Long-term technological development in commercial aircraft

TECHNOLOGICAL

FORECASTING

AND SOCIAL CHANGE

30, 149-166

(1986)

Long-Term Technological Development in Commercial Aircraft GEORGE

W. MECHLING,

JR.

ABSTRACT

Sahal tested two hypotheses in his initial investigation of long-term technological development. These two hypotheses arc learning by doing and scale of utilization. Sahal framed both hypotheses in a derived Gompertz form. He subsequently suggested the use of the Koyck form for the learning hypothesis, as well. He did not use it, however, because of relatively untractable correction difficulties that arise when estimating with it. This study refines Sahal’s methodology and investigative procedure. It significantly fails to empirically disconfirm either long-term hypotheses in both the Gompertz and Koyck form. This is a result that, generally speaking, Sahal’s work did not achieve. The artifacts the long-term technological development of which this study investigates are the commercial aircraft of what basically constitutes the old domestic trunk organization and the diesel-electric rail locomotives of the Class I roads. Upon establishing the explanatory significance of Sahal’s hypotheses, this study generates acceptable forecasts of further technological development. Finally, this study compares learning’s impact on the pace of technological change of both aircraft and diesel-electric locomotive technology. The methodology and procedure employed in this study, although possibly limited in application, substantially refine and improve Sahal’s prcv~ous effort.

The initial effort by Sahal in analyzing long-term technological development is attractive. This is due in large part to the fact that he couched his effort in a rudimentary theoretical framework consisting of testable hypotheses, rules of correspondence, and various postulate-like and law-like statements. This lends a desirable element of scientific rigor and generality to his investigation, which critics such as DeGregori and Linstone regard as provocative and engaging [6, 141. Unfortunately, less-than-compelling empirical results blunt the impact and significance of Sahal’s analysis. His shortcomings are several and this study will subsequently identify them. It will eliminate these shortcomings and in so doing lend support to Sahal’s basic rationale, which is to his credit. Patterns of Technological Innovation [26] and an earlier work [25] by Sahal address the long-term technological development of diverse artifacts. This study, however, will concern itself primarily with commercial aircraft, specifically the aircraft operating both domestically and internationally within what constitutes the old domestic trunk organization. It will also investigate the technological development of diesel-electric rail locomotives for the purpose of comparing learning’s impact on aircraft and locomotive technologies. Therefore, this study substantially limits its scope of investigation relative

GEORGE W. MECHLING, JR., received his Ph. D. in Economics from the University of Nebraska and is currently Assistant Professor, School of Business and Technology, Kearney State College, Keamey, Nebraska. Address reprint requests to George W. Mechling, Jr., School of Business and Technology, Keamey State College, Kearney, Nebraska 68849. 0 1986 Elsevier Science Publishing

Co., Inc.

0040--1625/86/$03.50

150

G.W. MECHLING,

JR.

to Sahal’s more ambitious undertaking, which includes diverse technologies of many artifacts. Despite its limited scope, this study is sufficient to initially lend significant credibility to Sahal’s original analyses of long-term technological development. This study is divided into five parts and a summary. Part One defines functional technical measures and discusses various premises that direct Sahal’s long-term analyses. These topics are briefly treated here, because they are treated at length elsewhere [26]. Part Two introduces the variables in the data set of Sahal’s original study of commercial aircraft, the formal estimating models he uses, and his original empirical results. Part Three identifies some reasons why Sahal’s empirical results are disappointing. This part also advances refinements both theoretical and methodological that lend investigations of his sort greater coherence, consistency, and scientific credibility. Such refinements necessarily entail a reconstruction of Sahal’s original data set. Part Four presents the empirical results of this study given the refinements it introduces in Part Three. These results vastlv improve those that Sahal originally generated. Furthermore, the estimates associated with this study are stable outside the sample set from which they are drawn. They therefore are not only statistically significant but they forecast as well. Part Five first introduces the empirical results of testing Sahal’s learning-by-doing hypothesis with respect to technological development associated with diesel-electric rail locomotives. It also criticizes Sahal’s original attempt to compare learning’s impact on the pace of change of diverse technologies. Finally, Part Five advances its own comparison of learning’s impact on the pace of change of the technologies of both commercial aircraft and rail locomotives. Part One’ The functional measure of the technology of some particular artifact is a quantifiable statement of the performance characteristics of the artifact or some subset thereof. Such a measure regards the artifact systemically, inasmuch as any change in the measure can be the result of a few or a host of relevant innovations that compose the artifact. It attempts to take into account all underlying innovations, major and minor, identified and otherwise, as a means of characterizing the technological phenomenon considered. Functional measures are also unambiguous, objectively measurable, and pragmatic. Thus they can indicate the innovative course a technology takes. Functional measures are also product specific. This implies that the sequential arrangement of technical relationships an economy produces must to some extent organize the activity of an economy itself [27]. Thus, the use of functional measures may be relevant to economic considerations as well as those that are technological. The functional measure Sahal selects to characterize the technology of commercial aircraft is the average airspeed of domestic air carriers. The functional measure he selects to characterize rail locomotive technology is average tractive effort or the force that the wheels of steam locomotives deliver against rails. This study subsequently adopts average seat-miles per hour and horsepower that domestic trunk aircraft generally speaking deliver to their aggregate domestic and international route systems and rated horsepower of the diesel-electric rail locomotives of the Class I roads. Sahal advances a number of premises concerning the evolutionary and systematic nature of technical change. One may regard these premises as having the status of theoretical postulates. They are not particularly original with Sahal, but he has collected and succinctly articulated them. We will briefly review them.

‘Most of what is presented

in this part and in Part Two is to be found in [26, Chapter 61.

