On Persistent Poverty in a Rich Country

T. M. Tonmoy Islam Center for Poverty Research

and Department of Economics

University of Kentucky tmisla2@uky.edu

Jenny Minier

Department of Economics University of Kentucky

jminier@uky.edu

James P. Ziliak Center for Poverty Research

and Department of Economics

University of Kentucky jziliak@uky.edu

September 2, 2010

PRELIMINARY

Abstract: Despite robust economic growth in the post-War era, there remain deep pockets of persistent poverty in the United States. We examine the origins of permanent income differences across counties using contemporaneous and historical Census data. Using a panel of U.S. counties from 1960 to 2000 and a long-difference dynamic panel-data estimator, we first test whether aggregate production technologies and rates of income convergence are the same across persistently poor and non-poor regions. We then use data from the late 19th and early 20th centuries to estimate the relative roles of culture, geography, institutions, and human capital in accounting for residual income growth differences across counties. We find evidence of significant regional differences in production technologies, but rates of convergence, which range from 7 to 9 percent, do not differ significantly between poor and non-poor regions. Illiteracy rates at the close of the 19th century are a key determinant of persistent poverty status at the close of the 20th century, suggesting long-term negative consequences for low initial human capital among persistently poor counties.

1

Between 1960 and 2000 real income per capita in the United States grew 175 percent and

aggregate poverty rates fell by half, from 22 percent to just over 11 percent. In spite of this

economic progress, poverty remains persistently high in several regions of the country,

suggesting that the gains from growth have not been realized equally. Figure 1 depicts counties

in which poverty rates exceeded 20 percent in each Decennial Census since 1960, which is the

definition of persistent poverty adopted by the USDA.1 The figure reveals that there are five

persistently poor regions of the country, encompassing 11 percent of all U.S. counties:

Appalachian Kentucky, the “Black Belt” region spanning the Carolinas to Alabama, the

Mississippi Delta region, the Texas “colonias” along the Rio Grande River, and Native American

reservations in the four corners states and the Dakotas. The difference in average per capita

incomes between these counties and other counties in the U.S. is significant: in 2000, average

income in the persistently poor counties was 72 percent of the non-poor county average. These

five regions differ greatly in racial, ethnic, geographic, and economic composition, yet share the

seeming puzzle of persistent poverty.

It is also interesting that these areas of persistent poverty occur within one of the richest

countries in the world. Much of the growth and development literature has concentrated on

explaining differences in standards of living across countries: why is income per capita about

$40,000 in the U.S. and similar countries, but only approximately $500 in many African

countries? Proposed explanations include differences in policy choices, institutions, and

geography, as well as factor accumulation. Since many of these potential determinants of

income per capita occur at the national level – monetary and trade policies, much of the system

1 In fact, the USDA defines a county as persistently poor if its poverty rate exceeds 20 percent in each Census since 1970 (http://www.ers.usda.gov/briefing/rurality/typology/maps/Poverty.htm). We extend this to include the 1960 Census. We note that the typography of persistent poverty is the same if one adopts a more stringent criterion of a 30 percent poverty rate, though fewer counties meet the criteria in each subregion.

2

of government – looking at subnational differences in incomes allows us to better understand the

relative importance of other factors that vary within a country. We utilize a neoclassical growth

framework to examine whether these differences in income, and the areas of persistent poverty

that have arisen, are due primarily to differences in aggregate production technologies, or

whether the historical roles of institutions, culture, geography, and endowments of human capital

have placed these regions on divergent growth paths.

The dynamic panel data model of Islam (1995) advanced the growth empirics literature

by explicitly allowing for heterogeneity in aggregate production functions via the inclusion of

permanent cross-country differences. This is attractive because a key determinant of steady-state

growth in the empirical model of Mankiw, Romer, and Weil (1992), which follows the canonical

Solow (1957) model closely and serves as the basis of Islam’s approach, is the initial level of

productive efficiency, and cross-country heterogeneity in productive efficiency seems likely.2

We apply these ideas to U.S. county-level data to identify why certain regions in an otherwise

wealthy nation remain mired in persistent poverty. Specifically, we assemble a panel of counties

across the five Decennial Censuses from 1960 to 2000 to estimate a dynamic panel data model of

conditional income convergence. In the full sample, we allow aggregate production technologies

to differ in terms of productive efficiency by including county intercepts. We also admit

potential heterogeneity in the production function parameters by estimating the dynamic income

model separately for counties classified as persistently poor versus those that are not poor. Lee,

Pesaran, and Smith (1997) discuss the issue of parameter heterogeneity in the cross-country

context, but as noted by Durlauf, Johnson, and Temple (2005), identification in these models is

perilous, and a possible alternative is to split the sample into groups likely to share similar

parameter values. Since our interest is in understanding what sets the persistently poor counties 2 Efficiency is also referred to as “technology” or “productivity.”

3

apart, we estimate separate models based on persistent poverty status and test whether rates of

conditional income convergence differ across regions. To correct for possible measurement

error at the county level, we estimate our income models with a long-difference GMM estimator

proposed by Hahn, Hausman, and Kuersteiner (2007), which has good finite sample properties

compared with other dynamic panel estimators such as the Blundell-Bond (1998) estimator.

With the estimated parameters from the income convergence models, we recover the

county-specific intercepts, which serve as proxies of initial productive efficiency. As Durlauf and

Quah (1999) argue, these intercepts are not nuisance parameters to discard, but rather serve as a

mechanism through which we can uncover permanent differences in income. Recent research has

emphasized culture, geography, and institutions as key determinants of long-run growth, and

these forces are likely embedded in the fixed effects (see, among many others, Grief 1994;

Rappaport and Sachs 2003; Acemoglu, Johnson, and Robinson 2005). These factors have

figured prominently in historical economic and sociological research on the development of the

antebellum South as well as Appalachia (Engerman 1966; Fogel and Engerman 1974; Billings

1974; Duncan 1999; Ransom and Sutch 2001; Eller 2008). We thus estimate a model that links

our modern county fixed effects to county-level data from the historical 1890 and 1900 Censuses

that contain rich data on land tenure, religious participation, nativity, and human capital, and

supplement it with data on geography including elevation and temperature.

Although much of the growth literature has been directed at understanding income

convergence across rich and poor countries, we are not the first to apply such models to regional

income growth within the U.S. Much of this work has centered on a panel of states (Barro and

Sala-i-Martin 1992; Evans and Karras 1996; Bauer, Schweitzer, and Shane 2006), but some has

also utilized county data (Rappaport and Sachs 2003; Clifton and Romero-Barrutieta 2006;

4

Higgins, Levy, and Young 2006). Rappaport and Sachs (2003) focus on changes in population

density, especially on the coasts, as opposed to income. Higgins, et al. (2006) use county-level

data from 1970-2000 to estimate income convergence rates, but they do not recover the county

fixed effects to identify the historical role of institutions, culture, and geography. Clifton and

Romero-Barrutieta (2006) pose a parsimonious model relating county poverty in 2003 to

geography and land tenure in 1910, but do not estimate the income-convergence process, and

they focus on poverty in Appalachia at a point in time as opposed to the broader set of

persistently poor regions over time. Thus, while we draw on several key ideas in the previous

research, our study differs in several dimensions in terms of methods, data, and emphasis.

We find evidence of significant regional differences in production technologies, but rates

of convergence, which range from 7 to 9 percent, do not differ significantly between persistently

poor and non-poor regions. Illiteracy rates at the close of the 19th century are a key determinant

of persistent poverty status at the close of the 20th century, suggesting long term negative

consequences for low initial human capital among persistently poor counties.

II. The Origins of Persistent Poverty: Some Preliminaries

On the eve of the 1960s the poverty status of a vast stretch of the United States was

bleak. In Figure 2 we present county poverty rates for 1959 based on income reported in the

1960 Census.3 The figure shows that county poverty rates in excess of 50 percent were common

in the South, and those in excess of 20-30 percent were the norm in the Midwest and Plains

states. With strong economic growth and expansion of income support as part of the Johnson

Administration’s Great Society programs, the poverty landscape changed dramatically over the

next decade. Figure 3 shows that county poverty rates in the 1970 Census were considerably

3 The United States did not produce its first estimates of poverty until the 1960s, but in the special tabulation the Economic Research Service of the USDA produced estimates for the 1960 Census. We thank Robert Gibbs of USDA for providing these data.

