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Gini and Lorenz

Gini and Lorenz are two related measures of inequality.  The Lorenz curve is a graph of the distribution of population and the distribution of wealth or income; the Gini measure is the decimal measure of the area below that curve, whose value ranges from 0 (complete equality) to 1 (all of the asset being measured is in the hands of those at the top of the distribution.

You'll be seeing these measures in future layers of the wealthandwant website.

For the purposes of measuring the concentration of land, two measures are of interest.  First, acreage.  Second, and much more meaningful in an urbanized society, land value.  Bill Batt has pointed out that a single acre in Manhattan (including an obsolete building which was prompty demolished) sold for about $250 million, more than the value of all the land above the Mohawk River in upstate New York.

Think about the implications this has for our distribution of wealth and income.

Mason Gaffney:  Full Employment, Growth And Progress On A Small Planet: Relieving Poverty While Healing The Earth

Georgists have focused on urban land, stressing its stupendous value p.s.f., and also its high value per capita. Some have favored ignoring rural areas completely, to placate the rural vote, and the putative empathy of urban Americans with their rural roots, and the supposed rural preservation of old cultural values. If those notions ever had merit, they do not today. George himself did not think they had merit in his day, either: his first book, Our Land and Land Policy (1871) went into great detail about the villainies (his word) involved in monopolizing rural land from the public domain. He demolished economist Francis A. Walker while exposing how Walker’s direction of the U.S. Census concealed the concentrated ownership of rural land – an early example of “How to Lie with Statistics.” In the process, George invented what today is called the Lorenz Curve, and influenced the U.S. Census to begin arranging data in a template geared to that curve, and to report on land separate from buildings (which it did until 1940).Read the whole article

Mason Gaffney: The Property Tax is a Progressive Tax

Mason Gaffney: The Relationship Between Property Taxation and the Concentration of Farm Land Ownership
Real wage rates, meanwhile since 1955, have not risen as fast as real land prices, and they haven't risen at all since 1975. This has raised the labor-price of land (the number of days/years a person must work at the average wage rate in order to raise the price of a farm.)  Coupling this with rising acres per farm, the labor-price of a farm roughly tripled, from about 6 years' wages (before payroll deductions) in 1954 to about 17 years' wages in 1987. That, of course, doesn't mean you could buy a farm in 17 years, unless you didn't eat anything and saved every penny of your wages to buy a farm. 

That is the mean size. At the same time, concentration of ownership was rising. That was the subject Henry George and Francis Walker debated way back in the 1880s. In the process Henry George invented something, later to be known as the "Lorenz Curve" - academicians are not generous about crediting Henry George with his various contributions to the discipline of political economy. Basically this Lorenz Curve is a way of measuring concentration by answering the question, what fraction of all the land is owned by the top ten percent. The curve extends from zero up to 100 percent. This curve has been reduced to a single figure, called the Gini Ratio, which is a measure of concentration which varies between zero and one. At zero, everyone has the same amount; at one, one person has it all. 

In 1900 the Census Bureau began publishing farm data ranked by acres per farm. Using those data, the Gini Ratio was .58 in 1900. By 1930 the GR had gotten up only to .63. This, remember, was the peak year of property taxes, before the property tax started waning. The GR began to rise faster, and by 1950 it was up to .70. It plateaued there for 15 years and then rose again to .76 by 1987. That is a high degree of concentration. (By comparison, GRs for personal income are much lower, about .40, and are much more stable over decades.) The accelerated rise since 1930 coincided with the rise of mean acres per farm, and both followed the fall of property tax rates. 

