1

Smith and Welch: Black Economic Progress After Myrdal

• “Inspired” by Gunnar Myrdal’s An American Dilemma (1944)– Story—Swedish: hired blacks– Bleak—American creed vs. black oppression (caste) is the

dilemma– Optimistic about future and cumulative process, but needed

something to “get it going”• Mechanization in South

• Government intervention

• Education (to disprove self-fulfilling prophecy)

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Has This Progress Happened?

• Smith and Welch argue emphatically that it has, at least for the1940-1980 period

• However, the authors are quick to note that:– Economic equality has not yet been achieved– Looking at 1980 there was cause for concern that the racial

convergence would not continue

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The Goal Is To Answer 4 Questions

• Question 1: What are the determinants of convergence in IB/IW between 1940 and 1980?

• Question 2: Are these opportunities still viable for continued convergence?

• Question 3: Can we develop an accounting of the sources of convergence (i.e. a picture of what happened)?

• Question 4: Method

To address these questions Smith and Welch use public use tapes of the decennial census from 1940-1980

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Table 1

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Table 2

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Table 4

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Table 8

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Table 9

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Table 11

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Table 11 (continued)

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Smith and Welch Model

• I = income = wage + salary + self-employed income• It = income in year t (t = 1940…1980)• Ib

t = black income in year t• Rt = Ib

t / Iwt = black income as % of white income (or

“gap”)• Ln Rt = ln Ib

t – ln Iwt (makes it easier to manipulate

things when linear and in natural logs—classic economics trick)

• Smith and Welch estimate determinants of ln Ibt and

ln Iwt. The goal is to see how much of observed

convergence in Rt is explained by each of the components of ln Ib

t and ln Iwt

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Smith and Welch Equations

• ln Ibt = (bb

ed,t * edbt) + (bb

south * southbt) + (bb

SMSA * SMSAb

t)+ (bbcentral city * central cityb

t )+ constantbt

• Where:– Edb

t = years of schooling for blacks in year t– Southb

t = 1 if lived in South in year t, 0 otherwise– SMSAb

t = 1 if lived in SMSA in year t, 0 otherwise– Central Cityb

t = 1 if lived in central city in year t, 0 otherwise

• Can also be written in matrix form: ln Ibt = Xb

t * Bbt,

where:– X = vector of characteristics that workers bring to market– B = vector of values the market places on the characteristics

• Equation for white workers is the same, but using the traits for white workers

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Brief Econometric Review

• We can observe ln Ibt, ln Iw

t, Xb

t, and Xwt; we must

estimate Bbt and Bw

t

• b is the slope of the line that minimizes the squared deviation of the errors

• b is interpreted as the impact of a one-year increase in education on income

• ( ln I) / ( X) = b = rate of change in income per unit change in X (NOT elasticity) edt

ln It

errorsb ed,t

const

edt = 1

Observations of edt and It

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Regression Results

• Smith and Welch estimate these equations for 8 experience classes, 5 years, and 2 races– 8 * 5 * 2 = 80 regressions– Results are reported in appendix

• Table 12 reports the 80 coefficients on education (bed,t). Main finding is that blacks receive less income per year of schooling than whites (bb

ed,t < bwed,t)

• Table 13 shows the difference (bwed,t - bb

ed,t)– Difference is declining over time– Causes of convergence? Education

• The question now is, how much of the convergence in the gap (from 1940-1980) is due to education changes? Must examine X and B…

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Decomposition Analysis: Technique

Ln Rt = Ln Rt – Ln Rt-1 = (xbt bb

t - xwt bw

t) - (xbt-1 bb

t-1 - xw

t-1 bwt-1)

– This is simply the change in the log of the gaps

• Adding and subtracting cross-terms, such as (xbt bb

t - xb

t bbt) = 0, yields the equation on page 529

• Example using t = 1980, t-1 = 1940: Ln R = (LnIb

80 - LnIw80) - (LnIb

40 - LnIw40) (i)

= [(xb80 – xw

80) - (xb40 – xw

40)]* bw40 (ii)

+ (xb80 – xb

40) * (bb40 – bw

40) (iii)

+ (xb80 – xw

80) * (bw80 – bw

40) (iv)

+ [(bb80 – bw

80) - (bb40 – bw

40)]* xb80 (v)

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Decomposition Analysis: What Are The Terms?

