Heteroskedastic errors - example 1

hi there in this video I'm going to be talking about a specific example of heteroscedasticity so the example which I'm going to give here is going to be let's say we're interested in finding out how an individual's wage level depended on their level of education so we might estimate that there is some sort of linear relationship between the level of wages which an individual obtains and their level of education so we're expecting here that B 2 is greater than 0 so as an individual has a higher level of education they can expect to obtain on average a higher level of wage so let's say we have a whole sample of data on individuals education level and their wage low so let's say we expect that as an individual's level of education increases then they can expect to obtain a higher level of wage however as an individual sort of level as an individual's level of education increases that individual also has more choice in terms of how they spend their time perhaps that individual cares a lot about money or earning a lot of money to take care of their family so they choose to become an investment banker which means that given their level of education they actually obtain a sort of above average level of wages or perhaps that individuals really interested in teaching so they're going to become a university lecturer whereby they earn a significantly lower salary than they would have done if they became an investment banker so know if I was to estimate this above model here then perhaps that would mean that I should fit a straight line to my data which on average shows the effects of Education on wages so perhaps the slope of this line is unbiased but note that the distance of points from the line on average is increasing along with my education variable along with my independent variable so in this circumstance we have the case of heteroscedasticity well sort of writing that mathematic we have that the variance of our sort of error so the distance of points from the line is increasing along with our independent variable education so perhaps it's equal to some sort of number times the level of education so in this circumstance the variance is increasing with education and this is in contrary to the gauss-markov assumption of homoscedasticity Rian's of our errors given our independent variable education should be a constant so in this circumstance we know that least squared estimates are or aliskiren estimators are no longer blue in specific there are other linear unbiased estimators which we'll come on to discuss in the future things which we call weighted least squares or generalized least squares which are also unbiased and lumineer but are better they have a lower sampling variance so that means that more often than not they will get closer to the true population parameter B to P if we use those techniques on the sample so in this circumstance we can see that least-squared estimators are no longer best intuitively what's happening is that there is some sort of error structure here and it's a predictable error structure and because we are not taking into account they sort of extra information in our estimators that means that our estimators aren't as accurate as they could be or aren't as reliable as they could be if we did take into account this extra information note that because of this heteroscedasticity we don't necessarily have bias in our estimate of the effect of Education on wages because our line still in general goes through the sort of center of the points here written mathematically we still can sort of assume that the expectation of our error given our independent variable education is equal to 0 so as education increases I don't in general get a sort of either an upward bias or a downward bias in my errors so my least-squared estimators are still bias in this circumstance

Channel: Ben Lambert

Views: 103,156

Rating: 4.9667773 out of 5

Keywords: heteroskedasticity, Heteroscedasticity, homoskedasticity, gauss-markov

Id: QlP25vfW0AA

Length: 4min 30sec (270 seconds)

Published: Mon Jun 03 2013