The Kuznets Curve and the Great U-Turn: Income Inequality in U.S. Counties, 1970 to 1990

by François Nielsen, Arthur S. Alderson
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Title:
The Kuznets Curve and the Great U-Turn: Income Inequality in U.S. Counties, 1970 to 1990
Author:
François Nielsen, Arthur S. Alderson
Year: 
1997
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American Sociological Review
Volume: 
62
Issue: 
1
Start Page: 
12
End Page: 
33
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English
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Abstract:

THE KUZNETS CURVE AND THE GREAT U-TURN:
INCOME INEQUALITY IN U.S. COUNTIES, 1970 TO 1990"
Franqois Nielsen Arthur S. Alderson

University of North Carolitza, University of North Carolina,
Chapel Hill Chapel Hill

We examine the determinants of inequality in the distribution of ,fanlily in-

conze in approxinzately 3,100 counties of the United States in 1970, 1980,

and 1990. Such a study provides a "window" on global trends in socirrl in-

equality during the period, which spans the tail end of the Kuzriets curve and

the more recent upswing in income inequa1it.y. Results from randonl-effects

regression models that control for urlmeasured heterogeneity anlong states

reveal the continued importance of the Kuznetsian pattern of declining in-

equality with economic development, a positive effect of urbanization on in-

equality, a declining positive impact of sector dualism, an increasing posi-

tive effect of educational heterogeneity, and a persistent effect of rncial du-

alisnz. Several variables associated with the recent upswing in inequality

lzave signi3cant effects: female labor-force participation (negative), fenznle-

headed households (positive), percent of the population over age 65 (changes

from positive to negative over the period), manufacturing employnlent (nega-

tive), and unenzployment (ambiguous). We also discuss nzethods of estimat-

ing the Gini coefficient for income inequality at the county level and mea-

sures of sector (farmhonfarm) dualism, racial (Black/White) dualism, and

educational heterogeneity.

The evolution of social inequality in the nets curve and the Great U-Turn. Kuznets course of human history is a central (1953, [I9551 1965) noted that income in- topic of stratification research (Lenski equality has an inverted-U shaped relation- [I9661 1984). While most sociologists view ship with economic development. Using data social inequality as multidimensional, in- for a handful of industrial societies in the volving power and prestige as well as in- nineteenth and twentieth centuries, he come, inequality in the distribution of in- showed that income inequality initially in- come is a tangible and measurable aspect of creased with industrial development, peaked inequality. Two major trends in inequality and leveled off, then declined with further have characterized industrial and developing development, with the exact timing of the de- societies in the twentieth century: the Kuz- cline differing somewhat across societies. In the United States, inequality peaked in the late 1800s and did not begin declining until

* Direct correspondence to Fran~ois Nielsen, Department of Sociology, University of North the late 1920s. Lampman (1962) found that, Carolina, Chapel Hill, NC 27599-3210 (francois- in the United States, a strikingly similar nielsen@unc.edu). An early version of this paper curve depicts the evolution of inequality in

was presented at the annual meeting of the the distribution of wealth, as distinct from American Sociological Association in Washing-

income, with the gap in the share of wealth

ton, DC., August 1995. Partial support for this re-

between rich and poor also declining sharply

search was provided by a summer stipend from

between the late 1920s and the middle of the

the Institute for Research in Social Science at the

century. Later research largely confirmed the

University of North Carolina at Chapel Hill. We

Kuznets-Lampman findings for the United

thank Gerhard Lenski, Rachel Rosenfeld, three ASR reviewers, and the ASR editors for their help- States (Williamson and Lindert 1980:281). ful advice. Lindert and Williamson (1985:345, fig. 2)

Atnericarz Sociological Review, 1997, Vol. 62 (February: 12-33)

Year Figure 1. Inequality in the Distribution of Family Income by Year: United States, 1929 to 1992

Note: Percent income share (right-hand scale) is based on personal income for 1929 through 1964 and on money income for 1947 through 1992. Personal income includes money income plus certain nonmonetary forms of income such as estimated net rental value to owner-occupants of their homes.

Sources: U.S. Bureau of the Census 1975, series G319-336; 1986, table 12; 1993, table B-7.

found parallel declines in income inequality experienced by other industrial societies in the twentieth century as well.'

The recent experience of industrial societ- ies, however, suggests an added twist to Kuznets's depiction of the evolution of in- equality associated with development. Williamson and Lindert (1980:5) saw in- equality as declining in the United States from the late 1920s to about 1950. The next two decades were characterized by a "curi- ous stability" at a relatively low level of in- equality. The period since 1970 has been characterized by a resurgence of income in- equality in U.S. society severe enough to be christened the "Great U-Turn" by Harrison

' Despite isolated skepticism (Papanek 1978), the Kuznets curve has also been documented for contemporary developing societies (Lecaillon et al. 1984; Gagliani 1987; Nielsen 1994; Nielsen and Alderson 1995).

and Bluestone (1988), who place the start of the upswing in inequality in 1969 for the dis- tribution of family income and in 1976 for the distribution of wages and salaries (1988:7, fig. 1.3; 119, fig. 5.2). The resump- tion of an upward trend in income inequality has been confirmed by several observers (Thurow 1987; Bluestone 1990; Levy and Michel 1991 ;Levy and Murnane 1992; Mor- ris, Bernhardt, and Handcock 1994). Figure 1 shows the evolution of inequality in the distribution of personal or money income among families in the United States from 1929 to 1992 (inequality is measured by the Gini coefficient or as the share of aggregate income accruing to the top quintile). The tail end of the decline in inequality associated with the Kuznets curve and the Great U-Turn are both clearly visible. A similar upswing in inequality has also been documented for the distribution of earnings for men in Canada, Sweden, Australia, and West Ger-

many (Green, Coder, and Ryscavage 1992), suggesting that the trend is international.

The long-term decline in inequality asso- ciated with industrial development repre- sented by the Kuznets curve and the more recent reversal of this trend in the Great U- Turn have been attributed to diverse causes. Indeed, the two historical episodes are dis- cussed in distinct literatures. Most theories of the causes of the inverted-U pattern of the Kuznets curve have been based on cross- national comparisons. In contrast, explana- tions of the Great U-Turn have been based largely on the U.S. domestic context. We combine these two theoretical threads in a model of inequality that accounts for both historical episodes. We then investigate the model's predictions using census data on in- come inequality in U.S. counties from 1970 to 1990.

INCOME INEQUALITY IN
U.S. COUNTIES IN THE LATE TWENTIETH CENTURY

The evolution of income inequality has tra- ditionally been investigated using historical data for individual countries (as in the admi- rable survey of the United States from colonial times to the 1970s by Williamson and Lindert 1980), or using cross-sections of contemporary countries (see the literature cited in Nielsen 1994 and Nielsen and Alder- son 1995). The relative scarcity of compa rable cross-national data over time has been a major problem in prior research (Gagliani

1987). Observations often have been too few to yield strong inferences (but see Nielsen and Alderson 1995). We avoid that problem by studying inequality in the distribution of income in approximately 3,100 counties of the United States over three decennial cen- sus periods from 1970 to 1990. Using coun- ties as units of analysis makes it possible to examine several thousand income distribu- tions at three points in time and over a wide range of social contexts.
Advantages of Counties

Although U.S. counties during the 1970 to 1990 period enjoyed levels of development that would place many counties among the most highly developed societies if they were
AMERICAN SOCIOLOGICAL REVIEW

independent political entities, they vary con- siderably in economic infrastructure. demo- graphic profile, and level of prosperity. Counties, as opposed to cities or SMSAs, represent the complete range of social land- scapes, from entirely rural to dense metro- politan areas. If one were to plot the 3,100 counties at the three time points on a graph relating income inequality to development, the 9,300 data points would span a wide "window" on the rightmost segment of the Kuznets curve. On the right side of the graph, the more prosperous counties in later periods might show evidence of the upswing in in- equality corresponding to the Great U-Turn. On the left of the graph, the least prosperous counties in the earliest periods might still trace the characteristic hump of the Kuznets curve, as Braun (199 1:247, fig. 6.3) claimed for non-southern counties as late as 1980.

