- pute a Cobb-Douglas type total input index and a residual which he then uses to estimate the trend coefficient for an aggro ate production function, yielding an estimate of .75 percent per year for the 1869—1953 period. This is essentially equiva- lent to what Tinbergen did, but with weights based on income shares rather than estimated pro- duction function coefficients. Solow does refer- ence Valavanis-Vail, but obvious] neither of them is aware of Tinbergen (1942) at t at point. _ journal of Economic Literature, Vol. XXXIV (September 1996) and “real” output series under the lead- ership of Simon Kuznets was expanded also to include capital series for major sectors of the economy, with contribu- tions by Daniel Creamer, Fabricant, Raymond Goldsmith, Alvin Tostlebe, and others. It seemed reasonably obvious to try and use such capital numbers in a more general productivity calculations The first such published calculation ap- pears in 1947 in Stigler’s book on Trends in Output and Employment where, after working pretty hard on the output and employment data, he presents (on p. 49), off-handedly, what looks like a “back of the envelope” calculation of efficiency, which he says “is usually defined as Out- put/(Input of Labor + Input of Other Resources),” for 12 manufacturing indus- tries. In 1952, Schmookler, who “had been Kuznets’ student at the University of Pennsylvania, published a detailed article on the “Changing Efficiency of the American Economy” in which he constructs an output over total input index with the intent “to describe the pattern and magnitude of technical change.”9 7 The .‘fraw-materials” assembled byrthe NBER were used repeatedly in sub— 8This was clearly foreshadowed in the earlier exchange between Copeland and Friedman quoted above. 9There are two major components in Schmook- ler's dissertation on which this article was based. The primary task of the thesis was the assembly and examination of a consistent series on patent— ing in the U.S., interpreting it as a measure of inventive activity. This art was ublished as Schmookier {1954). It is c ear that e intent was to bring these two parts together, with the patent series “explaining” the rowth in in ut—over-out- put series. In a thir , unpublis ed, chapter Schmookler tries to do just that and gets nothing. It is interesting to note that as the result of this outcome he leit the productivity measurement field and concentrated on the anal sis of patent data, perha s feeling that they are closer to and a more tangi le reflection of the actual processes of invention and innovation that he wanted to study. A generation later I will pursue the same mirage (Griliches 1990). ' “1996) i under the lead— :ts was expanded series for major y, with contribu- Lmer, Fabricant, vin Tostlebe, and inably obvious to al numbers in a vity calculation.8 d calculation ap- ' 5 book on Trends cent where, after l the output and esents (on p. 49), :s like a “back of on of efficiency, 5; defined as Out- Input of Other .ufacturing indus- iokler, gwho had at the University shed a detailed ng Efficiency of y” in which he over total input “to describe the le of technical assembled, by Jeatedly. in sub; - flawed in the earlier nd and Friedman ponents in Schmuck- 1is article was based. sis was the assembly ent series on patent- ; it as a measure of t was uhlished as r that e intent was ther, with the patent th in in ut-over—out- npublis ed, chapter hat and gets nothing. as the result of this .ctivity measurement as analysis of patent :y are closer to and a [3 actual processes of : he wanted to study. sue the same mirage Grilickes: The Residual 1327 TABLE 1 ‘ EARLY ESTIMATES or THE “RESIDUAL” IN U.S. Gsowru. (Percentage of Growthnot Accomted for by Conventional Inputs) Total Economy Agriculture In output ' per man or Source Period In output manhour Source Period In output Tinbergen (194.2) 1870-1914 27 100 Stigler (1947), 1904-1937 n.a. median 89 Barton and 1910—45 57 Selected Cooper manuf. iud's (1948) Schmookler 1869—1938 37 n.a. johnson 1900—20 24 (1952) manuf. (1950) 1923—29 50 1859-1928 31 88 1940-48 50 Fahricant 1870—1950 n.a.. 92 Ruttau 1910-50 (1954) (1956) beg. wts. 88 ' end wts. 71 Kendrick (1955) 1899—1948 p 87 manuf. i v I , Abramoviiz . 1869-1878 (1956) to 194453 48 86 Solow (1957) 1909-1949 52 88 n.a. — not available beg. wts. --- beginning period weights and wts. — end of period weights sequent studies, and in 1953 Kendrick was asked to systematize and develop this line of measurement more explicitly. Calculations based on his preliminary work were made by Fabricant in 1954, who may have been the first to empha- size loudly that most of the growth in output per unit of input has not been ex- plained and hence, “it follows that the major source of our economic advance has been a vastly improved efficiency” (p. 8). In 1956, a more detailed analysis “of basically the same data was published by Abramovitz, who identified productiv- ity with his computed index of “output per unit of utilized resources” and ch- served that “the lopsided importance which it appears to give to productivity increase” (in accounting for the growth , 'arr‘: in output per manhour) “should be . . . sobering, if not discouraging, to students of economic growth” and labeled the re- sulting index “a measure of our igno- rance.” Kendrick’s own similar results were already reported in the 1955 NBER Annual Report (Kendrick 1955, pp. 44— 47), but his magnum opus did not come out until 1961 (Kendrick 1961) and in the end he was overshadowed and did not get enough credit, in my opinion, either for providing the data to his “in~ terpreters” or for the detailed data con- struction effort behind it. Some of these computations, and the parallel ones made for agriculture, are summarized in Table 1. ‘ At the same time that the NBER was assembling data for the U.S. economy as 1328 a whole and for several of its major sec- tors, a parallel measurement effort was proceeding at the Bureau of Agricultural Economics of the USDA directed at the measurement of farm output and effi- ciency. In 1948, Barton and Cooper pub- lished a fully articulated and detailed output per unit of input index for the U.S. agriculture. Without computing such an index explicitly, Johnson (1950) used their data to estimate the magni- tude of the shifts in the aggregate agri— cultural production function in different periods, based on weights from esti- mated production functions, both linear and linear in the logarithms of the vari- ables}0 Theodore Schultz (1953) used the Barton and Cooper index to compute - the return to public investments in agri- cultural research. Ruttan (1954), as part" of his dissertation at the University of Chicago, constructed linear and geomet- ric output over input indexes for meat packing plants, interpreting these in- dexes as approximations to shifts in the underlying production function. He used base and end period weights to bound them, and included a reasonably com- plete discussion of the potential biases in such a construction. An extension of this work to the measurement of “The Con- tribution of Technological Progress to Farm Output" was published in Ruttan (1956). Against this historical background the 1957 paper by Solow may appear to be less original than it really was. Not the question, nor the data, nor the conclu- sion was new. Nor did using a geometric input index with shifting weights affect the results all that much. What was new and opportune in it, the “new wrinkle” (p. 312), was the explicit integration of economic theory into such a calculation and the use of calculus, which by then 1° Iohnson credits Tintner with stimulating his interest in this approach (personal communica- tion). . Journal of Economic Literature, Vol. XXXIV (September 1996) was being taught to most graduate stu- dents. It showed that one need not as- sume stable production function coeffi- cients to make such calculations and provided an approximation formula for any constant returns production function and, by implication, also an interpreta- tion of the earlier work that did not use this formula. This clarified the meaning of what were heretofore relatively arcane index number calculations and brought the subject from the periphery of the field to the center. It also connected it, indirectly, to Solow (1956) and growth theory and macroeconomics as it was to develop, and had an immense influence on subsequent work in both macro and micro economics. 1 All of the pioneers of this subject. were qhite clear about the tenuousness of such calculations and that it may be mis- leading to identify the results as “pure” measures of technical progress. Abra— movitz worried about possible measure- ment errors in his labor and capital se- ries, especially the omission of intangible capital accumulation through education, nutrition, and Ber, and also about not allowing for increasing returns to scale. Kendrick (1956) noted the omission- of intangible capital, such as B&D, from his total input construction. Solow empha- sized that he used “the phrase ‘technical change’ for any kind of shift in the pro- duction function” (emphasis in the origi- nal). He commented on the absence of good measures of capital utilization and he credited Schultz for “a heightened awareness that a lot of what appears as shifts in the production function must represent improvement in the quality of labor input, and therefore a result of real capital formation of an important kind” (fn. 6). Schultz, as mentioned earlier, ac- tually attributed such numbers to public lier and used them to compute a rate of return to them, influencing my sub- sequent work on returns to hybrid corn ber 1996) most graduate stu- it one need not as— ion function coeffi- :h calculations and mation formula for production function also an interpreta- 3rl< that did not use arified the meaning are relatively arcane .ations and brought 6 periphery of the t also connected it, (1956) and growth Inomics as it was to immense influence in both macro and of this subject were he tenuousness‘ of . . . that it may 93,: .; ., 1e results: as “pure” :al progress. Abra- t possible measure— lbor and capital se- mission of intangible through education, and also about not 1g returns to 7 ed the omission-mt -. .7 . :h as Ber, frorrihis " " ion. Solow empha- 1e phrase ‘technical of shift in the pro— 1phasis in the origi- on