Stem and Leaf Diagrams © Christine Crisp “Teach A Level Maths” Statistics 1.
Why you should study maths (and science and computing) at ...How does studying maths, science and...
Transcript of Why you should study maths (and science and computing) at ...How does studying maths, science and...
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Why you should study maths (and science andcomputing) at A-level
Martin O’ConnellInstitute for Fiscal Studies
July 2013
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Why choose A-level maths?
Opens lots of job opportunities ...
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Why choose A-level maths?
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Why choose A-level maths?
Could do many other jobs ... like working as an economist
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What is economics?
• Seeks to explain how individuals, businesses and governmentsmake decisions
• Why was the Samsung Galaxy S4 launch price £600? Why isit now £400?
• Why does government try to influence what we eat? What isthe most effective way of doing this?
• Uses maths to build theories about how people act
• And statistics to test and quantify these theories
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How does studying maths, science and computing (STEM)A-levels affect future earnings?
• Is taking more STEM A-levels correlated with higher wages?
• Do people who take STEM A-levels have higher wages onaverage?
• What happens when we control for other factors?• What is the magnitude of the effect?
• Can we pin down the causal effect?
• How will your future wages compare with what they wouldhave been if you took one less STEM A-level
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How does studying maths, science and computing (STEM)A-levels affect future earnings?
• Is taking more STEM A-levels correlated with higher wages?
• Do people who take STEM A-levels have higher wages onaverage?
• What happens when we control for other factors?• What is the magnitude of the effect?
• Can we pin down the causal effect?
• How will your future wages compare with what they wouldhave been if you took one less STEM A-level
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How does studying maths, science and computing (STEM)A-levels affect future earnings?
• Is taking more STEM A-levels correlated with higher wages?
• Do people who take STEM A-levels have higher wages onaverage?
• What happens when we control for other factors?• What is the magnitude of the effect?
• Can we pin down the causal effect?
• How will your future wages compare with what they wouldhave been if you took one less STEM A-level
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What does economic theory say?
• Employers are willing to pay productive workers more
• Taking STEM A-levels may
• Provide skills that makes someone who studies them moreproductive
• And may be a way of signalling to employers that you possessanalytical skills that will make you a productive worker
• In either case, we would expect taking STEM A-levels to beassociated with higher wages
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Testing the theory
• Is there evidence for this?
• And if so, how much more pay is associated with doing onemore STEM A-level?
• We want to know:
d logw
dSTEM= % increase in wage from doing one more STEM A-level
the marginal return to a STEM A-level (MR-STEM)
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Estimating MR-STEM
• Use data set on 956 people who studied A-levels
• Has information on:
• How many STEM and non-STEM A-levels they studied• Their weekly earnings at age 30• Other characteristics
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Estimating MR-STEM
Mathematical model:
logw = α + βSTEM
Stastistical model:
logw = α + βSTEM + u
Aim is to know numerical value of β
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Estimating MR-STEM
Mathematical model:
logw = α + βSTEM
Stastistical model:
logw = α + βSTEM + u
Aim is to know numerical value of β
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Relationship between STEM A-levels and wages
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Relationship between STEM A-levels and wages
l̂ogw = 5.94 + 0.13STEM
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Relationship between STEM A-levels and wages
• So on average doing 1 more STEM A-level is associated withwages at age 30 that are 13% higher
• Does this mean for every STEM A-level you do you canexpect to earn 13% more at age 30? ...
• No!
• People who take STEM A-levels may have othercharacteristics that lead them to earn more
• For instance they may also tend to take more non-STEMA-levels
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Relationship between STEM A-levels and wages
• So on average doing 1 more STEM A-level is associated withwages at age 30 that are 13% higher
• Does this mean for every STEM A-level you do you canexpect to earn 13% more at age 30? ...
• No!
• People who take STEM A-levels may have othercharacteristics that lead them to earn more
• For instance they may also tend to take more non-STEMA-levels
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Correlation vs. causation
• Most statistical analysis done by economists tries to separateout causality from correlations
• But this is much harder in economics than in the sciences
• Scientists can run controlled experiments in laboratoryconditions
• But in economics
• Experiments are very rare• So instead we need to use statistics to control for other factors
that may affect the outcome of interest
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Causal relationship between STEM A-levels and wages
• We need to control for other factors which
• Affect wages• And may differ among people who study different numbers of
STEM A-levels
• For instance
• Number of non-STEM A-levels• Whether they obtained a degree• Gender, region• And ability ...
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The ability problem
• Smart people may be more likely to select STEM A-levels
• And they may be more likely to get high paid jobs becausethey are smart
• So we risk mistaking the causal channel from ability to wages,for the causal channel from taking STEM A-levels to wages
• How can we control for ability ... ?