Using counties rather than nations as units of analysis has methodological advantages. Procedures of data collection and measure- ment used by the Census Bureau are the same across units, at least at the same time point, and when procedures do differ, they are well documented. In contrast, cross-na- tional data on income inequality are notori- ously delicate to compare (Menard 1986; Hoover 1989). Furthermore, many legal, edu- cational, and political institutions are shared by counties. These extraneous effects there- fore will not contribute to the noise confounding the effects of the structural vari- ables of interest.

Finally, counties observed at multiple time points constitute a time series of cross-sec- tions that incorporates variability both across units and over time. A data set with such a panel structure is potentially amenable to the use of powerful statistical techniques (based on pooling the cross-sections) that can increase efficiency of estimation (in the case of cross-sectional linear models) and can cor- rect for estimation inconsistency (in the case of models incorporating the lagged depen- dent variable).'

'Pooling county data over time is part of our future research agenda. Here we use a classical cross-sectional design for each of thc three ccn- sus years, using pooling techniques to control for the impact of ~lnmeasurcd characteristics of states.
Limitations of Counties

Counties are subject to a number of potential limitations:

First, because counties are subunits of a single national entity, they are more homog- enous and cannot cover as wide a range of variation in levels of development, social conditions, institutions, and culture as a cross-national sample.

Second, county boundaries may not de- limit autonomous and internally integrated social systems with respect to distributional processes. For example, following suburban expansion, the historical boundaries of a county may incorporate highly prosperous housing developments and low-income rural areas. The resulting high level of inequality does not necessarily indicate the level of in- equality in the county viewed as a social sys- tem. These areas may not interact much at all-they are juxtaposed within a boundary as a result of contingent processes. The theo- ries of income inequality discussed here, however, do not require that the population constitute a bounded system of interactions or an autonomous social or econornic sys- tem. The theoretical mechanisms discussed later typically associate a certain composi- tion of the population with respect to educa- tion, sector of economic activity, vital rates, and so on, with a certain level of income in- equality. They are "compositional" theories that treat a population purely as an aggregate of individuals. These theories can be tested with data on counties (or any other units with differing compositions on the relevant varl- ables) and would not be "fooled" by the jux- taposition in the example as long as relevant variables are measured.

A third potential problem with county data is that the population bases of data collected by official agencies may differ. For example, while the household census provides data on the population residing in the county, other data sources report characteristics of the population working in the county. The dis- crepancy between the two population bases can be considerable for counties in or near metropolitan areas where substantial numbers of residents commute to work across county boundaries. We circumvent this po- tential difficulty by using only data based on the population of residence.

Finally, one aspect of income distribu- tion-the political process broadly defined- is poorly capturzd at the county level. Al- though some aspects of the political process, such as the structure of the local elite, have been studied with county data (Tomaskovic- Devey and Roscigno 1996), political deci- sions affecting the distribution of income are made for the most part at levels other than the county level, especially in more recent periods. Counties, however, are subsets of larger units, the states, that do have a sub- stantial degree of political autonomy and can affect the distribution of income in several ways (Jacobs 1985). Fortunately, state-level effects can be controlled after a fashion. In the analyses reported below, we specify a random state-specific component of the er- ror term to simulate the overall impact of un- measured state-level variables on income in- equality in counties.
SOURCES OF INCOME INEQUALITY

Lindert and Williamson (1985) have pro- posed a comprehensive economic theory of the evolution of income inequality during de- velopment based on the historical experi- ences of Britain and the United States from the nineteenth century to the present. They identified three prime movers (i.e., mostly exogenous factors) of income inequality: (1) "rise and fall in sectoral imbalances in total factor productivity rates"; (2) "rise and fall of labor-force growth (e.g., due to demo- graphic transition)"; (3) "lagged acceleration of skills deepening" (pp. 368-69). In their in- terpretation, these three factors are treated as intermediate variables affected by more spe- cific measurable social changes. Labor-force growth, for example, may be affected by the demographic transition or immigration; the spread of education contributes to "skills deepening." In previous work (Nielsen 1994; Nielsen and Alderson 1995) we modified the Lindert and Williamson (1985) model by in- corporating the main mechanism of sector dualism discussed by Kuznets ([I9551 1965) and developed a "core" model of the rela- tionship between income inequality and de- velopment. Discussions of the Great U-Turn beginning in the early 1970s also generated theoretical conjectures and empirical inves- tigations of the causes of the upswing in in- equality. These two traditions-research on the Kuznets curve and the debate surround- ing the Great U-Turn-have evoked sets of explanatory factors that are largely nonover- lapping. We also investigate a potential fac- tor affecting inequality, racial dualism, which is central to the historical experience of the United States and not usually discussed in the other research traditions.
Income Inequality and Industrial Development

The Kuznets curve postulates a negative re- lationship between inequality and develop- ment for societies at relatively high levels of development. Williamson (199 1 :8) noted that this declining portion of the Kuznets curve is empirically robust and well documented. The level of development of most counties in the period from 1970 to 1990 corresponds to this declining segment of the Kuznets curve. In our empirical analyses, we use me- dian family income as the measure of eco- nomic development because it is a close sub-

stitute for gross domestic product per capita, a measure commonly used in cross-national research. We therefore predict that during the period under study, there is a negative rela- tionship between income inequality and level of development as measured by median farn- ily income.

Kuznets ([I9551 1965:264) speculated that income inequality in developing societies is typically higher in urban centers (with their enormous diversity of social conditions rang- ing from the destitute to wealthy industrial- ists) than in rural areas (which he viewed as populated by many small economic units of similar size and therefore inherently more egalitarian). Kuznets's conjecture, to the ex- tent that it can be applied to the urban-rural contrast in developed societies, predicts a positive association between income inequal- ity and urbanization. The issue is compli- cated by the positive correlation between urbanization and economic development. Highly urbanized counties are also likely to be more economically prosperous and there- fore have less inequality because of the nega- tive relationship between inequality and de- velopment. In zero-order associations, any independent positive effect of urbanization on inequality is likely to be overshadowed by the strong negative association between in- equality and development. Therefore, the hy- pothesis involving urbanization specifies a control for development. We use popueation density as a measure of the urbanization of a county. Kuznets's ([I9551 1965) discussion implies that, controlling for economic devee- opment, urbanizatiotl (measured as popula- tion density) has a positive effect on income inequality.

Kuznets' ([I9551 1965:269-75) explanation of the inverted-U pattern stressed the dualism between the traditional (agricultural) and modern (nonagricultural) sectors of a de- veloping economy. A society at an early stage of industrialization is characterized by the coexistence of a small modern industrial sector with high productivity and wages and a large traditional agricultural sector with low productivity and wages. As an increas- ing proportion of the labor force moves from the low-income traditional sector to the high- income modern sector, income inequality in- creases, levels off, and then decreases. This occurs as an automatic numerical consequence of the population transfers between sectors (Robinson 1976; Lydall 1977:205-25; Fields 1980; Lecaillon et al. 1984: 16-22; Nielsen 1994: 659, fig. 2).

