u.s. wages and salaries, a decomposition of wage and...

Outline_USA_7898_Rev.ppt 1

U.S. Wages and Salaries, A Decomposition of Wage and

Industry Effects: 1978, 1988, & 1998

Stephen Cooke8 October 2004

Dept. of Ag . & Resource Ec. SeminarUC Berkeley


Summary Slide

• Problem Definition• Literature review• The Theory• Results and Interpretation• Summary and Conclusions


Problem Definition


Per Worker and Per Capita Payments and Growth in U.S.: 1978, 1988, and 1998 (cpi 1998=100)

133,070113,42994,330Employment (thous.)

$ 18,189$ 16,522$ 15,353Per capita net

earnings

$ 5,147$ 4,559$ 2,890

Per capita dividends, interest and rent

$ 23,335$ 21,081$ 18,245Per capita total

199819881978Payments

$ 31,411 $ 29,666 $ 29,569 Per worker wages and

salaries


Per Worker and Per Capita Payments and Growth in U.S.: 1978, 1988, and 1998 (cpi 1998=100)

34.4%16.0%18.4%Employment

17.0%9.6%7.3%Per capita net earnings

1978/981988/981978/88Growth

24.6%10.2%14.5%Per capita total

57.7%12.1%45.6%Per capita dividends,

interest and rent

6.04%5.72%0.33%Per worker wages and

salaries


Per Worker Wages and Salaries in U.S.: 1978, 1998, and 1998 (cpi 1998=100)

6.04%5.72%0.33%Per worker wages

and salaries

1978/981988/981978/88Growth

80%92%53%Paired t-test, 1 tail

757575N (no. of sectors)

199819881978Payment

.079.071.058Thiel T’

1.811.430.24Skewness

$ 18,314$ 15,974$ 11,566Standard dev.

$ 31,411 $

29,666 $ 29,569 Per worker wages

and salaries


Table Determining the Source of Lower Wages

worst casePower and

BarrettLow wages

conventionalwisdom“past”High wages

Low paying industries

High paying industries

Explanations for low wages


Interpreting the Wage &Industry Effects

• Wage effect– Movement of high

quality factors toward or away from a region

– Solow (convergence)– Romer & Lucas

(divergence)

• Industry effect– Movement of high

value industries toward or away from a region

– Heckscher-Ohlin(convergence)

– Krugman (divergence)


Growth and Trade Policies

• If wage effect is negative, then– Increase investment in physical and human

capital, e.g., education and technology – Primary factors policies (labor vs capital?)

• If industry effect is negative, then– Increase competitive advantage by improving

local resources and institutions – Place policies (urban vs rural?)


Literature Review


Hamermesh, Daniel S. and Grant, James.• "Econometric Studies of Labor-Labor Substitution and Their Implications for

Policy." Journal of Human Resources, 1979, 14(4), pp. 518-42.

• Physical and human capital are complements and are jointly substitutable with raw labor.

• Future research should concentrate on substitution among workers


Bluestone, Barry and Harrison, Bennett

• "The Growth of Low-Wage Employment: 1963-86." American Economic Review., 1988, 78(2 (May)), pp. 124-28.

• The data suggest a rising low-wage share and growing wage polarization, at least after 1979. – The decline in unionization– The erosion in the real value of the minimum wage– The widespread existence of wage concession bargaining– Two-tier wage structures in a number of large industries. – The growing business practice of "outsourcing" to achieve

lower labor costs– The secular shift of capital from directly productive to overtly

speculative investment


Krueger, Alan B. and Summers, Lawrence H.

• "Efficiency Wages and the Inter-Industry Wage Structure." Econometrica: Journal of the Econometric Society, 1988, 56(2), pp. 259-93.

• Empirically tests and rejects classical competitive theories of wage determination by examining differences in wages for equally skilled workers across industries.

• These findings suggest that workers in high wage industries receive noncompetitive rents.


Bound, John and Johnson, George• "Changes in the Structure of Wages in the 1980's: An Evaluation

of Alternative Explanations." American Economic Review, 1992, 82(3), pp. 371-91.

• During the 1980's, there were large changes in the structure of relative wages, most notably a huge increase in the relative wages of highly educated workers.

• Our conclusion is that their major cause was a shift in the skill structure of labor demand brought about by biased technological change


DiNardo, John; Fortin, Nicole M. and Lemieux, Thomas.

• "Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach." Econometrica: Journal of the Econometric Society, 1996, 64(5), pp. 1001-44.

• de-unionization and supply and demand shocks were important factors in explaining the rise in wage inequality from 1979 to 1988.

• The decline in the real value of the minimum wage explains a substantial proportion of this increase in wage inequality, particularly for women.


