Income non-convergence and rural-urban earnings differentials: evidence from North Carolina.

I. Introduction

Considerable attention is currently focussed on the deteriorating social and economic condition of America's rural communities. Stagnant or worsening poverty rates, unemployment rates, and real incomes over the past decade - along with persistent and widening gaps between the economic performance of rural and urban areas - are well-documented indicators of the seriousness of this socioeconomic malaise [6; 8; 18]. Coming as it has after a period of relative prosperity - the so-called "rural renaissance" of the 1970s - the current crisis in rural America has generated a great deal of consternation among policymakers, social scientists, and other students of rural development.

Current concerns over rural economic decline coincide with the observation by a number of researchers that the spatial dispersion of income - measured by the variance of income or earnings per capita across geographic units - has increased over the past decade or so. This pattern of income non-convergence has been observed across countries [1], regions of the U.S. [3], and states [5], and is distinctly at odds with the theoretical predictions of standard neo-classical growth theory. A considerable recent literature that accounts for the effects of schooling, human capital accumulation, learning by doing, and endogenous technical change within the context of endogenous growth models seeks to generalize the standard growth model and clarify the conditions under which incomes may be expected to converge or diverge over time [2; 14; 17].

In fact, the recent increase in dispersion of income per capita and the widening disparity in the economic performance of rural and urban areas appear to be related phenomena. Consider Figure 1, which plots measures of income dispersion and rural-urban income differentials over time for North Carolina's 100 counties. There it will be observed that the coefficient of variation of earnings per capita (given by the solid line) fell during the first half of the 1970s, but has been rising steadily since 1976.(1) More striking is the remarkably similar behavior of the time series composed of the difference in earnings per capita between metro and non-metro counties (given by the dashed line). The strong correlation between these two series ([Rho] = .904) suggests that ascertaining the factors underlying the differential economic performance of rural areas vis-a-vis urban areas may hold the key to understanding the empirical puzzle embodied by the recent dynamics of income dispersion. Specifically, it begs the questions of what are the underlying forces determining real incomes, and how does the response to these forces differ between rural and urban areas.

This paper quantifies the magnitude of rural-urban differences in the response of earnings to key economic variables. Using county-level data for North Carolina, an empirical model of earnings determination is estimated that allows direct measurement of the impact on per capita earnings of the local stock of human capital, macroeconomic forces, and local labor market conditions. The econometric results indicate that (a) returns to schooling are significantly lower in rural areas than in urban areas; (b) there is no appreciable difference in the impact of macroeconomic forces on rural areas vis-a-vis urban areas; and (c) earnings in rural areas are more sensitive to local labor market conditions. Further analysis suggests that while macroeconomic forces have been the dominant source of earnings growth in all locations, divergence in per capita earnings between rural and urban areas has been largely attributable to local differences in human capital stocks and local labor market conditions.

The paper is organized as follows. The next section provides descriptive information on the study area. The following two sections describe the analytical framework for the empirical model, the data used, and some estimation issues. Next, the econometric results are presented and used to compute the contribution of key economic variables to observed trends in urban and rural earnings growth. The following section reassesses the link between rural-urban earnings differentials and income dispersion in light of our empirical findings. Concluding remarks are found in the paper's final section.

II. The Study Area

By most aggregate measures, North Carolina's economic performance has outpaced that of the rest of the nation over the past two decades. Between 1969 and 1990 real per capita income in North Carolina grew at a rate that was approximately 20% greater than the national rate, and the primary components of real income - earnings, capital income from dividends interest and rents, and transfer payments - grew at rates that exceeded the national average by 20% to 50% [ILLUSTRATION FOR FIGURE 2 OMITTED]. Only the state's agricultural sector fared worse than the national average, with farm earnings falling by an annual rate of 4.2% (as opposed to a decline of 3% per year nationally).

While economic growth has been impressive for the state as a whole, at a more disaggregated level the picture is considerably more mixed. North Carolina is composed of 75 rural counties and 25 metropolitan counties (as classified by the Bureau of Economic Analysis), with slightly less than half of the state's population living in rural areas. Table I provides information on the initial distribution of real income and income growth across counties over the period 1969-90. Two groups are of particular interest - the 10 counties that were initially better off and achieved income growth at rates in excess of the state average of 2.2%, and the 46 counties that started relatively worse off and achieved relatively low income growth. The first group comprises most of the state's major metropolitan centers and some adjacent counties. The second group is composed almost exclusively of rural counties, and primarily ones in which agriculture is a key industry within the county. The disparate economic performance of these two sets of counties - superior growth in a handful of "rich" urban counties and sluggish growth in a large group of "poor" rural counties - underlies the strikingly similar dynamics of earnings dispersion and rural-urban earnings disparities shown in Figure 1.