5

lower throughout much of the nation, especially in the South and Midwest. However, shades of

the five regions of persistent poverty already emerge as poverty rates remained in excess of 40

percent in many of the counties. Further progress against poverty continued through the 1970s as

Figure 4 shows, but comparing poverty rates in 1979 against those in 1989 in Figure 5 suggests

that gains against poverty abated in the 1980s. The economic expansion of the 1990s was

similar in strength to the 1960s, and as seen in Figure 6 poverty fell compared to 1989, but the

expansion was not enough to lift the poorest areas up to levels found elsewhere. Across Figures

2 to 6 it is clear that the poverty status of many counties that are identified as persistently poor in

Figure 1 improved over the past four decades, but poverty in many of those counties remained

four times higher than the national rate.

A fundamental question in the growth literature is whether the counties that have

emerged over the last four decades as persistently poor attained that status because of differences

in factor accumulation, or whether their status is due to differences in their aggregate production

functions – that is, their ability to use the factors that they have. In other words, do persistently

poor counties have lower levels of inputs like physical and human capital, or do they use the

capital they have less efficiently than other counties? We consider two types of differences in

production technology: differences in the initial level of a county’s “technology” and institutions,

and differences in the rate at which factors are transformed into output. We also focus on the

determinants of these underlying differences in initial conditions.

To fix ideas, the growth literature generally specifies that output or income is determined

by stocks of physical and human capital along with economy-specific “technology” or

“productivity,” which encompasses technology, institutions, and endowments of natural

resources. Table 1 illustrates some descriptive differences in incomes and observed human and

6

physical capital between the persistently poor counties and non-persistently poor (“non-poor”)

counties pooled across the 1960 to 2000 Censuses. In our sample there are 3,094 counties, 338 of

which are categorized as persistently poor.4 A data appendix provides details on the sources and

definitions of the variables. Not surprisingly, the persistently poor counties have lower per capita

real incomes, fewer people in the labor force, slower growth of the labor force, fewer high school

graduates, and lower new capital expenditures in manufacturing. The persistently poor counties

are also less urban, smaller (in terms of population), and have higher percentages of African

Americans. However, the bottom two panels of Table 1 indicate some signs of convergence

between the regions. In 1960, income per capita in the persistently poor areas was 62 percent of

the non-poor areas, but by 2000 it was 72 percent of non-poor income. Likewise, high school

completion rates in the persistently poor counties increased from 63 percent of the non-poor rate

in 1960 to 82 percent in 2000; and real capital spending increased from 7 percent of the non-poor

rate in 1960 to 17 percent in 2000. We more formally test for evidence of convergence below.

Many have argued that fundamental determinants of growth, such as geography,

institutions, and culture, explain more of the difference in growth rates than do current

differences in factor accumulation (Easterly and Levine 2001; Acemoglu, et al. 2005). To proxy

for these components of growth, we use historical data from the Censuses of the late 19th and

early 20th centuries. Since 1890 was the cusp of expansions in the logging and coal industries in

the U.S., we use 1890 data whenever possible (but for several variables that are not available in

1890, we use 1900 data).

Sociologists such as Duncan (1999) and Billings and Blee (2000) argue that the roots of

persistent poverty in Appalachia and the Mississippi Delta can be traced to social and economic

institutions that bestow ownership rights of land and resources to a select group of individuals— 4 There are 3,141 counties in the country, but data are missing on one or more variables on 47.

7

in the case of Appalachia to absentee coal and timber barons, and in the Delta to plantation

owners. Economists such as Fogel and Engerman (1974) and Ransom and Sutch (2001) have

made a similar case on the role of institutions on the economic development and growth in the

South in the decades following the Civil War, especially the economic organization of

sharecropping. Likewise, resettlement of Native Americans in the 19th Century often took the

form of removal from productive lands in the South and East to non-productive, arid lands in the

central Plains (Barrington 1999). This suggests that the extent of local ownership of land and

natural resources, sometimes referred to as land tenure, likely varies across the U.S. in response

to regional political institutions, and the higher the share of local land tenure, the more

productive income remains in the local community.

In the historic Censuses of the 19th and early 20th centuries, data were collected on the

number of improved and unimproved acres of farmland, distinguishing whether or not the

improved acres were owner-occupied. We thus construct a proxy for local institutions as the

fraction of farmland in the hands of local owners (Clifton and Romero-Barrutieta 2006).5 As

seen in Table 2, average land tenure in 1890 was higher in non-poor counties (80 percent)

compared to persistently poor counties (77 percent), and the variance lower. However, because

the differences are not striking, the empirical importance of historical land tenure on persistent

poverty today is not clear a priori.

Culture is also suggested as a possible source of persistent poverty, both across and

within countries (Banfield 1970; Billings 1974; Murray 1984; Grief 1994). Most prominent

among these is the role of religion in economic development, especially the argument made a

century ago by Max Weber that Protestantism (and Calvinism in particular) played a crucial part

5 Note that the sample size is smaller in Table 2 than in Table 1. As described in the Data Appendix we restrict our historic analysis only to counties without redefined borders between the relevant year (1890, 1900) and 1960.

8

in the economic success of Northern Europe compared to its southern neighbors who were

predominantly Roman Catholic. Barro and McCleary (2003) and Cavalcanti, Parente, and Zhao

(2007) provide some evidence in support of the Weber thesis in the cross-country context. In the

case of the U.S., religion-based cultural influences are determined by historic patterns of

immigration. 19th Century immigrants in the East, Midwest, and West tended to be dominated by

Roman Catholics, while those in the South were primarily Baptists. The early Scots-Irish who

settled northern and central Appalachia in the 18th Century tended to be Presbyterian, while later

immigrants from Germany tended to adhere to various movements within the Baptist faith as

well as Catholicism. The 1890 Census of Religious Bodies recorded the number of persons in a

county who claim membership in a church, both overall and by denomination. Table 2 includes

the means of the overall share of the population who are churched, as well as the share of some

major denominations. The table shows that differences in the share of the population counted as

church members are very small across poverty groupings, although the distribution across

religious affiliation varies considerably between the persistently poor and other counties. For

example, the share of residents who are Calvinist is twice as high in the non-poor counties,

which the Weber thesis would suggest greater economic growth in non-poor counties. However,

the non-poor counties are also have higher shares of Roman Catholics (5.9 versus 3.4 percent),

which is contrary to the pro-growth Weberian view. There is, however, twice the share of

Baptists in persistently poor counties compared to non-poor counties.

Geography, including mountainous terrain and temperature, is also often listed as a

barrier to riches (Gallup, Sachs, and Mellinger 1999; Acemoglu, et al. 2005; Iyigun 2005;

Rappaport and Sachs 2003; Rappaport 2007; Eller 2008). For example, the Appalachian

Mountains, which span from Mississippi to Maine, are rugged and densely packed with narrow

9

valleys, which make development a challenge. Likewise, the lowlands of the Mississippi Delta

were historically prone to flooding, another barrier to development. The hot and humid summers

of the South and the arid farmland of Native American reservations also pose challenges to

productivity.

In Table 2 we present two measures of geography, latitude (normalized relative to 90

degrees, so that larger values represent more northern locales), and the standard deviation of

elevation as a measure of how mountainous the terrain is. As expected based on the map in

Figure 1, Table 2 shows that persistently poor counties are located further south than non-poor

counties. The difference in the means between the poor and non-poor is about four degrees,

which is approximately the difference in latitude between Oxford, Mississippi and St. Louis,

Missouri. There is little difference between the persistently poor and non-poor counties in terms

of the standard deviation of elevation; the persistently poor are have slightly less variation than

do the non-poor.

Finally, economists have stressed the important roles of human capital endowments and

potential agglomeration economies in urban areas (for example, Glaeser, Kallal, Scheinkman,

and Shleifer 1992; Moretti 2004; Shapiro 2006). In the 1900 Census, individuals were asked

whether they could read or write, which leads to our focal historical measure of human capital,

the illiteracy rate. We also include the share of the county’s population that is foreign born,

while we use the share of the population residing in an urban area as our measure of

agglomeration economies. Table 2 shows that the most striking difference in the historical data

is in the human capital variables: counties that are classified as persistently poor today had

illiteracy rates more than three times higher than other counties in 1900 (36 percent versus 11

10

percent). Persistently poor counties also had urban shares 80 percent lower, and shares of

foreign-born residents 75 percent lower, than non-poor counties.

