Economic History Association
The Specification Problem in Economic History
Author(s): Robert William Fogel
Source: The Journal of Economic History, Vol. 27, No. 3 (Sep., 1967), pp. 283-308
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THE
JOURNAL
VOLUME XXVII
OF ECONOMIC
HISTORY
SEPTEMBER 1967
NUMBER 8
The Specification Problem in
Economic History
THE rise of the new economichistoryhas provokeda vigorous
debate on methodology.1At issue is the validity of the effortof
econometrichistoriansor cliometricians,as practitionersof the new
work are sometimes called, to apply the mathematicalmodels of
economics to the study of history. Some older historianshave attacked the use of such models on the ground that they violate the
empiricalcharacterof the discipline. In this view, the models employed by the cliometriciansrepresentan unwarrantedintrusionof
speculationinto an area of researchpreviouslylimited to the careful collection and presentationof facts. The most severe criticism
has been directed at the propensityof the new economichistorians
type, that
to deal with questions of the counterfactual-conditional
is, with questionswhich ask how the developmentof the economy
would have been altered by the absence of one or more of its observed features. It has been assertedthat the models which underlie the answersto such questionsare "figments"and that they cannot be verified.2Consequently counterfactualmodels are held to
This essay is a revised version of a paper originally presented to the First World
Congress of the Econometric Society which met in Rome, Italy, during September
1965. I have benefited from comments by Alfred H. Conrad, Ronald W. Jones,
Daniel McFadden, Yair Mundlak, Robert Mundell, Douglass C. North, William N.
Parker,Peter Temin, and Arnold Zellner.
1 The debate has already wound through nearly a score of essays. In addition to
the papers listed below see also those cited in R. W. Fogel, "The New Economic
History: Its Findings and Methods," The Economic History Review, XIX (Dec.
1966), especially pp. 642-43.
2 See, for example, Fritz Redlich, "New and Traditional Approaches to Economic
History and their Interdependence," JouRNALOF EcoNoMIc HISTORY,XXV (Dec.
1965), 480-95.
283
284
Robert William Fogel
be a direct threat to the integrity of economic history as an empirically confirmed description of the economic development of
nations.
These criticisms of the new work have received a strong fillip
from an unexpectedquarter.Robert L. Basmannhas recently suggested that economic histories are sources of decisive evidence
againstwhich the validity of econometricmodels should be tested.3
In so doing he appearsto treat the old economic histories as strict
compendiumsof facts or, at least, as empiricallyconfirmeddescriptions of the economieswith which they deal.4Hence Basmannhas
been interpretedas endorsingthe view that the findingsof the new
economichistoryare necessarilymore speculative-less solidly based
in facts-than were the findingsof the older work.
As an economic historianeager to increase the esteem in which
my disciplineis held, I certainlywould like to supportthe injunction
that Basmannhas directed at his fellow econometricians;however,
this injunctionmust be qualified.Economichistoriesshould not be
conceived of as a bed rock on which one may safely rest an econometricedifice. The belief that the older economichistoryis solidly
groundedin fact is an illusion. Actually, it is permeated with untested covert models and subliminal mathematical assumptions.
Hence, all of the pitfalls of econometricsand econometrichistory
are also present in the old economic history. Indeed, these pitfalls
are more dangerousin the old work than in the new because they
are more deeply concealed. The real differencebetween the new
economic historiansand their predecessorslies in the approachto
the specificationof models ratherthan in the frequencywith which
models are employed.
COVERT THEORY AND MATHEMATICS IN THE OLD ECONOMIC HISTORY
Concealed CounterfactualModels
It is widely agreed that the descriptionand explanationof economic development are the overriding objectives of research in
economichistory.As CarterGoodrichrecently put it, "If the study
3 Robert L. Basmann, "The Role of the Economic Historian in the Predictive Testing of 'Economic Laws,"' Explorations in EntrepreneurialHistory, 2d. ser., Vol. II
(Spring/Summer, 1965), pp. 159-86.
4 For a discussion of tie problem of "objectivity"and theory in economic history
see J. R. T. Hughes, "Fact and Theory in Economic History," Explorationsin EntrepreneurialHistory, 2d. ser., Vol. III (Winter, 1966), pp. 75-100.
The Specification Problem
285
of majoreconomic changes, and their analysis in terms of institutional factors,are not the centralbusinessof economic history,it is
hard to see what our business is."5However, one cannot determine
the economic effects-negative or positive-of the tariff,slavery,the
corporation,railroads,the Bessemerconverter,the reaper,the telegraph,the HomesteadAct, or interregionaltradewithoutconsidering
how the economywould have developed in the absence of such institutions, processes, and artifacts. Obviously these counterfactual
patternsof Americandevelopmentwere not observedand are not recorded in historicaldocuments.In order to determinewhat would
have happened in the absence of a given institution,the economic
historianneeds a set of general statements that will allow him to
deduce a counterfactualsituationfrom institutionsand relationships
that actually existed.
The foregoing suggests that the formulation of counterfactual
questions and the employmentof theories to settle these questions
is a long-standingpractice of economic historians.Yet recent discussionsrevealthat this procedureis not widely accepted. Indeed, it
has been singled out as the most novel and controversialfeature
of the new economic history. Here then is a paradox:a method of
analysisthat is widely used by economic historiansbut not widely
accepted by them, a practice that is both long-standingand novel.
The explanationof the paradoxlies in the fact that while reliance
on counterfactualstatements is a long-standingpractice of economic historians,both these statements and the theories on which
they rest are rarely made explicit. Quite the contrary, they are
usually disguised by a discussion which appears to be concerned
only with conditionsthat actually occurred.
A case in point is Eugene Genovese'shighly regardedessay "The
Significanceof the SlavePlantationfor SouthernEconomicDevelopment."6Genovese holds that the low level of manufacturingin the
ante-bellumSouth was due to the insufficiencyof Southerndemand
for manufacturedgoods. "Plantationslavery,"he writes, "so limited
the purchasingpower of the South that it could not sustain much
5 Carter Goodrich, "Economic History: One Field or Two?" JOURNAL OF ECONOMIC
HISTORY, XX (Dec. 1960), 533.
