6
votes
Accepted
How to prove that Adjusted R^2 is less than R^2
$$
SSRes=\sum_{i=1}^n\left(
y_i-\hat y_i
\right)^2\\
SSTotal=\sum_{i=1}^n\left(
y_i-\bar y
\right)^2
$$
$$
R^2=1-\dfrac{
SSRes/(n-1)
}{
SSTotal/(n-1)
}
$$
$$
\bar R^2=1-\dfrac{
SSRes/(n-k)
}{
SSTotal/(...
- 365
5
votes
Accepted
Variance of a random variable / Econometrics
$$E[(X-E[X])^2]$$
We FOIL the quadratic,
$$E[X^2 -2XE[X]+(E[X])^2]$$
We apply the expectation to each term,
$$E[X^2] -2E[XE[X]]+(E[X])^2$$
In the middle piece, $E[X]$ is a constant number that can be ...
- 3,161
4
votes
Accepted
Adding a subscripts for P (price) in equation
You should write:
$$
P_{i,j,k} = f(L_i,S_j, E_k).
$$
- 8,682
4
votes
Accepted
Functional form for regression in a hedonic pricing model
It is widely considered that economic theory does not suggest any particular functional form for a hedonic pricing model. See for example Cassel & Mendelsohn 1985 which references several sources ...
- 7,754
4
votes
Accepted
Why the subjective "Owners’ equivalent rent of residences" is included in the CPI?
There are host of reasons:
Rental houses are not randomly allocated across country. It is very likely that most rental houses are not directly comparable to non-rented houses. Of course sometime you ...
- 50.2k
3
votes
What is the difference between econometrics and statistics?
Econometrics is application of mathematics and statistics for the analysis of quantitative and qualitative economic data, in order to estimate various economic relationships, to test the correctness ...
- 137
3
votes
If a dummy variable is insignificant can I remove it from the regression?
Statisticians object to this kind of pre-testing. This is a form of stepwise regression, a methodology known to be problematic.
“Stepwise regression model-building is…pants.”
Two issues particularly ...
- 365
3
votes
Accepted
Expected Value / Econometrics
$$E\left[\frac{(y-\mu)^2}{\sigma^2}\right] $$
$\sigma^2$ is a constant,
$$\frac{1}{\sigma^2}E\left[(y-\mu)^2\right] $$
I assume $\sigma^2$ is notation for the variance of $y$, and thus $Var(y) = \...
- 3,161
3
votes
Accepted
Consistency of an estimator
The definition of "consistent" is that the estimator approaches the truth as the sample size grows large. The parameter of interest is presumably $\mu_y$, the population expected value of $y$...
- 3,161
2
votes
consistency and unbiasedness of ols estimator
We can write $\varepsilon_t=\sum_{s=0}^\infty \rho^su_{t-s}$.
Thus, $Cov(\varepsilon_t, C_{t-1}) = Cov(\sum_{s=0}^\infty \rho^su_{t-s}, C_{t-1})$.
We are given that $E[u_t|C_{t-1},\varepsilon_{t-1}]=0$...
- 3,161
2
votes
error specification of OLS regression models
By the definition of OLS estimator we can rewrite the $\hat\lambda$ as
$\hat\lambda=argmin \sum_{i=1}^{n}\epsilon_t^2$
From first order condition, we get $\hat\lambda=\frac{\sum_{i}^{n}(C_{t-1}-\bar{C}...
- 146
2
votes
lagged regression equation properties
OLS is consistent but biased. For consistency, we need $Cov(\epsilon_t, C_{t-1})=0$. The condition, $E[\epsilon_t|C_{t-1}]=0$ is sufficient for the covariance to be 0.
For unbiasedness, we need $E[\...
- 3,161
2
votes
Difference between M-estimators and Minimum Distance estimators
OLS is "the" linear estimator. When I hear "nonlinear estimator" in the context of econometrics, I'm thinking "anything except OLS". This isn't entirely true, as GLS is a ...
- 3,161
2
votes
How to get Customs data for importing companies?
How to access such data is often described in published papers using data on imports. For the US, see for instance:
Flaaen, Aaron, Ali Hortaçsu, and Felix Tintelnot. 2020. "The Production ...
- 3,029
1
vote
What is the difference between fixed effect regression and (panel) fixed effect regression?
Fixed effects regression is one of a broader class of panel econometric methods which take advantage of panel data to difference out unobserved variables which would cause biased estimators in a naive ...
- 11
1
vote
Accepted
CALCULATING REVENUES OF EACH PRODUCT IN RSTUDIO
I suggest looking at introductory R courses (Rstudio is not a programming language but merely an an IDE). It is meaningless to just copy paste some code when you do not understand it. Knowing the ...
- 3,146
1
vote
Accepted
How to find the share price with respect to the type of share?
I don't claim to be an expert on this so if someone else who knows more corrects me, I yield graciously.
Side note: The term is "preferred stock", not "preference stock". Though ...
- 300
1
vote
Is debt to GDP ratio a misleading statistic to show the level of indebtedness of a government?
It is good statistics for the level of debt country has.
What you describe is not level of debt. A country does not have higher level of debt just because debt has shorter maturity. Moreover, interest ...
- 50.2k
1
vote
Accepted
OLS with multiple indicator variables
This seems like a question about perfect collinearity.
Does $i1 +i2+i3 = 1$ always? If so, then you must exclude one of them if you want to include a constant. This would be the case if all the homes ...
- 3,161
1
vote
Interpretation of regression output for different models
Questions: (4)(5)(6)How to interpret the two coefficients of each of the models? What do we compare here? (7) How to interpret the 3 coefficients of this model? What is the main comparison?
Assuming ...
- 50.2k
1
vote
calculating a marginal effect for logit model
For marginal effects you can use margins. This is postestimation command so it should be run after you estimate your regression.
You seem to be running:
...
- 50.2k
1
vote
Accepted
Should I do Chi-square or T-test before running a regression?
Yes you should definitely test for whether the difference is statistically significant if your are going down the subsampling road instead of using interaction variables. That is you should test for ...
- 50.2k
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