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We Do Not Know the Inhabitants of Each Nation within the World for the Previous Two Thousand Years | The Journal of Financial Historical past

We Do Not Know the Inhabitants of Each Nation within the World for the Previous Two Thousand Years | The Journal of Financial Historical past

2023-09-04 21:14:16

Up to now 20 years, economists have estimated empirical workouts that rely partially on a broadcast work that reviews the inhabitants of each nation on the earth beginning within the 12 months 1 ce and even earlier. The existence of such information surprises these acquainted with analysis on inhabitants historical past; we’ve got solely a tough concept of the inhabitants of most components of the globe earlier than 1500. For a lot of nations, the statistical lacuna extends nearer to the current. Till the arrival of recent censuses, which in most nations began in the course of the nineteenth century, reckonings of the overall inhabitants for even the best-studied circumstances stay topic to appreciable error.

These workouts sometimes depend on McEvedy and Jones’s Atlas of World Inhabitants Historical past (hereafter MJ). Printed in 1978, this work reviews a inhabitants complete for the nations of the world at intervals of a century or half-century. MJ didn’t disguise the tough nature of their information, because the epigraph notes, and we should always distinguish what they report from the way in which others used their work. A number of economists level to a U.S. Census Bureau abstract that seems to endorse MJ’s estimates. The Bureau merely notes that MJ’s estimates for world inhabitants usually are not too totally different from the opposite, earlier outcomes.Footnote 1 As MJ state (pp. 353–4), nevertheless, that settlement is basically by building.

The drawbacks of utilizing such information are quite a few. MJ’s estimates, as they recommended themselves on the time of writing, lacked, in lots of circumstances, any agency basis. Usually, the estimates seem to mirror a judgment in regards to the nature of the economic system in query, rendering their use as financial proxies partially tautological. The MJ estimates are out-of-date for some nations; researchers have offered higher figures previously 40 years. Economists are likely to dismiss measurement error points by interesting to the implications of “classical” measurement error. MJ’s clearly acknowledged rounding guidelines imply the measurement error shouldn’t be classical. Non-classical measurement error create a number of alternatives for bias in regression fashions. Economists have compounded these weaknesses with unwise disaggregation practices.

Many economics articles, together with a number of extremely cited contributions within the main journals, depend on MJ for econometric workouts. This analysis has appeared within the main general-interest economics journals, in growth and growth-oriented journals, and in the primary discipline journals for financial historical past. A number of of those papers have been cited many instances.Footnote 2 The current paper raises severe questions in regards to the outcomes of any econometric train that depends on MJ.

If the proper inhabitants information have been accessible, we might re-estimate particular fashions that seem in revealed papers and assess the results of the measurement-error issues mentioned right here. That is clearly not doable as a result of we lack the proper information. What I do as an alternative is research the way in which MJ assemble and spherical their estimates. This allows us to attract on econometric literature to know the distinction between a mannequin estimated utilizing MJ and a mannequin estimated utilizing corrected inhabitants information. I then talk about extra particularly the way in which some economists have used this inhabitants information. A short replication train utilizing Nunn and Qian (2011) exhibits that some revealed outcomes usually are not strong to cautious consideration of the issues within the MJ information.


MJ report a collection of graphs of complete inhabitants in a rustic (or area), with labels at centuries or half-centuries. Determine 1 reviews the info for Germany in a format much like the figures MJ use to current most of their estimates.Footnote 3 For the 20th century and, in some circumstances, the nineteenth, MJ reproduce official census counts as mentioned by earlier students, typically adjusted for adjustments in nationwide boundaries.Footnote 4 Trendy censuses didn’t begin wherever till the late eighteenth century and weren’t widespread till the nineteenth century.


Notes: Inhabitants figures are in thousands and thousands, rounded by McEvedy and Jones as mentioned within the textual content. Years are centuries till 1600, then embrace the years 1650, 1750, and 1850. The unique determine is reproduced in Guinnane (Reference Guinnane2021, determine 1). I used to be unable to safe permission to breed that graph right here.

Sources: McEvedy and Jones (Reference McEvedy and Jones1978, p. 69), from datafile offered by James Fenske.

One would suppose from studying the economics literature that MJ report exact numbers based mostly on their evaluation of earlier works. Graphs comparable to Determine 1, together with MJ’s descriptions, recommend a unique image. “There are virtually no information on which to base a inhabitants estimate for Germany till we attain the late Center Ages” (McEvedy and Jones Reference McEvedy and Jones1978, p. 70). “Estimates of Poland’s inhabitants earlier than the 14th century are based mostly on nothing greater than basic concepts about doubtless [population – T.G.] densities” (p. 76). For the Maghreb, “There may be actually nothing on which to base any calculations earlier than the 19th century” (p. 220). These feedback are admirably frank, however MJ do, in truth, report inhabitants totals for Germany, Poland, and the Maghreb, and economists have used these observations to check hypotheses we view as necessary. MJ embrace a bibliography for every group of inhabitants estimates, however they sometimes don’t clarify how they used the references they checklist. For Burma, they word that the quantitative document consists of a single publication based mostly on a depend of homes in 1783 in addition to colonial censuses that started in 1871. But MJ report inhabitants sizes for that nation way back to 400 bce (pp. 190–92). This isn’t an remoted instance. In discussing the western hemisphere, they seek advice from debates present on the time they wrote, however these debates recommended giant ranges of estimates and pertain to the many years simply previous to European contact. But MJ present estimates for nations on this area going again many centuries. Most African entries have the identical taste; the one proof MJ cites refers back to the seventeenth century on the earliest, but they report estimates for 2 full millennia.