6 Eugene Genovese, "The Significance of
the Slave Plantation for Southern Economic Development," Journal of Southern History, XXVIII (Nov. 1962), reprinted
in Harry N. Scheiber, ed., United States Economic History (New York: Alfred A.
Knopf, 1964), pp. 149-65; also reprinted in Harold D. Woodman, ed., Slavery and
the Southern Economy (New York: Harcourt, Brace and World, 1960), pp. 223-33.
286
Robert William Fogel
industry.That industrywhich could be raisedusuallylacked a home
market of sufficientscope to permit large scale operation;the resultant cost of productionwas often too high for success in competition with Northern firms drawing on much wider markets."7
Genovese supports this conclusion with evidence that there were
far more poor in the rural South than in other ruralareas, that the
average expenditureper slave on food and supplies by plantation
owners was substantiallybelow the expendituresfor the same purpose by free farmers in the West, that the cost of productionin
Southern textile plants and iron works was higher than in the
Northern ones, and that the insufficientdevelopment of railroads
in the South aggravatedthe marketingproblemsof Southernfirms
by makingthe cost of distributingmanufacturedgoods higher in the
South than elsewhere.8
While Genovese appears to rest his case on "what was" rather
than on "whatmight have been,"his argumentis cruciallydependent on a series of implicit counterfactualstatementsand on a series
of theoretical assumptions.First, when Genovese argues that the
Southernmarketwas too small to permit the most efficient (lowestcost) level of production,he is assertingthe counterfactualproposition that if a bigger marketexisted, the cost of producingmanufacturedgoods in Southernfactorieswould have been lower than it
actually was. Since the condition asserted was not observed, the
propositionimplies the existence of long-runsupply functionsrelating the prices of the manufacturedgoods of Southern industries
to the quantitiesproduced.The propositionalso implies that Genovese had evidence which shows that these curves had negative
slopes.
Second, Genovese'sstatement that Southernindustry could not
compete with Northernfirmsbecause the smallnessof the Southern
marketmade Southernproductioncosts higher than Northernones
implies that if there had been a bigger market the differentialin
productioncosts between the North and the South would have fallen at least to a point at which distributionalfactors would have
enabled Southernfirmsto increasetheir share of sales in local markets. In this instance, demonstrationof the validity of the counterfactual statement requires the existence and a knowledge of the
supply curves of Northern firms in addition to those of Southern
7
8
Ibid., p. 161.
Ibid., passim.
The Specification Problem
287
firms. It further requires the existence and a knowledge of the
functional relationshipbetween the volume of sales and distributional costs in Southernmarkets for both Southern and Northern
firms.More specifically,Genovese implies that at the level of sales
he has in mind, the variousfunctionswere such that the sum of the
productionand distributioncosts of Southernfirmsin local markets
previously closed to them would have been less than the sum of
the same costs for Northernfirms.
Third, the statement that the size of the Southern market for
goods was limited by the existence of slavery implies the counterfactual proposition that in the absence of slavery the Southern
marketfor manufacturedgoods would have been larger than it actually was. Given the consuming groups into which Genovese divides the population,the basic condition for his propositionto be
valid is:9
(D'0 -]Po) + (D"o- iDEo)+ (D8- D- ) + (D -Df) > 0
where
DI
the slave owners'demandfunctionfor manufacturedgoods
to be used in the maintenanceof slaves
Dh-= the slave owners'demandfunctionfor manufacturedgoods
for all other uses
D= = the slaves'demandfunctionfor manufacturedgoods
D = the demandfunctionfor manufacturedgoods of nonslaveholding,free persons.
Symbols with bars refer to the slave period; those without bars
refer to the abolitionperiod.
=
Obviouslythe basic conditioncould have been satisfiedin a multitude of ways. If only ordinalcomparisonsof the pairedfunctionsare
allowed, there are 240 ways of satisfying the inequality. Genovese
did not clearly specify which of these alternativeshe had in mind.
The most that can reasonablybe inferredfrom his discussionis that
De- De > 0 and that Df - Df > 0. The restrictions reduce the
theoreticalalternatives,but the numberremaining(60) is still large.
Fourth, Genovese's comparisonof the difference in per capita
expendituresfor supplies in the West and South is relevant to the
9 This inequality must hold, not for all values of the functions, but only for the
range Genovese presumes to be relevant.
288
Robert William Fogel
effect of slavery on the demand for such goods in the South only
if it can be shown: (1) that per capita expendituresin the West
were higher than they would have been if some stated proportion
of Westernershad been slaves; (2) that the demand response of
Westernersto freedomfrom slaverywas functionallyrelated to the
demand response of Southernersto a change in their institutional
arrangements;and (3) that the first derivativeof this function was
positive.
Fifth, Genovese'semphasison the relative poverty in the South
supportshis argumentonly if income was an independentvariable
with a positive coefficientin an aggregate Southerndemand function for manufacturedgoods.
Sixth, the statement that the high cost of transportationhad an
adverse effect on the ability of Southern firms to compete with
Northern firms in the markets of the South implies the counterfactual propositionthat a reduction in Southern freight rates, all
other thingsbeing equal, would have increasedthe sales of Southern
firms.Genovesewas led to this position by implicit assumptionsregarding the relative positions of the cost functions for the production of boat and railroadservices. More importantthan the validity
of these particular assumptionsis the fact that Genovese's sixth
counterfactualpropositionconflictswith the central assumptionof
his second one. The latter implied both that the supply curves of
Northern manufacturingindustries had negative slopes and that
they were below those of Southernindustriesin the relevantrange.
If true, then in the extremecase of zero transportationrates, Southern firmswould have been unable to sell their goods anywhere in
the South. For in this circumstance,the delivered cost of Northern
goods would have been cheaper than their Southerncounterparts
throughoutthe South. In other words, high internaltransportcosts
acted like a tariffthat protected the internalmarketfrom the outside. The further a local market was from the boundariesof the
South,the greaterthe deliveredcost of Northerngoods and the better the competitive conditions for local manufacturers.Even if
Genovese'sprescriptionwould have increasedthe real income of the
South, it probablywould have retarded rather than advanced the
growth of an indigenousmanufacturingsector.'0
Thus although Genovese appearsto have written an essay about
10 This discussion abstracts from the income effect of a fall in transportationrates,
since that effect would probably have been quite small.
