U.S. Regional Growth And Convergence, 1880-1980

Kris James Mitchener, University of California-Berkeley
Ian W. McLean, University of Adelaide

Barro and Sala-i-Martin (1991, 1992) called attention to the striking degree of convergence in per capita incomes among U.S. states since 1880. In the wider focus adopted here, we stress the variety of regional growth experiences and the persistence of a substantial disparity in income and productivity levels for much of the period. These features 10d to be obscured in studies of regional convergence where only evidence from the start and end of the period is considered, and where the state-level figures are treated simply as data points useful in testing one hypothesis about a general tendency in the regional data.
We improve and extend state and regional income estimates derived by Easterlin (1957). We contribute evidence concerning the integration of goods markets. We show the extent to which measures of regional income disparities used in previous studies was the result of price effects, of demographic and labor market characteristics, and of underlying productivity differences across states. We highlight the special features of the West which have been neglected in most accounts of national economic development. And we offer a reinterpretation of the reasons for the marked convergence in state incomes which occurred over the past century.

1. State Nominal Income Per Capita
We begin by appending Easterlin's (1957) nominal state income per capita estimates for 1880, 1900 and 1920 to subsequent data for 1940, 1960 and 1980 published by the U.S. Department of Commerce. And we follow Easterlin's convention of examining changes in our series at 20 year intervals. Two striking features of the growth of the American economy since 1880 are revealed by the regional income per capita figures.
First, there was a remarkably wide dispersion of regional (nominal personal) incomes per capita in the late 19th century U.S. In 1880 there was a nearly tenfold difference between the richest (Nevada) and poorest (North Carolina) states, a gap similar in size to what is observed in 1990 between the United States and the Philippines. The wide dispersion in per capita incomes in 1880 has received less notice than the subsequent convergence, and no attempts have been made formally to account for it. This omission is surprising as the convergence since 1880 is impressive only because it occurred relative to the initial marked disparity.
Second, there occurred a long-run convergence in state incomes. When all states are standardized relative to the U.S. average level of income per capita, the standard deviation of this time series falls from 1880 to 1920, widens slightly between 1920 and 1940, but then resumes its downward trend. The state level per capita income data also suggest that the higher the initial (log) per capita income in 1880, the lower the subsequent growth rate in per capita income. Convergence across states is also seen when the sample is broken down into two subperiods, 1880 to 1940 and 1940 to 1980. Upon closer inspection, however, the dispersion in log per capita income is much less over the second subperiod than it is over the first. It is also striking that in 1880 the six states with highest per capita income are all western states. For the following 60 years, without the western states included in the sample there is very little convergence in growth rates.

2. Relative Prices across States
Citing a lack of reliable data on price levels by state, Barro and Sala-i-Martin computed "real" income by dividing state income per capita by the national values of the consumer price index. This may go some way to eliminating those trends in prices across time that are common to all states and regions. But it does not correct for differences in regional price levels at a point in time, nor for changes in the relationship between the price levels of different regions over time. Because there is no consumer price index across states that is benchmarked to a single year, we construct the next best alternative. We first gather price indexes for each of our six time periods. Then, at each point in time, we construct a relative price index which measures, for a particular year, how the price level for any given state deviates from the U.S. average.
We use data from Haines (1989) to construct 1880 relative state prices and follow Rosenbloom (1996) to construct data for 1900 from Haines' 1890 estimates. For 1920, we use BLS data on the 1920 city-based cost of living index to create state price relatives. We used similar procedures to create state price relatives for 1940, 1960, and 1980 using BLS data.
Two aspects of the resulting "relative" price estimates for the 48 states warrant emphasis. The first is that at the beginning of the study period there is a striking clustering of states by region when they are ranked on the basis of their price levels. The 10 states with the highest price levels in 1880 relative to the U.S. average are all located in the West, and nine out of the 10 states with the lowest price levels in 1880 are located either in the South or Midwest. By 1920, however, the regional concentration of states by their price levels has disappeared.
A second notable aspect of state price levels is their convergence between 1880 and 1940 - but not thereafter. Idaho and Montana, the states with the highest relative prices in 1880, were 40% higher than Kentucky, the state with the lowest price. By 1920, the difference in relative prices between the state with the highest relative prices and lowest had fallen to 21%, and by 1940 to a mere 4%. Between 1880 and 1940 the standard deviation in the relative price index falls from 8.64 to 1.00. Curiously, prices exhibit some modest divergence thereafter: the standard deviation rising to 2.45 by 1980.