The degree of inequality due to the differ- ence between the agricultural and nonagri- cultural sectors in average income is called sector dualism. Sector dualism is a function of both the difference between sectors in av- erage income and the relative size of the sec- tors (Lecaillon et al. 1984). Using cross-na- tional data, Nielsen (1994) and Nielsen and Alderson (1995) showed that sector dualism is significantly associated with overall in- come inequality and partially explains the inverted-U pattern of the Kuznets curve. In cross-national data, the impact of sector du- alism on inequality is greatest at relatively low levels of development. Developed soci- eties, including the United States, have low levels of sector dualism, in part because the agricultural sector is no longer a substantial fraction of the labor force (Lecaillon et al.

1984; Nielsen 1994:660, fig. 3). We use a measure of sector dualism based on a com- parison of farm and nonfarm earnings to es- timate dualism's effect on income inequality at the county level. Given the high level of development of counties in 1970 (and later) and their relative homogeneity compared to a cross-section of countries, we do not ex- pect the effect of sector dualism to be as strong as that found in cross-national data. Therefore, to the extent that sector dualism is still a determinant of inequality in the pe- riod under study, we predict that: (1) sector dualism has a positive effect on overall in- come inequality, and (2) the positive effect of sector dualism decreases over time.

Sector dualism measures the amount of overall income inequality that results from the difference in average income between sectors. The distribution of the population among sectors can also affect overall in- equality to the extent that inequality differs within sectors. If, as Kuznets ([I9551 1965: 264) believed, inequality is lower in the ag- ricultural sector than in the nonagricultural sector, it follows that a relatively large agri- cultural sector gives more weight to the more equal sector and results in lower overall in- equality (Nielsen 1994). Therefore, we con- trol for the size of the agricultural sector in our model (measured as percent farm popu- lation) and predict that, cor~trolling for sector dualism, size of the agricultural sector has a rzegative effect on income inequality.

The demographic transition, a major fea- ture of industrial development in which the early reduction in the death rate is not offset until later by a decline in the birth rate, has been implicated as an underlying cause of the inverted-U shape of the Kuznets curve. The position of a society along the demographic transition is indicated by the rate of naturzll irzcrease in the population, calculated as the difference between the birth rate and the death rate (Nielsen 1994:663, fig. 4). Ahlu- walia (1976) found a strong positive associa- tion between a population's rate of natural increase and income inequality In cross-na- tional data3 Pursuing an earlier suggestion of Kuznets ([I9551 1965:277-78), Lindert and Williamson (1985:368-69; Williamson 199 1 :25-27) argued that population growth tends to increase income inequality by in-

'Other researchers have documented an association between income inequality and the pro- portion of the population under age 15, a variable that is highly correlated with the rate of natural increase (Bollen and Jackman 1985a; Simpson 1990).

creaslng the supply of labor, especially of unskilled labor. Nielsen (1994) showed that the rate of natural increase has a positive ef- fect on inequality in cross-national data and attributed part of this effect to the fact that population growth is also a proxy measure of generalized dualcsm; that is, the degree of general social heterogeneity resulting from the uneven diffusion of industrial technology and culture (Lenski, Eenski, and Nolan 1991:401). The rate of natural increase is a proxy (possibly a crude one) for generalized dualism because it measures the gap between the early adoption of mortality-reducing modern technologies and the later adoption of modern attitudes toward reproduction and modern birth control methods. The effect of population growth on income inequality is expected to be smaller for U.S. counties, which are well past their demographic transi-

tions, than it would be in a cross-section of contemporary nations. To the extent that this demographic mechanism is at work in the period under study, and assuming that the demographic transition's effects decay over time, we predict that: (1) the rate of natural increase (birth rate minus death rate) has a positive effect on irlcorne inequality, and (2) this effect is stronger in earlier than in later periods.

Another major aspect of development is the diffusion of education. Beginning with Mill (1848) over a century ago, social scien- tists have believed that the spread of educa- tion, sometimes called "skills deepening" (Williamson 1991), is associated with reduced inequality.4 This is consistent with the standard economic argument that an increase in the supply of people with advanced edu- cational credentials should increase compe- tition for positions requiring these creden- tials and thereby reduce the wage differen- tlal between the educated and uneducated (Tinbergen 1975; Lecaillon et al. 1984:88). The spread of education, as measured by en- rollments in secondary schools, has a strong negative effect on income inequality in cross- national data (Simpson 1990; Nielsen 1994). This finding would be expected in a cross- national data set in which units of analysis

Lecaillon et al. (1984:86-90), however, dis- cuss plausible scenarios associating the spread of education with irzcrensed income inequality.

span the entire range of development levels. In such a context, educational expansion covaries so strongly with development that its relationship with inequality should be negative.

A few researchers have pointed out that the relationship between income inequality and educational expansion may differ among ad- vanced industrialized societies. Crenshaw and Ameen (1994) claimed that, even in a cross-national context, the relationship is re- versed and becomes positive at high levels of educational expansion, reflecting "a post- industrial regime with a new set of social in- equalities" (p. 11). Jacobs (1985) argued that the distribution of educational attainment af- fects the distribution of income through the dispersion of education rather than through the average level of education. To the extent that, for individuals, more education is asso- ciated with higher income, the distribution of educational attainment in a population is bound to have a compositional effect on in- come inequality, as the greater dispersion of educational attainment is translated, however noisily, into greater dispersion of income (i.e., inequality). At an aggregate level, in- come inequality should be positively associ- ated with a measure of the dispersion of edu- cational attainment in the population. Chiswick and Minces (1972), Chiswick (1974), Hirsch (1978), and Jacobs (1985) all reported positive associations between in- come inequality and inequality of educa- tional attainment. We investigate this hypo- thetical association using an indicator for educational heterogeneity that measures the diversity (dispersion) of educational attain- ment in the adult population of a county. We predict that, controlling for development, educational heterogeneity has a positive ef-

fect on income inequality.

The compositional hypothesis concerning the effect of the distribution of education on inequality has implications for comparisons of our model across periods. To anticipate some of the empirical results, we find a posi- tive association between educational hetero- geneity and the average educational attain- ment in a county, so that counties with high educational heterogeneity scores also have high proportions of high school and college educated adults (see also Nielsen and War- ren 1995). There is also a positive associa- tion between average educational attainment and economic development as measured by median family income. We speculate that in earlier periods, the spread of education at the county level was strongly associated with economic development and that its overall effect on inequality was negative-the same effect as that found in cross-national data. By 1990, the compositional effect of the educa- tional distribution grew stronger, and thus the effect of educational heterogeneity on in- come inequality should be increasingly posi- tive. Therefore, we predict that the positive effect of educational heterogeneity on income

inequality is stronger in later than in earlier periods.

Income inequality in the United States has historically been higher than in other ad- vanced industrial countries (Nielsen and Alderson 1995). One cause of the higher in- equality in the United States may be the na- ture of race relations. Systematic differences in income between the two major racial groups, Blacks and Whites, represent an ad- ditional source of inequality that could elevate overall income inequality in this country above that of other societies at simi- lar levels of industrial development. To cap- ture this, we use an indicator of racial dual- ism that measures income inequality in a county resulting from the difference in aver- age incomes between Black families and White families. The indicator of racial dual- ism is based on the same formula as sector dualism and is sensitive to the relative size of the racial groups and the difference be- tween them in average income. The racial composition of counties and the amount of racial dualism vary considerably by region.'