The Specification Problem
289
"whatwas,"his argumentis actuallyabout "whatmight have been."
His crucialpoints presupposea large numberof theoreticalrelationships. Taken together these relationshipsadumbratea massive and
highly complex model of Southerneconomic development during
the ante-bellumera.
It would be wrong to think that "The Significanceof the Slave
Plantationfor SouthernEconomic Development"is atypical. Quite
the contrary.The contributionof the essay rests not on its novelty
but on the skillfulmannerin which its authorhas summarizedand
synthesizeda set of views that are deeply embedded in the voluminous historical literature devoted to Southern economic development. Genovese's essay illustrates well the fundamental position
occupied by implicit counterfactualstatementsand implicit models
in economic historiography."
TheoriesThat ImpersonateFacts
Both those historianswho oppose the intrusionof mathematical
models into their domain, and those econometricianswho look to
historical studies as the ultimate basis for evaluating econometric
models, seem to assumethat the studies of the old economichistory
are compendiumsof facts-or at least that the evidence in such
works can be divided into mutually exclusive categories called
"facts"and "theories."Of course some of the evidence on which
economic historieshave been based can be classifiedunequivocally
as fact. Few would object to giving that title to the Congressional
Globe's report of the division of the Senate's vote on the Pacific
RailroadAct of 1864, to the Bureauof Statistics'reporton the total
value of duties collected on importsduring1870, or to the Commercial and Financial Chronicle'sreport of the closing price on New
YorkCentral Railroadstock for the last Friday of August 1875.
Yet there exists a large and importantcategory of evidence the
members of which are called and accepted as "facts"but which
are actually theories or involve theory in an essential way. Con11 Although it is not labeled as such, one of the earliest and best discussions of
the central position in economic and historical analysis occupied by counterfactual
conditional questions is contained in Fritz Machlup, The Political Economy of
Monopoly (Baltimore: Johns Hopkins Press, 1952), pp. 448-54. See also Ernest Nagel,
The Structureof Science (New York: Harcourt, Brace and World, 1961), pp. 588-92;
Carl G. Hempel, "The Function of General Laws in History," Journal of Philosophy
(1942), reprinted in Patrick Gardiner, ed., Theories of History (Glencoe, Ill.: The
Free Press, 1959), pp. 344-56; and Alfred H. Conrad and John R. Meyer, The Economics of Slavery (Chicago: Aldine, 1964), pp. 3-30.
290
Robert William Fogel
sider the economic historian who turns to page 139 of Historical
Statistics and observes that value-added in all commodity production was $2,690,000,000 in 1859 and $3,270,000,000 in 1869-an increase of 22 per cent between the two dates.12 It is, of course, a fact
that the second number is 22 per cent larger than the first one. If,
however, the economic historian uses this information as the basis
for the statement that the production of commodities increased by
22 per cent during the Civil War decade, he is implicitly invoking
theory.
The point is not merely that major components of the series were
estimated on the assumption that variables were related to each
other by linear functions whose constant terms are zero. Even if
Robert Gallman, the author of the series, had had direct and unquestionably accurate observations of all the underlying components, use of his series as a measure of the production of commodities would still involve theory. For one can determine the direction
and rate of movement of a collection of elements, when these elements have more than one dimension, move in more than one direction, and change at more than one rate, only by adopting a system
of weights which permits the aggregation of the elements into a
single-valued number. Which one of various alternative weighting
schemes ought to be used in a given aggregation process turns on
theoretical considerations. Hence the historian who uses Gallman's
series as an index of commodity production implicitly accepts the
theoretical propositions that led Gallman to aggregate by valueadded.
The weighting problems connected with the construction of national income accounts are, of course, well-known. Some readers
may consider their reiteration here as unnecessary or, even worse,
as irrelevant. After all, some of the best studies in economic history
were published long before the advent of national income accounts.
It might, therefore, appear that the category of facts to which I
have referred-facts which involve theory in an essential way-is of
limited importance in the writing of economic history. However,
while one can conceive of writing an economic history of the United
States without incorporating statistics on national income, it is inconceivable that a history of the American economy would omit the
12 Value-added is in constant dollars of 1879. United States Bureau of the Census,
Historical Statistics of the United States, Colonial Times to 1957 (Washington, D.C.,
1960).
The Specification Problem
291
discussion of such matters as the increase in the output of the
machinery industry, the Civil War inflation, the development of
regional specializationin production, the increase in the amount
of transportationservice provided by railroads,the development
of interregionaltrade, the mechanizationof agriculture,the concentrationof industry,and the effect of the transformationof industrial activity on real wages or the living conditionsof workers.
Of course, every one of these topics poses weighting problems
and theoretical issues similar to those posed by Gallman'sseries.
The output of the machine industry, for example, is not a single
good but a category of goods. While the output of most of the
membersof this category increasedduring the nineteenth century,
the output of some declined. Hence the conclusionthat machinery
production increased depends on a system which gives greater
weight to those products whose output rose than to those whose
output declined. Some economic historianshave traced the rise of
the machineryindustryfrom census reportson the value of its products-thus implicitly weighting physical output by current prices.
Still others appear to have based their conclusionsmerely on the
fact that most of the industry'scomponent series rose over timethus invoking an implicit weighting system that is only weakly
specified.
That the ubiquity of the weighting problem in economic history
is not more widely recognized appears to be due to an irony of
scholarship.Economic historians have long been critical of economic theoristsfor constructingoversimplifiedmodels based on the
assumptionof firms that produce only a single product all of the
units of which are homogeneous. Yet in practice historianshave
adopted the same assumption.They measure the growth of iron
mining,for example,by the tons of ore produced,thus ignoringthe
fact that not all tons of ore have the same content of iron, phosphorus, and other minerals.Differencesof this sort may make one
ton of high-grade ore the economic equivalent of three tons of
another ore. The same oversimplicationis involved when economic historiansmeasure the output of transportationservices in
undifferentiatedton-miles,meat productionin undifferentiatedbarrels, railroadtrack in undifferentiatedmiles, and grain in undifferentiated bushels.'3Whether or not measures that neglect all but
13 The last example is especially bizarre, since a bushel of wheat weighs 60 pounds
while a bushel of oats weighs only 32 pounds.