For a preliminary look at whether these historical differences in institutions, geography,

and human capital matter for the chances of being persistently poor a century later, in Table 3 we

specify a linear probability model of the probability that a county is persistently poor over the

period 1960-2000 as a function of historic Census data. In each regression, 273 counties (9.6

percent of the sample) are persistently poor. Column 1 of Table 3 contains a parsimonious

specification of persistent poverty as a function of institutions (land tenure) and geography

(temperature and terrain).6 The results in column 1 show that a percentage point increase in the

share of owner-occupied farmland in 1890 lowers the probability of being persistently poor a

century later by just under 10 percent, and living in the North reduces the chances being

persistently poor (a one degree move North lowers the probability by about 2 percent). In

columns 2 and 3 we present results from our preferred specifications that add measures of culture

and human capital to the regression model. Higher literacy rates, higher church membership

(especially Calvinist and Baptist), and higher urban population shares all significantly lower the

odds of being persistently poor. At the same time, the addition of these variables completely

wipes out any role for institutions and geography. In particular, as we show in columns 4 and 5,

omitting illiteracy causes the coefficient estimate on latitude and farm ownership to regain

statistical significance, and also causes the coefficient estimates on the shares of Baptists and

Catholics to become positive and statistically significant, while the coefficient estimate on the

share of Calvinists increases in magnitude but remains negative. Illiteracy is highly correlated

6 This is akin to the model estimated by Clifton and Romero-Barrutieta (2006). The dependent variable in their model is the poverty rate in 2003, rather than an indicator variable for persistent poverty for 1960-2000 as we use. In addition, we use two measures of geography—temperature and terrain—whereas they use only terrain.

11

with the prevalence of some denominations, in particular the share of Baptists in a county7, so

that models in columns 4 and 5 yield the spurious result that a higher share of Baptists increases

the probability of being a persistently poor county when in fact the driving force is county rates

of illiteracy. This result highlights the long-run importance of endowments of basic human

capital to county economic status. In the following sections, we turn to the growth literature to

examine more formally the mechanisms through which these historical factors affect modern

income levels while simultaneously accounting for current levels of factor accumulation.

III. Dynamic Model of Income Convergence

In neoclassical growth models such as the textbook model of Solow (1956), an economy

converges to a steady state determined by factors such as the economy’s rates of saving and

population growth, where income per capita grows at the rate of technological progress. To

illustrate, consider the human capital-augmented version of the Solow model following Mankiw,

Romer, and Weil (1992) and Islam (1995). The production function is given by

(1)

where Y is aggregate output, K and H are stocks of physical and human capital, L is the labor

force, and A is labor-augmenting technology, which grows at the exogenous rate g. Output is

invested in physical and human capital at the constant rates sk and sh respectively.

Under standard assumptions, an economy’s rate of convergence to its steady-state level

of income per capita (y=Y/L) can be derived:

ln ln 1 ln 1 ln 1

ln 1 ln 1 ln (2)

7 The correlation coefficient between the 1900 illiteracy rate and the share of church members in 1890 is 0.265; for Baptists, Calvinists, and Catholics, respectively, the correlations are 0.630, -0.189, and -0.163.

12

where λ=(n+g+δ)(1-α-γ). Thus, steady-state growth in income per capita depends on investment

in physical capital (sk), investment in human capital (sh), a term including population growth,

technological progress and depreciation (n+g+δ), initial income (y), and the initial level of

technology (A0). Furthermore, with reasonable assumptions about the values of α and γ (the

shares of physical and human capital, respectively, from the production function), the coefficient

estimate on the log of initial income can be used to infer the speed of convergence toward the

steady state (i.e., λ).

Traditionally, this has typically been estimated in the cross section, with an assumption

not only of identical production functions across economies (most commonly, countries), but

also of identical rates of technological progress; economies’ steady states still differ, based on

their savings and population growth rates. Under these assumptions, controlling for rates of

population growth and savings, an initially poor economy will “converge” to the same steady

state as an initially richer economy. This test of “conditional convergence” has received wide

support in the empirical literature.

However, moving to a panel framework, as in Islam (1995), allows for the estimation of

different initial levels of technology across economies (the rate of growth of technology is still

assumed constant across economies.) The workhorse specification in a panel data setting comes

from Islam (1995) (see also eqn (59) in Durlauf, et al. 2005):

1 (3)

where is the log of real income per capita for county i (=1,...,N) in year t (=1,...,T); is

the lag of the dependent variable; are time-varying rates of factor accumulation (new capital

investment, population growth rate, school enrollment rates); are time-invariant income

factors that may affect initial productivity (A0) such as geography and institutions; represents

13

unobserved, permanent differences across counties in productivity that do not vary over time;

is a macroeconomic shock common across counties but time varying; and is an iid error for

county i in year t. The parameter identifying the speed of convergence is .

By construction, unobserved productivity is correlated with and thus to

eliminate the latent heterogeneity we take differences

∆ 1 ∆ ∆ ∆ ∆ . (4)

where ∆ is the difference operator. Although is iid and uncorrelated with all right-hand side

variables, in differences, ∆ is MA(1) and thus correlated with ∆ . If the number of time

periods T is large, then the so-called Nickell bias of estimating (2) via OLS is small; that is, the

bias goes to zero as T goes to infinity (Nickell 1981). In our case, although the spacing of

measurement is per decade, the number of actual decades is small (T=5) and thus we will need to

instrument for the lagged dependent variable.

There are many possible estimators for the dynamic panel data model in equation (4).

For example, if we apply first differences, then under the assumptions of our model is a

valid instrument for ∆ , yielding the just-identified Anderson-Hsiao (1982) estimator.

Arellano and Bond (1991) proposed a more efficient GMM estimator, and Blundell and Bond

(1998) proposed a GMM estimator that was more robust in the presence of weak instruments and

when the true parameter on the lagged dependent variable approached unity. We instead use a

GMM estimator recently proposed by Hahn, Hausman, and Kuersteiner (2007) that has finite

sample properties at least as good as the Blundell and Bond estimator. Griliches and Hausman

(1986) showed that in the presence of mismeasured covariates, first differences tended to

exacerbate errors-in-variables bias relative to pooled OLS, and even relative to the within

estimator. However, taking wide differences, e.g. two-year or wider, had the effect of

14

attenuating bias from measurement error. Hahn, et al. (2007) apply this idea to the dynamic

panel case and suggest taking as wide a difference as possible while still retaining an instrument

for the lagged dependent variable.

In our model with Decennial Census data from 1960 to 2000 we estimate

∆ 1 ∆ ∆ ∆ ∆ . (5)

where ∆ is the three-decade difference operator. That is, the dependent variable is ∆

, the lagged dependent variable is ∆ , and the time-

varying covariates are ∆ . Note that the differenced time dummy

becomes a constant term because in long-difference form we are in effect left with a cross-

sectional model in equation (5). This approach retains as a valid instrument for the lagged

dependent variable. We in fact overidentify the model by including the t-3 and t-4 lags of the

time-varying productive factors, , as additional instrumental variables for the lag

dependent variable. In the case that the human and physical capital variables in X are strictly

exogenous, i.e. 0 , , then the ∆ serve as instruments for themselves. We test

this assumption against the alternative that human and physical capital should instead be treated

as predetermined to the income process of a county, in which case 0 and thus

the ∆ are dropped from the instrument set.

Specifically, define the matrix of regressors as ∆ , ∆ , 1 , the vector of

unknown coefficients as Γ 1 , , ∆ , and the matrix of instruments

, ∆ , , . Then the GMM estimator for the linear dynamic panel estimator

is Γ Ω Ω Δ , where Ω is an initial consistent estimate

of the weight matrix. For the two-step GMM estimator we take the identity matrix as the initial

15

weight matrix and then apply a heteroskedasticity-robust weight matrix in the second step.8 The

associated variance-covariance matrix is given as Γ Ω . Define

the Hansen (1982) J-test of the validity of the set of overidentifying restrictions as

Γ Ω Γ , which is distributed asymptotically chi-square with degrees of freedom

equal to the number of overidentifying restrictions. Newey and West (1987) show that it is

possible to test the validity of a subset of overidentifying restrictions as , where U

refers to the unrestricted model that includes Δ in the instrument set and R refers to the

restricted model without those instruments. The C-statistic is distributed asymptotically chi-

square with degrees of freedom equal to the number of restrictions.

The model in equation (5) assumes common production technology across counties, and

thus a common speed of convergence, except for the initial productivity embedded in . We

test this assumption by applying the long-difference GMM estimator to subsets of persistently

poor counties Γ and the non-poor counties Γ , and then conducting a Wald test for whether

convergence rates are similar as Γ Γ Γ Γ Γ Γ , which

is distributed asymptotially chi-square with degrees of freedom equal to the dimension of Γ.

In addition to examining the possible differences between aggregate production

functions between the persistently poor and other counties, we are interested in the extent to

which residual growth rates – also referred to as “technology” or “productivity” in the growth

literature – are explained by historical data. However, a consequence of differencing the model

in equation (5) is that it is no longer possible to identify , the vector of coefficients on the time-

invariant regressors Zi that in part determine initial productivity (e.g., culture, geography, and

8 Hahn et al. (2007) also discuss alternative, more efficient GMM estimators than the one we use here that take advantage of additional moment conditions in between year t and t-k.