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First, technical change is cumulative. Change builds on what already technologically exists. Thus, learning by experience is fundamental to the process and, as a consequence, innovation also tends to be localized or technology specific. Second, the experience gained does not always immediately have an impact on the behavior of a functional measure. Thus, significant gaps in time or cumulated production may exist between the acquisition of experience and its subsequent measurable effect on the measure. Third, technological guideposts that are designs pattern developing technologies along lines that exploit by degrees the innovative possibilities of the guidepost itself. Fourth, the evolution of a guidepost takes place with the disproportionate growth of its components, change in the material of its construction, and an increase in its structural complexity. These three processes bear on an artifact’s systemic evolution as a means of adapting it to changes in the scale of utilization. Eventually, however. changes in scale of utilization and learning will exhaust a guidepost’s exploitive possibilities in the absence of technological inputs not native to it if for no other reason than the applicability of physical laws. Fifth, a guidepost rarely develops in isolation from other technologies, however. Rather, artifacts of differing technologies are often combined into single devices creating a wholly new device altogether or radically altering at least one of the original artifacts. This phenomenon Sahal refers to as creative symbiosis, which offsets the eventual exhaustion of the exploitive possibilities of a particular guidepost. Sahal discusses more premises elsewhere [26]. The five that this study presents are, however, sufficient for Sahal to derive testable hypotheses of long-term technological development. Given that the exploitation of some device taken in isolation tends to eventually exhaust possibilities for improvement and refinement, the device is subject to a shortterm process of equilibration. Creative symbiosis and learning combine, however, to revise this equilibration path. Revisions of this sort constitute a long-term evolutionary process of disequilibration. The three hypotheses Sahal derives and two of which he tests seek to account for this long-term process. Using a Gompertz function Y = K exp [ -

exp (A - B,)],

(1)

Sahal formally depicts the phenomenon of equilibration where y is a functional measure of some technology, K is an equilibrium stage of development, and A and B are constants. Redefining terms, linearlizing the expression, internally substituting an expression of variation for K, and introducing stochastic elements into the derivation eventually yields In Y, = (1 -

A) PI + p2 (1 -

X) In X2* + hln Y,-l

+ (VI, + yU2,).

(2)

Here, 0 < A c 1 is a coefficient of equilibration (or rate of decay) and X2, is the explanatory variable of disequilibration or long-term development. The definition of X,, formally states the hypothesis to be tested. Sahal suggests two that are consistent with and follow from the above premises. The first consists of the claim that technological innovation depends on the accumulation of relevant experience of a practical nature. This is the learning-by-doing hypothesis. The second “has it’s origin in the observation that the characteristics of the environment surrounding the use of a” technological artifact “play an important role in its long term development.” This is the

G.W. MECHLING,

152

JR.

scale-of-utilization hypothesis and pertains to “the scale of the larger system within which a given technology is embedded” [26]. It thus remains to but specifically define variable XI, in a way that acceptably corresponds to these two hypotheses. Sahal proposes a variant of the learning hypothesis of accumulated experience that takes account of the fact that such an accumulation involves significant time lags. This may be formally depicted as: Y, = p, + p7X2, + p3xzr_, By the Koyck transformation

+ @4X2,-Z +

. .

and restated stochastically,

Y, = Pt(1 - A) + &Xx2, + hY,-

I

+

(e, -

he,_

Equation

(3) becomes (4)

,),

where 0 s A s 1. Sahal presents Equation (4) in log form although no compelling reason exists to do so. Equations (2) and (4) are remarkably similar. A significant difference exists, however, with respect to their error terms. One may assume the error term associated with Equation (2) to be randomly distributed. Consequently, the use of ordinary least squares (OLS) will estimate the model’s parameters. Equation (4), however, violates two classical OLS assumptions. Correlation exists between adjacent errors and between the error term and another variable in the argument, Y,,. Thus, OLS parameter estimates are both inconsistent and biased. Sahal deigns to attempt any estimation with the Equation (4) form.’ He opts instead to use the Equation (2) form to test his learning and scale of utilization hypotheses.

Part Two The functional measure Sahal selects for commercial aircraft route carriers is average annual airspeed (1933-1965). Values for this measure in the time period examined are readily available [8, 201. The measure he selects to correspond to the explanatory learning variable is the cumulated annual delivery of new aircraft purchased by the domestic trunks from 1947-1965. Values for this measure are not readily available and Sahal borrows from previous work by Phillips [21], who constructed such a series. Learning-curve and technical-progress-function literature usually associate learning with cumulated production 11, 151. Delivery figures on capital equipment are not inappropriate proxies for production figures of that equipment, however. Aircraft are made to order to specifications with some performance capability peculiar to the needs of those for whom the production is intended. Thus, the use of cumulated purchased deliveries is not exceptional despite the fact that military R&D, for example, contributes much to the development of commercial aircraft, and airframe manufacturers produce aircraft for more than just the domestic trunks. The measure selected to correspond to the explanatory variable of the scale of utilization hypothesis is the number of airfields and landing strips annually registered with the Federal Aviation Agency (FAA) from 1933 to 1965. Values for this measure are readily available [9]. The correspondence of such values to measures of scale is less

‘The difficulties

[to].

that estimating

such a form poses have not altogether

been satisfactorily

overcome.

See

COMMERCIAL AIRCRAFT DEVELOPMENT

I53

clear than with aircraft delivery figures and learning measures for which a substantial body of literature exists. All that Sahal will argue is that in transportation technology, “a relevant measure of overall system scale is a distance factor or some related variable such as route miles or number of ports” and that regional science studies indicate the existence of “significant regularities associated with the variation in distance factors” 1261. The results of Sahal’s regressions Learning by doing: InAS, = -0.11

that follow are not good.

+ 0.007*1nX~, + 0.991nY, -

(1.22)

(0.70)

R2 = 0.99, F = 989.04,

1

(Rl)

(19.8)

D-W = 1.23, N = 19(1947-1965);

and scale of utilization

lnAS, = 0.03 + 0.02* 1nX2, + 0.96ln Y,_, (0.5)

(2.00)

(R2)

(19.2)

R2 = 0.98, F = 825.9, D-W = 1.18, N = 33 (1933-1965). The values in parentheses are the t ratios of the estimates. Equation (2) shows that the coefficient of X2, in Equations (Rl) and (R2) is a composite where p: = (1 -

Qp,.

