Hybrid Corn Revisited: A Reply
Author(s): Zvi Griliches
Source: Econometrica, Vol. 48, No. 6 (Sep., 1980), pp. 1463-1465
Published by: The Econometric Society
Stable URL: http://www.jstor.org/stable/1912818
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Econometrica, Vol. 48, No. 6 (September,1980)
HYBRID CORN REVISITED: A REPLY'
BY Zvi GRILICHES
that a journal publishes a comment on a 24 year old paper. Nor does it
happen often that an empirical paper survives extrapolation and recomputation. I am
grateful therefore to Robert Dixon for taking on the effort of examining this early work of
mine and to the Editors for providing me with the opportunity for a brief comment on it.
In my original papers (Griliches [4, 5]) the diffusion of an economic innovation was
described by the logistic function with three parameters-the date of first commercial
availability, the rate of acceptance (diffusion), and the "ceiling." The choice of functional
form and the somewhat arbitrary division of the process into three main parameters was
made primarily for the usual econometric reasons: tractability, ease of interpretation, and
satisfactory fit. No claim was made that the assumed form represents some underlying
invariant or inherent "law" of diffusion behavior.
The main critical point of Dixon's comment is that subsequently available data exceeded
the "ceilings" that I assumed at the time. To that extent, my model (as of 1955-7) is clearly
wrong in retrospect both because of its assumption of a constant ceiling and because the
underlying process did not follow a fixed logistic curve exactly. It is possible, as Dixon
suggests, to substitute some other, less symmetric curve for it, such as the Gompretz, but to
get decent fits one would probably need at least a three parameter version of it. Adding
parameters to the curve itself or fiddling with the functional form is not an attractive
alternative, in my opinion. What one gains in fit one loses in interpretability. Instead, I
would now respecify the model so that the ceiling is itself a function of economic variables
that change over time.2
The economic characteristics of the new technology and the state of the economy define a
maximum feasible penetration level ("ceiling"). It is the amount of the new technology that
would be purchased (used) at that particular point of time if there were no uncertainty
about its true characteristics and profitability. It is defined as holding current prices and the
current distribution of the stocks of earlier technologies and sizes of firms constant. The
approach (diffusion) towards such an equilibrium level may be approximated adequately by
a logistic curve, representing the pattern of information spread and learning over time.
One can interpret what I did in the paper as analyzing the rate of diffusion towards such
"ceiling" as determined by the first main wave of hybrid corn varieties (the early hybrids
defined the availability date). Since new hybrid varieties were ultimately developed and
improved to fit various remaining nooks and crannies and since the supplies of the old
technology (open-pollinated seed) eventually dried up, ceilings shifted and the actual
numbers did not follow a single logistic curve all the way but rather a logistic type curve with
a shifting ceiling. It is not clear to me what is accomplished by fitting a single slope
parameter to a period that does not fit the concept of the original model (this comment
applies also to the Gompertz curve). The point is that the later slow upper tail is not the
property of the "acceptance" (diffusion) process, but may be rather a reflection of long lags
in the availability of well adapted hybrids for specific small regions of various states. In any
case, I would now use a model with an endogeneous and shifting ceiling parameter,
something that I believe can be implemented given the current state of econometric art.
Diffusion research emphasizes the role of time (and information) in the transition from
one technology of production or consumption to another. If all variables describing
individuals and affecting them were observable, one might do without the notion of
diffusion and discuss everything within an equilibrium framework. Since much of the
IT IS NOT OFTEN
1
Supported by NSF Grant No. SOC78-04279. I am indebted to Ariel Pakes for helpful comments.
I tried something like that in Appendix B of my thesis [3], but the state of econometric technology
at that time prevented me from pursuing it very far.
2
1463
1464
ZVI GRILICHES
interestingdataare unobservable,time is broughtin to proxyfor at least threedistinctsets
of forces:(1) the declineover timein the realcost of the new technologydue to decreasing
costs as the resultof learningby doing and to cumulativeimprovementsin the technology
itself;(2) the dying-offof old durableequipment,makingroomslowlyfor the new; and,(3)
the spreadof informationaboutthe actualoperatingcharacteristicsof the technologyand
the growthin the availableevidenceas to its workabilityandprofitability.In the workon
hybridcorn I focused on the third "disequilibrium"interpretation,and emphasizedthe
importanceof differencesin profitabilityboth as a stimulus towards closing the disequilibriumgapandas the determinantof the timeit takesto becomeawareof its existence.