16

institutions). It is still possible to recover estimates of with an auxiliary regression as follows

(Hausman and Taylor 1981; Hsiao 1986). Based on the GMM estimates from equation (5) we

construct an estimate of the fixed effect for each county as

1 , , (6)

where is the county-specific “time mean” and the other variables are similarly defined. We

then estimate a regression of the fixed effect on those factors that affect permanent differences

across counties as

, (7)

and thus identify . Provided that the unobserved initial conditions in 1960, the at the start of

our sample period, are uncorrelated with the Zi factors from the distant past then equation (7) can

be estimated via OLS.

IV. Evidence on Convergence

We first present estimates of the long-difference GMM model from equation (5) in Table

4. To recap, the dependent variable is the log difference of real per capita income between 1970

and 2000. The independent variables include the 1960-1990 lag difference in log income per

capita (yit-1), and the changes from 1970 to 2000 in the following (Xit): the percent of high school

graduates; real private capital expenditures in manufacturing; labor force growth; urban share;

and the share of residents who are black. For comparison purposes, in Regression 1 we estimate

equation (5) via OLS, while in Regressions 2 and 3 we use GMM. In the base case GMM model

of Regression 2 the instruments for the lagged dependent variable include the 1970-2000 change

in the Xit as well as the 1960 and 1970 levels of the Xit. In Regression 3 we exclude the 1970-

2000 change in the Xit from the instrument set and conduct pseudo-likelihood ratio tests (the C

statistic above) of the validity of their inclusion.

17

Regardless of the estimation method, per capita income levels are positively correlated

with lagged per capita income, and thus based on the specification in equation (1), per capita

income growth is negatively related with the lagged income level, implying conditional

convergence across U.S. counties. The rate of convergence implied by the models is found by

the transformation 1 log / , where time is the interval of data

measurement (here, 10 years) (Islam 1995).9 The estimated convergence rates presented in the

lower panel of Table 4 are quite consistent across the three specifications, at 0.08, and within the

range of estimates found in previous research at various levels of aggregation (e.g., Islam 1995 at

the cross-country level; Higgins et al 2006 at the county level). Other results of note in Table 4

are that per capita income growth is positively related with levels of human capital and urban

share, and negatively related to the share of the county population that is black. Given the semi-

logarithmic specification, the coefficients on the production function terms are more readily

interpreted in terms of elasticities. For example, the elasticity of per capita income with respect

to the share of high school graduates in Regression 2 is 0.23 and in Regression 3 is 0.13.10 In

Regression 2, the Hansen J-test of 101.6 rejects the null hypothesis that the overidentifying

restrictions are valid, but the test result of 9.98 in Regression 3 indicates that the restrictions are

valid at the 8 percent level. The estimated C-statistic of 91.6 thus confirms that our controls for

human and physical capital in the production technology should be treated as predetermined to

the income process for estimation.

One of our primary interests is in the extent to which aggregate production functions – or

the efficiency with which inputs (e.g., capital, labor) are transformed into output – of the

persistently poor counties differ from the production functions of other counties. As we saw in

9 The standard error for the convergence rate is found by the delta method (Wooldridge 2001). 10 In the semi-logarithmic specification of lny = a + b*x + u the elasticity is b*x.

18

Table 1, the persistently poor counties are different in terms of the levels of such inputs: they

have smaller, less well-educated labor forces, for example. To what extent are these lower

incomes explained by lower levels of inputs, and to what extent are they due to less efficient use

of the inputs? In Table 5, we repeat the analysis of Table 4 separately for the persistently poor

and non-poor counties.

Regressions 1-3 present results from the non-persistently poor sample, while Regressions

4-6 are for the persistently poor counties. Not surprisingly, the results in Regressions 1-3 are

very similar to those in Table 4, since the non-poor counties make up the overwhelming majority

of the full sample (2,752 out of 3,094). The estimates of the convergence parameter are also

quite similar, although slightly higher (this is also expected, since the persistently poor counties

over the 1960-2000 period have been dropped from the sample). As with the pooled sample, the

Hansen J-test and associated C-statistic point to the GMM model with ∆Xit excluded from the

instrument set (Regression 3)

Regressions 4-6 are estimated on the 338 persistently poor counties. While the effects of

lagged income growth and human capital are similar to those for the non-poor counties, most of

the other coefficient estimates differ substantially. For both the OLS and GMM regressions a

Wald test rejects the null hypothesis of equal coefficients between persistently poor and non-

poor counties, with a p-value of at least 0.02. Specifically, labor force growth is more strongly

and positively correlated with growth in the persistently poor counties, while the urban share –

which was strongly and positively correlated with growth in the non-poor counties – has little

effect. The return to physical capital accumulation is also higher in the persistently poor

counties, as the assumed Cobb-Douglas production function with diminishing returns to capital

would predict. Also, the negative correlation between growth and the share of black residents

19

seen in non-poor counties is not present in any of the persistently poor regressions. While the

coefficient estimates on the fraction having completed high school are comparable (except in

Regressions 3 and 6), recall that the level of high school completion is significantly higher in the

non-persistently poor counties: approximately 15 percentage points higher in the pooled sample.

Finally, for each model, Table 5 also presents estimated convergence rates. These are

quantitatively similar to those in Table 4 for the full sample, though the range is somewhat

wider. Although the Wald tests for equal convergence rates between persistently poor and non-

poor counties cannot reject the null for either OLS or GMM estimators, recall that these

estimates are for convergence within the groups (i.e., the persistently poor counties are

converging to a lower income level than are the non-poor; the results in Table 5 cannot provide

evidence for or against convergence across the entire sample).

V. The Origins of Persistent Poverty: Further Evidence

In Table 6, we report OLS estimates of equation (7) where the dependent variable is

residual growth rates (i.e., growth after controlling for the explanatory variables from our

preferred specification, Regression 3 of Table 4) from the entire sample. These residuals are

regressed on variables from historical Census data described in Section II. Recall that as a proxy

for institutions of land tenure, we include the percentage of farms operated by their owners. As

measures of geography, we include both a normalized measure of latitude and the standard

deviation of the county’s elevation. Finally, to proxy for culture, we include the population

shares of three major faiths in 1890: Baptists, Catholics, and Calvinists. We also include

historical data on illiteracy rates and urbanization to control for initial endowment of human

capital and the potential for agglomeration economies. In Regression 1, the variables are entered

linearly; in Regression 2, we include quadratic terms to allow for potential nonlinearities.

20

Interestingly, given the prevalence of the “fundamental determinants” argument in the

cross-country literature, these variables together explain only a small fraction of the variation in

residual income across counties: adjusted R2s are low in both regressions. Of course, even within

a country as large and geographically diverse as the United States, there is much less variation in

these factors as there is across countries.

In the specification with only linear terms (Regression 1), residual growth is negatively

correlated with higher shares of farms operated by owners, while the standard deviation of

elevation is positively correlated with residual growth. At first blush the latter two findings may

seem surprising, but given the linear probability results of Table 3 where once we controlled for

initial human capital and culture land tenure and variation in elevation had opposite signs than

expected (though no statistical impact), these results are less surprising. Counties with higher

shares of Baptists and Calvinists in 1890, higher shares of foreign-born residents in 1900, and

more urbanized in 1890, also have, on average, higher residual growth rates.

Allowing for quadratic relationships (in Regression 2) changes these implications

somewhat. In particular, there are inverted U-shaped relationships between residual growth and

normalized latitude, 1890 Baptist share, 1890 Catholic share, 1900 foreign-born share, and the

1900 illiteracy rate, i.e. residual growth is increasing at a decreasing rate in these factors. For

most of these variables, the maximum value of the marginal effect occurs at a fairly high level,

so that the correlation is increasing for over 90% of the sample. A notable exception is the

inverted U-shape relationship between latitude and residual growth, where the maximum value

occurring closer to the sample median (at a normalized latitude of 0.44; 61 percent of the sample

is below this level). Importantly, even though the negative link between initial income and

illiteracy does not occur until illiteracy rates reach 38 percent, this happens to be quite close to

21

the sample mean of persistently poor counties as identified in Table 2. The negative correlation

between residual growth and Catholic share, and the positive correlation between residual

growth and urbanization, seem to occur only at the highest levels of Catholic share and

urbanization, respectively.

In Table 7, we address whether these historical determinants of residual growth differ for

the persistently poor counties and other counties. In Regressions 1 and 2 of Table 7, we present

results for the non-poor counties, where the dependent variable is the residual growth rate from

Regression 3 of Table 5 (the regression on the non-poor subsample, with the regressors treated as

predetermined). Consistent with our earlier results, and as we expect given that the non-poor are

such a large portion of the full sample, Regressions 1 and 2 look quite similar to the full sample

results of Table 6.

