Land Endowments, Child Labor, and the Rise of Public Schooling (Tables and Figures)

Table 1: School Quality in U.S. South 1915 Years in School* Black White 9 6 1945 11 Pupil-Teacher Ratio** White 37 10 28 Black 62 34 Note: Averages of state-level averages of Southern states. *. Source: Collins and Margo (2006). **. Source: Card and Krueger (1992b). Author’s calculations. Table 2: Events Relating to School Quality Event Hookworm Eradication Year 1910 Adult Labor Yes Child Labor Yes School Characteristic – Fall in Cotton Production* 1920 Yes Yes Pupil-Teacher Ratio Immigration Exclusion Act 1924 Yes No – Agricultural Adjustment Act* 1933 No Yes School Term Length Cotton Mechanization 1940s No Yes – Brown v. Board 1954 No Yes – Civil Rights Act 1966 No Yes – Note: * Signifies an event responsible for narrowing racial differences in public schooling. The final three events occurred after racial differences in public schooling had already significantly narrowed. Moreover, the first affected school attendance before occurred after racial differences in public schooling had already significantly narrowed. Moreover, the first affected school attendance before racial differences in school attendance had significantly narrowed (Bleakley, 2007). Table 3: Attendance Rate Black * Cotton Ginned Per Acre I II III -0.583*** -0.342*** -0.338*** [0.165] [0.106] [0.106] Cotton Ginned Per Acre -0.092 Black 0.157 0.085 [0.202] [0.115] [0.102] -10.5*** -11.9*** -11.9*** [1.37] [1.22] [1.22] Year Trend 0.582*** [0.042] Constant School District Fixed Effects Year Fixed Effects Number of observations R2 Note: ∗∗∗ Significant at 1%. 62.7*** 65.0*** -1070*** [1.10] [0.856] [81] No No 9,184 0.26 Yes Yes 9,184 0.53 Yes No 9,184 0.51 Table 4: School Quality Black * Cotton Ginned Per Acre Cotton Ginned Per Acre Black Constant School District Fixed Effects Year Fixed Effects Number of observations R2 Note: ∗∗∗ Significant at 1%. Pupil-Teacher Ratio I II 0.527*** 0.403*** School Term Length III IV -0.66*** -0.17** [0.11] [0.12] [0.20] 0.173** 0.085** -0.40*** [0.09] [0.08] [0.07] [0.15] [0.10] 11.8*** 13.0*** -15.0*** -25.0*** [0.93] [1.0] [1.5] 36*** 28*** 145*** [0.7] [2.5] [1.0] [2.1] No No 9,262 0.38 Yes Yes 9,262 0.57 No No 9,112 0.14 Yes Yes 9,112 0.69 -0.15 [0.8] 120*** Table 5A: Cotton Ginned Per Acre, First-Stage November Weather Previous Year’s Cotton Price I II 0.194*** 0.087*** [0.02] [0.02] 0.171** 0.092** [0.01] [0.01] Year Trend -0.149*** [0.01] Constant School District Fixed Effects Number of observations R2 Note: ∗∗∗ Significant at 1%. 3.57*** 292*** [0.21] [24] Yes 4,592 0.60 Yes 4,592 0.65 Table 5B: Attendance Rate, 2SLS Black * Cotton Ginned Per Acre Cotton Ginned Per Acre Black I II III -0.477*** -0.431*** -0.919*** [0.258] [0.211] [0.205] -0.858*** -1.11*** -1.173*** [0.209] [0.177] [0.296] -11.0*** -11.8*** -11.9*** [1.64] [1.2] Year Trend [1.22] 0.582*** [0.042] Constant School District Fixed Effects Number of observations R2 Note: ∗∗∗ Significant at 1%. 67.1*** 55.0*** -1070*** [1.32] [1.15] [81] No 9,184 0.20 Yes 9,184 0.38 Yes 9,184 0.39 Figure 1: Pupil-Teacher Ratio in U.S. South Figure 2: School Quality in the Carolinas Figure 3A: Timing of the Supply-Side - Allocating State Funds t0 t1 School Board allocates state funds by race: W and B Blacks choose tS : time children are in school and not working + Profits from black child labor realized: w(1 − B), w: wage + White children attend school W : per capita funds for whites B: per capita funds for blacks t2 Racial inequality monitored: W −B White children earn income from returns to school quality: ρ(W ) + Law suit realized: γq(W − B), γ: cost, q(W − B): probability Figure 3B: Timing of the Demand-Side - Raising Local Tax by Race t0 t1 School Board raises local tax by race: T ∈ [W, B] Children attend school: tS (T ) = T + Profits from child labor: w(1 − T ), w: wage + Adult save from total wealth: s: saving + Household pays tax: T W : per capita funds for whites B: per capita funds for blacks t2 Wealth saved accumulates interest s = w(1 − T )+ w0 − T w0 : initial wealth and adult earnings Child earns income from returns to to school quality: ρ(W ) + Parent lives off of savings: rs, 1 r = 1+i , i: interest Figure 4: Georgia Cotton and Public School Quality Figure 5: School Term Length in Georgia Figure 6: Cotton Ginning in Georgia Figure IV – 500 1000 Thousands of Bales 1500 2000 2500 3000 Cotton Ginned in Georgia: 1910-40 1910 1920 1930 Year Source: U.S. Census Bureau. 