An important element in understanding rural-urban differences in income dynamics is the behavior of local labor markets. Figure 3 reveals a persisting gap between rural and urban unemployment [TABULAR DATA FOR TABLE I OMITTED] that has grown wider since the mid-1970s. To the extent that laborers in rural areas are less mobile and/or less able to shift from one type of employment to another, one would expect negative labor market shocks to have a greater impact on earnings in rural areas vis-a-vis urban areas [21]. The empirical analysis that follows seeks to measure the strength of these and other factors in the determination of earnings in different areas.

III. Analytical Framework

The analysis presented here concerns itself with per capita labor earnings, by far the dominant component of personal income.(2) Earnings ([Y.sub.E]) are the product of labor force participation (L) and wages (W). Following Tokle and Huffman, it is assumed that for any geographic area both L and W depend on the existing stock of human capital (H); permanent (anticipated) local labor market conditions ([Omega]); transitory (unanticipated) local labor market conditions ([Omega]); macroeconomic conditions ([Mu]); locational amenities ([Alpha]); the age distribution of the population ([Delta]); and other, miscellaneous socioeconomic variables ([Theta]) such as the ethnic composition of the local population and the industrial or sectoral composition of the local economy [20].(3) Thus, a reduced form per capita earnings equation of the following form can be written:

[Y.sub.E] = W(H, [Omega], [Omega], [Mu], [Alpha], [Delta], [Theta]) [multiplied by] L(H, [Omega], [Omega], [Mu], [Alpha], [Delta], [Theta]) = [Y.sub.E] (Y, [Omega], [Omega], [Mu], [Alpha], [Delta], [Theta]). (1)

Estimation of this earnings function has the potential of shedding light on the importance of several candidate explanations for spatial differences in economic performance. These include deficiencies in schools and other institutions supporting human capital development in rural areas [19], as indicated by differences in the response of [Y.sub.E] to H; greater sensitivity of rural areas to negative macroeconomic phenomena such as price shocks and recessions [6], as indicated by differences in the response of [Y.sub.E] to [Mu]; and greater mobility of rural workers (particularly younger and more educated workers) and attendant sensitivity of earnings to local labor market dynamics [21], as indicated by significant impacts of [Omega] and [Omega] on [Y.sub.E].(4)

IV. The Data and Econometric Model 

The earnings equation given in (1) was estimated using county-level, cross-sectional, time-series data for North Carolina. The unit of observation was the commuting zone designated by Killian and Tolbert [11]. There are 24 commuting zones in North Carolina, including eight that contain a small number of counties in adjoining states (Georgia, South Carolina, and Virginia). Data for these out-of-state counties were merged with North Carolina data in aggregating to the commuting zone level. The period covered was 1970 through 1990.

For each county, time-series data on earnings, education levels, local labor market conditions, demographic structure, and other economic variables were drawn from several sources and combined to form commuting zone aggregates. Earnings and population data were taken from the Bureau of Economic Analysis' Regional Economic Information System dataset. Per capita earnings were deflated by the U.S. Department of Commerce' GNP deflator.

County level data on educational attainment and demographic structure were available for the years 1970, 1980 and 1990 from the U.S. Census of Population and Housing. These were linearly interpolated to create a 21-year annual time series. The proportion of individuals aged 25 and up who had completed a high school degree was used as a proxy for human capital stock within each county. Demographic variables included the proportion of working age males and females in three age ranges (16-24, 25-54, and 54-65) plus the proportion of children under 16 and the proportion of elderly (over 65).

The Employment Security Commissions in North Carolina and adjoining states have published county-level data on unemployment for the period 1970-90. Using these data, ARMA models were estimated for each county's unemployment rate over the period. The one-step-ahead forecasts based on these models (i.e., the expected unemployment rate) were used as indicators of permanent (anticipated) local labor market conditions, while the difference between forecast and realized values of the unemployment rate was used as a proxy for transitory (i.e., unexpected) labor market shocks.(5)

County employment shares of service and retail industries, manufacturing, and agriculture for 1970 were used to control for differences in the sectoral composition of local economies. These data were from County Business Patterns. Additional independent variables included the real U.S. gross domestic product (as a proxy for macroeconomic conditions), the proportion of the population that is nonwhite, and a dummy variable with a value of 1 for metro counties and 0 for non-metro counties (using the Bureau of Economic Analysis classification). In order to test for differences in the impacts of key economic variables between rural and urban areas, interaction (slope) dummy variables were created by multiplying the metro dummy by the high school graduates, expected unemployment, unemployment shock, and GDP variables.

