National open university of nigeria introduction to econometrics I eco 355

3.3. Examples of a Relationship in Econometrics 
A simple example of a relationship in econometrics from the field of labor economics is: 
This example assumes that the natural logarithm of a person's wage is a linear function of 
the number of years of education that person has acquired. The parameter 
measures 
the increase in the natural log of the wage attributable to one more year of education. The 
term is a random variable representing all other factors that may have direct influence 
on wage. The econometric goal is to estimate the parameters, 
under specific 
assumptions about the random variable . For example, if is uncorrelated with years of 
education, then the equation can be estimated with ordinary least squares. 
If the researcher could randomly assign people to different levels of education, the data 
set thus generated would allow estimation of the effect of changes in years of education 
on wages. In reality, those experiments cannot be conducted. Instead, the econometrician 
observes the years of education of and the wages paid to people who differ along many 
dimensions. Given this kind of data, the estimated coefficient on Years of Education in 
the equation above reflects both the effect of education on wages and the effect of other 
variables on wages, if those other variables were correlated with education. For example, 
people born in certain places may have higher wages and higher levels of education. 
Unless the econometrician controls for place of birth in the above equation, the effect of 
birthplace on wages may be falsely attributed to the effect of education on wages. 
The most obvious way to control for birthplace is to include a measure of the effect of 
birthplace in the equation above. Exclusion of birthplace, together with the assumption 
that is uncorrelated with education produces a misspecified model. Another technique is 
to include in the equation additional set of measured covariates which are not 
instrumental variables, yet render 
identifiable. An overview of econometric methods 
used to study this problem was provided by Card (1999). 

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