1940 Appendix A Comparative Statics Proof for Proposition 1. Substituting the budget constraint, B = 1 − W , into (13), I maximize U (W ) = u(wW ) + βu(ρ(W ) − γq(2W − 1)). Maximizing yields wu0 (wW ) + βu0 (ρ(W ) − 2γq 0 (2W − 1)) = 0. Applying the implicit function theorem, I find that dW u0 (wW ) + wW u00 (wW ) = dw −w2 u00 (wW ) − βu00 (ρ(W ))(ρ0 (W ) − 2γq 0 (2W − 1))2 − βu0 (ρ(wW ))(ρ00 (W ) − 4γq 00 (2W − 1)) For utility functions such that |u0 (.)| ≥ |u00 (.)|, this derivative is positive. The maximization problem in (6) produces the following first-order conditions: ∂U : − u0 (c1 ) + βru0 (c2a ) = 0 ∂s ∂U : − wu0 (c1 ) + αβρ0 (tS )u0 (c2c ) = 0 ∂tS (11) (12) (7) is the standard Euler equation. Combining (7) and (8) indicates the relative prices of consumption in the denominators: u0 (c1 ) αβρ0 (tS ) w = u0 (c2a ) αρ0 (tS ) wr = u0 (c2c ) 1 (13) As w increases, the relative price of second-period child consumption decreases. Proof for Proposition 2. I separately compute the comparative static of tS with respect to each of the three proxies for race: w0 , α, and β. I seek to find whether each derivative has the same sign. I first define that φ−1 = (βρ00 (tS )u0 (c2c ) + αβρ0 (tS )2 u00 (c2c ))(u00 (c1 ) + βr2 u00 (c2a )) + β 2 w2 r2 u00 (c1 )u00 (c2c ) > 0. Indeed, all three derivatives are positive. First, −wr2 φu0 (c1 )u00 (c2a ) > 0. Finally, dtS dα dtS dw0 = wr2 βφu00 (c1 )u00 (c2a ) > 0. Second, dtS dβ = = −βφρ0 (tS )u00 (c1 )u0 (c2c ) − β 2 rφρ0 (tS )u0 (c2c )u00 (c2a ) > 0. Proof for Proposition 3. Recall that w reflects the returns to child labor. w was larger in cotton agriculture than in other forms of agriculture, and yet also declined during the early 1920s with the fall in cotton production and the mid-to-late 1930s decline in sharecropping and tenancy. I find that price effect: ≤ 0 income effect: ≥ 0 }| { z }| { dtS z 0 = φu (c1 )u00 (c1 ) + φαβr2 u0 (c1 )u00 (c2a ) + w(1 − tS )φαβr2 u00 (c1 )u00 (c2a ) dw (14) Whether a decline in the returns to child labor causes a rise in the demand for schooling depends on whether the price effect is larger than the income effect. The sum of the first two terms represents the price effect, which is unambiguously negative. An increase in the returns to child labor makes the combined first period and second period adult consumption relatively more attractive than second period child consumption as reflected by (9). As a result, demand for schooling falls. The third term in (10) corresponds with the income effect, which is unambiguously positive. As the returns to child labor fall, children must work more and attend school less to maintain the same level of first period household wealth. If the income effect is larger than the price effect, (10) produces the perhaps surprising result that children will attend more schooling when the returns to child labor rise. Proof for Proposition 4. Equation (10) suggests that black and white households could respond differently to changes in the returns to child labor based on their relative differences in their price and income effects. This proposition makes no claim about the sign of dtS dw for whites, but only that it is more negative for blacks. I proceed by assuming that the first and second derivatives of the utility function and returns to education function are bounded. Recall that a smaller value of α corresponds to black households. As α → 0 and the parameter is more likely to correspond with black households, only the first of the three terms remains non- zero and finite. In particular, this term is negative as previously signed, and dtS dw < 0. This argument suggests that the derivative takes on more negative values for black households. Proof for Proposition 5. For simplicity, I assume that time spent in school