V. Results

An earnings equation was estimated using 20 years of data from each of 23 commuting zones.(6) Given the time-series cross-sectional nature of the data, there was ample reason to believe a priori that significant correlation among disturbances existed, both contemporaneously (across commuting zones) and serially (within commuting zones). The econometric model was therefore estimated using the TSCSREG procedure of SAS, a generalized least squares estimator that accounts for both forms of error correlation. This method consists of (a) using OLS to compute consistent estimates of autocorrelation coefficients within each cross-section; (b) transforming the data to using a Cochrane-Orcutt procedure; (c) applying OLS to the transformed data to compute consistent estimates of cross-sectional error variances and covariances across counties; and (d) using the estimated variance covariance matrix to perform a standard GLS estimation [12, 622-25].

An additional complicating factor was introduced by the manner in which the educational attainment and demographic data were constructed. The very nature of their construction (through linear interpolation) rendered it likely that unobservable measurement error was embedded in most of the observations on these variables. In order to purge the potential inconsistency and bias attributable to this errors-in-variables problem, an instrumental variables (IV) estimation approach was taken. So long as the chosen instruments for the error-ridden variables are correlated with the true independent variable but uncorrelated with measurement error, the resulting parameter estimates will be consistent [4].(7) For the problem at hand, the U.S. inflation rate and the population density were selected as instruments that plausibly met this requirement. The education and demographic variables were first regressed against these instruments, and their predicted values were then used on the right hand side of the final regression equation.

Table II presents the econometric results. The dependent variable was the natural logarithm of per capita earnings. The logs of several right-hand-side variables of interest (high school graduates, U.S. GDP, and their interaction terms) were also used, primarily to reduce multicollinearity (which was severe when the levels of those variables were employed). In addition to the variables described earlier, state dummy variables for commuting zones containing counties in other states were included to account for possible fixed effects introduced by inter-state differences.

Table II. Regression Results(a)

Variable                                             Estimate

ln(High school grads)                                0.087(*)
                                                     (.020)
ln(U.S. GDP)                                         0.786(*)
                                                     (.021)
Expected unemployment                               -1.536(*)
                                                     (.082)
Unemployment shock                                  -1.305(*)
                                                     (.040)
ln(High school grads) x metro dummy                  0.102(*)
                                                     (.010)
ln(U.S. GDP) x metro dummy                          -0.007(*)
                                                     (.002)
Expected unemployment x metro dummy                  0.146(**)
                                                     (.065)
Unemployment shock x metro dummy                     0.222(*)
                                                     (.030)
Non-white population (%)                            -0.235(**)
                                                     (.033)
Males 16-24 (%)                                    -11.568(*)
                                                     (.351)
Males 55-64 (%)                                    -15.729(*)
                                                     (.952)
Females 16-24 (%)                                   -8.937(*)
                                                     (.258)
Females 25-54 (%)                                  -16.825(*)
                                                     (.418)
Females 55-64 (%)                                   -1.270(**)
                                                     (.493)
Elderly (%)                                        -12.134(*)
                                                     (.326)
Children (%)                                        -7.686(*)
                                                     (.231)
Agricultural employment share (1970)                -0.797(*)
                                                     (.114)
Service and retail employment share (1970)          -0.768(*)
                                                     (.147)
Manufacturing employment share (1970)               -0.463(*)
                                                     (.091)
Metro dummy                                          0.106(*)
                                                     (.008)
Georgia dummy                                       -0.089(*)
                                                     (.012)
South Carolina dummy                                -0.058(*)
                                                     (.009)
Virginia dummy                                       0.013(**)
                                                     (.006)
Intercept                                            5.096(*)
                                                     (.274)
[R.sup.2]                                             .952
Sample size                                            460

a. IV estimates using population density and U.S. inflation as
instruments for education and demographic variables (see text).
Dependent variable is the log of net earnings. Standard errors of
estimates are found in parentheses. * and ** indicate significance
at the 1% and 5% levels.

Nearly all of the parameter estimates are significant at the 1% level and of the expected sign. High school education,(8) U.S. GDP, and urban status were found to have a positive impact on earnings. Both permanent and transitory conditions in local labor markets were similarly found to have procyclical relationships with earnings, hence the negative coefficients on the two unemployment variables. The proportion of minority population was found to have a negative relationship with earnings. The coefficients on other demographic composition variables were all negative, which was not surprising given that the omitted demographic category variable was prime working age males aged 25 to 54. Finally, the coefficients on the variables indicating sectoral composition of local economies imply that earnings tended to be lower in areas that were initially more heavily dependent on agriculture, manufacturing, and service industries. This result is presumably a reflection of the decline of agriculture and certain historically important manufacturing industries (notably textiles) relative to other industries over the time period considered.