In a study using 1980 data for North Carolina counties, Niclsen and Warren (1995) found a ti-shaped relationship between overall Income in- equality and racial dualism. The curvilinear~ty is related to regional differences within the state: Counties with low racial dualism tend to be lo- cated in the Mountain region and are character- ized by relatively small Black populations and high inequality, while counties with high racial dualism are mainly Coastal Plain counties with relatively large poor Black populations and high income inequality. Counties with intermediate levels of racial dualism in the more developed Piedmont region have the lowest levels of income inequality.

Therefore we can test the prediction that,

controlling for other factors, racial dualism has a positive effect on income inequality.

According to an influential study by Wil- son (1980), the significance of race as a de- terminant of economic achievement declined in the postwar period. Others have argued that the decline in the significance of race was reversed during the 1980s as a result of the government's retreat from antidiscrimi- nation initiatives (Cancio, Evans, and Maume 1996). Insofar as systematic dis- crimination based on race has lessened over time, the importance of racial dualism as a component of overall income inequality should also decline. Therefore, we can test Wilson's general prediction that the effect of racial dualism on income inequality is stron- ger in earlier than in later periods against the alternative prediction-that its effect has not decreased or has become stronger.
The Great U-Turn

The upswing in inequality that began in 1969 for family income and in 1976 for earnings has generated a range of attempts to explain this reversal in the long trend toward declin- ing inequality (Thurow 1987; Bluestone 1990; Levy and Michel 1991 ; Levy and Murnane 1992; Ryscavage, Green, and Welniak 1992). The explanations have fo- cused on a few potential causes: the chang- ing role of women, the changing socioeco- nomic situation of the elderly, declining in- dustrial employment, and the international position of the United States.

Commenting on the upswing in inequality in the distribution of earnings, Thurow (1987) was blunt in implicating the role of increased labor-force participation by women:

What, then, is the cause of the rising inequality in the distribution of earnings? There are two major forces: (1) intense international competi- tive pressures, coupled with high unemploy- ment, and (2) a rising proportion of female workers. (P. 33)

Thurow (1987:34-35) argued that increased female-labor force participation contributed to the upswing in earnings inequality in two ways: (1) Because women are paid less and more often work part-time, greater participa- tion in the labor force by wotnen inflates the bottom of the earnings di~tribution.~

This trend, together with the increasing proportion of households headed by women, thus con- tributes to greater inequality in the distribu- tion of family income. (2) Assortative mat- ing causes high-income wives to be married to high-income husbands, amplifying the ad- vantage of high-earning families when both spouses are in the labor force. Bluestone (1990:28-32), while viewing other factors as more important causes of the rise in inequality in the 1970s, concurs that there is at least weak evidence for an influence of female la- bor-force participation. Thurow9s and Blue- stone's arguments lead to the prediction that,

controlling for otlzer factors, greater labor- force participation by women is positively

associated with income inequality.

Another trend related to the changing role of women has been the increasing proportion of female-headed households. Levy and Michel (1991:38-39) found that from 1973 to 1986, a period during which inequality in the distribution of family income was rising, the proportion of families headed by a single woman (among families with a head under age 65) increased from 1 in 8 to I in 5. Inso- far as female-headed families have lower- than-average incomes, this trend inflated the proportion of poor families (see McLanahan, Sosensen, and Watson 1989 concerning the implications of these trends for the "femini- zation of poverty"). The discussion by Levy and Michel (1991) leads us to expect that,

corltrolling for other factors, the percent of fanzilies headed by a single fenzale is posi-

tlvel)? nssoclated with in equal it)^.

Levy and Michel (1991:38) described the upward movement of elderly families in the distribution of income between 1973 and 1986 as a result of the fact that this genera- tion of elderly was the first to enjoy full ben- efits under the Social Security program. This, combined with the indexing of Social Secu- rity benefits, meant that the incotnes of eld- erly families were increasing. During the pe- riod under consideration, most elderly fami- lies joined the lower middle of the income distribution, while prior to that time they

Trends in the distribution of earnings of men and wornen are discussed in Levy and Michel (1991:6) and Bernhardt, Morris, and Handcock (1995).

were concentrated in the poorest segment of the distribution. The historical ascent of the elderly in the income distribution during the two decades under investigation implies a systematic pattern of change in the relation- ship at the county level between income in- equality and the proportion elderly (mea- sured as the percentage of the population over age 65). We predict, therefore, that (1)

in the earlier period (1970),the relative size of the elderly population is positively associ- ated with income inequality; and (2) in the later period (1990), the relative size of the elderly population is negatively associated with inequality.

Bluestone and Harrison (1982) and Harri- son and Bluestone (1988) popularized the term "deindustrialization" by tracing the far- reaching consequences of the erosion of the industr~al base of the United States in recent decades. Bluestone (1990:28-32) saw the de- cline in manufacturing employment as one of the main causes of two major trends since the early 1970s: the increase in the low-wage share of year-round full-time employment, and the increase in wage inequality. The de- cline in manufacturing employment contrib- utes to increased income inequality because the manufacturing sector is typically charac- terized by higher wages and a more equal wage distribution than is the service sector, so transfers of jobs from the manufacturing sector to the service sector produce more in- equality as well as a larger proportion of low- wage jobs. Ryscavage et al. (1992) identified the shift from goods-producing to service oc- cupations as one of the main factors behind the upswing in inequality. Although some re- cent empirical studies (e.g., Raffalovich

1993) cast doubt on the importance of de- industrialization in explaining the Great U-Turn, others (Lorence and Nelson 1993) cor- roborate it. We measure manufacturing etn- ployment and investigate the Bluestone- Harrison conjecture that manufacturing eltl- plo~~ment

has a rtegative effect on inequality.

Thurow (1987:33) also implicated rising une~nployment (which he viewed as a result, in part, of the weakening competitive posi- tion of the United States) in the upswing in inequality. More recently, Wood (1994) ar- gued that competition from low-skill nations has resulted in declining demand for unskilled labor in advanced industrialized soci-
AMERICAN SOCIOLOGICAL REVIEW

eties. The reduced demand for unskilled la- bor has tended to widen wage differentials between the skilled and unskilled. Where in- stitutional resistance to wider wage differen- tials has been great (as in continental Eu- rope) increased competition from low-skill nations has tended to express itself in rising unemployment. Where institutional resis- tance has been weak, as in the United States, the result has been widening wage differen- tials and greater income inequality. Wood's (1994) argument suggests that, in different institutional environments, high unemploy- ment and high income inequality are alterna- tive responses to the reduced demand for un- skilled labor, not phenomena connected by a direct causal link. As we cannot do justice here to the issues raised by Wood (1994), we test Thurow's simpler prediction that, at the county level, the unemployment rate has a positive effect on in equal it^.^
DATA AND MEASUREMENT

We collected data from various sources for the approximately 3, I00 counties and county equivalents of the United States in 1970, 1980, and 1990. The actual number of coun- ties varies from 3,103 to 3,141 depending on the year. Sources for all variables are listed in Table 1. Several variables, such as the mea- sure of income inequality, are based on math- ematical transformations of the raw data.
Itzconze Inequality

Our measure of inequality is the Gini coeffi- cient. This is calculated from the distribution of family income at the county level from the

