Additional regression results for Huang, Orazem and Wohlgemuth, “Rural Population Growth, 1950-1990: The Roles of Human Capital, Industry Structure and Government Policy”

A. Reduced Form Migration Regressions

In the model, income depends on human capital. Consequently, the effect of human capital on population growth given by equation (9) includes two effects: the direct effect and an indirect effect through income .

Additionally, county farm and nonfarm income are measured with error because of changes in data definitions over time. One method of correcting for measurement error is to use instrumental variables that are uncorrelated with the measurement error but correlated with the true value of the variable in question. Consequently, equation (7C) can be viewed as a first-stage equation in a two-stage estimation procedure or as an instrumenting equation for a relative income measure subject to error.

Measures of local government fiscal policy are endogenous to local population growth. Once again, instrumental variables can be used to identify these endogenous variables.

Substituting in all instrumental variables for endogenous income and government policy variables yields the reduced form regressions listed in Table B1. The summed reduced-form coefficients on the two human capital measures yield an estimate of the derivative in equation (9).

B. Structural Per Capita Income Regressions

The structural estimate of human capital on per capita income requires estimation of equation (6A). The sum of the two human capital coefficients can be taken as an estimate of . The estimates are reported in Table B2.

C. OLS versus GLS Estimates

Because we define the dependent variable in first-differenced form, county-specific fixed effects are eliminated. However, there may still be correlated errors in population growth for a given county over time. In Table B3, we replicate the estimate of overall county working population growth using controls for county-specific random effects. The GLS estimates are qualitatively similar to the OLS estimates reported in the paper.

Table B1: Reduced Form Estimates of Growth in Rural Population, by Age and Farm or Nonfarm Occupation, 1950-1990 (all variables in natural logarithms)
	20-64			20-34
	Total	Farm	Nonfarm	Total	Farm	Nonfarm
Median school years completed	-.169	.122	-.028	-.283	-.150	-.147
	(2.55)	(1.01)	(.34)	(3.04)	(.91)	(1.35)
% of population with high school degree	-.021	-.135	-.097	.027	-.102	-.066
	(.69)	(2.36)	(2.44)	(.64)	(1.31)	(1.28)
Distance to city with population > 100,000	-.044	-.009	-.063	-.059	-.005	-.077
	(5.21)	(.55)	(5.54)	(4.96)	(.23)	(5.27)
Herfindahl index of employment	-.132	.213	-.088	-.176	.238	-.068
	(7.68)	(6.74)	(4.03)	(7.28)	(5.53)	(2.41)
Rent	.118	.299	.051	.120	.373	.067
	(4.40)	(6.05)	(1.47)	(3.16)	(5.54)	(1.52)
State government highway expenditure	-.059	.078	-.056	-.091	.057	-.066
	(3.59)	(2.54)	(2.63)	(3.92)	(1.35)	(2.38)
Proportion on farm	-.025	-.158	.082	-.026	-.201	.074
	(3.25)	(11.0)	(8.16)	(2.35)	(10.15)	(5.74)
Proportion black	-.008	-.021	-.000	-.006	-.022	.004
	(2.93)	(3.94)	(.06)	(1.54)	(3.00)	(.92)
Proportion less than 15 years old	-.044	-.253	.127	-.145	-.194	.049
	(.93)	(2.91)	(2.10)	(2.18)	(1.64)	(.63)
Proportion 65 years and older	-.055	.089	-.093	-.036	.189	-.056
	(2.34)	(2.07)	(3.10)	(1.10)	(3.21)	(1.45)
Instruments
Per capita state taxes	.086	-.063	.052	.101	-.111	.052
	(3.30)	(1.33)	(1.56)	(2.73)	(1.71)	(1.21)
Percent of low income households	-.021	.092	-.046	-.011	.061	-.039
	(1.23)	(2.94)	(2.13)	(.47)	(1.44)	(1.38)
Average teacher salary	-.138	-.186	-.157	-.104	-.163	-.136
	(3.08)	(2.28)	(2.76)	(.47)	(1.46)	(1.85)
Cost of primary roads/mile	.003	.044	.011	.003	.079	.012
	(.34)	(2.58)	(.96)	(.21)	(3.38)	(.79)
Cost of secondary roads/mile	-.015	.019	-.026	-.018	-.005	-.022
	(2.00)	(1.38)	(2.69)	(1.71)	(.27)	(1.81)
Federal highway funds	-.039	.012	-.053	-.044	.028	-.050
	(3.51)	(.61)	(3.78)	(2.81)	(1.01)	(2.79)
Percent of union membership	.018	.004	.050	.031	-.005	.056
	(.91)	(.10)	(2.02)	(1.12)	(.09)	(1.74)
Soil suitability for roads	.018	-.005	-.018	-.002	-.012	-.039
	(.60)	(.091)	(.46)	(.04)	(.16)	(.79)
Soil suitability for roadfill	.015	-.084	.050	.024	-.090	.057
	(.60)	(1.90)	(1.62)	(.71)	(1.49)	(1.43)
% farm revenue in crops	–	-.044	-.027	–	-.055	-.045
		(4.55)	(4.00)		(4.15)	(5.24)
Average farm size (acres)	–	.033	-.051	–	.040	-.042
		(1.68)	(3.69)		(1.46)	(2.36)
Value of land, buildings per acre	–	.037	-.052	–	.092	-.034
		(4.34)	(3.72)		(3.34)	(1.89)
R^2	.42	.41	.32	.49	.44	.33
N	1224	1224	1224	1224	1224	1224