(5)

fi: is the value reported in Equations (Rl) and (R2), as noted by the asterisk, and is referred to as an unrestricted coefficient. fi2 is a restricted or exactly identified coefficient and is the coefficient of disequilibration that is associated with the explanatory affect of X2, on Y,. A is the rate of decay and the coefficient of equilibration and (1 - A) is the rate of adjustment. The t ratios indicate that fi$ is not significant for either Equation (RI) or Equation (R2). Our interest, however, is with the significance of &, The standard error of fi2 for both Equations (Rl) and (R2) can be disentangled from that of fi:, roughly yielding t ratios so small as to be virtually unreportable (0.00X) [ 131. The parameter estimates for variables X2,, accumulated delivery of aircraft and registered airfields and landing strips, respectively, are in no way statistically significant. Sahal’s results fail to establish any linear relationship between either of these two variables and the dependent variable the behavior of which he hypothesizes they explain. Part Three The poor statistical results Sahal’s study generates are primarily due to inconsistencies in method and unrefined correspondences. Significantly, these shortcomings are procedural flaws and have little if anything to do with the theoretical-like insights that form Sahal’s research program. Increased aircraft velocity is no doubt a technical achievement. The essence of this transportation mode’s appeal is obviously the advantage of its greater speed relative to other modes. Mere airspeed, however, is an incomplete indication as to what the development of such a technology involves. A perfunctory examination of that development reveals that composite materials that permit the construction of lighter, stronger, and longer airframes, more efficient fuels, lower weight-to-thrust ratios in more efficient engines, and transistorization of on-board electronic equipment are but a few of the

154

G.W.

MECHLING,

JR.

disparate technical improvements that in combination point to increased cartage capacity of the artifact, as well as speed [ 161. The function of the artifact not only involves movement at some velocity but the movement of what it carries at that velocity, as well. Thus, with respect to commercial aircraft, the functional measure that this study initially adopts is the capacity of the artifact to move a certain number of passengers at a certain velocity. This measure is seat miles per hour (SM/Hr).’ It is actually a crude power measure that one can also state in terms of ton miles per hour (TM/Hr) or horsepower (HPW). This study proceeds on the assumption that SM/Hr or its more refined variants (TMIHr and HPW) are more acceptable measures of the artifact’s technological function than its airspeed alone is. In testing the learning-by-doing hypothesis, Sahal borrows data from earlier work by Phillips 120, 211. Unfortunately, a gross inconsistency arises. The airspeed data Sahal borrows is airspeed data for all certified domestic route carriers. The accumulated delivery of new aircraft data he borrows to explain variation in that airspeed data pertains only to the domestic trunk carriers. Airspeed of both domestic trunks as well as all certified route carriers is readily accessible for the time period covered [9, 191. Thus, this study easily corrects this inconsistency and works with data pertaining to the domestic trunks only. In addition, domestic trunk carriers do not limit their activity to domestic routes. This study does not limit the contributions of acquired aircraft to domestic operations as Sahal does. To do so would involve great if not unnecessary accounting efforts to sort out that contribution from that to the total. Therefore, this study uses accumulated delivery of new aircraft to explain variation in the functional measure of the average domestic trunk aircraft flying the total system (domestic and international) in which the trunks operate. Airstrips and landing fields registered with the Federal Aviation Agency is an exceptionally gross explanatory measure. Such a measure comprises both public and private airstrips and landing fields that are paved/unpaved. lighted/unlighted, or some combination thereof. That domestic trunk carriers would frequent private unpaved and/or unlighted facilities seems unlikely. This study uses, therefore, only public paved and lighted facilities. This variable pertains to domestic U.S. facilities only. This requires this study to construct a functional measure of a magnitude appropriate for domestic U.S. operations in order to test the scale hypothesis. This presents no problem, because domestic-performance measures are as readily accessible as system and/or international ones [8]. Given the identification of shortcomings in Sahal’s previous study and the remedies that this study recommends. one can now detail the construction of its data set. Sahal’s data on commercial aircraft consist of annual observations from 1932 and 1947 to 1965 for scale and learning, respectively. Due primarily to the availability of the required explanatory data. this study adopts a different time period: the middle or late sixties through 1982. The FAA publishes monthly and yearly the number of airfields and landing strips on record with it (4, 91. The first time, however, that the agency had sufficiently retined this data for publication so as to identify the number of paved and lighted public airfields and landing strips on record was 1969. This study, therefore, tests the scale-ofutilization hypothesis using 14 annual observations of this more refined variable from 1969 through 1982. The Phillips data [2i] from which Sahal borrows his accumulated-delivery-of-newaircraft series to test his learning hypothesis is also suspect. Phillips does not describe in much detail how he formed this series. His figures are obviously public, but his

‘The use of this measure (SMIHr)

ia not

original to this

study; its use has precedent [24].