292
Robert William Fogel
one dimensionof a commoditywill mar the analysisof the economic
historiandepends on the nature of his problem and the characteristics of the commodity.
Economichistory is by no means the only discipline which must
contend with facts whose existence rests on theory. An object
painted in vermilionred can appear to be red or blue or an intervening color depending on the light source to which it is exposed.
The "true"or "actual"color of the paint can only be determined
by procedureswhich are derived from the theory of light.
SubliminalRegressionAnalysis
In general,the earlierthe period under study, the poorer are the
available economic data. As a consequence,the economic historian
frequently finds that numericalinformationcrucial to his analysis
is missing. In the absence of a desired set of data he often adopts
an alternativeone. Textbooksand monographsin economic history
thus use the rate of growthof pig iron as a substitutefor the rate of
growth of the output of the iron industry;miles of main line as a
substitute for the investment in, or sometimes the output of, railroads; spindles in operation as a substitute for the output of cotton textile mills; the distributionof horsepoweras a substitute for
the distributionof machinery;the movementof prices as a substitute
for the growth in the output of an industry;and the growth of receipts at New Orleans as a substitute for the growth of trade between the West and the South.
The methodological issue posed by this procedure is different
from the one discussed in the preceding section. That discussion
dealt with standardsfor transforminga vector or a matrix into a
scalarvalue. In the present case the issue is the functionalrelationship between two sets of numbers,given whatevermethod was used
to computethe membersof each set. What is most importantabout
the examplesI have cited (and the list could be greatly extended)
is the implicit and invariantassumptionthat the functionalrelationship between the designatedvariablesis of the form: y = ax.
THE EXPLICIT THEORY AND MATHEMATICS OF
THE NEW ECONOMIC HISTORY
The Recognitionof NonlinearRelationships
The thrust of the preceding discussionis that the new economic
historiansdeserve neither credit nor blame for introducingtheory
The Specification Problem
293
and mathematicsinto economic history. Theory and mathematics
have always been embedded in the writings of the discipline. In
the past, however, the theorizing was usually implicit. Moreover,
the functional relationshipswere often either weakly specified or
took a very simpleform.In the lattercase, the most commonassumption was that paired variableswere related by linear functionswith
a zero constant term.
The fact that the assumedformswere simple does not, of course,
mean that they were wrong. On a number of importantoccasions,
however, the linear forms assumed by historians have produced
badly biased estimatesas well as errorsin analysis.U. B. Phillips,for
example, believed that unless the rate of growth in cotton prices
was equal to the rate of growth of slave prices, the returnto slave
owners would decline. From this assumption,and from the fact
that the ratio of cotton to slave prices had declined rathersteadily,
he concluded that slavery lacked economic viability by the eve of
the Civil War.'4Phillips failed to give due recognitionto the fact
that equality in the rate of growth of the two prices is not a condition for a constantrate of profit,if the productivityof slaves was
increasing.As Conrad and Meyer have pointed out, the available
data do indeed indicate such a rise in productivity.'5Hence, an
assumptionof linearityled Phillipsto an erroneousconclusion.
The popularbelief that the outputof the ironindustrywas related
to pig iron by a linear function through the origin also appears to
be erroneous.Figure 1 shows that the rate of growth of the total
output of the iron industry departs noticeably from the rate of
growth of pig iron during most of the decades between 1880 and
1890.16On the average,output grew about 25 per cent more rapidly
than pig iron.The disparityis most markedduringthe three middle
decades of the period. From 1850 to 1860, the era of the first great
boomin railroadconstruction,the outputof the ironindustrygrew at
90 per cent of the pig iron rate. This correctionmakesthe 1850'sthe
poorest of the six decades for the iron industry. By contrast, the
14 Ulrich B. Phillips, "The Economic Cost of Slaveholding in the Cotton Belt,"
Political Science Quarterly,XX (June 1905), reprinted in Gerald D. Nash, ed., Issues
in American Economic History (Boston: D. C. Heath and Co., 1964), pp. 244-56.
15 Conrad and Meyer, Economics of Slavery, pp. 74-78.
16 The two series are taken from Stanley L. Engerman and Robert W. Fogel, The
Growth of the American Iron Industry, 1800-1860: A Statistical Reconstruction (in
progress). The total output series is the value of the gross product of the iron industry in dollars of 1860.
Robert William Fogel
294
100,00.Q
0
10,00
_S
1,0
0
10,
-
1, 000
Index of Pig Iron Production
100
1, 000
10, 000
FIGURE1.-Relationship between pig iron production and the total output of the
iron industry, 1830-1890.
1860's, which have been interpreted as an ordinary decade of expansion on the basis of pig iron statistics, emerge as an era of quite
rapid growth. This correction is of some significance to the debate
over the developmental effect of the Civil War, since the progress
of the iron industry has been made an issue in that dispute.'7
These two examples do not, of course, exhaust the instances
in which previously accepted assumptions of linearity have broken
down. The point is that some of the most important revisions of the
new economic history have arisen from nothing more than the dis17 Ralph Andreano, ed., The Economic Impact of the American Civil War (Cambridge, Mass.: SchenkmanPublishing Co., 1962), pp. 150, 165.
The Specification Problem
295
covery that the simple functions assumed in the past are poor descriptionsof the relationshipson which argumentswere anchored.
These are not cases in which theoriesreplacedfacts. They are rather
examplesof the substitutionof new theoriesfor old ones. The basis
for the substitutionis the discoveryof evidence that is incompatible
with the old assumptionsabout functional forms.
The RigorousSpecificationand Testing of Models
I have referredin severalplaces to the problemof weak specification, by which I mean the adumbrationof an equation or a set of
equations. Because so much of the theorizingin the past was implicit, weak specificationhas been the rule rather than the exception. Weakly specified theories are often difficult,if not impossible,
to subject to standard procedures of empirical verification.Thus
because of the vagueness of Genovese'smodel, his argumentabout
the effect of slavery on the size of the market and the growth of
industryin the South depends not on the absolute value of a few
parameters,but on the relative values of a large number of them.