Caldwell and Schindlmayr (Reference Caldwell and Schindlmayr2002, p. 200) emphasize the issue of helpful inhabitants estimates for a lot of the world, and even for Europe earlier than 1800. Inhabitants figures for the massive areas of the globe that when fell beneath European colonial domination could be the hardest a part of the issue. The essays on the Americas collected in Denevan (1992) doc debates that proceed. Carlos, Feir, and Redish (Reference Carlos, Feir and Redish2022, p. 522), for instance, word that within the early twentieth century, estimates of the pre-contact inhabitants of North America north of Mexico Metropolis ranged from 1.2 to 18 million individuals. Later efforts narrowed that vary to 1.2 to six.1 million individuals. The demographic consequence of colonial contact is one measure of imperialism’s impression on indigenous peoples, so these inhabitants measures carry appreciable interpretative weight. Persevering with variations of opinion don’t mirror a scarcity of analysis.Footnote 5

Systematic dialogue of MJ has been restricted, however specialists have a tendency to not be impressed. As Austin (Reference Austin2008, p. 1102) places it, “Should you search for McEvedy and Jones anticipating a treatise, detailing the unique proof and the reasoning behind the judgements by which it was transformed into useable information, you’ll be disenchanted.” In discussing one explicit research that depends closely on MJ, Austin (Reference Austin2008, p. 1002) says that “there may be merely no epistemological foundation for Nunn’s use of the phrase ‘information’ – actually, ‘issues which are given’ or granted – to seek advice from the guesses which have been made in regards to the inhabitants of future African nations in 1400.”Footnote 6

MJ’s effort displays an extended curiosity on the earth’s inhabitants from distant instances. MJ draw on these earlier efforts, which embrace Clark (Reference Clark1968) and Durand (Reference Durand1974). (On-line Appendix Desk A.1 summarizes the main examples.) Caldwell and Schindlmayr (Reference Caldwell and Schindlmayr2002) talk about the mental historical past of those analysis tasks, stressing their skepticism in regards to the obvious consensus within the figures. MJ’s effort differs from their predecessors in a single necessary respect: the sooner estimates pertain to giant areas or continents. MJ often report populations for the areas that correspond to trendy nation-states.

How did MJ derive inhabitants estimates from earlier than, as they are saying, there was something on which to base such estimates? Studying their descriptions and analyzing the figures suggests 4 overlapping approaches. In some circumstances, they state explicitly their reliance on considered one of these approaches, however extra typically, their methodology solely reveals itself within the estimates. First, they begin with the earliest official census and work backward. What Clark (Reference Clark1968, p. 61) calls “jobbing again” can yield good inhabitants estimates given the precise uncooked supplies and approach. The inhabitants of a rustic in 1500 equals its 1600 inhabitants minus deaths and web emigrants, plus births within the interval 1500–1600. Wrigley and Schofield (Reference Wrigley and Schofield1981, chapter 7) provide an instance of this method. They begin with the dependable census of England and Wales for 1841 and work again in time utilizing estimates of births and deaths, together with extra speculative estimates of web migration, to supply annual populations again to 1541. The problem for earlier intervals is that we hardly ever have something like good counts of births and deaths, a lot much less migrants, and the trouble calls for consideration to complicated sources. Creating the important occasions collection was the center of Wrigley and Schofield’s challenge.Footnote 7

Austin (Reference Austin2008, p. 1002) stresses that momentous historic occasions such because the rise of the Atlantic slave commerce enormously complicate such efforts. Few areas of the globe have been solely spared these destabilizing episodes. Generally we even lack the equal of a dependable end-period enumeration, such because the 1841 census for England and Wales. Current efforts to enhance historic African inhabitants counts present better-reasoned figures than MJ’s for that continent, however run right into a supply downside. The 20th-century colonial censuses that kind their end-period determine are themselves not terribly dependable. As well as, for Africa, we lack the sources that might enable us to estimate the sooner inhabitants will increase wanted for helpful “jobbing again.”Footnote 8

A touch comes from the suspiciously spherical development of inhabitants figures for single nations.Footnote 9 Desk 1 exhibits the general patterns; in lots of circumstances, MJ apparently devised a inhabitants estimate after deciding on a spherical determine for proportion progress. The numerous commonalities throughout nations are implausible. Particular person nation histories drive house the issue. In MJ’s reckoning, England’s inhabitants grew by 750,000 between 1600 and 1650, and by one other 750,000 within the subsequent half-century (McEvedy and Jones Reference McEvedy and Jones1978, p. 43). Austria added 250,000 individuals each 50 years between 1650 and 1800 (pp. 88–92). Thailand added 250,000 individuals in each the sixteenth and seventeenth centuries (p. 193). Burma’s inhabitants progress throughout the identical interval was 500,000 per century.


Second, MJ apparently wished their estimates to mirror their view that till the late medieval interval, inhabitants grew at a relentless charge. In disagreeing with an earlier creator on the precise complete world inhabitants for the 12 months 1000, MJ word that “our determine for AD 1, being 100m beneath the agreed determine for AD 1000, suits higher on the form of exponentially rising curve that everybody agrees finest describes mankind’s inhabitants progress” (p. 354). Because the citation implies, MJ additionally nervous about consistency between theirs and earlier estimates. Caldwell and Schindlmayr (Reference Caldwell and Schindlmayr2002, p. 199) name this “an instance of a harmful circularity,” whereas Biraben dismisses the MJ information after noting this reality.Footnote 10

Third, within the face of ignorance, MJ felt snug assigning an identical progress charges to locations they thought have been related. This apply likely underlies a lot of what we see in Desk 1. For 35 p.c of nations, MJ assign the identical determine to inhabitants progress between the years 1 and 1000.