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procedure is not. Phillips leaves one with the impression that those figures might be but actual acquisitions to equipment inventory. This does not necessarily include all additional new aircraft put to use, however. Commercial airlines often lease as many or more new aircraft than they initially purchase, and purchases often occur as part of lease-purchase arrangements, meaning that acquisitions of this sort have nothing to do with new aircraft. As a proxy for production, the number of new aircraft delivered for use to the fleets is not always clearcut and unambiguous. Leasing and lease-purchase arrangements appear to go back as far as the late 1950s. The construction of a data set of new aircraft put to use requires some sorting of the numerous kinds of use arrangements that exist. This study, therefore, constructs its own series subject to complete public view. The source for constructing such a data set are semiannual publications of Commercial Aircraft Fleets by AVMARK [5]. “Delivery” and “lease-delivery” are the two categories by which the publication lists newly manufactured aircraft put to use by the various fleets. Furthermore, AVMARK publishes the month of the year that such equipment goes into service. This is useful, because the functional or performance measures are annual averages and because the extent of a new aircraft’s contribution to some annual average depends on when in that year it went into service. Four aircraft going into service in December would thus constitute but one-third of an aircraft added to the fleet for that year but three and two-thirds for the year following. Thus, the use of the AVMARK source allows us the possibility of measuring relatively precisely the impact of accumulated new aircraft on its technological development. Although AVMARK data go back as far as 1949, that that was available for this study begins in 1964 and ends, as do the other explanatory series (public paved and lighted fields), in 1982; these data provide 19 annual observations. Consider now the construction of the data series of the functional measure (SM/Hr) that this study uses. The composition of what constitutes the domestic trunks for the period observed has been relatively stable.4 Northeast Airlines merged with Delta Airlines in 1974, Braniff ceased operation in 1979, and National Airlines merged with Pan American at the end of calendar year 1980. Thus, the domestic trunk organization remains virtually intact but for two exceptions. First, the domestic trunk organization did not include Pan American at the beginning of the period observed but did include the carrier by 1977. Given National’s merger with Pan American, this study factors Pan American’s performance data and new-aircraft acquisitions into domestic trunk operations for the entire period observed rather than attempt to factor it out entirely. Such an adjustment is possible at the levels of both total system and domestic operations. Second, domestic trunks were reorganized in 1981 into the Majors. The Majors differs from the old organization with the addition of Republic and USAir. This study factors these two airlines out of the aggregate Major data in order to maintain a consistent data series for the period observed. The sources of the functional measure data are the Handbook of Airline Statistics [8] and The OfJiciul Handbook of Airline Statistics [ 191. The Civil Aeronautics Board (CAB) publishes both. The Handbook last appeared for calendar year 1972, followed by two supplements for 1973-1974 and 197551976. The OfJiciul Handbook publishes monthly current and previous (corrected) year’s data. Both publications contain summary tables of numerous data categories. Manipulating some of these categories generates the func4American, Western.

Eastern,

TWA,

United,

Braniff,

Continental,

Delta,

National,

Northeast,

Northwest,

and

156

G.W. MECHLING,

JR.

tional measure that this study requires. The Handbook series, for example, publishes domestic information of the domestic trunks but not information for their total system. This study generates total system information by combining the domestic operations and international operations table of each of the individual carriers involved. The OfJicial Handbook publishes aggregated total system and domestic operations information for the Majors and/or domestic trunks. The Ojjicial Handbook, therefore, already makes the necessary aggregations, both domestic and international. In cases in which The Of/Sal Handbook reports operations of the Majors from 1981 on, subtracting Republic’s and USAir’s published individual summary tables of data from the two aggregates is a simple task. The data that this study requires are figured from the summary tables as follows. Wheels-off-wheels-on speed is equal to total revenue miles divided by total revenue hours. The number of seats per average aircraft is published in the tables but is also equal to total available seat miles divided by passenger revenue miles. SM/Hr is equal to the number of seats per average aircraft multiplied by the speed of the average aircraft. Finally, Equation (4) (the Koyck transform) presents difficulties of estimation that remain satisfactorily unresolved. That Sahal chooses, therefore, to avoid employing this form for purposes of estimation even though he argues for the appropriateness of its application is not surprising. This study does, however, provisionally employ it. The error term in Equation (4) is a moving-average (MA) error of the form e, - Xe,_, . Defining the MA error f, -

(6)

he,_ , = I/,,

and restating

U, in matrix form as a vector (7) ]+A2 -x 0 0

-A IfA2 --A 0 0

0 -A : : 0

. 0 .

* . . . -A

0 0 : 0 -A 1+X2

(8)

or

_u,_u:= CT2c$.“’

(91

The 4 matrix can be shown to be a component of the regression coefficients, @. jj = (X’$_‘x)-l

X’$_’

A SHAZAM subroutine Judge et.al [ 11) define as

of what is referred to as an Aitken estimator

_Y. [28] permits Aitken estimation

(10) with an MA matrix, which

I.

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1+a*

*I=

Y, -

0

0

0

0

0:

0

.. .:.

0

. . .

p

a:

1+a*...

0

0

0

0

hY,_,

:1

0

(Y

1+a*

The subroutine negative values The subroutine timate Equation

.

. . .

0

a

a

1+cY* (Y

157

(11)

(Y 1 + (Y=

requires that values for a be assigned prior to estimation. Thus, assigning to the off-diagonal (YSmakes matrices $ and IJJequivalents of each other. does not, however, permit restrictions. Thus, the subroutine cannot es(4) in its given algebraic form. Rearranging Equation (4), however, yields = (1 -

X)P, + p* X2,.

(12)

The left-hand side of Equation (12) is a new dependent variable (the variable of disequilibration). Searching for a value of lambda (X) between 0 and 1, the subroutine can estimate the coefficients of Equation ( 12). The search is complete when a particular value of lambda minimizes the residual sum of squares (RSS) of one of the regressions the subroutine runs. Assuming additivity, this study can restrict the coefficients of Equation (4) to values estimated with Equation (12) for purposes of determining the model’s goodness of fit and forecasting. This puts those estimates in a reportable form that is consistent with Sahal’s variant on the learning hypothesis (the Koyck transform). Part Four: Learning by Doing The observation period for estimation purposes runs from 1965 to 1976, with observations for 1977 to 1982 constituting the forecasting period. This study performs several separate estimations using both SM/Hr and mere trunk airspeed (AS) with the Gompertz Equation (2) and Koyck Equation (4) forms. Employing the rearranged Koyck form Equation ( 12) and regressing average airspeed of the trunks’ aircraft on accumulated deliveries of new aircraft will not converge the search.’ Using SM/Hr as the dependent variable convergence, however, occurs signihcantly. Restricting the estimates so generated yields the following model in the form of Equation (4): (SM / Hr), = 9407 + 3.2868 X2, + 0.806 (SM / Hr),_,; (67.025)

(R3)

(26.724)

R* = 0.9975, n = 12 (1965-1976), D-W = 2.8312, Theil = 0.250 (1977-1982). The values in parentheses are the t ratios of the estimated coefficients. The coefficient of the explanatory variable, cumulated delivery of aircraft, is statistically significant without question. This result fails to disconfirm Sahal’s learning-by-doing hypothesis. Note, however, that the estimation procedure will not generate an F statistic or a standard error for i, because the estimation procedure embeds that coefficient in the composite