U.S. censuses of 1970, 1980, and 1990. The Gini coefficient, which varies between 0 per- cent (perfect equality) and 100 percent (max- imum inequality), has the advantage that it is comparable with inequality measures available cross-nationally (World Bank 1990) and for the entire United States since 1947 (see Figure 1). Gini coefficients were calculated from the raw distributions, which are given as the number of families in various income

'Thanks to an anonymous reviewer for bring- ing Wood's work to our attention. Alderson is currently pursuing these isaues in the context of work on globalization.
Source "Year
Variable     1970     1980     1990
Income inequality (Gini x100)     Adams 1992a     Adams 1992b     USBC 1991
Median family income     USBC 1978     USBC 1992     USBC 1991
Population density     USBC 1978     USBC 1992     USBC 1992
Sector dualism     USBC 1992,     USBC 1992,     USBC 1992,
    USBC 1978    USBC 1984     USBC 1991
Percent farm population     USBC 1978     USBC 1984     USBC 1991
Ratc of natural increase             
(per 1,000 population)     USBC 1978     USBC 1992     USBC 1992
Educational heterogeneity     USBC 1978     USBC 1992     USBC 1991
Racial dualism     Adams 1992a,     USBC 1982     USBC 1991
    USBC 1978        
Percent of females in the labor force     Adams 1992a     Adams 1992b     USBC 1991
Percent female-headed households     USBC 1978     Adams 1992b     USBC 1991
Percent over age 65     USBC 1978     Adams 1992b     USBC 1991
Percent of labor force in manufacturing     USBC 1978     Adams 1992b     USBC 1991
Percent unemployed     USBC 1978     USBC 1984     USBC 1991
WSBC is U.S. Bureau of the Census             

categories (15, 17, and 25 income categories median is estimated by fitting a Pareto dis- in 1970, 1980, and 1990, respectively). The tribution to each interval, using formulas procedure requires estimating the Eorenz given by Allen (1938:407-408) or Klein curve, which plots the cumulative income (1962:150-54). Finally, the open-ended up- shares on the vertical axis against the cumu- per category is treated in a special way, also lative population shares on the horizontal based on fitting a Pareto distrib~tion.~ axis. To estimate the income share of an in- Given estimated points on the Lorenz come category, the average income of the in- curve (pi,Li), where piand Li represent the come category must be evaluated. Simple- cumulative population and income shares for minded procedures, like taking the category each income category i = I, . . . ,k (where k midpoint as the average income and dealing is the number of income categories), the with the open-ended top category by discard- value RLof the Gini coefficient is calculated ing it or taking its lower bound as the aver- using the formula given by Nygird and agk, yield mislkading Gini estimates. Instead, Sandstrom (198 1:292, eq. 8.10): we adapt a procedure used by the U.S. Cen- k-I

R, =Pk-, L(~l)(~,+l -PI-,). (1)sus Bureau, the Pareto-linear procedure. This is based on Pareto's (1897) observation that for upper income levels a plot of the loga-
Measures of Dualism

rithm of the number of recipients with in- come greater than a given level of income Measures of dualism are special cases of in- against the logarithm of income tends to equality measures. We use an approach based yield a straight line (Miller 1966:213-21; on the Gini coefficient (Nielsen 1994). For Spiers 1977; U.S. Bureau of the Census farmlnonfarm sector dualism. the Gini coef-

1980; Welniak 1988; also see Parker and Fenwick 1983). The Pareto-linear procedure

The details of the algorithm, which also

estimates the average income in the income

-handles special cases like empty categories and

category containing the median, and catego-

improbable Pareto slope estimates, are embodied ries below, as the category midpoint. The av- in a computer program PRLN.PAS in the Pascal erage income of income categories above the language developed by Nielsen.

ficient is calculated from figures for the farm population as a percent of the total popula- tion (p)and farm earnings as a percent of to- tal earnings (L), and derived from the gen- eral equation 1 for computing the Gini coef- ficient from points on the Lorenz curve. With only two sectors, farm and nonfarm, equation 1 with k = 2 reduces to

where p =pl and L =LI. The absolute value operator guarantees a positive value for sec- tor dualism when average farm earnings are greater than nonfarm earnings.

Racial dualism is estimated in the same way as sector dualism using equation 2, where p is the percent Black of all families and L is the aggregate income of Black fami- lies as a percent of the aggregate income of all families. Estimation of racial dualism in- volved several complications. First, we were unable to find county-level data on the aver- age income of families by race for 1970. We therefore calculated for 1970 a "pseudo-Gini" that uses the median instead of the av- erage as the measure of the central tendency of family incomes for Blacks and Whites. Second, we were also unable to find data on averagefamily income by race for 1990, and therefore we calculated racial dualism on the basis of average household income for Blacks and Whites in that year. Finally, for reasons of confidentiality, the U.S. Census Bureau suppresses income data for Blacks in counties with few Black families or house- holds. This initially produced many missing values for this variable. For counties where Blacks made up 0 to 5 percent of the popula- tion and data were suppressed, we assigned the value 0 to the racial dualism measure. The assumed value of 0 is a reasonable ap- proximation in such cases because in coun- ties with small Black populations, p and L are expected to be small in equation 2 and would yield small values for racial dualism. We coded racial dualism as missing for coun- ties where Blacks made up more than 5 per- cent of the population and income data by race were suppressed.
Educational Heterogeneity

Educational heterogeneity is calculated using Theil's (1972:6, eq. 1.6) formula for entropy:
AMERICAN SOCIOLOGICAL REVIEW

where In is the natural logarithm, n = 3, and pl, p2, and pj are the proportions of the adult population (ages 25 years old and older) without a high school degree, with a high school degree only, and with a four-year col- lege degree, respectively. Thus, the educa- tional categories are mutually exclusive. The entropy formula, originally derived by Shan- non (1948) in the context of information theory, has been interpreted more broadly by Theil (1972:13-15) as a general measure of dividedness, that is, the extent to which a given total (in this case the adult population) is evenly divided into parts (here, different levels of educational attainment). (For its ap- plication as a measure of political competi- tion, see Nielsen 1986.) Educational hetero- geneity assumes its maximum value when the adult population of the county is evenly distributed among the three categories of educational attainment, and its minimum value when the entire population is concen- trated in a single category.
MODEL ESTIMATION: RANDOM EFFECTS MODEL

We estimate linear regression models with income inequality as the dependent variable for the years 1970, 1980, and 1990. In any given year, our data set has a nested struc- ture, with counties nested within states. The data set is unbalanced because the number of counties differs by state. Data of this type are amenable to estimation methods that deal with potential heterogenei~ bias, or the con- founding effects of unmeasured variables

-

that are county-invariant within a state and that are omitted from the regression model (Hsiao 1986:5-6). All counties in a given state may be similarly affected by state-level processes, such as events originating in the state polity, that are not measured by the county-level variables in the model. Such characteristics of the state polity and other state-level processes that affect within-county income inequality uniformly would appear as an unmeasured state-specific, county-invariant error component, producing heterogeneity bias. Heterogeneity bias can seriously affect ordinary least squares coef- ficient estimates. The fixed effects model (FEM) and random effects model (REM) are commonly used estimation strategies de- signed to correct for unmeasured county-in- variant factors. Both methods address the heterogeneity problem by "simulating" the unmeasured county-invariant factors as state- specific intercepts. The model to be esti- mated can be written in general as

where i = 1,. . . ,Nand t = 1,. . . ,Ti, and by assumption E[ci,] = 0 and Var[ci,] = 0:. The subscript i denotes the state and t denotes a particular county within a state. Ti denotes the number of observations (counties) in state i, the indexing reflecting the unequal numbers of counties across states. In equa- tion 4, a0 represents the general intercept and ai represents the state-specific intercepts summarizing the effects of unmeasured fac- tors that affect counties homogeneously within a state. The FEM treats the state-spe- cific intercepts aias fixed effects to be esti- mated, equivalent to the regression coeffi- cients of indicator variables for states, while the REM treats aias a random component of the error term. The FEM is equivalent to ap- plying OLS regression to the data trans- formed by subtracting the state-specific means from the original~data, while the REM is equivalent to subtracting only a fraction of the state specific-means (Rosenfeld and Niel- sen 1984; Hsiao 1986:36).