3. Adjusting State Personal Income per Capita for Relative Price Differences
When adjusted for differences in price levels, the income per person for the West as a whole falls from being 90% above the national average to being 66% higher in 1880. It remains above the U.S. average over the entire century, although the margin declines relative to the unadjusted data. The Northeast looks similar to the West in that it is above the U.S. average from 1880 to 1980; furthermore, it is actually higher than the West's per capita income in 1920, 1940, and 1960. The Midwest's income per capita hovers around the U.S. average for our entire sample period, while that of the South is below the U.S. average for all periods, but converging on it, especially after 1940.
At the state level, and after adjustment for differences in state prices, Nevada still has the highest per capita income of any state in 1880; however, its income is now only 8.5 times as large as North Carolina's (still the poorest state) versus 10 times as large with no price adjustment. Of the 10 states with the highest price-adjusted per capita income in 1880, six of them are in the U.S. West. At the other end of the distribution, eleven of the twelve states with price-adjusted per capita personal income less than $100 in 1880 were located in the South. All 10 of the poorest states are still in the South in both 1940 and 1960, only falling to nine in 1980. By contrast, the 10 richest states in 1960 and 1980 continue to be drawn from all census regions.
With the U.S. average set at 100, the standard deviation of unadjusted state incomes in 1880 was 65, whereas the price-adjusted figure was 55. By 1900 the figures are 43 and 38 respectively, while by 1920 the difference has been eliminated (both 29). Thus a significant part of the regional dispersion in incomes in the Easterlin data for 1880 and 1900 is due to the effect of differences in regional price-levels.
When measured by price-adjusted income per capita U.S. regional growth over the long run includes some dramatic movers - both up and down. The Mountain states not only converge "from above" but overshoot the national average and actually fall below it. And the well-known catching-up of the southern states persists in the price-adjusted data, though it occurs mainly since 1940, enabling us to conclude that the catch-up of the South is not primarily a price phenomenon. In contrast, some - but not all - states in the upper echelon of price-adjusted per capita income in 1880 retain their ranking throughout the century. What is it about California, Nevada, New York, and Massachusetts that has allowed them to sustain their (relatively) high levels of per capita income over such a long period?

4. Labor Input by State
A state whose population has a higher (lower) than average masculinity, or work force participation rate, or proportion of its population of working age, will, ceteris paribus, have a higher (lower) income when measured in per capita terms. How much of the regional dispersion in per capita income in the U.S. and changes in it over time are due to these sources?
There is considerable initial dispersion in labor input per capita (the employment-population ratio), but the dispersion declines until 1940 after which there is little change. Eight of the 10 states that have the highest labor input per capita in 1880 are located in the West. By 1980, the 10 states with the highest labor input per capita come from all four major census regions. At the other end of the distribution there is a clearer geographical concentration. Six of the 10 states with the lowest labor input per capita are located in the Midwest region in 1880, but as the 20th century proceeds, southern states increasingly make up the majority of those with the lowest labor input per capita.

5. Partitioning Labor Input Per Capita
Underlying the variation in labor input per capita is a complex pattern of regional differences in gender ratios, age structure, and work force participation rates. Western states initially exhibited extraordinarily high proportions of males in their populations, including the seven states with the most males as a percent of total population in 1880. All of them had over 60% of their populations consisting of males. By 1920, nine of the 10 states with the highest masculinity were still located in the West. Indeed, at 20-year intervals, no western state had more females than males until 1960.
Both the West and Northeast exhibit high percentages of their total populations that are working age in 1880. The national average rises to 1940, with the Northeast registering the highest percentage of its population of working age. From 1960 onwards, when we use 15 and older as our definition of working-age population, there is little dispersion across regions in working-age population.
With our definition of the labor force, the U.S. average for male participation hovers between 77 and 80% over the entire sample period. In 1880, participation rates for males are highest in the West and South and lowest in the Midwest. Female labor force participation rates across states are very low initially, but rise rapidly over the course of the 20th century, from an average of 15% in 1880 to 52% by 1980, confirming Goldin's (1990) findings at the national level. Furthermore, we find a larger degree of initial variation across states and regions in female than in male participation rates.

