3
votes
Simultaneous Causality and Variance within a supply and demand model
$$(1) P_i = \beta_0 +\beta_1Q_i + \beta_2X_i +u_i$$
$$(2) Q_i = \delta_0 +\delta_1P_i + \delta_2W_i +v_i$$
Plugging (2) into (1) and simplifying yields,
$$P_i = \beta_0 +\beta_1(\delta_0 +\...
- 3,458
3
votes
Accepted
Measurement Error - Multivariate Case
To derive this you'll want to use the Frisch-Waugh-Lovell theorem.
Using the true variable, $x_2$, let $\widetilde{x_2}$ be the residual from a regression of $x_2$ on $x_1$,
$$x_2 = \delta_0 +\delta_1 ...
- 3,458
2
votes
Comparing degree of dispersion without calculating variance
The following might help, although whether it's simpler than calculating the variances will depend on the particular functions. Suppose the two distributions are of random variables $x_1$ and $x_2$. ...
- 8,311
2
votes
Why can we replace dependent variable y with the residuals e?
You are not replacing $y$ with $e$. We are replacing $y$ with $\hat{y}+\hat{e}$, which is the fitted value of $y$, given by $X\hat{\beta}$, plus the estimated value of the residual, given by $y-X\hat{\...
- 21
2
votes
Accepted
Variance of Quantile Regression
I cannot say how helpful this is for you but if your model is
$$y_i = a(u_i) + b(u_i)x_i, \;\; u_i|x_i \sim U[0,1] \;\;\forall i$$
Then
$$\text{Var}(y_i\mid x_i) = \text{Var}[a(u_i)\mid x_i] + x_i^...
- 33.4k
1
vote
Derivation of autocovariances Lewis (2021) RES
A useful implication of conditional mean independence is: $E[\varepsilon_{it}|\varepsilon_{ks}]=0 \implies E[\varepsilon_{it}\varepsilon_{ks}]=0,$ and more generally, $E[\varepsilon_{it}|\varepsilon_{...
- 3,179
1
vote
Why can we replace dependent variable y with the residuals e?
$$\big[ I-W(W'W)^{-1}W'+WC\big]y = \big[ I-W(W'W)^{-1}W'+WC\big](W\beta + e)$$
$$=\big[ I-W(W'W)^{-1}W'+WC\big]W\beta + \big[ I-W(W'W)^{-1}W'+WC\big] e$$
Analyzing the first term,
$$\big[ I-W(W'W)^{...
- 33.4k
1
vote
Sample weights in Stata: fweight vs. pweight
mean command with pweight gives you mean and sd estimates, which in turn gives you estimate of the coefficient of variation.
<...
- 503
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