All Questions
Tagged with estimators econometrics
20
questions
9
votes
1
answer
96
views
Adjusted R2 and bias
Consider the population $R^2$:
\begin{equation}
\rho^2 = 1- \frac{\sigma^{2}_u}{\sigma^{2}_y}
\end{equation}
This equation describes the proportion of the variation in $y$ in the population explained ...
- 185
4
votes
1
answer
96
views
Mathematical Step for consistency
Let me state my problem from the beginning:
Let $i$ be an index representing countries ($i = {1,2,\ldots,N }$), and $t$ represent time, denoted as available data for country $i$ ($t = {1,2,\ldots,T_i }...
- 309
0
votes
0
answers
20
views
Difference in differences to estimate differential impact of treatment?
I'm having some trouble thinking through the implementation of difference-in-differences / if DD is the best approach to use when I am comparing two groups who are both treated, but which I ...
1
vote
0
answers
28
views
I am looking for a method to estimate a threshold function for binary outcome data
A literature search yielded no obvious answers, so I wonder here if there any feasible methods to estimate the following.
Suppose I have data $Y_i, \vec X_i$ indexed by $i = 1, \cdots, N$.
Note that $...
1
vote
1
answer
74
views
Asymptotic property of estimators
I'm studying the asymptotic properties of estimators.
Let $\{ \hat{\theta}_T : T=1,2,3... \}$ be a sequence of estimators of the $p \times1$ vector $\theta \in \Theta $, and $T$ is the sample size. ...
- 321
10
votes
5
answers
2k
views
How do we know the true value of a parameter, in order to check estimator properties?
For example, we say that an estimator is unbiased if the expected value of the estimator is the true value of the parameter we're trying to estimate. However, if we already know the true value of the ...
- 103
3
votes
1
answer
237
views
Delta Method around zero is a N(0, 0)
I have this problem: $\sqrt N \hat{\theta} \sim N(0, V)$ where $E(\hat{\theta}) = \theta_{0} = 0$. I must find the asymthotic distribution of $\frac{N}{V}\hat{\theta}^{2}$ but if I use the Delta ...
- 33
0
votes
0
answers
139
views
Consistency of OLS estimator with unobservable variable
Suppose I have the next model
$Y_i = \alpha_i + \beta_i X_i + u_i$
where $u_i - N(0,\sigma^2)$ and $\alpha_i$ is unobservable, also $E(X_i \alpha_i) \neq 0$
My OLS estimator for $\beta_i$ is
$\hat{\...
- 101
1
vote
0
answers
290
views
GLS estimator - derivation
I'm stuck with the following question:
Given the model $$Y_t=\alpha+\beta X_t+u_t\,,$$ where the standard assumptions hold but $Eu_t^2=\sigma^2 X_t^2$, derive the GLS estimator.
Basically, all Gauss ...
- 309
1
vote
1
answer
166
views
How to prove that $\hat\theta_n$ is a consistent estimator of $\theta$ if and only if $a_n \rightarrow \infty $ as $ n \rightarrow \infty$
Suppose that $\hat\theta_n, n \in \mathbb{N}$, is a sequene of estimators of $\theta \in \mathbb{R}$ such that $$a_n (\hat\theta_n - \theta) \xrightarrow{d} \mathcal{N}(0, \sigma^2)$$ for some ...
- 25
0
votes
1
answer
923
views
Econometrics: How to Derive the OLS Estimators of a log-log model
Consider the following two simple linear model specifications:
$log(y) = \beta_0 + \beta_1log(x) + u$ $(1)$
$log(y/x) = \alpha_0 + \alpha_1log(x) + v$ $(2)$
where y and x are two random variables for ...
2
votes
1
answer
975
views
Compare the variances of restricted and unrestricted estimators?
Problem
Given a linear model $y_i = \beta_1 + \beta_2 x_i +\epsilon_i, \quad i = 1, \dots, n$
I need to compare the variance ordinary least squares estimator of $\beta_2$ without the restrictions and ...
- 27
0
votes
0
answers
30
views
What determines the precision of my estimator?
I suppose I want to run the following regression:
$$y_{ist} = \beta_0 + \beta_1 \tau_{st} + \beta_2 T_t + \beta_3 \tau_{st} T_t + \epsilon_{ist} $$
$\tau_{st}$ is my continuous treatment variable. ...
3
votes
1
answer
3k
views
Use of Weighting Matrix (GMM)
While conducting estimation via the Generalised Method of Moments, or GMM, I understand that we need to minimise the following expression:
$Q_n(\theta)=g_n(\theta)'W_ng_n(\theta)$
Where $g_n(\theta)$...
- 294
0
votes
0
answers
907
views
How to prove variance of OLS estimator in matrix form?
I am reading Wooldridge's Introductory Econometrics (2000), don't judge me, old version = cheap second hand book, and in the page P94 Theorem 3.2 of Multiple Regression Analysis, it says that:
$$
Var(...