‘None of the regressions

run minimize the RSS for 0 G i <

I

158

G.W. MECHLING,

JR.

dependent variable and subsequently restricts the coefficient values found for Equation (12). Although this deficiency is not desirable, one may assume i’s significance as well as that of the model’s, inasmuch as i’s standardized coefficient is 0.83757 in Equation (R3) and that of the explanatory variables’ is significant only at 0.17293. Furthermore and of particular importance, Equation (R3)‘s Theil Inequality Coefficient [22] is substantially less than one, indicating that the model will forecast. Thus, the estimated learning coefficient appears to be not only stable within but stable without the estimation set. Employing the Gompertz form (Equation (2)) with mere airspeed as the regressand generates the following results. InAS, = 2.7834

+ 0.015566*lnX2,

(2.1084)

+ 0.524 I ~~zAS,_~;

(0.76927)

(R4)

(2.1801)

R2 = 0.9735, F = 165.043, n = 12 (1965-1976), D-W = 1.1106. Autocorrelation is insufficiently present in the above regression model to warrant correction. The f ratio indicates that fiz is not significant. Our interest is not with fi$, however, but rather with p2 as to whether or not it is significant. Disentangling its standard error from that of fi; yields a t ratio of roughly 0.878. This indicates the failure of the learning hypothesis to explain change in the functional measure of mere airspeed. Applying the Gompertz form to the functional measure this study adopts, where X2, is still the accumulated deliveries of new aircraft, the following is generated. lnSM/Hr,

= 1.4570 (4.1501)

+ 0.0159505*lnXZ, (1.7032)

+ 0.860661n(SM/Hr),_

I;

(R5)

(22.937)

R2 = 0.9974, F = 1704.114, n = 12 (1965-1976), Theil = 0.683 (1977-1982), DW = 2.6798, (YI2 = 0.025. Autocorrelation is probably not present in Equation (R5), so no correction of that sort was made. The coefficient for the explanatory variable in Equation (R5) is a composite, as is the case with Eqrlation (R4). The t ratio of 6; indicates the lack of statistical significance for that composite. Disentangling the standard error for pZ from that of the composite yields, however, a t ratio of roughly 2.78. Thus, using the functional measure of SM/Hr, Sahal’s learning hypothesis in the Gompertz form has explanatory power. Furthermore, the estimates are stable outside the estimation set, because the Theil statistic indicates that this model also forecasts. The question does arise as to the legitimacy of comparing the relative effectiveness of the Gompertz or Koyck forms of the learning hypotheses when using the simple (AS) or composite (SM/Hr) functional measures. The values of all the data series generally and for the most part change in the same direction with the passage of time. Thus, the presence of collinearity is a distinct possibility. Inspection of the correlation matrices of Equation (R4) does in fact indicate its presence.6 The correlation between variables in the argument is high. Thus, standard errors tend to be high and t ratios low for the estimates even in the face of high R’s.

‘Provided

by the author on request

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Collinearity in Equation (R3) is not an issue because its estimates are from Equation (12). The question then arises as to whether or not estimating Equation (R4) like Equation (12) would generate results that compare more favorably with Equation (R3). Thus, this study initiated a search procedure like that that estimated Equation (12), with the exception that the subroutine needed only to supply values for A in the composite dependent variable, because the errors of this model are random. The results follow: InAS, = 2.7821 (131.61)

+ 0.015547*lnXZ,

+ 0525lnAS,_,;

(R6)

(5.0018)

R* = 0.9735, n = 12 (1965-1976), Theil = 2.866 (1977-1982). Initially, using the composite functional measure (SM/Hr) in Equation (R3) appears to have no advantage over the simple (AS) measure. The composite coefficient for XZ, (the learning data) isAcertainly significant. With Equation (R3), however, the significance of one coefficient (A) is uncertain. With Equation (R6) two are uncertain. More than likely, the fir of the composite coefficient (Equation (5)) is significant, but one cannot disentangle its standard error from that of ST, because the search procedure does not generate a standard error for X.Puthermore, and of substantial importance, despite whatever significance may exist for p2, the regression model fails to forecast (Theil = 2.866). Thus, this study leads us to prefer the composite functional measure (SM/Hr) over the simple one (AS). Part Four: Scale of Utilization This analysis differs from the foregoing in several minor ways. The use of FAAregistered airstrips and landing fields dictates the use of functional measures that pertain to only the domestic operations of the domestic trunks. Furthermore, the availability of the data necessarily limit the analysis to only 14 annual observations (1969-1982). We therefore choose not to test the forecasting capability of this hypothesis; the number of observations are too few. In addition, no call to employ the Koyck form to test this hypothesis exists, because it pertains to learning. We will, therefore, estimate only the coefficients of the Gompertz form that Sahal derived. Operating under the assumption that domestic airspeed of the domestic trunks (the simple functional measure) is more closely linked to the refined explanatory measure of public paved and lighted airstrips and landing fields registered with the FAA than is the gross measure of all airstrips and landing fields so registered, this study generates the following results: InAS, = 3.9717 (5.0917)

+ 0.024959*lnX2, (1.6468)

+ 0.31395lnAS,_,;

(R7)

(2.2112)

R* = 0.7091, F = 13.407, n = 13 (1970-1982), D-W = 1.5001, (Y/ 2 = 0.025. The r ratios (in parentheses) indicate that the composite coefficient of the explanatory variable is not significant and that the D-W statistic indicates the absence of autocorrelation Disentangling the standard errors of the composite yields a t ratio of roughly 2.13 for &. Thus, the explanatory power of the scale hypothesis using the simple functional measure (AS of the domestic trunks’ domestic operations) remains insignificant at a level of 5% or less. The same is not true for the composite functional measure (SM/Hr).

G.W. MECHLING,JR.