For methodological and substantive rea- sons, we present the REM estimates of the regression models. First, the FEM estimation algorithm can be interpreted substantively as "throwing away" for estimation purposes all between-state variation present in the data. The FEM procedure therefore consumes much information. Second, the REM has been shown to be asymptotically efficient relative to the FEM (Tuma and Hannan 1984).~

'The REM, FEM, and OLS estimation proce- dures yielded similar substantive patterns. Fur- thermore, results indicate that state-specific fac- tors represent only a small proportion of the error variance in the fully specified models, suggest~ng that the FEM is not needed with these data (see below and footnote 16). Further discussion of fixed-effects and random-effects models can be

We carried out preliminary OLS regression analyses of the models giving careful atten- tion to outliers and influential cases, using the various regression diagnostics available in the SYSTAT statistical program (Belsley, Kuh, and Welsch 1980; Bollen and Jackman 198%; Wilkinson 1990a:154-56, 1990b). Our strategy was to eliminate cases that ap- peared unduly influential on the basis of a combination of criteria (Studentized residual, Cook's D, influence in partial regression plots). We excluded from the analysis 149 counties in 1970 (4.7 percent of the 1970 data set), 112 counties in 1980 (3.5 percent of the 1980 data set), and 137 counties in 1990 (4.4 percent of the 1990 data set). Ex- clusion of these cases affected the substan- tive results only in 1980. The effect of popu- lation density changed from significantly negative to significantly positive when influ- ential cases were removed, consistent with the results for 1970 and 1990. The effect of the percent of the population over age 65 changed from significantly negative to non- significant, consistent with the expected evo- lution of this effect over time from positive to negative. To assess the comparison of co- efficients over time implied by some of the theoretical predictions, we performed one-tailed significance tests for the three possible differences across time points (1980 -1970, 1990 -1980, and 1990 -1970).'O Finally, we checked the matrices of independent vari- ables for severe collinearity and found none."

found in Judge et al. (1980:336-38), Hsiao (1986:41-7), and Greene (1990:480-98). We es- timated the REM models with the LIMDEP pro- gram (Greene 1992, chap. 29). The OLS regres- sions and diagnostics for influential cases were carried out with SYSTAT (Wilkinson 1990a). The figures were produced with SYGRAPH (Wilkinson 1990b).

''The OLS results, correlations and basic sta- tistics, and significance tests for comparisons of coefficients between time points are not pre- sented. These tables are available from the authors on request.

" The minimum Jolerance value found for all (OLS) estimated coefficients was ,195 (for fe- male-headed households in 1990), corresponding to a variance inflation factor of 5.13, well below the cutoff of 10 often taken as indicative of excessive collincarity (Neter, Wasserman, and Kutner 1990:408-11).
lected Independent Variables: U.S. Counties, 1970

Independent Variable Constant Median family income (log) Population density (log) Sector dualism Percent farm population Rate of natural increase Educational heterogeneity Racial dualism Perccnt females in the labor force Percent female-headed households Perccnt over 65

Model Model Model 1 2 3

15 1.59*** 159.50a** 130.18***

(80.456) (72.167) (53.697)

-29.6 16*** -34.367*** -24.630a** (-61.562) (-53.877) (-39.266)

1.060**"

(11.200)
-.030***

(4.958) .039***

(8.485)
-,007

-

(.913)
-8.680"'

-

(14.048) -.183***

(1 8.872) ,001

(-. 106) --.327***

(19.567) .079***

(6.033)
Percent of labor force in manufacturing Percent unemployed     --    --    -.076*** (-19,529) -.038 (-1.833)
R2 Rho Number of counties         
Note: Numbers in parentheses are r-statistics.
*p < .05 **p<.Ol ***11 < ,001 (two-tailed tests)
       

Model 4

134.45***

(45.732)

-27.383*** (-34.423)

.786**'

(8.284) .024'**

(4.133) .043***

(9.348) .043***

(3.922)

4.21 1 ***

(6.595) .132***

(12.338)
.0 12

(1.385) .176***

(8.042) .I 1O***

(6.232)

-.063*** (-16.038)

,033

(1.655)
RESULTS

Regression results are shown in Table 2 (1970), Table 3 (1980), and Table 4 (1990). The independent variables are roughly di- vided into two sets. The first set comprises variables that originate in general theories of income inequality and development, often in the context of the Kuznets curve. These in- clude economic development (logged median income), urbanization, the effect of labor- force shifts out of agriculture (sector dual- ism and percent farm population), the rate of natural increase, and the spread of education, measured here as educational heterogeneity. We have added to this set racial dualism, a factor that is particularly relevant to the U.S. context. The second set includes variables evoked in discussions of the Great U-Turn in the past two decades: female labor-force par- ticipation, female-headed households, per- cent population over age 65, manufacturing labor force, and the unemployment rate.
Income Ineq~tality and Industrial Development

Referring to the 1970 results in Table 2, Model 1 includes only the general measure of development, logged median income, to evaluate the predicted negative association of income inequality with development. The
lected Independent Variables: U.S. Counties, 1980

Independent Variable Constant

Median family income (log)

Population density (log)

Sector dualism Percent farm population

Rate of natural increase Educational heterogeneity Racial dualism Percent females in the labor force

Percent female-headed households Percent over 65

Model
1

144.88***

(70.693)

-25.662*** (-53.530)

-

-

-

-

-.

-

-

-

-

Percent of labor force in manufacturing
-

Percent unemployed -

R2 Rho Number of counties

Note: Numbers in parentheses are t-statistics.

Model
2

142.04***

(67.796)
-27.982***

(-5 1.920) .560***

(7.151) ,002

(-,503) .071 ***

(13.110)
,027"'

(3.442) 1 1.022*'*

(14.978) .299***

(24.676)

-

-

-

-

-

Model Model
3 4

136.18*** 129.57***

(55.502) (45.741) -23.154*** -23.297***

(-39.832)

-

-

-

-

-

(-35.244) .356***

(4.422) -.004

(-,946) .070***

(12.545)

,003 (.289) 6.504***

(8.479) .161***

(10.905)

-.054*** -,056*** (-7.438) (-7.75 1) .293*** .201***

(29.625) (13.320)

,008 -.018 (.768) (-1.192) -.072*** -.054***

(-1 9.395) (-14.183) -.191*** -.096**' (-1 3.623) (-6.758)

*,I < .05 **p<.01 ***11 < ,001 (two-tailed tests)

negative effect is strongly significant: In 1970, median family income alone explains 67 percent of the variance in income inequal- ity. Comparing this figure with the results for later years in Tables 3 and 4, the explanatory power of median family income declines regularly over time-W2 = .537 in 1980 and R2 = .401 in 1990-suggesting that variables other than a county's level of development became increasingly important.'2

l2 The zero-order (OLS) correlations between income inequality and logged median income are -.837, -.739, and -.649 in 1970, 1980, and 1990, respectively. Even in 1990, median income is the independent variable most strongly associated with income inequality.