The Gini Ratio has been criticized because it deals only with the concentration among existing farms, and doesn't take into account all of the former farmers who left the business. To adjust for this, we can simply add them to the distribution of the farms as farmers with zero land. There are 4-1/2 million farms that died between 1935 and 1988. If you add in the farmers with zero acres of land to the lowest bracket, that raises GR for 1988 from .76 to .92, a radical rise of inequality since 1930 (.63). But calculating the ratio this way gives you a better sense of how concentration has shot up during and since the Great Depression. In the Great Depression (1930-1941), six million farms provided a refuge for the urban jobless and homeless. Today, that refuge is closed.
  • Mining has taken over the Appalachians, where farmers could make moonshine.
  • Farming has been taken over by forestry and recreation in the Ozarks. ...
Land in farms of 1,000 acres and over actually dropped (nationally) by 15 percent from 1900 to 1910, the only drop on record. Now, however, 34 percent of all irrigated land is in the top bracket, farms of 2,000 acres and over. Control of irrigated land means control over water. Control of water gives control over arid lands roundabout. Ownership and control based on water have become highly concentrated. For farms with irrigated land, the Gini Ratio is .82, substantially higher than the GR of .76 for all farms. 

From 1930-87, the fraction of all farm acres in units of 1,000 acres and over rose from 28% of the total to 62% of the total. That is a rise of 123% over the 1930 base. That rise in degree of concentration is impressive, all by itself. At the same time, however, the mean value per acre in the largest spreads was rising much faster than that of other farms. In result, the value of the real estate (land and buildings) in these giant spreads rose from 8% of the total in 1930 to 38% of the total in 1987. That is a rise of 375% over the 1930 base. 

The second thing that makes the trivialization humbug is a statistical principle called "regression fallacy." Many people, otherwise bright, are thicker than mud when it comes to picking up on this principle, so there must be some mental block built into the culture. Once you see this "cat," however, it's pretty simple and straightforward. It says that the degree of concentration you find in any distribution depends on what you choose as the ranking variable. If you want to compare the concentration of value with the concentration of acreage, you can't rank the farms by acreage and then take the top bracket and ask what the value is. You have got to re-rank them by value, and these are entirely different rankings with an entirely different collection of farms in the top bracket, and naturally these are more valuable farms.

This reranking, farm by farm, is almost impossible to do from published census data, which come in large groups. But I managed to do it with some other series, and I can vouch for the fact that if you do rewrite the data by value, you get a higher - not a lower - degree of concentration in terms of value than in terms of acreage. 

So, for those two reasons, concentration of land ownership is not only high but it has risen at a very rapid rate. Read the whole article

Mason Gaffney: Rising Inequality and Falling Property Tax Rates
Vanishing Farmers and Unaffordable Farms
The Vanishing Middle Class;  Gini Ratio
The Rise of Land Quality in Vast Farms
Rising Land Share and Rising Ratio of Price to Cash Flow
National Data
Concentration of irrigated land
Land Concentration for Farms Ranked by Sales
Lack of buildings on latifundia
Lack of family labor on latifundia
Comparisons Among States
Lesser Improvement of Land in States with Larger Farms
Urban Influence
Association of Property Taxation and Land Improvement

It is a common belief that property tax relief is "good for farmers." It certainly raises the private share of economic rent. That in turn raises the investment grade of farmland and encourages its purchase as a store of value, a place to park slack money. This may be at odds, however, with using it as a vehicle for enterprise and an outlet for workmanship. Lower farm property taxes are associated with lower ratios of capital to land, and labor to land, both over time and among states. They are also associated with bigger mean farm size and less equal distribution of farm sizes.

In the sections that follow, I first document the rise of inequality in the distribution of farmland that followed a sharp drop in farm property tax rates after 1930. Then I show, by cross-sectional analysis, a positive relationship between higher property tax rates and more intensive use of farmland, which in turn is associated with more equal distribution of farmland. Conversely, I find property tax relief associated with underuse and underimprovement of land.

A priori, a tax on buildings works to suppress building and to penalize smaller farmers, whose building to land ratio is higher than that of bigger farmers. The findings seem to show, therefore, a stronger countereffect, proincentive and pro-subdivision, of the other part of the property tax, the part based on land value.
Now, however, 34 percent of all irrigated land is in the top bracket, farms of 2,000 acres and over. (10) Control of irrigated land means control over water. Control of water gives control over arid lands roundabout. Ownership and control based on water have become highly concentrated. For farms with irrigated land, GR = .82, (11) substantially higher than the GR of .76 for all farms. ...