160

ln(SM / Hr), = 1.5881 and 0.27103*lnX2, (5.6616)

(4.0278)

+ 0.66439ln(SM

/ Hr),_ r);

(R8)

(9.6859)

R’ = 0.9958, F = 1307.605, n = 13 (1970-1982), D-W = 3.0239. The regression model (Equation (R8)) evinces no autocorrelation of any significance. The unrestricted or composite explanatory coefficient despite the presence of multicollinearity is decidedly significant. Furthermore, the coefficient of disequilibration is itself also decidedly significant. Disentangling its standard error from that of the composite yields a t ratio of 6.60. Thus, it would appear that Sahal’s scale hypothesis also finds significant empirical support. Summarizing the results of Part Four. we can make the following observations. First, the more complex functional measure (SM/Hr) appears to be superior to mere airspeed insofar as generating test results that support Sahal’s hypotheses. Second, consistency in the data set’s construction no doubt enhances the results of the analyses. Sahal’s mix of certified route carrier and domestic trunk data detracts rigor from his efforts. This study lends credibility to the hypotheses that Sahal framed but for which he could not generate empirical support. By employing both the Koyck and Gompertz formal variants of the learning-by-doing hypothesis, this study determines that this hypothesis can also explain and forecast variation in the functional measure of the technological artifact under analysis once the shortcomings in Sahal’s earlier work are eliminated. With respect to the scale hypothesis, the results despite their statistical validity are somewhat less convincing. Owing to limitations of published data, this study could only test the explanatory power of the hypothesis. More data permitting a test of the forecast capability of the scale hypothesis might ease this drawback. We conclude, however, that Sahal’s hypotheses in general do receive substantial empirical support, given improvements in the conduct of their analyses. Part Five Research of industrial productivity in the United States discloses for the most part gross unevenness of growth across sectors of industries. Table I provides the necessary comparisons [ 181. Efforts to explain this unevenness, although extensive, have generally been inadequate. This lack of adequate explanation is referred to as the “differential productivity puzzle” (DPP) [ 171. Most economists are reluctant to attribute differences in productivity growth to inherent differences in the technologies of the various sectors and/or industries. This reluctance stems more than likely from their bias for explanations that are price-theoretical alone. In addition, economists quantify productivity measures in terms of total factor and/or labor productivity. Such measures are efficiency measures, and for economists they are proxy measures of technological change, as well. Thus. the economist measures technological change in terms of the (productivity) variables it might very well determine. As a consequence, the economist cannot address such a possible connection unambiguously. The question, Does some particular technology in fact have its own peculiar pace at which it evolves and thus does that technology affect productivity in its associated industry differently than does the technology associated with some other industry‘? is open and at best improperly asked. Nelson and Winter are two economists who come close to addressing this question with the acknowledgment that a technology may follow particular trajectories. They do not speak at all, however. to the issue that what might also be important along with the trajectory taken is that trajectory’s pace [ I8 1. Sahal, concerned with making a case for his hypotheses, also sought to explore the

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TABLE 1 Growth in the Private Business Economy by Industry Group and Industry (1948-1%6) Percentage Yearly Change in Total Factor Productivitv

Private Domestic Business Economy Farming Mining Metal Coal Crude petroleum and natural gas Nonmetallic mining and quarrying Contract Construction Manufacturing Nondurables Food, except beverages Beverages Tobacco Textiles Apparel Paper and paper products Printing Chemicals Petroleum refining Rubber products Leather products Durables Lumber Furniture Stone, clay, glass Primary metal products Fabricated materials Machinery except electric Electric machinery Transportation equipment and ordnance Instruments Miscellaneous and manufacturing Transportation Railroads (Nonrail) Local railroads and bus lines Intercity passenger Water transportation Air transportation Pipelines-

Percentage Yearly Change in Output ner Worker

2.5 3.3 4.2 2.4 5.2 3.2 2.6 1.5 2.5 2.6 3.0 2.2 1.1 4.0 1.9 2.5 2.7 4.9 3.0 3.9 1.7 2.4 3.5 2.9 2.4 I .6 I .9 2.6 3.7

3.1 5.6 4.6 2.9 5.8 2.3 3.2 2.0 2.9 3.2 3.4 2.9 2.7 4.3 2.2 3.0 2.7 6.0 5.5 4.0 1.7 2.8 3.9 2.9 3.2 2.1 2.2 2.7 -4.1

3.2 2.9 3.5 3.4 5.2 2.1

3.2 3.7 4.0 3.7 5.8 2.3

I.0 0.5 8.0

1.5 0.7 8.2 9.1

possibility that differences between technologies might provide some hint as to the differential productivities existing across industries. He did this by comparing the exactly identified or restricted coefficients of the explanatory variables estimated for his tests of the learning hypothesis.’ This approach is not necessarily inappropriate. His regression models are of the Gompertz form, meaning they are logarithmic. The estimates of the model’s restricted parameters are, therefore, linear transformations of what economists ‘Chapter

6 126).

162

G.W. MECHLING, JR.

