National Replication vs. Regional Replication ---- How Reliable is the OLS-Based Evidence of College Wage Premium?

Haogen Yao, Steve SimpsonTeachers College, Columbia University

Sui Yang, Shi LiBeijing Normal University

38% of the world’s tertiary graduates 33% of the world’s GDP in 2011huge diversities within the 2 nations

The Studies Replicated

The Race between Education and Technology (Goldin and Katz, 2008)

Summary: Apply the basic regression and aggregated indicators (yearly-national level) to find that the relative lag of college graduate supply is the main reason of expanding wage premium.

Universal high school and mass higher education (Wang, 2009)

Summary: Use extended Mincer earning function and the Chinese Census data to find a very high marginal return to higher education for both urban and rural populations.

Problem statement: We know OLS is problematic. Before applying advance methods like IV and RD, maybe we should firstly ask HOW reliable (unreliable) the OLS-based evidences are? Here is a straightforward answer relying on large-scale datasets: regional replication.

The Implementation

Wang (2009)Data. 1% sample of the 2005 Chinese CensusMethod. Includes variables indicating the lengths of 4 levels of education, with individual characteristics and provincial dummies controlled

Our ReplicationData. 20% resampling of the 1% sampleMethod. The same regression with the same set of variables/ But not sure if they are constructed in identical way/ Replication for the nation and the six administrative divisions

Goldin and Katz (2008)Data. Yearly CPS and Census (when available) data, 1915-2005Method. Regress the college-high school wage premium (log ratio) on relative supply, with institutional factors and time trends controlled

Our ReplicationData. Same for national replication, but 1976-2010 CPS for regional replication b/c previous data are inappropriateMethod. while the original one weighed data by gender, race and experience, we use personal weight but control these 3 factors in regression/ Use the national equation to predict regional premium

The United State

.3.4

.5.6

.7.8

1920 1940 1960 1980 2000year

Actual Premium Predicted Premium

Figure 1. College Wage Premium for the US

Result from Goldin and Katz (2008)

Our Result

.2.4

.6.8

1970 1980 1990 2000 2010

Wage Premium for Pacific

.3.4

.5.6

.7.8

1970 1980 1990 2000 2010

Wage Premium for Middle Atlantic.3

.4.5

.6.7

.8

1970 1980 1990 2000 2010

Wage Premium for East North Central

.2.4

.6.8

1970 1980 1990 2000 2010

Wage Premium for Mountain

The Model Works for 52% of the US Population

.3.4

.5.6

.7.8

1970 1980 1990 2000 2010year

Actual Premium for the US Actual Premium for the RegionPredicted Premium for the Region

Figure 5. Wage Premium for West North Central

.3.4

.5.6

.7.8

1970 1980 1990 2000 2010

Wage Premium for West North Central

.4.5

.6.7

.8.9

1970 1980 1990 2000 2010

Wage Premium for South Atlantic

THE DIFFERENCERelatively optimistic actual premiums evolutions for WNC and SA, and the predicted ones are even more optimistic

.3.4

.5.6

.7.8

1970 1980 1990 2000 2010year

Actual Premium for the US Actual Premium for the RegionPredicted Premium for the Region

Figure 5. Wage Premium for West North Central

WHYVariable Construction?

Omitted Variable?

.2.4

.6.8

1970 1980 1990 2000 2010

Wage Premium for New England

.4.6

.81

1970 1980 1990 2000 2010

Wage Premium for East South Central

.4.6

.81

1970 1980 1990 2000 2010

Wage Premium for West South Central

.3.4

.5.6

.7.8

1970 1980 1990 2000 2010year

Actual Premium for the US Actual Premium for the RegionPredicted Premium for the Region

Figure 5. Wage Premium for West North Central

THE DIFFERENCE: Quite obvious…

WHYThe quality of “supply” variable? Industrial structure? Path dependency? SES?

Yes fixed-effect can close the gap between lines, but it gives an elasticity of substitution between skilled and unskilled as high as 9, much higher than the suggested one of 1.4

China

020

4060

80

Primary LowerS UpperS HigherAttainment (assuming the same yearly return within a level)

Urban Accumulated Rural AccumulatedUrban Marginal Rural Marginal

Return to Education in China (%) by Replication

020

4060

8010

0

Primary LowerS UpperS Higher

Return to Education in China (%) by Wang

lower estimates

Larger gap of return to higher education

Lower marginal return of higher education, BUT still can tell it is big

Our data does not allow for a strict classification of rural/urban population. Our urban group contains rural residents that may drag the estimates down

Pretty high marginal return of higher education

020

4060

80

Primary LowerS UpperS Higher

East

020

4060

80

Primary LowerS UpperS Higher

South Central

020

4060

80

Primary LowerS UpperS Higher

Urban Accumulated Rural AccumulatedUrban Marginal Rural Marginal

South Central

Similar shapes are found for East and South Central. About 57% of the Chinese population live in these two regions.

020

4060

80

Primary LowerS UpperS Higher

Northeast0

2040

6080

Primary LowerS UpperS Higher

North

020

4060

80

Primary LowerS UpperS Higher

Urban Accumulated Rural AccumulatedUrban Marginal Rural Marginal

South Central

THE DIFFERENCELow overall returnsUpper secondary education looks too “risky” to the rural Northeast: Those entered college gain big, while losers swallow the pain of 3-years cost with no human capital accumulation.

WHYIndustrial Structure?

Market openness?

Over college-oriented high school education?

020

4060

Primary LowerS UpperS Higher

Northwest0

2040

6080

Primary LowerS UpperS Higher

Southwest0

2040

6080

Primary LowerS UpperS Higher

Urban Accumulated Rural AccumulatedUrban Marginal Rural Marginal

South Central

THE DIFFERENCENo strong marginal return to higher education. And it seems for Northwest the priority should be lower secondary education

HintThese are the real RURAL China

-20

24

Primary LowerS UpperS Higher

North NortheastEast South CentralSouthwest Northwest

Marginal Returns (%) for Rural China

-10

12

34

Primary LowerS UpperS Higher

North NortheastEast South CentralSouthwest Northwest

Marginal Returns (%) for Urban China

Closer look at the marginal returns

The low return to upper secondary education is as eye-popping as the high return to higher education

02

46

8

Primary LowerS UpperS Higher

Urban (Wang) Rural (Wang)Urban (Replication) Rural (Repl ication)

Marginal Return (%) for China

To Sum Up The study is simple and straightforward-- Firstly have a national replication to make

sure we get results similar to the original study’s, then compare them to regional results. By looking at the nation-region disparities, we are able to assess the OLS-based evidence of college wage premium.

GK(2008) and Wang(2009) advocate mess higher education, but our replications caution on this suggestion. Even assuming the OLS results are enough for causal identification, mess higher education may only benefit half of the population for both countries. Since we are unable to perfectly replicate the two studies, the best way to clear up the worry is regional replication from the authors.