is a linear function of school quality: tS (T ) = T .61 This assumption produces the following household maximization problem: U (s, T ) = u(w0 + w(1 − T ) − s − T ) + βu(rs) + βαu(ρ(T )) (15) The comparative statics follow similarly to that of the previous section. Specifically, scale the returns to child labor in (6) additively by one. 61 This assumption is consistent with Card (1999). B Correcting Education Data The annual reports contain several typographical errors, and I correct them to the best of my ability by taking advantage of the many totals provided. In some years, the reports aggregate the data by county when it has at least one city as an independent school district, in addition to by race. Statelevel totals are always available to aggregate the county- and city- totals. Additionally, the reports often divide the data into its components, and report the aggregate as well. For example for teachers, the reports typically list both the total amount of teacher as well as the amount of male and female teachers. In some cases the reports provide more than one level of disaggregation, such as dividing total enrollment once by gender and then separately by grade. Finally for space constraints, when many categories existed such as in sources of revenue, the reports often aggregated some of them and listed them as Other to ensure that the total could be checked against all of the sources of funding. I check the accuracy of the reported data by computing totals for all of these levels of disaggregations. I consider a typographical error as potentially arising when a discrepancy exists between my computation and the state report’s computed total. I also check the report’s computed totals using the same sets of checks to assess whether the typographical error is with the raw data. I can correct typographical errors by exploiting all of these different checks at once by identifying which cell is consistently causing my totals to not correspond with that of the report’s. If there is one cell that is a typographical error but every other cell involved in each of the sums is correct, then I can identify the problematic cell by noting that it appears in multiple checks. The amount it should be corrected by reflects by how much the amount that each check is consistently incorrect. For example, suppose a county’s amount of black male teachers is misreported, but all other information about its teachers are correctly reported. Figure 1 provides such an example. There are 3 race totals and 3 gender totals, and all 6 sum correctly except for that of black teachers and that of male teachers. Both are 1 less than what is reported, so I change black male teachers from 11 to 12. In a few cases where it was difficult to identify the incorrect cell, it was clearly the case that either a decimal or a number’s digit was inadvertently omitted. These typographical errors are relatively straight-forward to identify if they are not in the ones place because they produce discrepancies that are large in magnitude. Finally, I classify some numbers as typographical errors if they change drastically in one year and then return to their original value in the following for a category that is unlikely to vary so much. For example, in Figure 2, I do not expect that number of black students attending public schools in Stewart County increased by 7,002 from 1,760. Instead, the number for 1915 is most likely 1,762, given a total enrollment of 3,356. The amount of typographical errors is not trivial, though they generally improve with each year’s report. Moreover, there are generally more delineations provided over time, which helps to identify typographical errors more easily. It is not clear whether some county superintendents provided incorrect accounts to the state superintendent or simply the state superintendent’s office incorrectly presented some of the county’s data. W hite Race Black T otal M ale 22 11 34 Gender F emale 45 11 56 T otal 67 23 90 Figure 1: Teachers in Berrien County, 1909 District Stewart 1914 1760 Year 1915 8762 1916 1954 Figure 2: Average Daily Attendance for Black Children