Lastly, particularly earlier than 1500, MJ tended to purpose from the character of an economic system and the inhabitants they thought it might assist. They’re hardly ever express about this tactic, however it exhibits via remarks comparable to “doubtless inhabitants densities” within the passage about Poland quoted earlier. To the extent that they estimate inhabitants on this means, MJ’s figures mirror not the inhabitants of a selected nation at a cut-off date, however their views in regards to the inhabitants density in line with the sort of economic system MJ thought the nation had. Since they don’t declare any severe information of the economic system or of the variety of individuals it could assist, the idea for this reasoning is unclear.Footnote 11


A number of of the articles mentioned later rely partially on estimates reported by the late Angus Maddison. Maddison famously constructed, up to date, and used a database that provided estimates of inhabitants and GDP/capita for a lot of the world’s nations, once more, in some variations, going way back to the 12 months 1 ce.Footnote 12 For the final main revision of his estimates, Maddison says of his inhabitants information: “The next detailed estimates for 1500 onwards rely closely on monographic nation research for the main nations. To fill holes in my dataset I draw on McEvedy and Jones (Reference McEvedy and Jones1978). For the previous millennium and a half, I exploit their work extensively” (Maddison Reference Maddison2001, p. 230). Maddison provides that he depends on MJ quite than earlier accounts as a result of MJ are “essentially the most detailed and finest documented” (p. 230).

Thus, for a lot of locations earlier than 1500, Maddison’s database simply reproduces MJ’s figures. This isn’t all the time the case, nevertheless; Maddison was capable of incorporate the fruits of analysis revealed between 1978 and his personal publication. This led to some substantive revisions, however these revisions mirror the analysis literature’s emphasis. He up to date 23 p.c of MJ’s observations for the 12 months 1000, for instance, and 40 p.c of the observations for 1500. Nearly all of Maddison’s adjustments for the 12 months 1000 have been in non-European nations (eight of 9 nations that modified have been outdoors Europe). For 1500, this sample adjustments; 10 of 16 adjustments are for European nations, and in 1700, 8 of 12 are for Europe. These adjustments mirror contributions from the analysis literature.

Some particular person adjustments are a lot bigger, nevertheless. Maddison added 50 p.c to Mexico’s inhabitants for the 12 months 1000, and he doubled Peru’s inhabitants in that very same 12 months (Maddison Reference Maddison2001, desk B-5, p. 235). He elevated the inhabitants of the territory that might change into the USA by 125 p.c for the 12 months 1500. For later intervals, particularly within the twentieth century, Maddison revises the MJ estimates extra comprehensively. In 1850, 84 p.c of Maddison’s 51 observations have values totally different from MJ’s, though the common absolute distinction (3 p.c) is smaller than for earlier years.Footnote 13


Relative to “good” information for each nation on the earth, how far fallacious will MJ take us? It’s price reviewing some basic penalties of measurement error for the sorts of linear fashions that almost all researchers use.Footnote 14 Denote the true inhabitants of nation i in 12 months t as Ṗit. The MJ estimate is Pit. The distinction between MJ’s estimate and the true inhabitants is the measurement error ε it, such that Pit = Ṗit + ε it. Classical measurement error is the particular circumstances the place ε it is additive and uncorrelated with Ṗit. We’ve got two basic implications. First, classical measurement error within the dependent variable alone doesn’t bias estimates. The ε it are swept into the regression error time period, and the one consequence is a few effectivity loss. Second, measurement error in any regressor implies bias in all of the estimates.

Think about the next regression:


$[{{rm{Y}}_{{rm{it}}}}{rm{ = alpha + beta }}{{rm{X}}_{{rm{it}}}}{rm{ + gamma }}{{rm{P}}_{it}}{rm{ + }}{{rm{mu }}_{{rm{it}}}}{rm{,}}]$

the place Pit is the mis-measured variable. Whereas I write Equation (1) for a panel framework, that’s not vital for what follows. Classical measurement error in Pit implies that the estimate for γ might be smaller in absolute worth than it will be if we might use Ṗit as an alternative. The estimate is attenuated. The estimate for β will even be biased in methods we can not ordinarily signal. The issue arises from the correlation between the measurement error ε it and the regression error time period μit, which is why some researchers make use of instrumental-variable strategies in utilizing the MJ information as a regressor. The fixed-effects estimator doesn’t essentially yield unbiased estimates within the presence of even classical measurement error. Fastened results solely “offers with” measurement error if the errors in Pit are, for every nation i, the identical for all years. In that case, the measurement error turns into a part of the estimated nation fastened results (Deaton Reference Deaton1997, pp. 108–110).Footnote 15

Classical measurement error within the dependent variable ordinarily doesn’t bias regression estimates as a result of the measurement error is added to the regression disturbance time period. This consequence requires that the measurement error be additive: Pit = Ṗit + ε it. One frequent case of non-additive measurement error seems when the dependent variable is the ratio of two variables and the denominator is measured with error. Think about a standard instance: an urbanization determine is fashioned because the variety of individuals residing in cities divided by MJ’s inhabitants estimate. Rewriting Equation (1),


$[{{rm{C}}_{{rm{it}}}}{rm{/}}{{rm{P}}_{it}}{rm{ = alpha + beta }}{{rm{X}}_{{rm{it}}}}{rm{ + }}{{rm{mu }}_{{rm{it}}}}{rm{,}}]$

the place Cit is the city inhabitants. Utilizing MJ’s inhabitants estimate implies that the denominator is the true inhabitants plus measurement error, Pit = Ṗit + ε it. Substituting and re-arranging, we’ve got:


$[{{rm{C}}_{it}} + {rm{alpha }}({{rm{dot P}}_{it}} + {varepsilon _{it}}) + {rm{beta }}{{rm{X}}_{{rm{it}}}}({{rm{dot P}}_{it}} + {varepsilon _{it}}) + {mu _{{rm{it}}}}({{rm{dot P}}_{it}} + {varepsilon _{it}})]$

The ratio within the unique dependent variable makes the measurement error multiplicative and causes bias in estimates of β. Extra usually, if measurement error shouldn’t be classical, then we have to mannequin the error. Hyslop and Imbens (Reference Hyslop and Imbens2001) talk about a number of circumstances, together with one the place measurement error in a regressor results in overestimates of that coefficient as an alternative of the attenuation we anticipate with classical measurement error.

What does this imply for econometric research that used mis-measured inhabitants estimates? If we keep the belief that the measurement error is classical, we will say two issues. When inhabitants is the dependent variable, the estimates could also be much less environment friendly, however there ought to be no bias resulting from measurement error alone. If inhabitants is a regressor, however, then the estimate for inhabitants might be attenuated. Moreover, the opposite estimates on this case might be biased and inconsistent. Thus, utilizing inhabitants as a “management” can result in bias even for variables not thought to undergo from measurement error. If the error shouldn’t be classical, however, then we can not say a lot with out modeling the measurement error.

Whereas economists are likely to assume that measurement error is all the time classical, on this case, we all know that this isn’t the case. MJ state that they’ve rounded their estimates in ways in which make the measurement error rely on the true worth. This rounding applies to each nation and each interval, however the rounding rule is dependent upon the inhabitants measurement. This implies the measurement error is dependent upon inhabitants measurement:

All figures are rounded on the next system: beneath a million to the closest .1 million, between one and 10 thousands and thousands to the closest .25 million, between 10 and 20 million to the closest .5 million and between 20 and 100 thousands and thousands to the closest million. Above 100 million the rounding is to the closest 5 million, above a billion… to the closest 25 million. (McEvedy and Jones Reference McEvedy and Jones1978, p. 9)

Thus, MJ inform us that they create measurement error that’s bigger for bigger populations. We can not know exactly the implications of MJ’s rounding guidelines. We will, nevertheless, simulate the “true” populations to get a really feel for the way a lot bother the rounding could cause. I exploit a Monte Carlo train to simulate the rounded-off portion of every inhabitants estimate. Including that rounded portion to MJ’s reported numbers yields a simulated “true” inhabitants. We will then ask whether or not that simulated “true” inhabitants is correlated with the error attributable to rounding. This train can solely tackle the measurement error attributable to rounding; the opposite flaws stay. Desk 2 exhibits the consequence: the rounding induces a excessive diploma of correlation between the measurement error and the inhabitants. This consequence holds for 4 totally different assumed purposeful kinds for the rounding error, together with two which are uneven in several methods. The correlation stems from MJ’s totally different guidelines for various measurement classes.


On-line Appendix Part 2 reviews particulars of this simulation together with two extra assessments of the significance of this rounding. The primary makes use of the populations of the 50 United States for the interval 1900–1970. The second makes use of the populations of nations all over the world for the interval 1960–2020. In each circumstances, I apply MJ’s rounding guidelines and study the correlation between the true values and the errors created by rounding. Rounding for the U.S. states doesn’t persistently suggest correlation, whereas for the nations of the world, the correlation between the true worth and the measurement error is appreciable. The nations dataset is the nearer analogy to MJ as a result of the nations span your entire vary of their rounding guidelines.

MJ’s rounding process creates a definite downside when a rustic’s inhabitants crosses one of many thresholds implied by their rounding rule. Portugal, they report, had a inhabitants of 900,000 in 1400 and 1.25 million in 1500 (p. 103). These figures suggest that Portugal’s inhabitants elevated by 350,000 individuals, or 39 p.c, in these 100 years. Taking the rounding into consideration, nevertheless, implies higher and decrease bounds for the inhabitants estimate in each 1400 and 1500. The true enhance may very well be as small as 19 p.c or as nice as 58 p.c.

The non-classical nature of the measurement error in MJ poses a significant issue for any estimates that depend on it. We will consider earlier, revealed work beneath the belief of classical measurement error, and that’s not a nasty place to begin. However MJ’s rounding applies to each nation and interval of their information, which signifies that none of the usual intuitions based mostly on classical measurement error actually apply.


Many economists who use MJ’s figures consider inhabitants (or a by-product comparable to inhabitants density) as a proxy for an financial combination comparable to output. Critics comparable to Caldwell and Schindlmayr (Reference Caldwell and Schindlmayr2002) and Austin (Reference Austin2008) word MJ typically use concepts in regards to the economic system to derive an estimate of inhabitants measurement, thus making the inhabitants estimates a poor proxy for an financial combination. That is very true in locations and instances for which the inhabitants information are skinny. As famous, MJ defend an estimate for medieval Poland by referring to “doubtless inhabitants densities.” In a extra express instance, MJ talk about agricultural circumstances in a area that includes the trendy states of Columbia, Venezuela, and the Guyanas to defend their assumption that till 1500, Colombia all the time accounted for two/3 of the area’s inhabitants (McEvedy and Jones Reference McEvedy and Jones1978, p. 302).