• (i) represents the change in the percentage gap• (ii) is the “characteristic” or “main” effect

– This is the value of the increased education among blacks evaluated at the white return in 1940

• (iii) is the “direct effect” of race– This term is negative and evaluates the in characteristics

from 1940-1980 against the race “penalty” (difference in coefficients) in 1940

• (iv) is the year interaction term– Measures the difference in 1940 characteristics evaluated

against the change in white returns between 1940 and 1980

• (v) is the “race-year interaction”– The value of the relative change in coefficients evaluated

against the characteristics of black workers in 1980

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Decomposition Analysis: Interpreting The Terms

• (ii) The “characteristic” or “main” effect measures the income convergence due to convergence in black and white worker characteristics (measured at the market rate of return for whites in 1940)

• (iii) The “direct effect” of race accounts for the fact that the increase in black characteristics did not receive the 1940 market return for whites; those workers received bb

40 < bw40, so we must

subtract the difference from the income growth anticipated by the characteristic effect

• (iv) The year interaction term accounts for the impact of s in payments to characteristics for whites between 1940 and 1980 on relative black wages (i.e. if return to a white trait and blacks have “less” of that trait black’s experience a relative gain)

• (v) The “race-year interaction” measures the income convergence attributable to convergence in race-specific coefficients (or the convergence in market “prices” of characteristics)

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Decomposition Analysis: An Example

1. Main effect: [(11-12)-(6-9)]*9 = [(-1)-(-3)]*9 = 18%

2. Race effect: (11-6)(4-9)= 5 *(-5) = (-25%)

3. Year interaction: (11-12)(7-9)= (-1)*(-2) = 2%

4. Race-Year interaction: 11*[(6-7)-(4-9)] = 11*[(-1)-(-5)] = 11*4 = 44%

1940 1980

xb40 = 5.70 (6)

bb40 = 3.88 (4)

xb80 = 10.90 (11)

bb80 = 6.12 (6)

xw40 = 9.38 (9)

bw40 = 8.69 (9)

xw40 = 12.47

(12)

bw40 = 6.94 (7)

Bla

ckW

hit

e

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The Smith And Welch Story

• So, if black workers were treated like whites were in 1940, and years of ed. from 6 to 11, then black-white wage gap would have closed by 18%; this effect accounts for (.18/.75) = 13.5% of convergence

• But blacks were not treated like whites—they got less per year. Thus black ed. would have had to grow faster than white ed. to keep up. Did it? No, and we must adjust the main effect accordingly; (18-25)= -7%

• Also, white returns to ed. changed since 1940, so we must adjust for that; = 2%

• But the racial difference in returns declined by 4% points between 1940 and 1980, so we must give that relative improvement to black workers in 1980. This effect increased the relative black wage by 44%!

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What Is Going On In The Race-Yr Interaction Term?

• Smith and Welch argue that the large magnitude of race-year interaction is partly an error, but mostly represents improvements in school quality (so it should be added to the main effect)– If the decrease in racial difference of returns is due to an

increase in school quality, than this term is the measurement error on years

• Card and Kreuger argue that at most 20% of the race-year interaction (or 8.8% of overall improvement) can be attributed to improved educational quality– If the gain is due to a decrease in discrimination, then it is a

large decrease

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Table 12

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Table 13

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Table 14

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Table 15

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Table 16

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Table 19

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Table 20

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Migration’s Impact

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Table 29

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Table 30

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Smith And Welch’s Conclusions: The Good News

• Significant wage convergence from 1940-1980• Most of the convergence is due to 3 sources

– Improvements in education—accounts for 18-25+44 = 37% of convergence

– Migration—accounts for 15% of convergence– Civil Rights Legislation—accounts for between 0% and 44%

of convergence (though Smith and Welch seem to believe it is closer to 0%)

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Smith And Welch’s Conclusions: The Bad News

• Not much room left for migration to affect wages• Ib / Iw has stagnated since 1970 (not necessarily true through

1990’s); see Table 14• Historical trend of strong improvements among new entrants

reversed after 1980; see Table 15• Poverty has risen again• Growth slowed from 1970 through 1990 (1990’s saw “top

heavy” growth• Relative value of skill has increased• Opportunities for improvements in quality have diminished

– Migration to North

– Improvements in South

– Urban schools are failing