Alternatively(see, e.g., David [2]), one can focus on reasons(1) or (2), in whichcase the
existingsize distributionof firmsor the existingage distributionof the equipmentto be
replacedbecomes one of the major determinantsof the rate of "diffusion"or, perhaps
more usefully an explanationof how and why "ceilings"shift over time. The relative
importanceof these forcesvariesfromtechnologyto technologyand the optimalmode of
analysisis likelyto be quitesensitiveto thatandto the kindsof dataavailableto the analyst.
In any case, all such approacheslay stress on the economic determinantsof diffusion
althoughthey differin the emphasesthat they put on them.
InmyoriginalpaperI emphasizeddifferencesin "profitability"
as the majordeterminant
of the rate of diffusionand claimedin a finalfootnote that all otherpossibledeterminants
such as variouspersonalvariablessuggestedby sociologistscould be given an economic
interpretation.Thisled to some controversyin the pagesof RuralSociology(see Brandner
and Strauss[1]; Griliches[6 and7]; Havensand Rogers[8]). If I were to rewriteit today,I
would still take the same position but add "andvice versa" at the end of that footnote.
I wouldlike to note, for the benefitof those who have not read the originalpaper,that
besidesestimatingand analyzingrate of diffusionparametersat the state level, the paper
contains also an analysisof the same parametersat a lower level of aggregation(crop
reportingdistricts),3andseparateanalysesof factorsaffectingthe date of firstavailabilityof
the newtechnologyin the differentareasandfactorsaffectingthe "ceilings"of the diffusion
process as then estimated.In addition,I would like to alert the interestedreadersto a
numberof importantsubsequentwritingsin thisgeneralarea:David [2], Mansfield[9, 10],
Nabseth[11], and Pakes [12], amongothers.
Harvard University
ManuscriptreceivedSeptember,1979.
REFERENCES
[1]
[2]
[3]
[41
[5]
[6]
[7]
[8]
3
L., AND M. A. STRAUSS: "Congruence versus Profitability in the Diffusion of
Hybrid Sorghum," Rural Sociology, 24 (1959), 381-383.
P. A.: "A Contribution to the Theory of Diffusion," Stanford Center For Research in
DAVID,
Economic Growth, Memorandum No. 71, June, 1969.
GRILICHES,
Z.: "Hybrid Corn: An Exploration in Economics of Technological Change," Ph.D.
Thesis, Department of Economics, University of Chicago, 1957.
: "Hybrid Corn: An Exploration in the Economics of Technological Change,"
Econometrica, 25 (1957), 501-522.
: "Hybrid Corn and the Economics of Innovation," Science, 132 (1960), 275-280.
: "Congruence versus Profitability: A False Dichotomy," Rural Sociology, 25 (1960),
354-356.
: "Profitability versus Interaction: Another False Dichotomy," Rural Sociology, 27
(1962), 327-330.
HAVENS,
A. E., AND E. M. ROGERS: "Adoption of Hybrid Corn: Profitability and Interaction
Effects," Rural Sociology, 26 (1961), 409-414.
BRANDNER,
Dixon could not have reproduced that since the underlying data were never published.
HYBRID CORN: REPLY
1465
[9] MANSFIELD, E.: "Technical Change and the Rate of Imitation," Econometrica, 29 (1961),
741-766.
: Industrial Research and Technological Innovation. New York: Norton, 1968.
[10]
[11] NABSETH, L., AND G. RAY: The Diffusion of New Industrial Processes. London: Cambridge
University Press, 1974.
[12] PAKES,A.: "A Simple Aggregate Diffusion Model, Estimation Techniques and a Case Study in a
Secondary Country," Falk Institute Discussion Paper 7613, The Maurice Falk Institute,
Jerusalem, Israel, 1976.