Austin stresses that this method makes their estimates hostage to concepts about an economic system and financial change. It’s a explicit downside for Africa as a result of we all know comparatively little about that continent’s financial historical past. Maddison (Reference Maddison2001, p. 238), for instance, adopts MJ’s estimates for Africa as opposed to earlier options as a result of MJ “assumed a extra dynamic progress course of.” That’s, Maddison most well-liked MJ’s inhabitants estimates as a result of he agreed with their evaluation of the African economic system. Neither Maddison nor MJ provide impartial proof in regards to the African economic system. To the extent MJ assigned inhabitants estimates based mostly on their perceptions of financial efficiency, a regression utilizing inhabitants as a proxy for progress tells us extra about MJ than about financial progress.


Researchers who use MJ’s information deal with them as in the event that they suggest impartial observations; put in a different way, if there are N nations listed for a given 12 months, this displays N items of knowledge. This isn’t all the time true, for 2 distinct causes that I’ll name “comfortable” and “laborious” clones. MJ themselves create the comfortable clones. Frankly admitting that they lack significant information, they assign to some nations the inhabitants dynamics of nations they suppose are related. Generally they make this method express. After concluding that Afghanistan has no helpful inhabitants information earlier than the 20th century, MJ say that “Maybe the very best method is to check Afghanistan with Iran” (McEvedy and Jones Reference McEvedy and Jones1978, p. 156). What they did, in truth, was to imagine that Afghanistan had half the inhabitants of Iran in yearly earlier than 1900. The measurement error for Afghanistan thus has two sources. The Afghan numbers share any measurement error within the figures for Iran, they usually additionally undergo from the error implied by any deviation of Afghanistan’s true inhabitants dynamics from Iran’s.

MJ consists of many comfortable clones. Kenya and Uganda, for instance, had an identical populations via 1800, though the textual content doesn’t say why. In some circumstances, they attraction to the concept neighboring nations ought to have related inhabitants progress charges: “… the truth that inhabitants doubled in most European nations between A.D. 1000 and 1300 could be taken as robust proof for it doing so in different European nations for which direct proof is missing” (p. 11). Thus, of their reckoning, Poland, Hungary, and Czechoslovakia every grew 20 p.c between 1000 and 1100. Within the fifteenth century, European Russia and China every grew by one-third. As late as 1600–1700, Romania and Austria every grew by 11.11 p.c. Tender clones most likely underlie the patterns we see in Desk 1.


A closing downside displays each MJ’s estimates and the way in which some economists have used them. MJ report many populations for areas quite than trendy nations. Some economists create country-level populations out of the areas by allocating the regional inhabitants among the many constituent trendy nation-states. I’ll name the ensuing nations “laborious clones.” Within the cross-section, these clones differ in measurement throughout the area. By building, nevertheless, within the time collection, all members of a clone group share the inhabitants progress charge MJ assigned to the area. Arduous clones account for an particularly giant portion of the African country-level observations, however they seem in different components of the world, as effectively. In Nunn and Qian (2011), laborious clones account for 76 p.c of the observations in Africa, 36 p.c in Europe, and 41 p.c in Asia. In Ashraf and Galor (Reference Ashraf and Galor2011), the clones are related for these continents; three-quarters of their Western Hemisphere nations are clones.Footnote 16

The literature consists of two alternative ways to create nations out of areas. Nunn (Reference Nunn2008, p. 170) assumes that the relative sizes of the populations inside every area are the identical as reported for 1950. Nunn and Qian (2011) don’t say explicitly how they disaggregated the areas, however for many nations, their inhabitants figures are much like Nunn’s, so the method might be related.Footnote 17 Ashraf and Galor (Reference Ashraf and Galor2011, Reference Ashraf and Galor2013) disaggregate the areas by assuming that every nation inside a area has the identical inhabitants density in every year. Basically, the ensuing “nation” populations created by the 2 strategies differ within the cross-section; Nunn and Qian’s Nigeria in 1500 shouldn’t be the identical measurement as Ashraf and Galor’s. But each cloning strategies suggest that Nigeria has the identical progress charge between any two years. This progress charge is solely the speed implicit within the area from which Nigeria is cloned.

Arduous cloning provides additional error to MJ’s guesses; how a lot is one thing we can not say exactly as a result of we have no idea the true populations of the clones in these years. We will, nevertheless, research the implications of those two strategies in contexts the place we’ve got the equal of legitimate country-level numbers. For the years 1900–1970, I constructed a panel from the inhabitants of the 50 United States as reported within the decennial census. I then combination the state populations into 4 customary areas. The state populations (which we all know) are analogous to the unknown nation populations that tough cloning makes an attempt to recuperate. The U.S. areas are just like the areas within the MJ e book. I apply each the Nunn-Qian and Ashraf-Galor strategies to estimating the inhabitants of every state within the interval 1900–1960, as if all I knew was the inhabitants of every state in 1970 (for Nunn-Qian) and the state space and regional inhabitants in every year 1900–1970 (Ashraf-Galor). Desk 3 summarizes the errors these strategies produce. In most years, the Nunn-Qian method produces smaller errors than Ashraf-Galor, though these errors are nonetheless giant. Solely in 1960 did the median error from the Nunn-Qian method fall beneath 5 p.c of the particular state inhabitants. The Ashraf-Galor method produces a smaller median error within the early years, however the variance of the errors utilizing this methodology is giant. The 2 sorts of error usually are not extremely correlated within the cross-section.Footnote 18