refer to as (constant) partial elasticities. Elasticities are ratios of percentage changes of the dependent variable to like changes of the independent [3]. This is particularly useful inasmuch as these estimates are not affected by differences in the magnitudes that variables assume in different (technological) populations. A particular difficulty arises, however. The results of any such comparison of elasticities of different technologies regarding the differential impact learning may have on their respective development are not valid. The data of the explanatory variables of theye regressions are learning data and therefore are cumulated. Due to the log transformations, percentage changes through such series from observation to observation depend on the point at which the cumulative process begins. The corresponding percentage changes of the dependent variable remain unchanged, because its series is not cumulative. Consequently, the parameter estimates themselves will always vary depending on the point at which the analysis itself should happen to begin. One cannot then regard any comparison between the parameter estimates associated with the explanatory variables from different regression models as meaningful. The point at which cumulation and analysis begin for each of the regressions cannot be anything other than arbitrarily determined, generally speaking. Fortunately, the difficulty outlined in the preceding paragraph does not apply to linear models of the Koyck form, such as Equations (4) and (12). The point at which cumulation happens to begin with raw data affects only the intercept and not the estimates of slope, in which we are interested. A comparison, therefore, between estimated learning parameters of different technologies is possible as long as one in some way takes dimensional and magnitudinal differences into account. This part attempts to compare diesel-electric rail locomotives of the Class I roads in the United States and the domestic airline trunks with respect to learning’s impact on the pace of change of their respective technologies. Such a comparison is possible: both types of artifacts can be measured in cartage, so their respective functional measures can be similarly denominated. Sahal limits his analyses of locomotives to steam locomotives. The functional measure he uses is tractive effort of force of wheel against rail: a popular measure for those artifacts. Such a measure does not, however, indicate the amount of cartage the artifact can accomplish. Only a power measure can do this. The Association of American Railroads provides such information in the form of aggregated rated horsepower and number of power units for Class I railroads in the U.S. Rail System. The association also provides data on the installation of new and rebuilt power units in the system [2, 231. These data consist of 13 annual observations from 1972 to 1984. Given the period covered, the information pertains only to diesel-electric equipment. This study constructs from this information data series of rated horsepower of the average power unit and cumulated installation of new and rebuilt units. SM/Hr is at best a crude power measure. This measure can be further refined and made denominationally similar to the power measure of the rail locomotives. Dividing available ton-miles by available seat-miles and multiplying by SM/Hr yields ton-miles per hour (TM/Hr) of the average aircraft. Multiplying TM/Hr by 5.33 transforms this more refined measure into the horsepower (HPW) the average aircraft delivers to the total system. The results of testing the learning-by-doing hypothesis follow, where Xzr is the cumulated delivery of new aircraft. HPW, = 10320 + 3.4941X*, (42.944) R’ = 0.9947,

+ 0.724HPW,_,;

(16.696)

n = 12 (196%1976),

Theil

= 0.219 (1977-1982).

(R9)

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The parameter estimate for the explanatory variable is decidedly significant. Its stability apparently extends outside the estimation set, given the Theil statistic’s indication that the model can forecast. One may assume that the lagged dependent variable is also significant, inasmuch as its standardized coefficient is 0.78873 and that of the explanatory variable is 0.22513. Thus, with little reservation we can use this regression in place of Equation (R3) (SM/Hr). The number of observations for rail locomotives is but i3. The current study, therefore, tests only the explanatory power of the learning hypothesis. The regression results follow, where XTc is the cumulated installation in the system of new or rebuilt locomotive units. HPW, = 701.09

+ 0.012216X,,

(68.716)

+ 0.672HPW,_,,

(RlO)

(9.5367)

R2 = 0.9171, n = 12 (1973-1984). The parameter estimate for the explanatory variable of cumulated installation of new and rebuilt power units is also decidedly significant. One may also regard the coefficient of the lagged dependent variable as significant, inasmuch as its standardized coefficient is 0.88353 and that of the explanatory variable is 0.11384. The question now remains, To what extent do the parameter estimates for the variables differ? One must, however, take into account magnitudinal differences in the variables that the two regressions involve if such a comparison is to be meaningful. One way to overcome magnitudinal differences between the dependent variables in each data set would be to measure the relative change in the variables of disequilibration against a corresponding per-unit change in their respective explanatory variables. A semilog model of the form In Y; = pr + PzX2, + 24i

(13)

will generate precisely this sort of information. Conveniently, the model measures the explanatory variables in both Equation (R9) and Equation (RlO) in artifact units. Thus, multiplying the estimate of p2 by 100 yields the constant percentage change in Y, perunit change in the explanatory variable. Specifying the $ matrix with the appropriate values that converged using the GLS subroutine in the initial search procedure, we can estimate p2 (the learning coefficient of both technologies) for comparative purposes only with In (HPW, -

A HPW,_ ,) = (1 -

h)P,

+ P2X2r.

The results follow for aircraft and diesel-electric In (HPW, - 0.724HPW,-,)

= 9.2667

F = 304.398,

(RI 1)

(17.447)

= 6.5562

+ 0.000015538X2,;

(495.32) F = 87.424,

respectively:

n = 12(1965-1976).

In (HPW, - 0.672HPW,_,)

R2 = 0.8974,

technology,

+ 0.00025907x2,;

(543.43) R2 = 0.9682,

locomotive

(14)

n = 12(1973-1984).

(9.3501)

(RW

G.W. MECHLING,

164

JR.

The parameter estimates for both regressions are significant. Each additional aircraft delivered increases the functional measure of the commercial fleets examined by a constant 0.0259%. Each additional installation of new or rebuilt locomotive units increases the functional measure of that technology by a constant 0.001554%. Learning in aircraft technology clearly appears to outpace learning in diesel-electric technology. Such a finding is not inconsistent with the comparison that Table I makes between the total and labor productivities for railroads and air transportation. If such a conclusion is to have some warrant, however, one must first determine whether or not both slope estimates are significantly different from each other and whether or not the slope estimate for aircraft technology is significantly greater than that for diesel-electric locomotive technology. Employing an F test at the 2.5% level of significance, we find that the variances of the respective dependent variables for Equations (RI 1) and (R12) are statistically the same. This permits the use of a scheme that generates a small sample test statistic employing pooled variances and the difference between the estimates of the slope parameters in Equations (RI I) and (R 12) [ 121. The hypotheses are

Ho : PA = PL, 0.00025907

(HI)

= 0.000015538

or H Al

: PA

+

H A2

: PA

G= PL,

PI_,

and

where the critical tzo,.tw,.s.Hnd.“, , for HAI and HAI are 2.845 and 2.528, respectively. The test statistic generated is 9.75, which clearly rejects the null hypothesis and permits the acceptance of both alternatives. Given the length of the data series, this study estimated the parameters of Equation ( 14) for an upper portion of the aircraft series ( 197 l-l 982) to determine the extent to which the constant percentage change that Equation (Rl 1) estimated is constant for the entire series. The results of the semilog form for this set of observations follow: In (HPW, - 0.268 HPW,_,)