The search for the data needed to estimate these parametersis, at
present, so difficultthat a conclusive test of Genovese'sargument
could easily occupy a lifetime.
The prevalenceof weak specificationin much of the literatureof
economic history weakens the claim that such work constitutes an
empirically confirmed description of American economic development. The dichotomy which some historians have introduced
between facts and theory-and the high esteem showeredon the former as comparedwith the latter-has produced an economic historiographyof uneven quality. The problem is not that these historians have been too concerned with the integrity of their facts
but that they have been insufficientlyconcerned with the nature
of their conceptions of the interrelationshipsbetween these facts.
Because of this neglect they have failed to produce a body of rigorously specified relations among facts, a body of relations so constructedas to be readilyamenableto empiricalconfirmationor contradiction.Consequently,even where the facts of economic history
have been establishedbeyond a reasonabledoubt, the theoretical
networks that bind them together, as well as the implicationsdeduced from the facts and the theories, frequentlyfall in the realm
of conjecture.
Under these circumstancesthe new economichistoryhas focused
296
Robert William Fogel
largely on the task of reformulatingthe vague theories of received
history into rigorouslyspecified and testable statements. An outstanding example of this work is Albert Fishlow's analysis of the
propositionthat Americanrailroadswere built ahead of demand.18
While the proposition is frequently couched in language which
suggests that railroadswere built into unsettled territory,this form
of the hypothesis is so patently in errorthat Fishlow immediately
rejects it. New railroadsbuilt in the West during the 1850'salmost
invariablytraversedterritorieswith populationdensities of from 18
to 45 personsper squaremile-a level which indicates a substantial
developmentof agriculture.
Fishlow arguesthat it is more meaningfulto conceive of the hypothesisas suggestinga disequilibriumsituationin which the demand
curve for transportationserviceoriginallylies to the left of the firm's
average cost curve. Over time the demand curve shifts to the right
until finally average revenues exceed average cost. From the specification Fishlow derives two testable implications. First, during
the early years of such a road'soperation,profitrates should be less
than alternativerates. Second,there should be a positive correlation
between current profits and the age of the enterprise. Statistical
tests contradict both implications,and hence Fishlow rejects the
hypothesis.
It would be wrong to leave the impressionthat the inherited
corpus of the discipline contains only false theories. The rigorous
specificationand testing of theoriesby the new economichistorians
have also contributedto the advanceof the disciplineby confirming
the validity of past argumentsand procedures.Thus Fishlow'sindex
of net real capital formationin railroadsreveals that new miles of
mainroad and capitalformationdid indeed grow at nearly the same
rate during the nineteenth century and hence supports much researchbased on that assumption.19
Even more strikingis Paul David's test of competingexplanations
of the accelerated employment of mechanical reapers during the
18 Albert Fishlow, American Railroadsand the Transformationof the Ante-Bellum
Economy (Cambridge: HarvardUniversity Press, 1965), ch. iv.
19 Albert Fishlow, "Productivityand Technological Change in the Railroad Sector,
1840-1910," in Output, Employment and Productivity in the United States After 1800,
Conference on Research in Income and Wealth, Studies in Income and Wealth, National Bureau of Economic Research, Vol. 30 (New York: Columbia University Press,
1966), Tables 2 and 6.
The Specification Problem
297
1850's.20One theory attributesthe accelerationto a rise in wheat
prices and economies of scale in the utilization of the reaper. The
combinationof these factors, it is said, led farmersto expand the
size of their farms.The second theory stressesthe scarcity of farm
labor and the rise in wages relative to the price of capital. In a deft
analysis,David shows that ratherthan conflicting,the two theories
are compatiblecomponentsof a largermodel. He develops a threshold function which relates the farm size at which it became profitable to substitute the reaper for hand labor to the ratio between
the cost of reapers and the price of labor. David then shows that
the rise in the relative price of labor during the 1850'sreduced the
minimum acreage at which it paid to introduce the reaper, while
the rise in the price of grain provided an incentive to expand the
acreage beyond the thresholdpoint. David's estimates suggest that
the rise in the relative price of labor was twice as importantas the
growth of farm size in promotingthe employmentof the reaper.
The Searchfor "Efficient"Models
The attemptto transformeconomichistoryfroma disciplinebased
on implicit, weakly specified, and untested theories to one based
on rigorouslyspecified and empiricallywarrantedtheories is a prodigious and frustrating enterprise. The greatest obstacle is the
paucity of data. Much has been said in recent years about the
tendency of historiansto exaggerate the shortage of data. While
there is some truthto this charge,the fact is that statisticalevidence
bearing on many importantissues in Americaneconomic history is
exceedingly sparse. Hence the most crucial determinantof success
in the quest for the empiricalconfirmationof theories is the ability
of the economic historian to specify models that are exceedingly
"efficient"in the utilizationof data.
Usually when we speak of efficiencyin econometricswe refer to
the selectionof estimatingproceduresthat make the varianceof the
sampling distributionsof regression coefficientsa minimum. This
problem does, of course, arise in economic history. The data required for the direct measurementof characteristicsthrough regressionanalysis,however, are often wanting. In this circumstance
20 Paul David, "The Mechanization of Reaping in the Ante-Bellum Midwest," in
Henry Rosovsky, ed., Industrializationin Two Systems: Essays in Honor of Alexander
Gerschenkron(New York:John Wiley and Sons, 1966), pp. 3-39.
298
Robert William Fogel
"efficient"specificationrequires the discovery of a model capable
of producingthe desiredmeasuresfromonly those fragmentsof data
which are available. Hence econometrichistoriansrarely have the
luxuryof solving their analyticalproblemsby takingrefuge in large,
complicated equation systems. They must search instead for constructs which, while simple, are neverthelesscapable of describing
the realitieswith which they are concerned.Simple models contain
few parametersand are, therefore, "efficient"with respect to the
available data. The preponderanceof simple models in the new
economic history requires no apology. "Complex"and "elaborate"
are not synonymsfor "powerful."And the epithet for a simplemodel
which has great explanatoryforce is "elegant."