Valletta, Robert G.

• "Effects of Industry Employment Shifts on U.S. Wage Structure,1979-1995." Federal Reserve Bank of San Francisco Economic Review, 1997, 1, pp. 16-32.

• Earlier analyses revealed that average earnings are lower, and earnings inequality is higher for service-producing workers than for goods-producing workers.

• During the period 1979–1995 the results show at most a small effect of industry employment shifts on growing inequality in male hourly earnings.


Calmon, Paulo Du Pin; Conceicao, Pedro; Galbraith, James K.; Cantu, Vidal Garza and Hibert, Abel.

• "The Evolution of Industrial Earnings Inequality in Mexico and Brazil." Rev Development Economics, 2000, 4(2), pp. 194-203.

• Mexico and Brazil show increases in wage dispersion over time, and a strong negative correlation is found with the rate of real economic growth.


The Theory


Hanna and LaCroixWage and Industry Indices

0101

1010

1111

0000

nnnn

nnnn

nnnn

nnnn

NWNWNWNWNWNWNWNW

=•

=•

=•

=•00

01

10

11

_

_

nn

nn

nn

nn

NWNWWageLaCroix

NWNW

WageHanna

=

=

01

11

00

10

_

_

nn

nn

nn

nn

NWNWIndustryLaCroix

NWNWIndustryHanna

=

=


Hanna and La Croix Wage Indices

0W 1W

)( iWf

0E

1EA

B

E

iW 1−iW

)( 1/iWf

E

0E

1E

C

D

0W 1W

)( iWf

)( 0/iWf


Contradictory Results

• For both Hanna and La Croix indices:(Wage index)( Industry index) = Total index

• Hanna total index = La Croix total index• However:

Hanna wage index ≠ La Croix wage indexHanna industry index ≠ La Croix industry index

• Sometimes they are contradictory!• Needed: a consistent and defensible wage index


Avg. wages as a function ofavg. sector wages

AB

0E

1E

0W 1W

)( iWf

iW 1−iW

1iW

D

C

F

0iWW


Wage index derivation• Assume a continuous, twice-differentiable, concave

quadratic average wage function in which the region’s industrial structure is constantW = Σi(ai0 + ai1wi - ai2wi

2) • This functional form implies that skilled and less skilled

labor are imperfect substitutes in all industries. • Then apply a second-order Taylor series expansion to

W=f(wi)• Adapt Shepherd's lemma in which the 1st derivative of

a logarithmic Cobb-Douglas cost function equals the factor share

• Diewert’s quadratic lemma: the geometric mean of two 1st order approximations equals a second order measure


Wage decomposition equation andthe Theil inequality index (T’)

Total effect = wage effect + industry effect

)1ln()/(ln)(½)/ln( 011001 µ+++=∑ iii

ii wwssWW

( )∑=i

ii WwsT ln'

W: avg. overall wage/jobw: avg. sector wage/job s: share sector’s wage billu: industry effect i: sector; time: 0..1

Theil inequality index (T’)


jW1

01W

*11W1

1W

11W*0

1W jn

jj WWW ...| 21

0E

A

1E

0E 1E

*1E

Wage and Industry Effects as Substitution and Output Effects

E0E1: Total effect (+)

E0A: Wage Effect (+)

AE1: Industry Effect (-)


Change in the Theil Inequality index (overall between sectors, T’ and wage effect, TF’)

w,/W: ratio of avg. sector wage per job to overall average

ni: ratio of labor in sector i to overall labor

i sectors; time 0..1T ∈ {0, log(n)}Conceicao & Galbraith,

2000, pp. 65, 68

( ) ( )

( ) ( )∑

∑

++=

++=

•

•••

i i

iii

i

iiii

iiiiiiii

Ww

WwWwnWwn

nnnWwWwT

WwnWwnnWwWwT

ii 0

10111

0

1011'

'

)(

)(log)()log(log)log()(

)()log()log()(_)5(

( )

( )∑

∑

+=

+=

•

••

i i

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Ww

WwWwWwnT

WwWwnT

0

1011

'

'

)(

)(log)(1)log(

)(1)log(_)13(

Theil (T’) effect = industry + wage effects

Theil wage effect (TF’)


Results and Interpretation: U.S. Wages and Salaries


U.S. Wages and Salaries (cpi 1998=100)

$92-$38$130

$87-$18$105

$5-$20$25

A. diff. W/J

$12,255,497,700$31,4116.04%Total-$5,010,139,942$31,411-2.37%Industry$17,265,637,642$32,1648.41%Wage