Rural-urban differences in the effects of key economic variables are reflected in the interaction terms. These are most readily understood by comparing the implied elasticities for urban and rural commuting zones (Table III). Education's impact on earnings is strikingly greater in urban areas: the urban elasticity of earnings with respect to education is more than double that of rural areas (.189 vs. .087). In contrast, earnings are only slightly more sensitive to macroeconomic forces in rural areas than in urban areas. This result is at odds with the arguments of several authors who assert that income and employment are more strongly affected by business cycle trends in rural areas, particularly in the rural South [6; 13].

Finally, local labor market conditions - as proxied by expected and unanticipated unemployment - have a significantly larger impact on earnings in rural areas than in urban areas. This finding is consistent with evidence presented by Topel regarding the volatility of the earnings of different types of workers [21].(9) Specifically, his model of local labor markets predicts that the earnings of older and less mobile workers are more strongly affected by negative forces (both permanent and transitory) than their younger and more mobile counterparts, largely due to the greater ability of the latter to migrate.

Table III. Elasticities of Earnings with Respect to Key Variables

Variable                                Urban           Rural

High school graduates                    .189            .087
U.S. GDP                                 .779            .786
Expected unemployment rate(a)           -.075           -.104

a. Evaluated at the sample mean.

[TABULAR DATA FOR TABLE IV OMITTED]

Trend Decomposition 

Combining the estimated earnings elasticities of key variables with information on trends in those variables enables measurement of the contribution of specific factors to observed earnings growth. Totally differentiating equation (1) and dividing through by [Y.sub.E] yields the growth accounting identity:

[Mathematical Expression Omitted]

where [[Epsilon].sub.H], [[Epsilon].sub.GDP], [[Epsilon].sub.EU] denote the elasticities of earnings with respect to high school education, U.S. GDP, and expected unemployment, respectively, and a "^" denotes percentage growth. The residual is the sum of the growth rates of all other variables on the right hand side of our estimating equation (weighted by their elasticities).

Equation (2) decomposes earnings growth into shares attributable to human capital stock (education), national (macroeconomic) effects, and local (labor market) effects. Table IV presents measures of these growth shares computed using the earnings elasticities from Table III and observed trend growth rates in both rural and urban areas.(10) The estimates are presented for the 1970s, the 1980s and the entire 1970-90 time period.

Several interesting conclusions emerge from the data presented in Table IV. First, national (macroeconomic) effects dominate human capital and local effects in terms of overall contribution to earnings growth. This is the case in both rural and urban locations, over the entire 21 year period and in both sub-periods. Second, the contribution of education to earnings growth has been distinctly lower in rural areas than urban areas over the period of observation. This is primarily due to the much smaller elasticity of rural earnings with respect to education. Furthermore, education's contribution to earnings growth fell between the 1970s and 1980s. Third, the contribution of local labor market conditions to earnings growth has been consistently greater in rural areas than in urban areas. Additionally, these local effects have gained in importance over time in both locations.

VI. Income Non-convergence Revisited

As indicated in the introductory section of this paper, a strong correlation exists between the observed pattern of income dispersion and rural-urban earnings differentials over the past two decades. We are now in position to reconsider this empirical regularity in light of the results presented in the previous section.

Macroeconomic trends were found to have had a dominant impact on earnings and earnings growth in North Carolina over the past two decades. However, the econometric results indicate little difference between rural and urban areas in the effect of these macroeconomic trends on earnings: the size of the estimated difference - while statistically significant - was very small in magnitude. Correspondingly, the absolute contribution of macroeconomic trends to earnings growth varied little between rural and urban areas.(11) The solution to the empirical puzzle embodied in Figure 1 would thus appear to lie someplace other than in the purportedly greater sensitivity of rural areas to national business cycles.

Two types of rural-urban differences in the determinants of earnings were detected: (a) differences in returns to the stock of human capital (education); and (b) differences in the sensitivity of earnings to local labor market conditions (both expected and unexpected). These factors underlie the relative movements of rural and urban earnings in North Carolina over the past two decades or so, and, by extension, explain a considerable proportion of the increase in income dispersion since the mid-1970s.

Beginning with differences in returns to education, national data indicate that the proportion of both high school- and college-educated persons has been growing faster in urban areas than in rural areas, at least since 1980 and probably even longer [15]. This is true for North Carolina as well, and is due to a combination of in-state migration from rural counties to metropolitan centers, migration into North Carolina from outside the state, and rural-urban differences in expenditures on schools and facilities [16]. The combination of increasingly better-educated urban dwellers and distinctly higher returns to education in urban areas (i.e., a greater concentration of jobs for high-skilled workers) is clearly consistent with growing disparities between rural and urban incomes.