The strategyI have describedis illustratedby Paul David's study
of the mechanicalreaper.David did not derive his thresholdfunction for reapersfrom a regression.In principle he could have proceeded in this manner.One could estimatesuch a functionby drawing a sample of counties and determiningthe size of the smallest
farm which employed the reaper, the delivered price of reapers,
and the averagewage of hand labor in each county. However, it is
a herculeanif not impossibletask to collect these data. Consequently
David deduced the equation from a specificationof the conditions
under which farmerswould be indifferentbetween the choice of a
reaper and hand labor. It turned out that this equation had only
three parameters:the rate of depreciation,the rate of interest, and
the rate of substitution between reapers and man-days of labor.
Data on these parameterswere readily available.
Similarly,Fishlow could have based his test of the hypothesis
that railroadswere built ahead of demand on an attempt to produce statisticaldemand and cost functions.While this approach,if
successful,would have yielded informationthat permitted Fishlow
to develop new lines of inquiry, its cost in terms of data requirements was prohibitive.Instead, as we have seen, Fishlow deduced
implicationsof the model that couldbe tested with relativeease.
The ContinuingProblem of MisspelcifiedModels
To say that the new economic historiansattempt to be rigorous
in the formulationand testing of models does not mean that they
have conqueredthe specificationproblem.Determinationof whether
a given model adequately describes the reality with which one is
concernedremainsthe most difficultchallengeof historicalanalysis.
The Specification Problem
299
Model misspecificationdogs the heels of the new generationas it
did the previous one. Indeed, with the attempt to employ mathematicalmodels for the measurementof characteristicsand the resolution of issuespreviouslyeschewed, the problemhas intensified.
That misspecificationis still a criticalissue is pointed up by Peter
Temin'srecent essay, "LaborScarcityand the Problemof American
Industrial Efficiency in the 1850's."'21Temin's central objective is
clarificationof the issuesinvolvedin the attemptto relate differences
in the development of British and Americantechnology to differences in their factor endowments.By casting the argumentwithin
the frameworkof a two-sectormodel, Temin effectively dispels the
confusionthat surroundedearlierdiscussions.Muchof this confusion
stemmedfrom a failure to recognizethat the existence of a capitallabor ratio in American manufacturingwhich differed from the
capital-laborratio of Britishmanufacturingdoes not necessarilyimply that the two nationshad differenttechnologies-that is, does not
necessarilyimply that their manufacturingsectors were described
by differentproductionfunctions.As Temin points out, the capitallabor ratios of the two nations could differ, although both of their
industrieswere describedby the same productionfunction, if their
factor-priceratios differed.
Temin is not content merely to exploreissues of logic. He goes on
to arguethat the weight of availableevidence actuallysuggeststhat
in the 1850'smanufacturingtechnologywas the same in the United
States as it was in Great Britain. This, in turn, leads him to the
startling conclusionthat the American"realwage" was. below the
British "real wage" and hence that the United States was laborabundant.Temin does not pretend that he has proved these heretical propositions,but he does hold that they are probablytrue or at
least consistentwith currentlyavailableevidence. In what follows I
will attempt to demonstratewhy this claim cannot be accepted.
Temin'sargumentrests on the contentionthat it is reasonableto
describethe U.S. economyof the 1850'sby the followingproduction
functions:
where
(1)
(2)
T)
QM -g(L, K)
QA
-f(L,
QA
- the output of agriculture
21 JOURNAL OF ECONOMICHISTORY,XXVI
(Sept. 1966),
277-98.
300
Robert William Fogel
QM=
L =
T =
K =
the output of manufacturing
labor
land
capital.
Among the assumptionsthat are crucial in the development of
his argumentare the following: (a) Equations(1) and (2) are both
homogeneousof degree one and have positive first and negative
"own"second derivatives."In other words, there are no economies
or diseconomiesof scale, factorsof productionare never redundant,
and there are diminishingreturnsto any single factor."22(b) The
outputof manufacturingwas used both for consumptionand as capital. -(c) The output of agriculture was used only for consumption. (d) Land was used only to produce agriculturalcommodities.
(e) Capital was used only in manufacturing.(f) Capital did not
depreciate.
The last four assumptionsare obviously at variancewith reality.
Are these departuresfrom reality justifiablesimplificationswhich
clarifythe crucialissues without significantlyalteringthe substance
of the argument?In at least two of the cases they are not. Temin
attemptsto justify assumption(d)-the exclusionof land from the
manufacturingproduction function-on the ground that it is the
assumptionof H. J. Habakkukand E. Rothbarth,the authorsof two
well-knowndiscussionsof the nexus between factorproportionsand
the developmentof Americantechnology.23
This is a frail argument. Because their models are not clearly
specified, it may be reasonableto infer that Habakkukand Rothbarth meant to exclude land from the manufacturingproduction
function,but this is by no means the only plausiblereadingof their
essays. Moreover,Temin makes equation (2) do double duty. He
uses it not merely to explicatethe positionsof Habakkukand RothIbid., p. 295. Since I am following Temin's notation, it is worth noting that he
does not use subscripts to distinguish between labor employed in agriculture and
labor employed in manufacturing. It should be understood, however, that the L of
f(L, T) and the L of g(L, K) do not necessarily represent the same magnitude.
Similarly when the symbol QA is used as the dependent variable in equation (1), it
stands for the total output of the agricultural sector. But when QA is used below as
an independent variable, as in equations (3) and (8), it represents only that part
of agriculturaloutput which becomes an intermediateproduct.
23 H. J. Habakkuk, American and British Technology in the Nineteenth Century
(Cambridge, [Eng.]: The University Press, 1962); and E. Rothbarth, "Causes of the
Superior Efficiency of U. S. A. Industry as Compared With British Industry," Economic Journal,LVI (Sept. 1946), 383-90.
22
The Specification Problem
301
barth,but also to interpretactualfeaturesof the economy.The contention that he is following the argumentof his predecessorswill
not justify the second use of equation (2). Therefore,Temin holds
that the omission of T from the equation does not impair its use
as a vehicle for the analysisof the U.S. economybecause the symbol
stands for ordinaryland (not land containingminerals), very little
of which was employed in manufacturing.