Regressions also include dummy variables for each decade, measures of average county rainfall, January and July temperature, and a dummy variable for Shannon County in South Dakota.

t-statistics in parentheses.

Table B2: Regressions Explaining Log Per Capita Income as Functions of Human Capital and Local Labor Market Factors (all variables in natural logarithms)
	Aggregate	Farm	Nonfarm
Median school years completed	.176	.469	.141
	(2.28)	(3.99)	(1.78)
% of population with high school degree	.170	.039	.160
	(4.66)	(.69)	(4.26)
Distance to city with population > 100,000	-.030	-.026	-.041
	(3.02)	(1.70)	(4.00)
Herfindahl index of employment	-.136	-.035	-.129
	(6.95)	(1.16)	(6.39)
Rent	.413	.364	.447
	(13.7)	(7.82)	(14.3)
Proportion on farm	-.067	-.130	-.020
	(7.86)	(9.96)	(2.23)
Proportion black	-.010	-.026	.003
	(3.07)	(5.24)	(.84)
% farm revenue in crops	.018	-.017	.026
	(2.90)	(1.87)	(4.15)
Average farm size (acres)	.044	.146	-.005
	(3.48)	(7.54)	(.35)
Value of land, buildings per acre	.095	.166	.057
	(7.78)	(8.98)	(4.62)
Average January temperature	.086	.104	.069
	(4.09)	(3.25)	(3.22)
Average July temperature	-.770	-.677	-.795
	(4.06)	(2.34)	(4.08)
Average annual rainfall	-.156	-.009	-.200
	(4.14)	(.15)	(5.21)
R^2	.86	.79	.84
N	1224	1203	1224

Regressions also include dummy variables for each decade.

t-statistics in parentheses.

Table B3: Reduced Form Estimates of Growth in Rural Population Aged 20-64, 1950-1990 (all variables in natural logarithms)
	OLS	GLS
Median income	.086	.110
	(2.65)	(3.34)
Median school years completed	-.171	-.209
	(2.59)	(3.18)
% of population with high school degree	-.022	-.010
	(.74)	(0.33)
Distance to city with population > 100,000	-.046	-.047
	(5.35)	(5.03)
Herfindahl index of employment	-.129	-.122
	(7.48)	(6.93)
Rent	.097	.084
	(3.48)	(2.95)
State government highway expenditure	-.060	-.061
	(3.66)	(3.58)
Proportion on farm	-.022	-.022
	(2.82)	(2.72)
Proportion black	-.008	-.008
	(2.96)	(2.72)
Proportion less than 15 years old	-.023	.012
	(0.48)	(0.23)
Proportion 65 years and older	-.061	-.017
	(2.57)	(0.71)
Instruments
Per capita state taxes	.083	.090
	(3.18)	(3.36)
Percent of low income households	.015	.020
	(0.72)	(0.95)
Average teacher salary	-.147	-.151
	(3.29)	(3.31)
Cost of primary roads/mile	.003	.002
	(0.36)	(0.21)
Cost of secondary roads/mile	-.017	-.017
	(2.26)	(2.17)
Federal highway funds	-.041	-.038
	(3.73)	(3.48)
Percent of union membership	.019	.010
	(0.99)	(0.50)
Soil suitability for roads	.017	.015
	(0.59)	(0.47)
Soil suitability for roadfill	.016	.019
	(0.66)	(0.72)
R^2	.42	.42
N	1224	1224

Regressions also include dummy variables for each decade, measures of average county rainfall, January and July temperature, and a dummy variable for Shannon County in South Dakota.

t-statistics in parentheses.

GLS estimate allows for correlation in county error terms over time.