What does this train inform us about disaggregating MJ’s areas? The Nunn-Qian methodology assumes that inhabitants progress charges inside every area are related over time. The strategy goes fallacious for areas with a state like California, which skilled particularly speedy progress within the twentieth century. In 1900, California’s inhabitants accounted for 34 p.c of the “West” area; in 1970, it was 57 p.c. That is most likely why the Nunn-Qian method improves monotonically higher over time; the Seventies weights higher approximate the inhabitants distribution in 1960 than in 1900. It additionally illustrates the hazard of their analysis, which begins with MJ’s estimates for 1000. Between the years 1000 and 1950, there was loads of alternative for the nations inside a area to develop at totally different charges, producing a model of the issue famous for California.Footnote 19 Ashraf and Galor’s method, however, requires that the inhabitants densities for nations inside a area be an identical. This method fares poorly within the U.S. case due to the unequal inhabitants densities inside some U.S. areas; the “Midwest” area, for instance, consists of states like Ohio (204 individuals per sq. mile in 1900) in addition to states like North Dakota (9 individuals per sq. mile). The belief is unlikely to carry at any cut-off date, and the discrepancy between assumption and actuality might change over time with the introduction of recent crops or different adjustments that result in uneven financial growth throughout the area. The U.S. expertise might not present a strict analogy to the areas these two strategies try to disaggregate, however this train highlights how far fallacious issues can go if robust assumptions don’t maintain. The U.S. case additionally highlights the questions that we would wish to ask earlier than disaggregating information on this means. Do we actually know sufficient in regards to the sub-regional patterns within the Sahel in 1000, for instance, to divide up a regional inhabitants?

See Also

The laborious clones play an particularly necessary position in Africa. MJ report solely 12 areas for Africa. Nunn (Reference Nunn2008)’s Africa has 52 nations, whereas Nunn and Qian (2011)’s have 47.Footnote 20 Three-quarters of the African observations are thus clones. Given the distinction in strategies, we anticipate Nunn-Qian and Ashraf-Galor to assign totally different populations to the identical nation, however the variations could be large. On-line Appendix Determine 1 reviews the distribution of the ratio of Ashraf-Galor’s clones to Nunn-Qian’s for the Outdated World in 1500. This determine illustrates the nice vary in values for a given place and time that consequence from cloning the MJ areas. In Africa, this ratio ranges from .192 (Malawi) to .61 (Nigeria) via South Africa (1.003) to Congo (2.208) and Côte d’Ivoire (2.887).Footnote 21

The disaggregation issues account for under considered one of two totally different sources of measurement error for laborious clones. The primary comes from MJ itself; MJ’s regional estimates are themselves noisy and rounded. Cloning assigns that noise to every of the country-level figures and provides extra error as a result of we don’t actually know what the precise allocations inside a area ought to be. This extra disaggregation error is, by definition, negatively correlated for nations inside a given MJ area and 12 months. The cloned inhabitants estimates can’t be “appropriate.” The implications for change over time, nevertheless, are the identical: each clone from a given area should develop on the identical charge, the expansion charge MJ assigned to the area. Breaking these areas up into observations doesn’t create extra info. It simply creates clones.

Econometric Implications of Arduous Clones

We can not re-estimate earlier fashions utilizing appropriate inhabitants information as a result of that’s clearly not accessible. The very best examine on the implications of cloning could be to dispense with the disaggregation and re-estimate the fashions utilizing the models MJ reported. Since that examine would require redefinition of all the opposite variables as effectively, it lies past the scope of this paper. We will, nevertheless, present that counting on clones considerably impacts the outcomes of revealed analysis. The next dialogue solely considers two circumstances and focuses on this challenge alone. Desk 4 considers the baseline outcomes from Nunn and Qian (2011), which research the previous query of whether or not the potato’s introduction within the Outdated World brought on inhabitants progress. The regressions use the inhabitants of all nations within the Outdated World at century intervals between 1000 and 1900, together with the years 1750 and 1850. The dependent variable is all the time inhabitants. Though they report and talk about different specs, Nunn and Qian give attention to fashions by which the regressor of curiosity is the interplay between an index of the fraction of a rustic’s land that’s appropriate for potato cultivation and a dummy for the years 1750 and later. They regard this interplay as a proxy for the impact of the potato’s precise introduction.Footnote 22 Each specification consists of 12 months and nation fastened results. Some fashions haven’t any extra controls; we give attention to fashions that embrace the “baseline” controls.


Desk 4, Column (1), reproduces the consequence from Nunn and Qian (2011, desk IV, column (1)). As they stress, the interplay implies that the potato’s introduction elevated inhabitants sizes within the years 1750 and later. Once we drop the African clones (Column (2)), nevertheless, the purpose estimate (and the common marginal impact) are now not considerably totally different from zero. Dropping all clones (Column (3)) doesn’t produce this impact; the issue seems to be the African clones. However, if we drop all of Africa (Column (4)), the purpose estimate and common marginal impact (AME) change into even smaller. On condition that about three-quarters of the African observations are clones, it’s troublesome to know whether or not Africa typically doesn’t match the story or if there’s something explicit to African clones.

