national replication vs. regional replication ---- how reliable is the ols-based evidence of college...
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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 2011
huge 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
WHY
Variable 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
02
04
06
08
01
00
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
02
04
06
08
0
Primary LowerS UpperS Higher
East
02
04
06
08
0
Primary LowerS UpperS Higher
South Central
02
04
06
08
0
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.
02
04
06
08
0
Primary LowerS UpperS Higher
Northeast0
20
40
60
80
Primary LowerS UpperS Higher
North
02
04
06
08
0
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.
WHY
Industrial Structure?
Market openness?
Over college-oriented high school education?
02
04
06
0
Primary LowerS UpperS Higher
Northwest0
20
40
60
80
Primary LowerS UpperS Higher
Southwest0
20
40
60
80
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
Hint
These 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 (Replication)
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.