Our main interest, however, lies in comparing these estimates (Regressions 1 and 2) for

the non-poor sample with estimates for the persistently poor subgroup. Regressions 3 and 4

include results for the persistently poor counties, where the dependent variable is the residual

growth rate from our preferred specification, Regression 5 of Table 5 (estimated with the

regressors treated as exogenous). As indicated at the bottom of the table, formal Wald tests

strongly reject the null hypothesis of equal coefficients.

Comparing Regressions 1 and 3, a number of the qualitative and quantitative estimates

are quite different. While farm ownership has a negative and statistically significant correlation

with residual growth for the non-poor sample, the correlation is not statistically different from

zero among the poor counties. Among the non-poor counties, the standard deviation of elevation

is positively and statistically significantly correlated with residual growth, but this effect changes

sign and loses statistical significance among the persistently poor. This may suggest additional

22

nonlinearities or contingencies in the relationship: a county that is rich enough (through other

means) to pave roads through the mountains, or large enough to have a less mountainous area

where production can more easily be located, may be able to capitalize on mountains for their

amenity value, while poorer counties (or counties with no flat area at all) struggle with

transportation and access.

In Regressions 1 and 3, the coefficient estimate on Baptist share is positive and

statistically significant in both regressions, while the estimates on Calvinist and Catholic shares

are not statistically significant in either case. For both the foreign-born share and the illiteracy

rate, the effects are opposite in sign but statistically significant in both samples. A higher

percentage of foreign born in 1900, and a higher illiteracy rate in 1900, are positively correlated

with residual growth in the non-poor sample, but negatively correlated with growth in the

persistently poor sample. (Recall from Table 2 that the persistently poor counties had, on

average, much higher illiteracy rates in 1900, and much lower percentages of foreign born

residents.) Finally, the positive and statistically significant correlation between urbanization in

1900 and residual growth in the persistently poor sample does not appear in the non-poor sample.

Regressions 2 and 4 include quadratic terms for all of the regressors. There are several

nonlinear relationships worth discussing. Among the non-poor sample, the nonlinear

relationship between residual growth and illiteracy found in Table 6 remains, and the nonlinear

relationship between residual growth and urbanization strengthens. The implied maximum of

the marginal correlation between illiteracy and residual growth occurs at an illiteracy rate of 49

percent; only 56 counties (3 percent of the sample) have illiteracy rates higher than this. The

implied minimum of the U-shaped relationship between urbanization in 1890 and residual

growth occurs at an urban share of 36.5 percent, which 86 percent of the sample is below. For

23

the persistently poor sample, the quadratic specification seems to be “overfitted” for the

comparatively small sample. The only statistically significant coefficient estimate is on the

Baptist share entered linearly, which remains positive. However, of interest is the negative

coefficient estimate on illiteracy that is opposite in sign from those in the non-poor sample,

suggesting potential long term negative consequences for low initial human capital.

VI. Conclusion

Deep pockets of poverty persist in several regions of the United States despite the

widespread availability of technology and the lack of institutional barriers to labor mobility

across county and state borders. To examine the sources of persistent poverty across regions we

estimated a dynamic panel data model of conditional income convergence using county-level

data from the past five Censuses. We also recovered county-specific estimates of residual

income to examine the influence of fundamental determinants of income; namely, the roles of

culture, geography, human capital, and institutions based on measures from historic Censuses of

1980 and 1900.

Our estimates from a long-difference GMM estimator suggest that there are significant

regional differences in production technologies between counties that are persistently poor

versus non-poor: in particular, income growth is more highly correlated with capital spending

and the growth of the labor force in the persistently poor counties, and less correlated with the

urban share of the county. Despite this, rates of income convergence, which range from 7 to 9

percent, do not differ substantively between poor and non-poor regions. In terms of fundamental

determinants, we found an inverted U-shaped relationship between residual growth and our

measures of geography, culture, and human capital; that is, initial income is increasing at a

decreasing rate in these factors. Perhaps most compelling of the fundamental determinants is the

24

role of initial human capital. Counties with high rates of illiteracy in the late 19th century were at

much greater risk of being persistently poor a century later, suggesting long-term negative

consequences for low initial human capital among persistently poor counties. An implication of

these results is that to overcome such barriers to riches, these counties must invest heavily in

human capital development to catch up to their richer neighboring counties.

VII. References Acemoglu, D., S. Johnson, and J. Robinson (2005), “Institutions as the fundamental cause of

long-run growth,” in P. Aghion and S.N. Durlauf, eds., Handbook of Economic Growth, vol. 1. Amsterdam:. North-Holland Elsevier: 385-472.

Anderson, T., and C. Hsiao (1982), “Formulation and Estimation of Dynamic Models Using

Panel Data,” Journal of Econometrics 18(1): 47-82. Arellano, M., and S. Bond (1991), “Some Tests of Specification for Panel Data: Monte Carlo

Evidence and an Application to Employment Equations,” The Review of Economic Studies 58 (2): 277-297.

Banfield, E. (1970), The Unheavenly City. Boston: Little, Brown and Company. Barrington, L. (1999), “Editor’s Introduction: Native Americans and U.S. Economic History,” in

L. Barrington, ed., The Other Side of the Frontier: Economic Explorations into Native American History, Westview Press.

Barro, R., and R. M. McCleary (2003), “Religion and Economic Growth,” American

Sociological Review 68 (5): 760-781. Barro, R., and X. Sala-i-Martin (1992), “Convergence,” Journal of Political Economy 100 (2):

223-251. Bauer, P., M. Schweitzer, and S. Shane (2006), “State Growth Empirics: The Long-Run

Determinants of State Income Growth,” Social Science Research Network. Billings, D. (1974), “Culture and Poverty in Appalachia: A Theoretical Discussion and

Empirical Analysis,” Social Forces, 53, 2, 315-323. Billings, D., and K. Blee (2000), The Road to Poverty: The Making of Wealth and Hardship in

Appalachia. New York: Cambridge University Press.

25

Blundell, R., and S. Bond (1998), “Initial conditions and moment restrictions in dynamic panel data models,” Journal of Econometrics 87(1): 115-143.

Cavalcanti, T., S. Parente, and R. Zhao (2007), “Religion in macroeconomics: a quantitative

analysis of Weber's thesis,” Economic Theory 32: 105-132 Clifton, E., and A. Romero-Barrutieta (2006), “Institutions v. geography: sub-national evidence

from the United States,” International Monetary Fund Working Paper. Duncan, C., (1999), Worlds Apart: Why Poverty Persists in Rural America, New Haven:

Yale University Press. Durlauf, S. N., P. Johnson, and J. Temple (2005), “Growth Econometrics,” in P. Aghion and

S.N. Durlauf, eds., Handbook of Economic Growth vol. 1.. Amsterdam: North-Holland Elsevier: 555-677.

Durlauf, S. N., and D. Quah (1999), “The new empirics of economic growth,” in J. Taylor and

M. Woodford, eds, Handbook of Macroeconomics vol. 1. Amsterdam: North-Holland: 235-308.

Easterly, W., and R. Levine (2001), “What have we learned from a decade of empirical research

on growth? It's Not Factor Accumulation: Stylized Facts and Growth Models,” The World Bank Economic Review 15(2): 177-219.

Eller, R (2008), Uneven ground: Appalachia since 1945. Lexington: The University Press of

Kentucky. Engerman, S. (1966), “The Economic Impact of the Civil War,” Explorations in Economic

History 3: 176-99. Engerman, S., and R. Fogel (1974), Time on the Cross: The Economics of American Negro

Slavery. Boston: Little Brown. Evans, P., and G. Karras (1996), “Convergence revisited,” Journal of Monetary Economic 37

(2): 249-265. Gallup, J., J. Sachs, and A. Mellinger (1999), “Geography and economic development,”

International Regional Science Review 22(2): 179-232. Glaeser, E., H. D. Kallal, J. A. Scheinkman and A. Shleifer (1992), “Growth in Cities,” The

Journal of Political Economy 100(6): 1126-1152. Greif A. (1994), “Cultural Beliefs and the Organization of Society: A Historical and Theoretical

Reflection on Collectivist and Individualist Societies,” The Journal of Political Economy. 102(5): 912-50.

26

Griliches, Z, and J. Hausman (1986), “Errors in Variables in Panel Data,” Journal of Econometrics 31: 93-118.

Hahn, J., J. Hausman, and G. M. Kuersteiner (2007), “Long difference instrumental variables

estimation for dynamic panel models with fixed effects,” Journal of Econometrics 140(2): 574-617.