Figure 2 provides a more detailed view of the evolution of the relationshir, between in- come inequality and economic development. The scatterplots of income inequality by logged median income show increasing scat- ter around a strong negative relationship. Nonparametric regression curves fitted by Distance-Weighted Least Squares (McLain 1974; Wilkinson 1990b:236) suggest that part of the increasing scatter around the lin- ear trend is a result of increasing nonlinearity of the regression line, as the relationship tends the origin in later Years. Although the most Pros- perous counties (in terms of median income) in 1970 had the lowest income inequality, by

Table 4. Unstandardized GLS Coefficients for Regression of Income Inequality (Gini x 100) on Se- lected Independent Variables: U.S. Counties, 1990

Model Model Model Model
I 2 3 4

Constant Median family income (log) Population density (log) Sector dualism Percent farm population Rate of natural increase Educational heterogeneity Racial dualism Perccnt femaies in the labor force Percent female-headed households Percent over 65 Percent of labor force in manufacturing Percent unemployed

R~ Rho Number of counties

Note: Numbers in parentheses are r-statistics. < .05 **]I < .01 < ,001 (two-tailed tests)

1990 this pattern is reversed so that among the most prosperous counties greater median income is associated with increased income inequality.

Model 2 includes the entire set of variables relating to economic development. Model 3 introduces, in addition to logged median family income, the variables involved in the debate surrounding the upswing in inequal- ity and the "disappearing middle-class" (Levy and Michel 1991). Model 4 is the full model that includes all the independent vari- ables. We focus on Model 4.

In Table 2, Model 4, the coefficient for population density-our measure of urban- ization-is significant and positive, as ex-

pected from Kuznets's ([I9551 1965) conjec- ture concerning the greater range of status in urban settings compared to rural settings. The effect is positive in Model 4 even though the zero-order correlation is negative (-,296). The effect of population density on inequal- ity remains positive in later years (Tables 3 and 4). The impact of the shift of the labor force away from agriculture is captured by sector dualism and percent farm population. The classical expectation is that sector dual- ism has a positive effect on income inequal- ity because it represents inequality resulting from the difference in average income be- tween agriculture and the rest of the econ- omy, and that percent farm population has a
2         0     0         I     .    7-4
    3.0    3.5     4.0     4.5     5.0     3.0     3.5     4.0     4.5     5.0
        hledian Income (log lo), 1970            Median Income (log lo), 1980

Median Income (log lo), 1990 Median Income (log 10)

Figure 2. Relationship between Income Inequality and Median Family Income: U.S. Counties, 1970, 1980, and 1990

Note: Nonparametric regression curves fitted by distance weighted least squares (DWLS) with tension .05. The bottom-right graph compares the nonparametric regression curves for the three years.

negative effect because it captures the effect labor-force shifts between the agricultural of low income inequality in the agricultural and nonagricultural sectors have become a sector (Nielsen 1994). The regression results minor determinant of within-county income fall short of this expectation, as both vari- inequality in recent decades. ables have a significant positive effect on in- The coefficient for the rate of natural in- come inequality in 1970. In 1980 and 1990, crease in population is significantly positive the effect of sector dualism vanishes (the in 1970. nonsignificant in 1980. and signifi-

1970-1980 decline is significant), while the cantly positive again in 1990. The positive coefficient for percent farm population re-effect is in the predicted direction, as the rate mains significant and positive. This ambigu- of natural increase is assumed to affect in- ous pattern is consistent with the view that come inequality directly by affecting the sup- ply of labor and indirectly as a proxy for gen- eralized dualism. The irregular pattern over time, however, was not predicted, as a more monotonic decline in the coefficient over time would be expected as counties move further away from their demographic transi- tions.

Educational heterogeneity has a strong positive effect on income inequality in 1970: The greater the heterogeneity of educational attainment in a county, the greater the in- equality of the distribution of income. The positive effect of educational heterogeneity emerges in the multiple regression equation where other variables are controlled, even though in 1970 the zero-order association of this variable with income inequality is strongly negative (-,455). This contrast is consistent with the pattern of a positive asso- ciation between educational heterogeneity and mean educational attainment (and there- fore with economic development), which confounds the ~ositive effect of educational heterogeneity on inequality with the negative effect of economic development in the zero- order relationship. The positive effect of edu- cational heterogeneity on income inequality increases significantly after 1970 (the in- crease between 1980 and 1990 is particularly pronounced), while the zero-order correlation changes from negative to positive (-,455, -.168, and ,343 in 1970, 1980, and 1990, respectively). The correlation between educational heterogeneity and median family income decreases over the period (.676, ,474, and ,181). This pattern is consistent with an increasing impact of educational heterogene- ity on income inequality combined with the spread of educational heterogeneity from centers of development to outlying areas.

Wilson's (1980) argument regarding the declining significance of race implies that the effect of racial dualism on iicome inequality should wane in more recent periods as U.S. society moves further away from ra- cial discrimination. In fact, racial dualism has a strong significant and positive effect on income inequality in 1970, and the effect shows no sign of disappearing in 1980 and 1990, although there is a statistically signifi- cant decline in the coefficient between 1980 and 1990 (from .16 1 to ,115). This consis- tency is even more remarkable given that ra- cial dualism is measured in somewhat differ- ent ways for the three periods. We conclude that racial dualism remains a strong compo- nent of overall income inequality in contem- porary U.S. society, despite a small decline in its impact.

The Great U-Turn

Thurow (1987) confidently implicated in- creased female labor-force participation as a major culprit in the recent upswing in in- equality. Thurow predicted a positive effect of female labor-force participation on income inequality. The coefficient for female labor- force participation in Model 4 for 1970 is not significant (Table 2). For both 1980 and 1990, however, the effect of female labor-force par- ticipation is strongly significant and nega- tive-the opposite of Thurow's expectation. It seems that the net impact of the increase in labor-force participation by women, which has been considerable,I3 has been to create more families with total incomes closer to the center of the income distribution, lessening the trend toward greater inequality caused by other aspects of social change during the pe- riod (Ryscavage et al. 1992).

Another aspect of the changing role of women, the percent of households headed by females, has more disturbing consequences. This variable has a strongly significant posi- tive effect on income inequality in 1970, and its effect increases in both magnitude and significance in 1980 and 1990. This suggests a substantial role for this variable in the up- swing in income inequality since 1970. The effect of the size of the elderly population (percent over age 65) exhibits a more com- plex pattern over time. In 1970 (Table 2), the percent over age 65 has a strongly significant positive effect on income inequality, reflect- ing the fact that elderly families were a rela- tively disadvantaged segment of the income distribution. The effect in 1980 (Table 3) is nonsignificant, and in 1990 (Table 4) the ef- fect is strongly significant and negative. (The decline in the value of the coefficient be- tween 1970 and 1990 is strongly significant.) This reversal in the direction of this effect is consistent with the scenario proposed by

"Average female labor-force participation is 36.7, 44.8, and 52.0 percent in 1970, 1980, and 1990, respectively.

Levy and Michel (1991), who described the average elderly family as moving up in the income distribution in the 1970s and 1980s because of the increasing impact of the So- cial Security program on cohorts reaching re- tirement age during that period and the in- dexing of Social Security benefits.