To sum up,
  • rising acreages mean there are fewer farms overall.
  • Rising labor prices per farm mean aspiring farmers who lack prior wealth can no longer buy in.
  • Rising Gini Ratios mean acreage is less equally shared among a given number of farms.
  • Rising Gamma factors mean the higher quality land is moving into bigger farms.
  • The Gamma data are confirmed by rising shares of cropland and irrigated land in vast farms.
  • Rising P/C ratios reflect a higher LSREV, and they mean it is harder for a newcomer to acquire any farm acres.

The combination means the agricultural ladder has been pulled up. Entry is nearly impossible for farmers lacking outside finance; exit and latifundiazation proceed apace. These changes accompanied and followed a 40 percent drop in farm property tax rates.  ...


A result of rising concentration is the separation of land from capital. With some exaggeration, American latifundia are now lands without buildings, but buildings cluster on smaller farms, many without enough land. This implies at least three points.

  • First, building wealth is more equally distributed than land wealth.
  • Second, the property tax would be more progressive if changed to a pure land tax, exempting buildings.
  • Third, many latifundia are not being used to their potential, while capital on some small farms is undercomplemented with land. I support the case first using national data, and then by comparing states.
It is awkward that the 1987 Census of Agriculture defines "farm size," and ranks farms, only by acres rather than value.  ...

Concentration of irrigated land

The yield per acre of most crops stays level or rises with harvested acres per farm. At the same time, sales per dollar of real estate fall somewhat. (21) The most likely reason is that the quality of harvested land rises with quantity. There is, to be sure, a trade-off between quality and quantity, but there is also a bond. Whoever can afford more can afford better. Which effect is stronger? The question must be resolved by data.  ...

Comparing different crops, high values of GR go with crops that are mostly irrigated. For example, 85 percent of tomato acres and 14 percent of silage corn are irrigated. For tomatoes, GR = .91; for silage corn, GR = .52. (26)
(26) Those who find GR index numbers too abstract will find more meaning in these raw data. For tomatoes, the top acreage bracket contains 1.1 percent of the farms, 45 percent of the harvested acres, and 52 percent of the irrigated acres in tomatoes. For silage corn, the top bracket contains 1.0 percent of the farms, 11.3 percent of the harvested acres, and 26 percent of the irrigated acres in silage corn. ...

Lack of buildings on latifundia

The 1940 Census of Agriculture was the last to separate $L from $B, overall. In 1940 the building share of real estate value ($B/[$L+B], or BSREV) was .69 in the lowest acreage bracket, .31 for all farms, and .12 for farms of 1,000 acres and over. (36)

(36) 1940 Census of Agriculture, Vol. 3:80. An earlier insightful article on the subject is D. Weeks, "Factors Affecting Selling Prices of Land in the 11th Federal Farm Loan District," Hilgardia 3, no. 17 (1929):459-542.

AELOS (1988) gives no comparable comprehensive data, but it does give two series that test the point and have the advantage of disaggregation. One is for "owner-operators" and one for "landlords with debt." For the owner-operators, ranked by acres per farm, BSREV was .63 for farms under 10 acres; .29 for all farms; and .12 for farms of 2,000 acres and over. (37) Building values are much more equally distributed among these farms than land values. ...

The inverse relationship between PTR and GR is particularly consistent and noteworthy.  ...


One may at least firmly conclude that large farm units are less improved and less peopled than small and medium-sized farms. There are two possible interpretations. One is that big farms are more efficient, getting more from less, but that is refuted by their getting less output per $L. The other is that Veblen was right, many of them are oversized stores of value, held first to park slack money and only secondly to produce food and fiber, and complement the owner's workmanship. The Florida 9 [the high LSREV states] may represent a home grown rural "third world" of large, underutilized landholdings that preempt the best land and force median farmers onto small farms on low-grade land.

The issue cannot be settled in a few words, but the implications for tax policy are the same either way. If large units are more efficient, they can bear heavier taxes. If they are less efficient, heavier PTRs will induce them to release surplus land for others, which will tend at the margins to equalize factor proportions, moving more states from the Florida toward the Wisconsin model. Read the whole article

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Wealth and Want
... because democracy alone hasn't yet led to a society in which all can prosper