Temin provides no justificationat all for assumption (c)-that
agriculturalcommoditieswere used only for consumption.This is
certainlyan unacceptableassumption.Firms employed in the processing of agriculturalcommoditiesaccounted for more than 50 per
cent of the value added by the manufacturingsector in 1860.24Consequently, a more appropriatespecificationof the manufacturing
productionfunction is that given by equation (3).
QM- g(L,
K,QA)).
(3)
But then it follows from equation (1) that the manufacturingproduction function can also be written as
- h(L, K, T),
(4)
QM.
since land is an argumentof QA. Thus, Temin'sexclusionof T from
the manufacturingproductionfunction is not justified by the observationthat little land was directly employed in manufacturing.
Both equations (3) and (4) are superiorto equation (2) as a descriptionof the ante-bellummanufacturingindustry.
As noted earlier, Temin assumes that manufacturingtechnology
was the same in GreatBritainas in the United States;let us call this
assumption(g). Assumption(g) means that equation (2) also describes the British manufacturingsector. Temin offers two reasons
for adoptingthis assumption.First, casualexaminationof subsectors
of manufacturingsuch as iron, textiles, etc., reveals that essentially
the same techniqueswere practiced in both countries.Second, the
techniques employed in each country were known by and were
available to the entrepreneursof the other country. Here again
Temin'sevidence is insufficientto establishhis proposition.Even if
each of the subsectorsin the United Stateshad the same production
function as the correspondingsubsectorin England, the aggregate
24 Robert E. Gallman, Value Added by Agriculture, Mining, and Manufacturingin
the United States, 1840-1880 (unpublished Ph.D. dissertation, University of Pennsylvania, 1956), pp. 357-58.
302
Robert William Fogel
manufacturingproductionfunctionsof the two countriescould differ. This would occur if the percentage distributionof output by
subsectorsin the United States differedfrom that of Great Britain.
Such structuraldifferencesappearto have existedin the ante-bellum
era. Food processingwas a more importantindustryin the United
States than in GreatBritain;and in the case of the iron industrythe
reversesituationobtained.Thus, Temin'scontentionthat subsectors
in the two nations had identical productionfunctions may well require a conclusionthat is the opposite from the one which he embraced, namely, that the aggregateBritishproductionfunction differed from that of the Americanfunction.
What then are the implicationsof Temin'sassumptions?And how
would his findingsbe alteredif assumptions(c), (d), and (g) were
changed along the lines suggested above? These questions can be
answeredmost expeditiouslyif the productionfunction is taken to
Use of an explicitfunction simplifiesthe mathebe Cobb-Douglas.25
matics without diminishingthe force of the argument.
In Cobb-Douglasform, equation (2) becomes
QM = GLa1 Ka2;
a, + a2
1.
(5)
It can be shown that correspondingto equation (5) is a function
called the factor-pricefrontierwhich is given by
1
1
al
r - PMa2Ga2w a2
(6)
where
r
_ the money rental rate of capital
PM = the price of QM
w
G
=
=
the money wage of labor
an index of technological efficiency.
Dividingboth sides of the equationby PMyields
1
a1
i - GW-2
w a2
(7)
where i is the nominalinterestrate and w equals w/Pm. Temin calls
w the "realwage" and holds that equation (7) is also a "factorprice"frontier.When equation (7) is graphed,we have the curve
shown in Figure 2.
25
Such a productionfunction meets Temin's specification.
The Specification Problem
303
It will be noted that W"and i are related negatively. Hence, as
Temin points out, given G, a, and a,-the parametersof both the
production function and equation (7)-i can rise only if w falls,
and vice versa. Moreover,if the British manufacturingfunction is
frontiermust
identicalwith equation (5), the British"factor-price"
be identical with the equation (7). It follows that if the nominal
interestrate in the United States (ia) exceeded that of GreatBritain
then Wa would have to have been below that of Wb. This
(ib),
U.- S. and G. B.
Interest Rate
(i)
a
b
Wa
a)b
Wb
~
frRealw age'
FiGURE2.-Hypothetical "factor-price"frontier for Great Britain and the United
States when technologies are identical. (The subscript b denotes British prices and
the subscript a denotes U.S. prices.)
then is the logic that leads Temin to the proposition that "real
wages"were lower in the United States than in Great Britain.
It is easy to see fromequation (7) that if Americais moreefficient
than GreatBritain (if the Americanvalue of G exceeds the British),
the factor-pricecurves of the two nations will differ. Under this
circumstanceboth Americanfactor prices could exceed their corresponding British factor prices (See Figure 3). Consequently,
Temin requiresidentical technologiesin order to be able to argue
that a relativelyhigher Americaninterestrate implies that its wage
rate was relatively lower. Since Temin's evidence was inadequate
304
Robert William Fogel
to establish assumption (g), he has not eliminated the possibility
that the United States was both labor- and capital-scarce.And this
dual scarcityis the traditionalposition of economic historians.
The traditionalposition could be maintained,even if British and
Americantechnologieswere identical,by using a more realisticpro-
Interest
G. B.
Rate
(i)
a
U. S.
--
,
I
~I
w
b
"Real Wage
(w)
a
FIGuRE 3.-Hypothetical "factor-price"frontiers for Great Britain and the United
States when technologies differ or the production functions have three inputs. (Subscript b denotes British prices and subscript a denotes U.S. prices.)
ductionfunctionthan the one which Temin chose. Equation (8) includes QA as an input in manufacturing.
QM = GLal
a, + a2 +
Ka2 Qaa3;
a.3
(8)
Correspondingto equation (8) we have equation (9).