Hansen, L. (1982), “Large Sample Properties of Generalized Method of Moments Estimators,”

Econometrica 50(4): 1029-1054. Higgins, M., D. Levy, and A. Young (2006), “Growth and Convergence across the United States:

Evidence from County-Level Data,” The Review of Economics and Statistics 8(4): 671-681.

Hausman, J., and W. Taylor (1981), “Panel Data and Unobservable Individual Effects,”

Econometrica 49(6): 1377-1398. Hsiao, C. (1986), Analysis of Panel Data, Cambridge, MA: Cambridge University Press. Islam, N. (1995), “Growth Empirics: A Panel Data Approach,” The Quarterly Journal of

Economics 110(4): 1127-1170. Iyigun, M. (2005), “Geography, Demography, and Early Development,” Journal of Population

Economics 18(2): 301-321. Lee, K., M., H. Perasan, and R. Smith (1997), “Growth and convergence in a multi-country

empirical stochastic Solow model,” Journal of Applied Econometrics 12(4): 357-392. Mankiw, N. G., D. Romer, and D. N. Weil (1992), “A Contribution to the Empirics of Economic

Growth,” The Quarterly Journal of Economics 107(2): 407-437. Moretti, E. (2004), “Workers’ Education, Spillovers, and Productivity: Evidence from Plant-

Level Production Functions,” The American Economic Review 94(3): 656-690. Murray, C. (1984), Losing ground: American social policy, 1950-1980. New York: Basic Books. Newey, W. K. and K. D. West (1987). “Hypothesis Testing with Efficient Method of Moments

Estimation,” International Economic Review 28(3): 777–787. Nickell, S. (1981), “Biases in Dynamic Models with Fixed Effects,” Econometrica 49(6): 1417-

1426. Ransom, R., and R. Sutch (2001), One kind of freedom: The economic consequences of

emancipation, 2nd edition. New York: Cambridge University Press.

27

Rappaport, J. (2007), “Moving to nice weather,” Regional Science and Urban Economics 37(3): 375-398.

Rappaport J., and J. Sachs (2003), “The United States as a Coastal Nation,” Journal of

Economic Growth. 8(1): 5-46. Shapiro, T. (2006), “Race, homeownership and wealth,” Washington University Journal of Law

and Policy 53. Solow, R. (1956), “A Contribution to the Theory of Economic Growth,” Quarterly Journal of

Economics 70(1): 65-94. Data Appendix

Data on income, population, civilian labor, private capital expenditure, persons living in

poverty, number of high-school degree holders, number of African-Americans, land tenure,

religiosity, geography and institutions have been collected from various sources. A summary of

variable definitions and their measurement units is shown in Appendix Table 1.

The summary statistics in Table 1 of the text, and the dynamic panel model estimates of

income per capita in Tables 4-5, utilized county-level Census data from the 1960-2000 Decennial

Censuses. The USA Counties Basic Information database of the Census Bureau provided

information on many of the variables for 1980-2000 Census. Included in this database are county

per capita income (average income earned by the residents of the county), the total population of

the county, civilian labor force residing in the county (defined as the number of people over the

age of 16 in the county who are not employed in the armed forces and are not institutionalized),

number of people living in urban areas in the county (defined below), number of African-

Americans living in each county, persons living under the poverty-level in the county according

to the official poverty definition of the US, and the proportion of residents residing in the county

who are over the age of 25 and have at least a high school degree. These data are publicly

available from the URL: http://www.census.gov/support/DataDownload.htm.

28

The corresponding variables for the years 1960 and 1970 were collected from the County

and City Data Book of the Census (1962 and 1972), which are available on the website of ICPSR

(Inter-University Consortium for Political and Social Research). This site is maintained by the

University of Michigan. Data collected from ICPSR has been obtained from the URL:

http://www.icpsr.umich.edu/icpsrweb/ICPSR/studies/2896/system.

In this analysis, the growth rate of labor force in each county has been used. This growth

rate has been defined as the percentage change of civilian labor force in a country from one

decade to the next. To construct this variable for 1960 we obtained the corresponding

information on labor force from the 1950 Census to construct the 1950-1960 change.

The definition of what constitutes as an urban area has changed over time. In 2000, the

definition of urban areas was a core census block groups or census block that had at least 1000

persons per square mile and the surrounding census blocks that have a population density of at

least 500 persons per square mile (http://www.census.gov/geo/www/ua/ua_2k.html). So, a city

with a population density of at least 1000 people per square mile and the surrounding suburbs

with at least 500 people per square mile would be considered to be an urban area. For the years

1960, 1970, 1980 and 1990, the definition of an urban area was less stringent; any area that was

one of the Census designated places with more than 2500 people, or was incorporated in an

urban area (http://www.census.gov/population/censusdata/urdef.txt) was considered to be an

urban area. Therefore, for those areas, people living in a city or a town with at least 2500 people

or, living in an area that was historically considered to be urban would be considered to be living

in an urban area.

Private capital expenditure in the manufacturing sector (measured in millions of US

dollars) of each county for the years 1960, 1970 and 1980 has been obtained from the County

29

and City Data Books of various years. Private capital expenditure has been defined as either a

permanent addition or a major change made by a manufacturing firm and/or the addition or

replacement of any machinery or equipment in the plant (and whose depreciation account was

maintained). The data for 1990 and the definition of capital expenditures have been obtained

from the 1992 Census of Manufactures Report on each county

(http://www.census.gov/prod/1/manmin/92area/92manufa.htm). The 1990 data are in pdf format,

and thus a pdf-to-Excel converter was used to convert the data from pdf to Excel, and then

exported to Stata. Private capital expenditure data for the year 2000 has been obtained from US

Counties Basic Information database. The data from 1960 to 1990 were converted to real 2000

dollars using the personal consumption expenditure deflator from the Bureau of Economic

Analysis (BEA).

For the summary statistics in Table 2 of the text, as well as the regressions in Tables 3, 6,

and 7, historic data on geography, institutions, culture, and human capital were obtained from

various sources. The latitude of each county has been obtained from the Census 2000 U.S.

Gazetteer Files (http://www.census.gov/geo/www/gazetteer/places2k.html). The TIGER

database of Census stores latitude data as decimal degrees, instead of degrees, minutes and

seconds for ease of calculation. Therefore, if latitude of a certain area is 37 degrees, 25 minutes

and 40.5 seconds, it is recorded as 37.427916 by Census (http://www.census.gov/cgi-

bin/geo/tigerfaq?Q20). The decimal degree latitude of each county has been divided by 90 to

normalize it. The closer the value is to 1, the further the county is from the equator, and thus, the

more north/colder that county is relative to the equator. This measure shows the severity of

weather of a county. For example, Los Angeles County, CA has a latitude of 34 degrees 5

minutes and 18.6 seconds, but in decimal degrees, it has been recorded as 34.08851degrees.

30

After normalizing it, the value is 0.3787. Similarly, Cook County, IL has a latitude of 41 degrees

50 minutes and 15.3 minutes, and it is 41.8376 degrees. After normalizing it, the value is 0.4648.

Data on the standard deviation of elevation of each county has been obtained from

Rappaport and Sachs (March, 2003) and has been provided by Jordan Rappaport of the Federal

Reserve Bank of Kansas City. Elevation data were measured in feet, and it measures how high

the land is from sea-level. This data measures how varied the terrain of a county is. The higher

the standard deviation, the more extreme the terrain of the county; the lower the standard

deviation, the terrain is more or less constant. So, if a county has terrain near sea-level and also

high mountains, it is going to have a high value of standard deviation. On the other hand, if a

county has more or less uniform terrain (all the land near sea-level, or all the land are high-lands,

but without much variation in height) the value of standard deviation is going to be low.

Historical data of variables that proxies institution and culture, like percentage of foreign-

born living in a county, land tenure of a county, number of county residents living in urban areas

(areas that have been legally incorporated as cities, towns or boroughs,

http://www.census.gov/population/www/documentation/twps0027/twps0027.html) and number

of illiterate people in a county (number of people living in the county who cannot read or write)

have been collected from the 1890 and 1900 Census Database. The percentage foreign-born was

defined as the proportion of people living in a county who were not born in the United States.

Land tenure has been defined as the total area farmed by owners of those respective farms in a

given county, divided by the total amount of farmland in the county. This number was not given

explicitly; what was given was the number of farm owners who farmed 0-9 acres of farmland,

10-19 acres, 20-49 acres, 50-99 acres, 100-499 acres, 500-999 acres and 1000+ acres. The mid-

point of each segment was multiplied by their respected number of farm owners (for 1000+ acres

31

of farm segment, the number of farmers was multiplied by 1000 to estimate the total number of

farmland owned by farmers farming 1000+ acres) and then they were added together to get the

total acres of farmland farmed by owners.