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The ability problem
We can control for people’s test scores when they were younger
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Estimating MR-STEM II
Mathematical model:
logw = α+βSTEM + γ1non STEM + γ2degree + γ3gender+
γ4region + γ5ability
Stastistical model:
logw = α+βSTEM + γ1non STEM + γ2degree + γ3gender+
γ4region + γ5ability + u
Now β tells us % increase in wages associated with one moreSTEM A-level, holding non STEM - ability constant
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Estimating MR-STEM II
Mathematical model:
logw = α+βSTEM + γ1non STEM + γ2degree + γ3gender+
γ4region + γ5ability
Stastistical model:
logw = α+βSTEM + γ1non STEM + γ2degree + γ3gender+
γ4region + γ5ability + u
Now β tells us % increase in wages associated with one moreSTEM A-level, holding non STEM - ability constant
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The answer
After doing this we get:β = 0.09
If two groups of people have the same number of non-STEMA-levels, degree status, gender, live in the same region, and got thesame test scores aged 10 ...... but one group did one more STEM A-level ...... on average their wage at age 30 would be 9% higher
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The answer
After doing this we get:β = 0.09
If two groups of people have the same number of non-STEMA-levels, degree status, gender, live in the same region, and got thesame test scores aged 10 ...
... but one group did one more STEM A-level ...
... on average their wage at age 30 would be 9% higher
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The answer
After doing this we get:β = 0.09
If two groups of people have the same number of non-STEMA-levels, degree status, gender, live in the same region, and got thesame test scores aged 10 ...... but one group did one more STEM A-level ...
... on average their wage at age 30 would be 9% higher
![Page 27: Why you should study maths (and science and computing) at ...How does studying maths, science and computing (STEM) A-levels a ect future earnings? Is taking more STEM A-levels correlated](https://reader034.fdocuments.in/reader034/viewer/2022050315/5f77a204ce80c3032e3403e1/html5/thumbnails/27.jpg)
The answer
After doing this we get:β = 0.09
If two groups of people have the same number of non-STEMA-levels, degree status, gender, live in the same region, and got thesame test scores aged 10 ...... but one group did one more STEM A-level ...... on average their wage at age 30 would be 9% higher
![Page 28: Why you should study maths (and science and computing) at ...How does studying maths, science and computing (STEM) A-levels a ect future earnings? Is taking more STEM A-levels correlated](https://reader034.fdocuments.in/reader034/viewer/2022050315/5f77a204ce80c3032e3403e1/html5/thumbnails/28.jpg)
Conclusive proof that each STEM A-level will earn you 9%more by age 30?
• More like evidence of an effect around this size
• Economists will always argue about empirical findings (part ofwhat makes it fun!)
• Here we might ask
• Is relationship between STEM A-levels and wages really linear?• What about the influence of school and/or parents?
• But evidence that studying maths is likely to result in higherearnings is very strong
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Conclusive proof that each STEM A-level will earn you 9%more by age 30?
• More like evidence of an effect around this size
• Economists will always argue about empirical findings (part ofwhat makes it fun!)
• Here we might ask
• Is relationship between STEM A-levels and wages really linear?• What about the influence of school and/or parents?
• But evidence that studying maths is likely to result in higherearnings is very strong
![Page 30: Why you should study maths (and science and computing) at ...How does studying maths, science and computing (STEM) A-levels a ect future earnings? Is taking more STEM A-levels correlated](https://reader034.fdocuments.in/reader034/viewer/2022050315/5f77a204ce80c3032e3403e1/html5/thumbnails/30.jpg)
Conclusive proof that each STEM A-level will earn you 9%more by age 30?
• More like evidence of an effect around this size
• Economists will always argue about empirical findings (part ofwhat makes it fun!)
• Here we might ask
• Is relationship between STEM A-levels and wages really linear?• What about the influence of school and/or parents?
• But evidence that studying maths is likely to result in higherearnings is very strong
![Page 31: Why you should study maths (and science and computing) at ...How does studying maths, science and computing (STEM) A-levels a ect future earnings? Is taking more STEM A-levels correlated](https://reader034.fdocuments.in/reader034/viewer/2022050315/5f77a204ce80c3032e3403e1/html5/thumbnails/31.jpg)
So why choose A-level maths?
• It opens lots of interesting careers paths (without closing anyoff)
• And it is very likely to lead you to earn more money!
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So why choose A-level maths?
• It opens lots of interesting careers paths (without closing anyoff)
• And it is very likely to lead you to earn more money!