Econ B: L11

Question 1

Give some examples of types of functional forms that may imply a non-linear relationship between y and x but not a non-linear model?

Answer 1

squared, interaction terms, logs (see slides 7->10)

Question 2

eg (cont. use)) Given wage(hat)=5+0.5educ:
What does this imply?
What are the 2 options around this?

Answer 2

Implies each additional year of education will increase wage by £0.5 but this i unrealistic (inc. returns to educ.)
2 options:
1) specify a non linear model (bad)
2) specify a linear model using logarithms (good!)

Question 3

eg) suppose % increase in wage is same given each additional year of education:
1) What is the regression equation for this?
2) How will β1 be interpreted?

Answer 3

1) log(wage) = β0 + β1educ +u
2) %∆wage ~=(100β1)∆educ

On average, holding all other factors fixed:
A one year change in educ leads to a (100β1)% change in wages.

Question 4

Steps to making a logarithmic model?

Answer 4

1) Define y=log(wage)

2) Mechanics of OLS are same tf just do same as usual

Question 5

What is a semi-elasticity model?

Answer 5

A log-level model; y is in log form and x is in level

Question 6

What is an elasticity model?

Answer 6

Log-log model: both sides are in logarithmic form

Question 7

Given an elasticity model, what will the interpretation of β1 be? (2)

Answer 7

Elasticity of y wrt x1
tf:
%∆y~=β1%∆x1

Question 8

What is a level-log model? What is the interpretation of it?

Answer 8

y is in normal form, x is in log form (ie. log(x)):

∆y~=(β1/100)%∆x

Question 9

3 advantages of taking logs?

Answer 9

1) when y > 0, models using log(y) as the dependent variable often satisfy the MLR assumptions more closely than models using the level of y.
2) Strictly positive variables often have conditional distributions that are heteroskedastic or skewed; taking the log can mitigate, if not eliminate, both problems.
3) Taking logs usually narrows the range of the variable, in some cases by a considerable amount. This makes estimates less sensitive to outlying (or extreme) observations on the dependent or independent variables.

Question 10

2 standard examples where you may take logs?

Answer 10

1) If positive monetary amount (can’t have -ve pounds)

2) If large integer values (eg. pop)

Question 11

What form do variables in years normally appear in?

Answer 11

Their original form

Question 12

A variable that is a proportion or a percent can appear in either original or logarithmic form, although there is a tendency to use them in level form. Why?

Answer 12

any regression coefficients involving the original variable whether it is the dependent or independent variable will have a percentage point change interpretation

Question 13

Difference between percentage point change and percentage change?

Answer 13

eg) if U goes from 8% to 9% this is an increase of one percentage point
But a 12.5% increase from the initial U level (see slides)
using logs means we are looking at % change in U rate

Question 14

2 limitations of logs?

Answer 14

1) can’t be used if a variable takes on zero/negative values

2) If log is on dependent variable can be more effort to predict/transform it back to the original variable

Question 15

Note:

Answer 15

Not legitimate to compare R^2s from models where y is DV in one and log(y) is DV in other; measures explain variations in different variables!

Question 16

When could you use logs on a variable that includes 0 (non-negative)? What would the interpretation be? When would this not be suitable to do?

Answer 16

If you did log(1+y); interpretations are the same except for at y=0 it is undefined. Not suitable if data on y are dominated by 0s!