Religious data on total church attendance and followers of different denominations,

namely Baptists, Calvinists and Catholics, have been obtained from the 1890 Census of

Religious Bodies. Data on the number of Baptists, Catholics, Calvinists and total church

members in a county have been collected from the 1890 Census of Religious Bodies. In this

paper, the Baptist denomination includes Regular (North, South and Colored), Freewill, General,

Primitive and Old Two-Seed denominations. The Calvinists denomination includes Welsh

Calvinist, Presbyterian (Northern and Southern), Cumberland Presbyterian (Regular and

Colored), United Presbyterian, US Reformed Church and American Reformed Church

Organizations. All these historical and religious data can be obtained from the ICPSR database:

http://www.icpsr.umich.edu/icpsrweb/ICPSR/studies/2896/system.

A number of counties changed their area and many new counties formed over time. Large

counties were split to form new counties and some counties were merged to form a new county.

For example, Manitou County in Michigan does not exist anymore and was merged with other

neighboring counties. These redrawing of county boundaries posed a problem because different

social indicators data (such as population, number of people illiterate in the county, land tenure)

changed whenever county boundaries were changed. To ensure that the changing of county

boundaries did not pose a problem with the regression analysis, only counties whose shape

remained the same from the years 1890 onwards were used in the analysis. Data on whether

county boundaries have changed over time has been obtained from the website of Newberry

Library (http://www.newberry.org). The library has electronic files of state maps from different

32

periods that show how the counties in each state evolved over time. The maps for the year 1890

were compared with those of current day (which are also available in the website of Newberry

Library) to see which counties did not change their shape between 1890 and present day.

However, during the time of this analysis, the library did not have data on the evolution of

county shapes for the state of Georgia, and this data has been obtained from the website:

http://www.FamilyHistory101.com.

Appendix Table 1: Description of Variables Used in the Regressions Variable Description Measurement Units Per Capita Income ($)

Average income earned by the residents of the county

In dollar amounts; values from 1960 to 1990 have been converted to 2000 dollars using the personal consumption expenditure deflator from the Bureau of Economic Analysis (BEA)

Population Total number of people living within the boundary of a county

In absolute value

Fraction in Labor Force The number of people over the age of 16 in the county who are not employed in the armed forces and are not institutionalized, divided by the population of the county.

Between 0 and 1

Growth in Labor Force The increase in civilian labor force in a country from one decade to the next

Between 0 and 1

33

Fraction High School Graduate Capital Expenditure

The number of residents over the age of 25 with at least a high school degree in the county, divided by the population of the county A permanent addition or a major change made by a manufacturing firm and/or the addition or replacement of any machinery or equipment in the plant (and whose depreciation account was maintained).

Between 0 and 1 In millions of dollars, and the values have been converted to real 2000 dollars using the personal consumption expenditure deflator from the Bureau of Economic Analysis

Fraction Living in Urban Area

The number of residents living in an urban area as defined by the Census, divided by the total population

Between 0 and 1

Fraction Black The number of African-Americans living in a county, divided by the total population

Between 0 and 1

Land Tenure in 1890 The total area of farmland farmed by their respective owners in the year 1890, divided by the total area under cultivation in a county in 1890

Between 0 and 1

Share Churched in 1890

The total number of people who attended church services in 1890, divided by the total number of people living in the county in 1890

Between 0 and 1

Share Baptist in 1890 The total number of people in a county who identify themselves as Baptists (Regular (North, South and Colored), Freewill, General, Primitive and Old Two-Seed denominations) in 1890, divided by the total population in 1890

Between 0 and 1

Share Calvinist in 1890 The total number of people in a county who identify themselves as Calvinists (Welsh Calvinist, Presbyterian (Northern and Southern), Cumberland Presbyterian (Regular and Colored), United Presbyterian, US Reformed Church

Between 0 and 1

34

and American Reformed Church Organizations) in 1890, divided by the total population in 1890

Share Catholic in 1890 The total number of people in a county who identify themselves as Catholics in 1890, divided by the total population in 1890

Between 0 and 1

Latitude The absolute value of latitude of a county (obtained from the Census)

Between 0 and 1

divided by 90 to obtain the normalized value

Std Dev of Elevation The standard deviation of elevation of a county

In feet

Urban Share in 1890 The number of residents living in an urban area as defined by the Census, divided by the total population in 1890

Between 0 and 1

Share Foreign Born in 1900

The number of residents living in the county who were not born in the United States in 1890, divided by the total population

Between 0 and 1

Illiteracy Rate in 1900 The number of people who cannot read or write in a county in 1890, divided by the total number of people living in the given county in 1890

Between 0 and 1

35

36

37

38

39

40

41

Table 1: Summary Statistics of Social Indicators for Counties by Persistent Poverty Status Not Persistently Poor Persistently Poor Mean Standard

Deviation Mean Standard

Deviation Pooled 1960-2000 Census Data Per Capita Income ($) 12,429 4,839 8,615 3,410 Population 78,576 260,310 24,368 48,481 Fraction in Labor Force 0.423 0.065 0.355 0.057 Growth in Labor Force 0.166 0.309 0.056 0.219 Fraction High School Graduate 0.588 0.188 0.431 0.172 Capital Expenditure ($millions) 34.676 142.399 5.405 19.781 Fraction Living in Urban Area 0.372 0.299 0.251 0.251 Fraction Black 0.070 0.118 0.252 0.247

1960 Census Data Per Capita Income ($) 6,918 1,894 4,295 1,343 Population 61,536 214,978 22,530 41,197 Fraction in Labor Force 0.360 0.038 0.305 0.045 Growth in Labor Force 0.069 0.324 -0.125 0.201 Fraction High School Graduate 0.361 0.105 0.227 0.073 Capital Expenditure ($millions) 14.857 72.808 1.112 3.129 Fraction Living in Urban Area 0.335 0.287 0.213 0.234 Fraction Black

0.076

0.131

0.271 0.259

2000 Census Data Per Capita Income ($) 18,431 3,813 13,199 1,958 Population 97,237 307,612 27,855 60,596 Fraction in Labor Force 0.478 0.048 0.395 0.039 Growth in Labor Force 0.144 0.166 0.068 0.117 Fraction High School Graduate 0.789 0.074 0.642 0.071 Capital Expenditure ($millions) 38.741 163.346 6.419 23.038 Fraction Living in Urban Area 0.415 0.309 0.272 0.260 Fraction Black

0.067

0.110

0.250

0.249

Observations 2,756 338 Notes: “Persistently poor” counties have poverty rates of at least 20% in 1960, 1970, 1980, 1990, and 2000. “Not persistently poor” are all others. Per capita income and capital expenditures are in real $2000 based on the personal consumption expenditure deflator.

42

Table 2: Summary Statistics of Historical Indicators for Counties by Persistent Poverty Status Not Persistently Poor Persistently Poor Land Tenure in 1890 0.800 0.117 0.766 0.146 Share Churched in 1890 0.294 0.120 0.311 0.157 Share Baptist in 1890 0.064 0.081 0.131 0.099 Share Calvinist in 1890 0.019 0.022 0.009 0.016 Share Catholic in 1890 0.059 0.089 0.034 0.122 Latitude 0.431 0.050 0.382 0.039 Std Dev of Elevation 0.097 0.170 0.060 0.071 Urban Share in 1890 0.132 0.220 0.025 0.105 Share Foreign Born in 1900 0.100 0.107 0.026 0.074 Illiteracy Rate in 1900 0.110 0.134 0.356 0.222 Observations 2,287 245 Notes: “Persistently poor” counties have poverty rates of at least 20% in 1960, 1970, 1980, 1990, and 2000. “Not persistently poor” are all others. The historic Census data include only counties without redefined borders between the relevant year (1890, 1900) and 1960. See the Data Appendix for detailed variable definitions.

43

Table 3: Linear Probability Estimates of the Probability of Being Persistently Poor

Variables (1) (2) (3) (4) (5)

Farm Owner Percentage in 1890

-0.098(0.047)

0.040 (0.048)

0.033(0.050)

-0.157 (0.050)

-0.202(0.050)

Normalized Latitude

-1.746(0.116)

-0.103(0.166)

-0.136(0.167)

-1.753 (0.151)

-1.362(0.159)

Std. Dev of Elevation

-0.084(0.045)

-0.045(0.042)

-0.031(0.042)

-0.067 (0.045)

-0.060(0.044)

Foreign-born Percentage in 1900

0.075(0.071)

-0.021(0.081)

0.107 (0.075)

0.029(0.085)

Urban Share 1890

-0.071(0.028)

-0.081(0.028)

-0.155 (0.029)

-0.138(0.030)

Illiteracy Rate 1900

0.839(0.045)

0.852(0.050)

Church Share 1890

-0.193(0.046)

0.016 (0.047)

Baptist Share 1890

-0.316(0.086)

0.335(0.081)

Calvin Share 1890

-0.623(0.261)

-1.382(0.272)

Catholic Share 1890

-0.021(0.071)

0.163(0.075)

Constant

0.926(0.058)

0.057(0.087)

0.062(0.087)

0.981 (0.077)

0.850(0.078)

Adjusted R2 0.091 0.215 0.213 0.101 0.119Observations 2,498 2,474 2,474 2,474 2,474 Persistently poor 237 237 237 237 237

Notes: Standard errors are in parentheses. The dependent variable is a binary variable equal to one for counties that are persistently poor between 1960 and 2000 and zero otherwise.