= 10.212 (426.67)

+ 0.00023229x2,;

(Rf3)

(16.798)

R* = 0.9658, F = 282.173, n = 12(1971-1982). All estimates in Equation (R13) are significant. Furthermore, an F test at the 1% level of significance indicates that the respective variances of the dependent variables from Equations (R 1 I ) and (R 13) are statistically similar. This again permits the generation of a small sample test statistic and the framing of the following hypotheses:

Ho : PA = ( 1965- 1976) 0.00025907

PA (1971-1982)

=

0.00023229

WI

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DEVELOPMENT

or

(196551976)

(1971-1982)

The critical f2”,.“, is 2.845, and the test statistic generated is 0.6545, well within the region of acceptance. The estimated coefficients are therefore not significantly different from each other. Although the locomotive series is too short to conduct this kind of experiment, the results of Hypothesis (H2) can now indicate that at least in part the results of comparing aircraft and locomotive technology are not particularly functions of select portions of the data series. Rather, those results admit of some generality and, therefore, claim some legitimacy. Summary and Conclusions Given the employment of some methodological rigor, this study generates empirical results that lend some support to Sahal’s hypotheses concerning long-term technological development. The approach to making intertechnological comparisons of the pace of change that we conducted in this study in Part V is no doubt an improvement on Sahal’s earlier attempt. Our approach, however, must be regarded as tentative. Constant percentage rates of change seem intuitively unrealistic and, therefore, have comparative use only. Furthermore, the procedure we used in Part V is woefully specific and is applicable only to a linear estimation of raw data in the Koyck form. Finally, the connection between relative rates of productivity growth and the pace of technical change at this point has little theoretical linkage. An empirical relationship between but two industries and their associated technologies hardly warrants generalization. One could, of course, explore the possible existence of further consistency in such relationships. To find this consistency in conjunction with theoretical insights that could lend it a dimension of causality, however, would be the remarkable achievement. References I. Abernathy,

W.. and Wayne,

K., Limits of the Learning

Curve, Harvard

Business

Review 52,

109-I 19

(1974). 2. Activity Report-Diesel

EIecrric Locomofives, CS-56. Association of American Railroads, Washington, D.C.. monthly. 3. Chaing, H., Fundamental Methods of Mathematical Economics. McGraw-Hill, New York, 1971, pp. 3 19-320. 4. “Civil Aircraft Facilities”, U.S. Department of Transportation News, Office of Public Affairs, Washington, D.C., monthly. 5. Commercial Aircrqft Fleets. AVMARK Inc. and Lockheed Georgia, a division of Lockheed Corporation, Washington, D.C., semi-annual. 6. DeCregori, T., Book Review, Journal of Economic Issues 27, 349-350 (1983). 7. Dhrymes, P.. Distributed Lags. North-Holland, New York, 1981, p. 114. 8. Handbook ofAirline Statisrics. Civil Aeronautics Board, Washington, D.C., 1973, 1975, 1977, biannual. 9. Handbook of Statistics, Federal Aviation Agency, Series Q, Government Printing Office, Washington, D.C., annual. IO. Judge, G., W.E. Griffiths, R.C. Hill, H. Ltitkepohl, T. Lee, Introduction to the Theory and Practice of Econometrics. John Wiley, New York, 1982, pp. 736-741. Il. Judge. G., W.E. Griftiths. R.C. Hill, H. Ltitkepohl, T. Lee, The Theory and Praclice of Econometrics. John Wiley, New York, 1985, p. 299. 12. Kleinbaum, D., and Kupper. L., Applied Regression Analysis and Other Multivariable Methods. Duxbury Press, Boston, 1978, p. 100. 13. Kmenta, J., Elemenrs of Economefrics. Macmillan, New York, 1971, pp. 442-446.

166

G.W. MECHLING.

JR.

14. Linstone, H., Book Review, Journul of Technological Forecasting and Social Change 22, 367-369. 15. Martino, J., Technological Forrcustirqfor Decision Making. 2nd ed., North-Holland, New York. 1983. pp. 98-109. 16. Mowery, D.. and Rosenberg, N., The Commercial Aircraft Industry, in Government and Technical Pro,q ress. R. Nelson, ed.. Harvard University Press, Cambridge, 1984, pp. 101-161. 17. Nelson, R., and Winter. S., Growth Theory from an Evolutionary Perspective: The Differential Productivity Puzzle, American Economic Review 65. 338-344 (1975). 18. Nelson, R., and Winter, S., In Search of Useful Theory of Innovation, Research Poliq 6, 36-76 (1977). 19. Ofjirial Handbook of Airline Sraristics, The, Department of Transportation, Washington, D.C., monthly. 20. Phillips, A., Air Transportation in the U.S., in Technical Change in Regulated Industries. W. Capron ed.. The Brookings Institution, Washington, D.C., 1971. 21. Phillips, A.. Technology and Marker Snucture. D.C. Heath. 1971, pp. 104-109. 22. Pindyck, R., and Rubinfeld, D., Economerric Models and Economic Forecasts, McGraw-Hill, New York, 1981, pp. 364-365. 23. Railroad Facts, I584 Edition, Association of American Railroads, Washington, D.C., 1984, p. 52. 24. Rosenberg, N., A.M. Thompson, S.E. Belsley, Technological Change and Productivity Growth in the Air Transport Industry. NASA Technical Memorandum 78505, Washington, D.C., 1978. 25. Sahal, D.. Technological Progress and Policy, in Research. Development and Technologicul Innovation. D. Sahal, ed., D.C. Heath, Lexington, Mass., 1980, pp. 171-198. 26. Sahal, D., Patferns of Technological Innovation. Addison-Wesley, Reading, Mass., 1981. 21. Sraffa, P., The Producrion of Commodities by Means of Commodities. 2nd ed.. Cambridge University Press, Cambridge, England, 1963. 28. White, K., A General Computer Program for Econometric Methods-SHAZAM, Economerrics, 239-240 (1978). Received I Februury

1986; revised 24 May 1986.