the absence of sital utilization and for “a heightened of what appears as tion function must nt in the quality of cfore a result of real an important kind” -ntioned earlier, ac- numbers to public to compute a rate ifluencing my sub— rrns to hybrid corn Griliches: The Residual 132.9 research (Griliches 1958). Most writers echoed Abramovitz’s conclusion that such calculations should be interpreted, primarily, as providing an “indication of ' where we need to concentrate our atten- tion.” At this point the gauntlet had been thrown: even though it had been named “efficiency,” “technical change," or most accurately a “measure of our ignorance,” much of observed economic growth re- mained unexplained. It was now the turn 11 The search for “explanations” of such residual measures of roductivity growth (technical change) will be t e topic of the sequel to this note. of the explairna-rs.ll REFERENCES ABBAMOVI’IZ, MUSES. “Resource and Output Trends in the United States- since 1870,“ Amer. Econ. Reo., May 1956, 46(2), pp. 5—23. BARTON, GLEN THOMAS AND COOPER, MARTIN R. “Relation of Agricultural Production to In- puts," Rev. Econ. Statist, 1948, 30(2), pp. 117- 26. COPELAND, MORRIS A. "Concepts of National In- come," in Studies in income and wealth. Vol. 1, New York: National Bureau of Economic Re- search, 1937, pp. 3—63. COPELAND; Morons A. AND MARTIN, E. M. “The Correction of Wealth and Income Estimates for . Price Changes," in Studies in income and ' wealth. Vol. 2. New York: National Bureau of Economic Research, 1938, pp. 85—135; includ~ ing discussion by MILTON FREEMAN. FABRICANT, SOLOMON. Economic progress and economic change. 34th Annual Report. New York: NBEB, 1954. GRILICHES, ZVI. “Research Cost and Social Re- turns: Hybrid Corn and Related Innovations,” ]. Polit. Econ., Oct. 1953, 56(5), pp. 419-31. .“Measuring Inputs in Agriculture: A Criti- cal Survey,” ]. Form Economics, Dec. 1960, 42(5), p . 1411—27. . "'Fhe Sources of Measured Productivity Growth: United States Agriculture, 1940—1960," I. Polit. Econ., Aug. 1963, 71(4), pp. 331-46. . "Patent Statistics as Economic Indicators: A Surve ," Econ. Lit, Dec. 1990, 28(4), pp. 1661-1 07. HEADY, EARL 0. AND DILLON, JOHN L. Agricul- tural production functions. Ames, Iowa: Iowa State U. Press, 1961. HICKS, JOHN R. “The Valuation of the Social In- gzme,” Economico, N. 3., May 1940, 7, pp. 105— IOHNSON, D. GALE. “The Nature of the Supply Function for Agricultural Products,” Amer. Econ. 3673., 1950, 40(4), pp. 539—54. JORCENSON, DALE W. AND CRILICHES, ZVI. “The Explanation of Productivity Change,” Rev. Econ. Stud, June 1967, 34(3), pp. 249—83. KENDRICK, JOHN W. “Productivity,” in Govern- ment in economic life. Ed: SOLOMON FABRI- CANT. 35th Annual Report, New York: NBER, 1955, pp. 44—47. . Productivity trends: Capital and labor. New York: NBER, 1956. , . Productivity trends in the United States. Princeton, NI: Princeton U. Press, 1961. MENDERSHAUSEN, HORST. “On the Si 'ficance of Professor Douglas’ Production fiction,” Econometrica, Apr. 1938, 6(2), pp. 143—53. RUTTAN, VERNON W. Technological progress in the meatpacking industry, 1919—47. Washing— ton, DC: USDA, 1954. ._ "The Contribution of Technological Prog- ress to Farm Output: 195 1533212. Econ. Sta- tist, 1956, 38(1), pp. 61—69. SCHMOOKLER, JACOB. “Invention and Economic Development.” Un uh. Ph.D. dissertation, U. of Pen lvania, Phi adel hia,,1951. .“T {Changingfi' 'iciien‘cy of the Ameri- can EcOnOmy: Econ. Statist, 1952, 34(3). p‘p. 214-321. 3‘ . "The Level of Inventive Activity,” Rev. Econ. Statist, May 1954, 36, pp. 183—90. SCHULTZ, THEODORE W. The economic organiza- tion of agriculture. New York: McGraw—Hill, 1953. SMITH, VICTOR E. “An Application and Critique of Certain Methods for the Determination of a Statistical Production“ Function for the Canadian Automobile infantry, 1917—1930." Unpublished PhD‘. di‘sserta'hl’oii, Department of Economics, :f‘Urj‘ Evanston, IL, - . in... r ....-‘::. SOLOW, ROBERT M'.‘ “A Contribution to the The- ory of Economic Growth,” Quart. ]. Econ, Feb. 1956, 70, p. 65-94. .“Tec nical Change and the Aggregate Pro- duction Function,” Heo. Econ. Station, 1957, 39(3), pp. 312—20. STIGLER, GEORGE ]. Trends in output and em- ployment. New York: NBER, 1947. TINBERGEN, IAN. Econometric. Gorinchem: }. Noorduijn en zoon n. v., 1941. . “Zur Theorie der Langfirstigen Wirt- schaftsennvicklung,” Weltwirts. Archie. 1, Am- sterdam: North—Holland Pub. Co., 1942, pp. 511—49; reprinted in English translation in JAN TINBEBCES. Selected papers. North-Holland, 1959. ' TINTNEB, GERHARD. “A Note on the Derivation of Production Functions from Farm Records," Econometrica, Jan. 1944, 12(1), p. 26—34. .“Some Applications of'Mu tivariate Analy- sis to Economic Data,” ]. Amer. Statist. Assoc, Dec. 1946, 41, pp. 472—500. U.S. DEPARTMENT OF LABOR. BUREAU OF LA- 1330 journal of Economic Literature, Vol. XXXIV (September 1996) BOB STATISTICS. Trends in multifactor ro- VALAVANIS-VAIL, STEFAN. “An Econdmetric ductiuity, 1948—81. Bulletin No. 2178. ash- Model of Crawth: U.S.A. 1869—1953," Amer. ingtou, DC: US. Department of Labor, 1983. Econ. Rea, 1955, 45(Sup), pp. 208—21 ...
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