The finding that earnings in rural areas are more sensitive to local labor market conditions is consistent with the conventional wisdom regarding the "brain drain" from rural to urban areas within North Carolina. Because the rural labor force tends to be older and less mobile, it is more vulnerable to negative labor market shocks than the (younger) urban labor force. As elsewhere in the U.S., unemployment in North Carolina's rural areas has consistently been higher than urban unemployment; moreover, while unemployment has been trending downward in both areas, the two rural and urban rates have been diverging since 1975. This, in combination with the more negative effect of unemployment on earnings in rural labor markets, is again consistent with the widening of the rural-urban income gap.

VII. Concluding Remarks

This paper has sought to quantify the impact of key economic variables on per capita earnings. Econometric results indicated strikingly larger returns to schooling in urban areas, substantially larger impacts of local unemployment shocks (both transitory and permanent) on earnings in rural areas, and little difference between the two areas in the response of earnings to macroeconomic forces. Decomposition of trends over the 1970-90 period indicated that macroeconomic forces have been the dominant source of earnings growth in both areas, but that spatial differences in human capital stocks and local labor market conditions underlie the relative movements of rural and urban earnings over the past two decades or so.

The research that has been reported here is distinguished by its use of county-level data for the measurement of the determinants of earnings. By comparison to state level data used in much of the research on income dispersion, county-level data provides a richer source of information for testing hypotheses related to local markets. At the same time, however, analysis for only one state is somewhat limiting. A useful extension, then, would be to maintain the same level of disaggregation but to broaden the geographic scope of analysis to other states (or groups of states).

Finally, the results that have been presented here have strong implications regarding labor force mobility and the dynamics of migration. Specifically, they point to migration as a key force effecting equilibrium in local labor markets. Explicitly incorporating migration into an analysis of the determinants of rural-urban earnings differentials - say, through the use of panel data - represents another potentially fruitful useful extension of this research.

The author gratefully acknowledges the insightful comments of Stefan Goetz, Barry Goodwin, Tom Grennes, Alastair Hall, Dale Hoover, Ron Schrimper, Paul Siegel, Wally Thurman, Mike Walden, and an anonymous reviewer.

1. Examination of personal income data extending back to 1929 indicates that income dispersion had been steadily decreasing up to the mid-1970s.

2. As of 1990, earnings accounted for slightly over 70% of total personal income in North Carolina.

3. Wages and labor force participation are likely to be affected differently by the same variable. However, it is reasonable to assume that the direction of effects of the key variables of interest here - human capital stock, local labor market conditions and macroeconomic conditions - will be the same.

4. Other explanations of rural-urban differential that are not tested within the current framework include inadequacies in publicly-supported infrastructure such as roads and telecommunications facilities [7], and shortages of capital and technical assistance for would-be rural entrepreneurs [9].

5. This procedure is in the same spirit as that used by Tokle and Huffman, but differs in that it uses time-series methods to generate forecasts and residuals instead of fitting quadratic trend equations to the data [20].

6. One year of data was lost for each of the commuting zones in order to generate forecasts of the unemployment rate. One of the commuting zones was dropped from the sample because employment data for the early years of the sample period were unavailable.

7. The estimates using a particular set of instruments need not yield the minimum asymptotic variance, however [10, 533].

8. I experimented with using the proportion of college graduates in the adult population in place of the proportion of high school graduates. This yielded very similar results to those presented here in terms of the magnitude, sign, and level of significance of the parameter estimates.

9. Note, however, Topel's model also predicts anticipated and unanticipated local labor market shocks to have opposite effects on wages - i.e, that the sign on anticipated local unemployment should be positive. In his model, increases in expected future demand for labor increases in-migration (in anticipation of future wage increases), thereby depressing current wages. That the results here imply lower earnings accompanying increases in expected unemployment may be due to the fact that spatial differences in demographic structure are controlled for explicitly. Alternatively, it may indicate that the negative impact of greater expected unemployment on current labor force participation outweighs the positive impacts on current wages.

10. For ease of interpretation, the values in the table are expressed as the percentage contribution of each variable to earnings net of the residual term in equation (2). In all cases this residual was negative, and hence the gross percentage contribution of each variable to overall earnings growth is even greater than that reported in Table IV.

11. That the percentage contribution of U.S. GDP to net earnings growth in rural areas was about six percentage points greater than that of urban areas is attributable to relative differences in the magnitude of education and local effects across areas.

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