$29,56940.0%cpi$11,8280.0%1998/78

$11,611,059,709$31,4115.72%Total-$2,393,457,563$31,411-1.14%Industry$14,004,517,272$31,7716.85%Wage

$29,66672.6%cpi$21,5310.0%1998/88

$549,319,582$29,6660.33%Total-$2,314,081,551$29,666-1.37%Industry$2,863,401,134$30,0741.69%Wage

$29,56940.0%cpi$11,8280.00%1988/78

A. Changein W

real avg.W/J

growth rate

Year/index


U.S. Wage & Salaries Wage and TheilIndices: 1978 to 1998

Wage decomposition (%)6.05.70.3T-effect

Theil inequality index (T’ between industries only)-2.4-1.1-1.4I-effect8.46.81.7W-effect

.016.007.012T’-total

-.033-.014-.019T’-industry.049.021.031T’-wage

1998/781998/881988/78Index


The Fat Epidemic: He says it’s an illusion

• Dr. Jeffrey Friedman (Rockefeller U.)– Obesity researcher at Howard Hughes Medical

Institute– “national data do not show Americans growing

uniformly fatter” (NYT 6/8/04, p. D5)– “from 1991 to present … the lower end of the weight

distribution, nothing has changed, not even by a few pounds … only the massively obese, the very top of the distribution is there a substantial increase in weight, about 25 to 30 pounds”


Wage Effects on Avg. Wages

• An across the board proportionate change in wages per job (sign - or +) regardless of the distribution

iS

iW iW

iS

1W 0W 0W 1W


Negative Industry Effects Cause a Decrease in the Mean

C. Low value industries that expand (↑)(L) = (+)( -)

(skewed to the right, µ3 > 0)

D. High value industries that contract(↓)(H) = (-)(+)

iS

iW1W 0W

iS

iW1W 0W


1978 U.S. Frequency of Jobs by Wage (cpi 1998=100)

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

14,000,000

$61,

671

$51,

403

$47,

554

$44,

406

$43,

488

$40,

273

$38,

912

$36,

613

$35,

007

$33,

171

$29,

849

$28,

230

$26,

338

$25,

608

$24,

422

$21,

059

$19,

792

$18,

115

$14,

253

Wage/job/year

# of

jobs


1978 U.S. Frequency of Jobs by Wage (cpi 1998=100)

0

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

12,000,000

14,000,000

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Wage/job/year

# of

jobs


1978 Frequency of jobs by salary(cpi 1998=100)

05,000,000

10,000,00015,000,00020,000,00025,000,00030,000,00035,000,00040,000,00045,000,00050,000,000

$10,

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$15,

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$20,

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$25,

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$30,

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$40,

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$45,

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$50,

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$55,

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$60,

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$65,

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$70,

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$150

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Wage/job/year

# of

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1978


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)2

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πσ

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hpdfGaussian

Silverman, B. W. Density Estimation for Statistics and Data Analysis. 1986


Summary and Conclusions


Summary• I developed a CES average wage function

– Derived 2nd order approximation using Taylor series– CES is exact

• Industry effect seems more important than it is because the wageeffect has industry effect characteristics– Technology bias– Substitution of skilled for unskilled labor and vice versa within industries– High skill – high wage industries becoming more or less so

compounds the perception of actual industry effect

• Thiel index shows that the negative industry effect can result in greater wage equality and conversely for the wage effect


Table Determining the Source of Wage Change

worst casePower and

BarrettLow wages

conventionalwisdom“past”High wages

Low paying industries

High paying industries

Explanations for low wages


Growth and Trade Policies

• If industry effect is negative, then– Increase competitive advantage by improving

local resources and institutions – Place policies (urban vs rural?)


References• Conceicao, Pedro and Galbraith, James K. "Constructing Long and

Dense Time-Series of Inequality Using the Theil Index." Eastern Economic Journal, 2000, 26(1), pp. 61.

• Cooke, Stephen “Wage and Industry Effects in U.S. Regional Income, 1840 to 1987: A CES Wage Index Method” J. of Econ. History 63(2003): 1131-1146.

• Diewert, W. E., “Exact and Superlative Index Numbers” Journal of Econometrics 4(May):115-45, 1976.

• Hanna, Frank. “Contribution of Manufacturing Wages to Differences in per capita Income.” Review of Economics and Statistics 33(Feb. 1951): 18-28.

• La Croix, Sumner. “Economic Integration and Convergence: A Second Decomposition Method” J. of Econ. History 59(1999): 773-785.

• Silverman, B. W. Density Estimation for Statistics and Data Analysis. London; New York: Chapman and Hall, 1986.

• Theil, Henri. Economics and Information Theory. Chicago,: Rand McNally, 1967.

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