Inclusion of the percentage of the labor force employed in manufacturing in Model 4 permits an evaluation of the deindustrial- ization argument of Bluestone and Harrison (1982) and Harrison and Bluestone (1988). The relative size of the manufacturing labor force has a strongly significant negative ef- fect on income inequality in 1970 (Table 2). This negative effect remains stable in 1980 and 1990, providing strong support for the deindustrialization thesis.

Unemployment is another aspect of the deindustrialization argument. In the simple version of this argument, international com- petition is viewed as generating unemploy- ment, which produces greater inequality in the income distribution (Thurow 1987; but see Wood 1994). The percent unemployed in Model 4 yields ambiguous results. The effect of the unemployment rate is nonsignificant in 1970, but in 1980 it is negative and strongly significant, suggesting that unemployment reduces income inequality, contrary to the prediction. In 1990, however, the effect of un- employment is again nonsignificant.14

For the full regression model (Model 4) R2 ranges from ,750 in 1980 to .807 in 1970, suggesting that these independent variables taken together are powerful determinants of variation in income inequality across U.S. counties.
Unmeasured State Effects

The use of the REM procedure was motivated by a desire to take into account the possible presence of unmeasured state-spe- cific factors affecting county-level income inequality uniformly within a state. Unmea- sured outcomes of autonomous state-level political activity, for example, would be ex- pected to behave in this county-invariant,

l4 This ambiguous pattern of effects is consis- tent with Wood's (1994) view of income inequal- ity and unemployment as alternative responses to the reduced demand for low-skill labor.

state-specific manner (Jacobs 1985). The relative impact of the state-specific compo- nent of the error term can be estimated by the rho coefficient shown for each regression model in Tables 2, 3, and 4. Rho is a mea- sure of the correlation among the error terms of counties due to the presence of the state- specific component. Thus a high value of rho indicates that unmeasured state-specific fac- tors have a strong impact on the variation in income inequality among countie~.'~

The pattern is similar for each census year: The estimated value of rho is highest in Model 1, which includes only logged median income and is therefore most likely to be under- specified, with values for Model 1 of ,301, .492, and .459 in 1970, 1980, and 1990, re- spectively. As explanatory variables are add- ed in Models 2, 3, and 4, the estimated value of rho decreases, indicating that the unmea- sured state-specific component is progres- sively accounted for by variables included in the models. In Model 4, values of rho are ,069, ,169, and ,087 for the three census years. These small estimated values of rho suggest that variables in the full regression model (Model 4) capture most of the state- specific factors (including those related to state-level policy outcomes) that affect in- come inequality within counties.I6
CONCLUSION AND DISCUSSION

We have examined the processes affecting inequality in the distribution of income in

U.S. counties in 1970, 1980, and 1990 in the hope of gaining insights into two major his- torical trends that characterize industrialized societies in the twentieth century: the declin-

l5 Rho is estimated as

Var(u) Vnr(u)+ Vnr(e)' where u denotes the state-specific county-invari- ant error and e denotes the ordinary regression error that varies over both states and counties (Greene 1992:303). l6 The small estimated values of rho also sug- gest that attempting to unravel state effects on in- come inequality by explicitly measuring state- level variables (such as average AFDC payments) is unlikely to be a productive strategy. There is little evidence in our results for state-specific ef- fects of any kind after controlling for the county- level variables.

ing level of income inequality that has mark- ed industrial development during the later part of the Kuznets curve, and the upswing in inequality since the early 1970s. We have examined the impact on income inequality of two sets of factors: variables related to the impact of industrial development on income inequality in the context of the Kuznets curve, and variables invoked in the more re- cent debate surrounding the upswing in in- equality.

Our regression models of income inequal- ity, which control for unmeasured state-spe- cific effects with REM estimation, reveal several distinct patterns. Results suggest the continued importance of the Kuznetsian pat- tern of declining income inequality with eco- nomic development, even though in recent years the association has become increas- ingly convex to the origin, indicating increas- ing income inequality in the most prosperous counties. Controlling for economic develop- ment, urbanization has a positive effect on inequality, supporting an early suggestion by Kuznets. Sector dualism effects associated with labor-force shifts from agriculture to other sectors of production have a minor im- pact on variation in county-level income in- equality during the period investigated. The rate of natural increase in population, which is strongly associated with inequality in cross-national data, is also a weak predictor of income inequality in counties of an indus- trial society during the later part of the twen- tieth century. However, heterogeneity of edu- cational attainment has an increasingly strong positive impact on income inequality from 1970 to 1990, suggesting a new role for the education distribution in determining in- come inequality in advanced industrial soci- eties. Racial dualism, which measures the amount of inequality resulting from the dif- ference in average income between Blacks and Whites, has a surprisingly strong and persistent effect on income inequality during the period studied.

With respect to variables that have been invoked in the Great U-Turn debate, our re- sults exonerate at least one variable suspected of contributing to the upswing in in- equality since 1970: Instead of the predicted positive effect of female labor-force partici- pation on income inequality, this variable has an increasingly strong negative effect. In
AMERICAN SOCIOLOGICAL REVIEW

agreement with the expectation of most ob- servers, however, the percentage of female- headed households is a strong contributor to income inequality. The effect on inequality of the percent of the population over age 65 tracks historical changes in the position of this group in the income distribution that took place over the two decades under study-from a positive effect in 1970, when the elderly were a much more disadvantaged group than today, to a negative effect in 1990, when the elderly assumed a more cen- tral position in the income distribution. The percent of the labor force in manufacturing has a strong negative effect on income in- equality at all time points, consistent with the deindustrialization argument, while the ef- fect of the unemployment rate on inequality shows no clear pattern.

The declining importance of some of the factors traditionally associated with the im- pact of industrial development on income in- equality (such as sector dualism and popula- tion growth associated with the demographic transition) and the increasing importance of new factors (particularly educational hetero- geneity and variables representing new living arrangements, such as female-headed households and female labor-force participa- tion) suggest that the determination of in- come inequality in advanced industrial soci- eties is the outcome of a new set of processes. Our analyses provide a glimpse of some of the features of this new causal regime. Clearly, further research is needed to fully elucidate the nature of distributional pro- cesses in advanced industrial society.

Frnngois Nielserz is Associate Professor of Soci- ology at the University of North Cnrolirta nt Chapel Hill. He is contirzuing research with Arthiir Alderson on tlze relationship between in- come ineqiiality ancl developrnerzt, iising both cross-rzational clata and clata or1 United States courzties. He is also docng research on simulation rnodels of incorne distribution, the emergence of regions in the European Urziorz, sociobiology, arzcl tlze influence of Protestantism on the early devel- oprnent of industrial capitalisnz in Europe.

Arthur S. Alderson is a P1z.D. studerlt irz sociol- ogy at the Urziversity of North Carolirza at Chapel Hill. hz the fall of 1997, he will join tlze faculty at hlcliarza Urziversity in Bloorningtorz. Irz aclclition to his corztirzuirlg work with Frarz~ois Nielsen on irz- corne irzeqiiality, hls research ir~terests irzclucle comparative ancl lzistorical sociology, political and ecorzornic sociology, and international devel- opment. His rlissertation research is rlevoted to the problematic of globalizatiorz. He is the autlzor (with Fran~ois Nielse~z) of "lrzcome Inequality, Developntelzt, and Dualisrn: Results frorn arz UII- balanced Cross-National Panel" (American Sociological Review, 1101. 60, 1995, pp. 674-701).
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