6. Labor Productivity across States
Dividing each state's price-adjusted income per capita by its labor input per capita yields a measure of labor productivity, or more precisely, price-adjusted state personal income per worker. As with nominal income per capita, the western states are prominent among those with the highest labor productivity in 1880: five of the top 10 are located in the West (four more are located in the Northeast). Nevada still holds the top spot. And as was the case with income per capita, the South has nine of the 10 states with the lowest productivity levels in 1880. Nevada, is now only 5.7 times more productive than North Carolina (the least productive) compared with the tenfold difference in nominal income per capita and the gap of 8.5 with the price-adjusted series between the highest and lowest ranked states. Thus the dispersion in the 1880 data has been significantly reduced by moving to a measure of labor productivity; nonetheless, it remains substantial and still requires explanation. The standard deviation of the productivity values relative to the U.S. average declines from 1880 to 1920, then increases slightly in 1940 before continuing its narrowing. From 1880 to 1980, the standard deviation falls from 37 points relative to the U.S. average to just 10 points. Regional data also show this general trend of declining dispersion.
We can now summarize how each of these transformations affected the dispersion in the data. The dispersion in 1880 income per capita across states is reduced by 16% when we adjust the series for differences in prices across states, and declines by nearly 44% when we adjust the series for demographic factors and prices. In 1920, the dispersion in nominal state per capita income is reduced by 11% after adjusting for prices and by 25% after accounting for demographic factors. Prices slightly increase the dispersion of the income per capita data in 1940, but the productivity effect continues to reduce the variance across states. By 1980, there is little dispersion in the nominal income per capita data across states, prices only reduce the dispersion by 2%, but demographic factors combined with prices reduce the standard deviation by 22%.
We can also reassess the evidence on convergence by using our productivity series. A clear negative relationship between initial income per worker and the growth rate in income per worker still exists from 1880 to 1980. However, the initial dispersion in log productivity is considerably less than the initial dispersion in log state income per capita. When we move to a measure of productivity, the convergence relationship still exists from 1880 to 1940, although the relationship appears weaker. Furthermore, the 10 states with the highest initial productivity are not dominantly from the West as was the case with the state nominal income per capita data. An important part of the convergence story has thus been explained by moving to a series that adjusts for the variation between states in labor input per capita.

7. Analysis of Interstate Variation in Nominal Income Per Capita
For a given year, if the income per capita figure for any state is expressed relative to the U.S. average, then the difference between the two can be decomposed into the portion arising from the state in question having: (1) a price level that is above or below the national average; (2) a labor input per capita that is higher or lower than the average; and (3) a level of productivity per worker that is greater than or less than that for the country as a whole. The relative contributions of each to the overall difference in income from the U.S. average serves as a convenient summary indicator of the proximate reasons why any state departs from "average" income levels. To illustrate, the West had a relatively high income in 1880 due in equal measure to its relatively high level of productivity, its relatively favorable labor input per capita, and a relatively high price level. Over time, and as western incomes converged on the U.S. average from above, productivity differences come to account for most of the (continuing) higher western incomes, with the favorable labor input per capita in the region contributing much less, and price differences little (or negatively). By contrast, the relatively low Southern incomes are explained (in this framework) for most of the period almost entirely by the region's relatively low productivity. Neither prices nor labor input per capita in the South were very different from the U.S. averages until after 1940.
In a separate exercise we illustrate the significance of the variation in labor input per capita across states and regions. We take as given the levels of labor productivity previously estimated. The impact on incomes of variations in labor input per capita across regions is striking. For example, incomes in the West in 1880 are 26% higher than they would have been in the absence of that region's higher (than national average) level of labor input per capita. This premium fades to around 10% in 1900 and 5% in 1920 as the West's labor input per capita declines relative to that of the U.S. as a whole. In the South, the lower than average labor input per capita has a consistently negative effect on incomes. In each of 1920, 1940 and 1960 incomes were about 6% lower than they would have been with U.S.-average labor input per capita.

References
Barro, Robert J. and Xavier Sala-i-Martin (1991), "Convergence across States and Regions," Brookings Papers on Economic Activity, No. 1, 107-182.
Barro, Robert J. and Xavier Sala-i-Martin (1992), "Convergence," Journal of Political Economy, Vol. 100, No. 2 (April), 223-251.
Easterlin, Richard A. (1957), "State Income Estimates" in Everett S. Lee, Ann Ratner Miller, Carol Brainerd, and Richard A. Easterlin, Population Redistribution and Economic Growth: United States 1870-1950, Vol. 1 (Philadelphia: The American Philosophical Society), 701-759.
Goldin, Claudia (1990), Understanding the Gender Gap: An Economic History of American Women (New York: Oxford University Press).
Haines, Michael R. (1989), "A State and Local Consumer Price Index for the United States in 1890," Historical Methods, Vol. 22, No. 3 (Summer), 97-105.
Rosenbloom, Joshua L. (1996), "Was there a National Labor Market in the Late Nineteenth-Century United States? New Evidence on Earnings in Manufacturing," Journal of Economic History, Vol 56, No. 3 (September), 626-656.