Sat 28 Dec, 2019 08:45 am
Let’s say we have a true model for health that goes h=c+bw+ci+u where w is weight and i is income. Now this means that holding weight constant a one unit change in income on average causes a c unit change in health. Now let’s assume income and weight are correlated. We we regress health on only income we will get a larger coefficient estimate. Now this is generally referred to as omitted variable bias. But I don’t see where the bias is. Isn’t the coefficient just larger because we are not holding weight constant? Isn’t this model just as valid?
Let's say that income and weight are loosely correlated but not strongly correlated. The bias comes in because some of the effect that should be assigned to weight will be assigned to income instead making it look like a stronger influence than it really is. If income and weight are very strongly correlated, then you can't tell if the effect is weight or income.
I do know there is a strong correlation between height and income. In 2007 an inch of height was worth about $789 in annual income.
I assume there is some correlation between height and weight.