The following three specs repeat (2)–(4) utilizing Nunn and Qian’s information however use the Ashraf-Galor definition of clones. The outcomes differ considerably, however the general message is identical. On this mannequin, it doesn’t matter how we assemble the clones; dropping Africa’s clones, all clones, or all of Africa has the identical impact as with Nunn and Qian’s definition. Desk 4 holds two classes. First, the Nunn-Qian consequence relies upon critically on the inclusion of Africa or its clones. This will not maintain for all of Nunn and Qian’s specs, though On-line Appendix Part 4 demonstrates the identical downside of their totally versatile method. Second, and extra usually, on this instance, it doesn’t a lot matter how we assemble the laborious clones. This follows from together with country-level fastened results. Since identification comes from within-country change and because the clones, nevertheless constructed, all have the identical progress charges because the areas from which they’re disaggregated, in such a mannequin, the error created by cloning doesn’t rely on how the clones are constructed.Footnote 23

Fastened-effects fashions can not remedy measurement error typically, as I harassed earlier. Even the nations that aren’t clones within the Nunn-Qian or Ashraf-Galor datasets have rounding error plus the measurement error inherent in MJ’s guesses. This replication train makes a slim and particular level. I’ve proven that first, Nunn and Qian’s outcomes rely on together with African observations which are actually clones, and second, there isn’t a necessary distinction between the extra measurement error created by two alternative ways of making laborious clones.Footnote 24 Absolutely those that will depend on MJ sooner or later ought to at the least dispense with the clones and use as their models of study the areas that seem within the inhabitants information.


To acquire a extra particular concept of how economists use these information, I examined each paper that cites MJ that was revealed in one of many “High 5” economics journals via 2020.Footnote 25 I put aside many of those papers for the remainder of this dialogue. This checklist features a few articles that cite MJ however don’t use the info in econometric workouts. Shiue and Keller (Reference Shiue and Keller2007, p. 1194), for instance, cite MJ and different authorities as implying that their two areas, China and Europe, had related populations on the finish of the eighteenth century. Rogers (Reference Rogers1994, p. 467) cites MJ to defend the belief that long-term inhabitants progress charges have been practically zero till comparatively not too long ago. This utilization appears in line with the spirit by which MJ provide their estimates. I additionally put aside papers that solely use MJ’s estimates for 1900 and later. By that date, the data MJ reviews comes virtually solely from affordable census reviews (though they spherical even these figures). This consists of articles comparable to Acemoğlu, Johnson, and Robinson (Reference Acemoğlu, Johnson and Robinson2001).Footnote 26

A primary query pertains to dates; the MJ information are extra suspect in earlier intervals. The 12 months 1500 doesn’t kind a magical dividing line, however it’s the earliest 12 months for which we’ve got something like dependable estimates for populations of even most European nations, which are likely to have the best-founded estimates. A number of articles rely in a severe means on MJ’s inhabitants estimates from earlier than 1500. Ashraf and Galor (Reference Ashraf and Galor2011) report econometric outcomes that rely critically on inhabitants information from the years 1, 1000, and 1500. Inhabitants is the variable of curiosity in Nunn and Qian (2011), which begins with the 12 months 1000. Nunn (Reference Nunn2008) makes use of the 1400 estimates alone.Footnote 27 A number of different papers additionally depend on information from 1500–1800.

A second challenge is whether or not MJ’s inhabitants figures kind the dependent variable or a regressor. Many articles use inhabitants because the dependent variable, the place it does least hurt beneath the belief of classical measurement error. These embrace Ashraf and Galor (Reference Ashraf and Galor2011, Reference Ashraf and Galor2013) and Nunn and Qian (2011).Footnote 28 In others, the MJ information scale the dependent variable. As famous beforehand, this implies the measurement error within the dependent variable shouldn’t be classical, and the estimates are biased in unpredictable methods. Acemoğlu, Johnson, and Robinson (Reference Acemoğlu, Johnson and Robinson2005)’s urbanization regressions are an instance.

Some articles, nevertheless, create regressors from MJ’s estimates. This checklist consists of Iyigun (Reference Iyigun2008) in addition to Gennaioli and Voth (Reference Gennaioli and Voth2015). Iyigun (Reference Iyigun2008) research whether or not navy strain from the Ottoman Empire helped cut back battle amongst European states within the early-modern interval. The econometric fashions depend on annual observations for the interval 1450–1700. The dependent variables measure intra-European battle. The controls embrace measures of Ottoman navy strain in addition to the populations of Europe and, in some specs, the Ottoman Empire’s. Iyigun (Reference Iyigun2008, p. 1476) describes the inhabitants information as a proxy for financial “measurement and power.” The estimated impact for European inhabitants measurement is imprecisely estimated in most specs, whereas the Ottoman inhabitants variable is extra exactly estimated however switches indicators, relying on the dependent variable. The purpose estimates for each inhabitants variables should be attenuated if that is classical measurement error, so we can not actually say whether or not Europe turned extra peaceable merely due to financial progress, nor can we assess the implications of Ottoman financial circumstances for European battle. Furthermore, the estimates for his major variable of curiosity, the extent of Ottoman navy incursions into Europe, could also be biased due to the measurement error in inhabitants.

Gennaioli and Voth (Reference Gennaioli and Voth2015, desk 3) tackle a associated query, and their inhabitants figures trigger related bother. They research the determinants of battle success in early-modern European conflicts. The authors set this up as a horse race between fiscal power on the one hand and inhabitants measurement on the opposite. Larger fiscal power permits a state to pay extra mercenaries and assist extra allies. Inhabitants measurement might matter in early-modern warfare as a result of bigger populations make it simpler to discipline bigger armies. In most specs, the fiscal variable has a constructive and vital impact on battlefield success, whereas the relative populations of the 2 combatants have virtually none. They conclude that “Variations in inhabitants measurement shouldn’t have a scientific impact on the possibility of battlefield success” (Gennaioli and Voth Reference Gennaioli and Voth2015, p. 1430). This consequence might mirror nothing greater than the measurement error in MJ’s estimates.