1
i=Ga2
al
M
a2 PA
a3
2
(9)
It will be noted that a curverelatingi and w (Temin's"factor-price"
frontier) now has the price of agriculturalcommodities (PA) as a
shift parameter.Thus, even if the value of G in the United States
was the same as the British value, the American "factor-price"
frontierwould lie to the right of the British one (see Figure 3) as
long as Americanagriculturalprices were below those in GreatBrit-
The SpecificationProblem
305
ain. But this is the price relationshipthat actually obtained. Consequently it is possible that both the Americaninterest rate and the
"realwage" exceeded those which prevailed in Great Britain (see
Figure 8). Here again the rejectionof one of Temin'sassumptions
-in this case assumption(c) -leads one back to the traditionalconclusion that both capital and laborwere scarce in the United States
during the ante-bellumera. Such a dual scarcity is more credible
than Temin's contention that labor was abundant.26Clearly, the
abundant input during the ante-bellumera was natural resources
(land, minerals,and forest resources).Abundantnatural resources,
especially land, made the price of agriculturalgoods lower in the
United States than in Great Britain.
I have stressedthat the rejectionof assumption(c) reinstatesthe
propositionthat in Americaboth capital and labor were scarce relative to land. This dual scarcity (a condition in which both ia > ib
and W'a > wb) underminesTemin'sattempt to infer, from the fact
that the Americaninterestrate exceeded the Britishrate,27the conclusion that less capital per worker was employed in the United
States than in Great Britain (that is, that La/Ka exceeded Lb/Kb).
The inadmissibilityof Temin'sinferenceis demonstratedin Figure4,
where the slope of line I gives the ratio of the interest rate to the
and the slope of line II gives
"realwage" in Great Britain (ib/Vb)
for the United States.Since
the value of the same ratio (ia/Wa)
lb
a2 Lb
ZWb
--(0
la
a2La
a,
10)
Kb
and
ia
(11)
a, Ka
it follows that
28 A persistence of the dual scarcity, of course, required costs of, and/or barriers
to, international movements of both factors and commodities. These barriers did in
fact exist and took the form of transport costs, information costs, tariffs, and factor
immobilities. The last barrier may merely have reflected the nonmonetary cost an individual incurredwhen he uprooted himself from his homeland.
27 I have accepted Temin's contention that the rate of return in American manufacturing during the ante-bellum era was higher than the rate of return in British
manufacturing.While this contention seems plausible, it should be noted that Temin
does not provide data on manufacturing. The rates he cites pertain to government
bonds (Temin, "Labor Scarcity," p. 291). Hence, the validity of his claim that
manufacturingwas "consistently"more profitable in the United States than in Great
Britainduring the ante-bellum era is not beyond doubt.
Robert William Fogel
306
La
Ka
ia
_
Lb
Lb
Kb
a
~~~~(12)
lb
-:-.
Wb
Thus when the slope of line I exceeds that of line II, the United
States employs less labor per unit of capital (or more capital per
unit of labor) than does Great Britain. Figure 4 shows that the slope
Interest.
Rate'
G.B.
a
"Real Wage"
b
aa)
a
FIGURE4.-Relationship between relative interest rates and relative capital-labor
ratios under conditions of dual scarcity-Great Britain and the United States. (Subscript b denotes British prices and subscript a denotes U.S. prices.)
of line I may exceed the slope of line II even though the American
interest rate is greater than the British rate.
Finally, it should be mentioned that Temin's use of the term "real
wage" to describe the ratio w/PM and his characterization of equation (7) as a factor-price frontier are extremely unfortunate and
have led to much confusion regarding the interpretation of his essay.
While equation (7) is a factor-price frontier in a one-good model,
it is not such a frontier in a two-good model. For w/Pm is not the real
wage of workers but their marginal physical product. It would be
The SpecificationProblem
307
the real wage, in a world of more than one final product, only if
workers spent all of their income on the output of manufactured
goods. Since this condition never obtained, equation (7) is a marginal-physical-productfrontier.
Thus, even if one accepts assumptions (c), (d), and (g), the
function which relates the interest rate to the real wage is given
by equation (13):
i
where P = y1PM+ y2PA=
/PM\
a
1
al
( _) a2Ga2W a2
P
an index of commodityprices;
(13)
= 1)
+
(Y1 ?Y2
y1= the share of income spent on Qm
share of income spent on QA
72=the
w= the real wage = w/P.
It follows from equation (13) that the Britishand Americanfactor-price frontiers could have differed because the real price of
U.S. manufactures(PM/P) exceeded the real price of British manufactures.This, indeed, is what one would expect to observe given
the U.S. abundanceof land, the cost of transportation,tariffs,and
factor immobilities.For since
PM
1(14)
Y1 +
2 V PM)
the larger quantity of land in ante-bellum America would have
caused PA/PM to be lower there than in GreatBritain.Consequently,
PM/Pwould have been higherin the United States.
In this circumstance,the fact that the interest rate in the United
States exceeded that of Great Britain does not necessarily imply
that Americawas labor-abundant,even under the assumptionsof
Temin's model, if the criterion for abundance is either: (1) that
the Americanreal wage was less than the Britishreal wage; or (2)
that the ratio of the real wage to the interest rate was lower in
the United States than in GreatBritain.Temin recognizesthis point
but his discussionof it is obscure.28While he identifieslabor abund28
Ibid.,p. 290.
308
Robert William Fogel
ance with the existence of a low "realwage," his "realwage" is, as
has been pointed out, the marginalphysical product of labor ( ').
Since the real price of manufacturedgoods createsa wedge between
the real wage (w) and the marginal physical product of labor ( w),
the former (w) may be relativelyhigh even though the latter (w)
is relativelylow. Consequently,under Temin'scriterion,the United
States may be labor-abundanteven though its high real wage induces a large flow of foreign workersinto the country.
I do not mean to suggest that Temin'scriterionfor labor abundance is unreasonable,but rather that his terminologyis confusing.
His language tends to suggest contradictionswhen in fact none
exists.
To state that Temin'smore sensationalfindings stem from specification errors by no means implies that the contributionof his
essay was negative. Quite the contrary: Despite the questionable
validity of his specificationof the manufacturingproductionfunction, his paper does much to clarify the nexus between factor endowments and the divergence of Americanand British technology
duringthe nineteenthcentury.Thus, Temin'sessay effectively demonstrates both the promise and the pitfalls of the new economic
history.29
ROBERTWILLiAMFoGEL, Universityof Chicago
At press time it was discovered that a factor of proportionalitywas inadvertently
omitted from equations (6), (9), and (13). The omission does not affect the argument. It merely changes the scale in which the efficiency index is measured.
29