44

Table 4: Dynamic Panel Estimates of Income Convergence

(1) (2) (3)

OLS GMM

∆Xit exogenous GMM

∆Xit predetermined Lag Income per Capita

0.442

(0.016) 0.436

(0.018) 0.460

(0.026) Fraction High School 0.364

(0.046) 0.396

(0.047) 0.236

(0.075) Capital Spending (x1000) 0.042

(0.029) 0.069

(0.021) -0.156 (0.185)

Labor Force Growth 0.013 (0.015)

0.026 (0.012)

-0.031 (0.025)

Urban Share 0.093 (0.013)

0.085 (0.013)

0.159 (0.036)

Black Share -0.288 (0.049)

-0.222 (0.045)

-0.191 (0.163)

Constant 0.193 (0.010)

0.187 (0.010)

0.221 (0.020)

Convergence Rate

0.082 (0.003)

0.083 (0.004)

0.077 (0.006)

Hansen's J (p-value) 101.582 [0.000]

9.975 [0.076]

C-statistic 91.607 [0.000]

Observations 3,094 3,090 3,090 Notes: Asymptotic standard errors are reported in parentheses. The p-value for the chi-square distribution is reported in square brackets.

45

Table 5: Dynamic Panel Estimates of Income Convergence, by Persistent Poverty Status Non-Persistent Poverty Persistent Poverty

(1) (2) (3) (4) (5) (6)

OLS

GMM ∆Xit

Exog

GMM ∆Xit

Predet OLS

GMM ∆Xit

Exog

GMM ∆Xit

Predet Lag of Income

0.435

(0.016) 0.395

(0.020) 0.454

(0.030) 0.431

(0.049) 0.433

(0.043) 0.375

(0.052) Fraction High School

0.356 (0.047)

0.440 (0.050)

0.180 (0.070)

0.501 (0.145)

0.449 (0.134)

1.016 (0.277)

Capital Spending (x1000)

0.041 (0.029)

0.064 (0.021)

-0.158 (0.172)

0.247 (0.158)

0.145 (0.140)

0.371 (1.249)

Labor Force Growth 0.010 (0.013)

-0.001 (0.014)

-0.031 (0.024)

0.187 (0.048)

0.210 (0.044)

0.165 (0.087)

Urban Share 0.101 (0.014)

0.096 (0.014)

0.202 (0.035)

0.024 (0.049)

-0.001 (0.047)

-0.076 (0.127)

Black Share -0.321 (0.053)

-0.326 (0.049)

-0.209 (0.131)

-0.123 (0.139)

0.019 (0.112)

0.340 (0.336)

Constant 0.199 (0.011)

0.202 (0.010)

0.238 (0.017)

0.155 (0.037)

0.172 (0.031)

0.034 (0.069)

Convergence 0.083 (0.004)

0.093 (0.005)

0.079 (0.007)

0.084 (0.011)

0.084 (0.009)

0.098 (0.014)

Hansen's J [p-value] 147.290 [0.000]

7.575 [0.181]

17.363 [0.067]

5.762 [0.330]

C-statistic

139.715 [0.000]

11.601 [0.041]

(1) vs (4) (2) vs (5) (3) vs (6) Equal Coefficient Wald Test [p-value]

14.524 [0.024]

26.043 [0.000]

20.988 [0.002]

Equal Convergence Wald Test [p-value]

0.007 [0.931]

0.662 [0.415]

1.710 [0.190]

Observations 2,752 2,752 2,752 338 338 338Notes: Asymptotic standard errors are reported in parentheses. The p-value for the chi-square distribution is reported in square brackets.

46

Table 6: Pooled Regressions, Second-Stage Results (1) (2)

Farm Owner in 1890 -0.243 (0.029)

-0.220 (0.236)

Farm Owner in 1890, squared -0.021 (0.158)

Normalized Latitude 0.070 (0.098)

4.349 (1.214)

Normalized Latitude, squared -4.901 (1.454)

Std. Dev of Elevation 0.197 (0.025)

0.140 (0.046)

Std. Dev to Elevation, squared 0.024

(0.048)

Baptist Share in 1890 0.401 (0.051)

0.542 (0.099)

Baptist Share in 1890, squared -0.491 (0.196)

Calvin Share in 1890 0.338 (0.154)

-0.036 (0.332)

Calvin Share in 1890, squared 4.615

(3.034)

Catholic Share in 1890 0.016 (0.042)

0.158 (0.085)

Catholic Share in 1890, squared -0.327 (0.149)

Foreign-born Share in 1900 0.215 (0.047)

0.607 (0.119)

Foreign-born Share in 1900, squared -0.893 (0.292)

Illiteracy Rate in 1900 0.042 (0.029)

0.468 (0.075)

Illiteracy Rate in 1900, squared -0.606 (0.102)

Urban Share in 1890 0.075 (0.017)

-0.058 (0.043)

Urban Share in 1890, squared 0.165

(0.060)

Constant 9.023 (0.051)

8.053 (0.267)

Observations 2,473 2,473 Adjusted R2 0.108 0.132

Notes: The dependent variable is residual growth from the pooled, pre-determined model (Regression 3 of Table 4). Standard errors are in parenthesis.

47

Table 7: Second-Stage Results by Persistently Poor Status Not Persistently Poor Persistently Poor (1) (2) (3) (4)

Farm Owner in 1890 -0.280 (0.030)

-0.384 (0.249)

-0.110 (0.065)

-0.075 (0.462)

Farm Owner in 1890, squared

0.064 (0.165)

-0.040 (0.327)

Normalized Latitude 0.042 (0.102)

4.346 (1.222)

-0.296 (0.248)

-2.747 (4.357)

Normalized Latitude, squared

-4.961 (1.458)

3.125 (5.390)

Std. Dev of Elevation 0.208 (0.024)

0.166 (0.046)

-0.160 (0.105)

-0.437 (0.276)

Std. Dev of Elevation, squared

-0.004 (0.047)

0.778 (0.705)

Baptist Share in 1890 0.268 (0.054)

0.312 (0.103)

0.309 (0.084)

0.661 (0.224)

Baptist Share in 1890, squared

-0.243 (0.199)

-0.905 (0.503)

Calvin Share in 1890 0.188 (0.153)

-0.669 (0.338)

0.025 (0.486)

-1.336 (0.867)

Calvin Share in 1890, squared

9.638 (3.125)

12.272 (6.392)

Catholic Share in 1890 0.030 (0.045)

-0.012 (0.095)

-0.071 (0.070)

-0.186 (0.188)

Catholic Share in 1890, squared

0.060 (0.193)

0.184 (0.237)

Foreign-born Share in 1900 0.301 (0.049)

0.533 (0.119)

-0.462 (0.123)

-0.746 (0.469)

Foreign-born Share in 1900, squared

-0.482 (0.296)

0.610 (0.964)

Illiteracy Rate in 1900 0.244 (0.035)

0.594 (0.089)

-0.160 (0.052)

-0.203 (0.143)

Illiteracy Rate in 1900, squared

-0.601 (0.143)

0.005 (0.144)

Urban Share in 1890 -0.008 (0.016)

-0.149 (0.043)

0.163 (0.068)

0.111 (0.170)

Urban Share in 1890, squared

0.205 (0.059)

0.119 (0.225)

Constant 9.078 (0.053)

8.181 (0.270)

8.879 (0.121)

9.368 (0.912)

(1) vs (3) (2) vs (4) Equal Coefficient Wald Test [p-value]

1692.543 [0.000]

1673.917 [0.000]

Observations 2,236 2,236 237 237 Adjusted R2 0.133 0.159 0.204 0.212

Notes: The dependent variable in Regressions 1 and 2 is residual growth from the pre-determined model estimated on the non-persistently-poor counties only (Regression 3 of Table 5). The dependent variable in Regressions 3 and 4 is residual growth from the exogenous model estimated on persistently poor counties only (Regression 5 of Table 5). Standard errors are in parenthesis.