A 3rd challenge pertains to how the authors confront the potential of measurement error within the inhabitants information. Acemoğlu, Johnson, and Robinson (Reference Acemoğlu, Johnson and Robinson2002) and Acemoğlu et al. (2008) explicitly talk about measurement error and use IV strategies to deal with measurement error in regressors. Others take a unique method. Ashraf and Galor (Reference Ashraf and Galor2011, p. 2011) declare:

Probably the most complete worldwide cross-country historic estimates of inhabitants and earnings per capita because the 12 months 1 CE have been assembled by Colin McEvedy and Richard Jones (1978) and Angus Maddison (2003), respectively. Certainly, regardless of inherent issues of measurement related to historic information, these sources stay unparalleled in offering comparable estimates throughout nations within the final 2,000 years and have, due to this fact, extensively been considered customary sources for such information within the long-run progress literature.

They don’t argue that MJ’s information meet any explicit customary. Fairly, they know of nothing higher (it’s “unparalleled”) and everybody else makes use of it (it’s the “customary supply within the long-run progress literature”).

Nunn and Qian (2011, p. 616) tackle measurement error extra explicitly, however their dialogue consists of basic statements that aren’t related to the MJ information:

Accuracy is an apparent concern for historic information that span such a very long time horizon and broad cross-section. Nonetheless, classical measurement error in our consequence variables is not going to bias our regression estimates. Equally, any systematic measurement error that varies by time-period or by nation is captured by the nation and 12 months fastened results, that are included in all specs.

Inhabitants is their dependent variable, so they’re appropriate that if the measurement error is classical, it doesn’t bias their outcomes. They supply no purpose to suppose that is true, and, as famous, MJ say it’s not true. The second assertion about fastened results is equally true however irrelevant to the case. Neither of those excessive assumptions is probably going. Nor can they be true concurrently.


We all know the inhabitants of the USA in 2020 to a excessive diploma of accuracy. For historic episodes, we would not all the time do as effectively, however we will positively do higher than MJ. Palma, Reis, and Zhang (2020), for instance, present improved estimates for Portugal (1527–1850) by combining two units of historic estimates with some even handed reasoning. Comparable approaches could also be doable for different instances and locations. Federico and Tena-Junguito (Reference Federico and Tena-Junguito2022) present appreciable enchancment over MJ for the interval since 1800 by making higher use of revealed information. Earlier intervals might require totally different approaches. Refining the estimates for Poland in 1400, for instance, might not simply require consulting extra revealed works, but additionally unique analysis utilizing, for instance, basically archeological strategies. However it may be executed. It will not be helpful to claim that as a result of we can not know the inhabitants of Poland in 1400 with the identical accuracy as we will in 2020, there isn’t a level in utilizing historic inhabitants counts. The alternative excessive is extra frequent and pernicious: many economists take the view that the accuracy of historic information doesn’t matter as a result of it can’t be as exact as trendy reviews.

We will do, and have executed, higher. Think about one instance. MJ’s estimates suggest that the inhabitants of England and Wales grew at a median annual charge of .32 p.c within the interval 1600–1650. Wrigley and Schofield’s figures put that charge at .5 p.c. For the interval 1650–1700, the estimated progress charges are .26 in MJ and –0.07 in Wrigley and Schofield; for 1700–1750, they’re .10 and .26. The variations are substantial. MJ missed the inhabitants stagnation of the second half of the seventeenth century and considerably understated the inhabitants progress of the primary half of the eighteenth century. Inhabitants figures immediately underlie, any assertion about per-capita GDP or its progress charge and are thus central to understanding the Industrial Revolution. We will do a lot better than MJ’s guesses for a lot of nations, particularly within the interval since 1500 (e.g., Vos Reference Vos2014, pp. 366–69).

Econometric estimates that depend on MJ kind a selected literature that takes a “cross-country regression” method to financial progress, political economic system, and associated questions. Economists differ on the usefulness of the final analysis technique, and those that favor such research might insist that some information are higher than none. Even those that take this view, nevertheless, ought to concentrate on the pitfalls of the supply and the way in which some use it. As I’ve famous, Acemoğlu and his co-authors have a tendency to make use of MJ as rigorously as one can. Others have compounded MJ’s weaknesses by attempting to create info that’s not within the supply. A few of the analysis mentioned right here appeals to the concept classical measurement error doesn’t trigger bias in linear fashions when the measurement error impacts solely the dependent variable. This commentary is mathematically true however not related to the MJ information.

This paper paperwork a collection of issues in a broadcast supply that underpins many articles revealed within the main general-interest economics journals. Publication in these shops has robust skilled rewards and conveys indicators. One sign is that if everybody does one thing inappropriate, then it’s advantageous. A second sign discourages the unique work vital to enhance the idea of our information. The researchers who did the groundwork on which MJ relies understood themselves as contributing to a broader literature within the social sciences. Their contributions have been rewarded inside their very own niches. The identical applies to the entire effort that went into establishing the appreciable info on historic economies that Maddison summarizes. To the extent the occupation indicators a scarcity of curiosity in such work, it’s unlikely we are going to ever be taught extra about, for instance, the inhabitants of Poland in 1400.

This dialogue holds a less complicated lesson. Many economists at the moment obtain a dataset and merge it into different datasets with out consulting the unique sources. Inspecting MJ’s e book is instructive. The introduction explains the issue of non-classical measurement error. A take a look at the graphs (comparable to my Determine 1) would lead most to deal with the info with appreciable warning. Anybody taking a look at MJ’s maps for Africa ought to marvel why their Africa has so many nations within the information.

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