Summary
Summary Applied Microeconometrics (FEM11087)
- Course
- Institution
Notes from AME's knowledge clips, lectures and exercise lectures.
[Show more]
Seller
Follow
lauraakkermans2000
Reviews received
Content preview
fMODULE 1: LINEAR REGRESSION MODELSIntroduction to empirical methods: linear regression models
1. Introduction: linear regression model
- Empirical analysis
> Use data
Test a theory
Estimate relationship between variables
> First step is to clearly define your research question
Economic model
Intuitive and less formal reasoning (observation & existing scientific evidence)
- Single regression model
> We have two variables, y and x
We are interested in ‘explaining y in terms of x’ or ‘how y varies with changes in x’
For example: House prices and average income in a neighbourhood
- How does the average house prices in a neighbourhood changes when income changes
Positive association. Formula:
- Ceteris paribus relationship
> Simple linear regression model:
> Ceteris paribus = other factors held fixed
> If the factors in u are held fixed:
- Zero conditional mean assumption (gives another useful interpretation)
E(u|x) = E(u) = 0
For example:
What is the expected value of y, for a given value of x ^^
1
,Keep asking yourself…
- Can we draw ceteris paribus conclusions about how x affects y in our example?
> We need to assume E(u|x) = E(u) = 0
>> Zero conditional mean assumption
>> What does it mean in our example?
>>> Assume u is the same as amenities
>>> Then, amenities are the same regardless of average income
*E(amenities | income = 10,000) = E(amenities | income = 100,000)
Means: amenities (voorzieningen) is same regardless incomes
* If we think that the amount and quality of amenities is different in
richer than in poorer neighbourhoods then previous assumption
does not hold
* We cannot observe u, so we have no way of knowing whether or not
amenities are the same for all levels of x
2. Estimation and interpretation
- Given graph: each dot is a neighbourhood, positively related
- Estimate by ordinary least square estimates (OLS)
> Select a random sample of the population of interest
Using stata to add the values
> In stata
Income was in 1000 €, when average income increases by 1000, the average
houseprice increases by about 16000 €, ceteris paribus
Output tell us that expected houseprice = equal to -95000 when the income is 0
Does not make sense, cause we do not have negative prices but that is
cause income can not be 0 (> this way good interpretation)
2
,- Multiple regression model
> Difficult to draw ceteris paribus conclusions using simple regression analysis
is 2nd cp? Depends; if error is not correlated
> Multiple regression model:
> Multiple regression analysis allows us to control for many other factors that
simultaneously affect the dependent variable (better predictions also)
3. OLS assumptions for unbiasedness
- Unbiasedness of OLS = Expected value of estimator = population parameter
- Assumptions needed:
MLR1: Linear in parameters
MLR2: Random sampling
MLR3: No perfect collinearity
MLR4: Zero conditional mean, i.e., E(u|x)=0
> Assumption MLR1: Linearity in parameters
> Assumption MLR2: Random sampling
* We have a random sample of size n, following the population model
* If sample is not random, selection bias
> Assumption MLR3: No perfect collinearity = no perfect linear relationships
* In the sample (and therefore in the population):
None of the independent variables is constant, and
There are no exact linear relationships among the independent variables
Example:
3
, Perfect collinearity
- Estimation simply does not work
- Some softwares give error message and no/strange results
- Stata drops one variable automatically/arbitrarily and then estimates a
model that does not suffer from this problem:
But it may not be the variable you would prefer to drop, so i) start by
defining model properly and, only then, ii) estimate it
Imperfect collinearity
- Model works but is problematic, imprecise estimates
- Beware of x’s with high correlation
- Symptoms of imperfect collinearity (for example, between x1 & x2):
Big F-stat (x1, x2 jointly significant) but
small t-statistics (for example x1 and x2 individually insignificant)
> Assumption MLR4: Zero conditional mean (important and complicated)
Next step is to do hypothesis testing: do we need additional assumptions to do inference?
YES:
4. Assumptions for inference (gevolgtrekking/conclusie)
- Inference - hypothesis testing
> We make two additional assumptions:
MLR5: Homoskedasticity
MLR6: Normality
> MLR1 - MLR6: OLS estimator is the minimum variance unbiased estimator
- Assumption MLR5: homoskedasticity
> Variance of error term is the same regardless of the values of the independent
Variables:
> Importance of error term same for all individuals
> Magnitude of uncertainty in the outcome of y is the same at all levels of x’s
Example: in which figure is the homoskedasticy assumption most likely to be satisfied?
B less variation for small x, more for large x
So in figure A the assumption is most likely to be satisfied
> If assumption does not hold, then we have heteroskedasticity:
> In case of heteroskedasticity:
* SE and statistics used for inference can easily be adjusted
→ ALWAYS use heteroskedasticity-robust standard errors
4
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lauraakkermans2000. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $11.47. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
83100 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now