Summary EMF P1 - Most important topics and Interpretation of Regressions
12 views 0 purchase
Course
Empirical Methods in Finance (323063M6)
Institution
Tilburg University (UVT)
In this summary, the main topics for the Part 1 exam of EMF taught by Vincenzo Pezone are outlined. Additionally, there is also a page on interpreting regressions using dummies and logarithms, for example.
If you memorize this summary, you are guaranteed to get a (high) passing grade.
Most important topics
Bivariate & Multivariate Linear Regression Model
Bivariate
Ordinary Least Squares (OLS)= Methodology that we use to estimate the coefficients
1. Take vertical distances (defined as ûi) between each point
2. Take the square of each distance and sum them
- Some distance can be positive or negative so that’s why we square it
3. Find the estimated coefficient α ^ and ^β that minimize the sum of the squared residuals
Population regression function: yi= α + βxi + ui
- Sample regression function: yi= α ^ + ^β xi + ûi
OLS properties:
1. Unbiasedness; on average α ^ and ^β are equal to the true values of 𝛼 and 𝛽
2. Efficiency; no other estimator has smaller Var(α ^ ) and Var( ^
β ¿¿
In order for the properties of the OLS estimator to hold, some important assumptions must
hold at the same time.
There are also large sample properties of OLS:
1. Consistency: the estimates will converge to the true values when N increases to infinity
2. Asymptotic Normality: estimates are normally distributed in large enough samples
Bivariate OLS assumptions:
1. Population model is linear in parameters
2. Random sample from the population
3. Sample variation in explanatory variable
4. The error u has an expected value of zero
5. Homoscedasticity: the variance of the error u is constant and finite for any value of the
explanatory variable x
6. Normality; the population error u is independent of the explanatory variables x and is
normally distributed -> only for hypothesis testing
These assumptions guarantee that the OLS estimators α ^ and ^β are the Best Linear
Unbiased Estimators (BLUE)
Best: have the minimum variance
Linear: linear estimators, linear combinations of y
Unbiased: if on average they are equal to the true values
Estimator: are estimators of the true values α and β
Standardized Coefficients are useful since there is no need to worry about units of measurement
and provide more meaningful economic interpretation.
- How much 1 SD of x increases y
Logarithm is used in regressions for various reasons:
1. Rescale the data so that their variance is more constant -> overcome heteroscedasticity
2. Positively skewed distribution closer to a normal distribution
3. Constant percentage increase -> means the coefficients can be interpreted as elasticities
o Log-log is also called elasticity of y with respect to x
o Semi-elasticity: level-log model
^ and ^β
Standard Error: estimate the precision of α
- Larger error variance σ² -> larger var -> less precise estimates
Three measures that help calculate the Goodness of Fit of the model:
1. Total Sum of Squares (TSS)= ESS + RSS
o Total variation in y
1
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 juliareuvers. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $6.42. You're not tied to anything after your purchase.
