## Solved – How do instrumental variables address selection bias

I'm wondering how an instrumental variable addresses selection bias in regression. Here's the example I'm chewing on: In Mostly Harmless Econometrics, the authors discuss an IV regression relating to military service and earnings later in life. The question is, "Does serving in the military increase or decrease future earnings?" They investigate this question in the … Read more

## Solved – Is regression discontinuity a form of instrumental variable regression

I understand that regression discontinuity determines changes in the fitted line (or coefficient) at the point in a variable which defines whether the person received the treatment/intervention. It has been said that, as such, RD is a form of instrumental variable regression? Does this mean it is a special case of regression of which heckman … Read more

## Solved – Can someone please explain to me what the particular scenarios mean

"The set of points in \$mathbb{R}^2\$ classified ORANGE corresponds to {\$x:x^Tβ>0.5\$}, indicated in Figure 2.1, and the two predicted classes are separated by the decision boundary {\$x:x^Tβ=0.5\$}, which is linear in this case. We see that for these data there are several misclassifications on both sides of the decision boundary. Perhaps our linear model is … Read more

## Solved – Can someone please explain to me what the particular scenarios mean

"The set of points in \$mathbb{R}^2\$ classified ORANGE corresponds to {\$x:x^Tβ>0.5\$}, indicated in Figure 2.1, and the two predicted classes are separated by the decision boundary {\$x:x^Tβ=0.5\$}, which is linear in this case. We see that for these data there are several misclassifications on both sides of the decision boundary. Perhaps our linear model is … Read more

## Solved – Understanding the homoscedasticity assumption

I can't understand how this works: \$e\$ is the error term and \$x\$ is the explanatory variable. \$\$Var(e|x) = E(e^2|x) – [E(e|x)]^2\$\$ I know that \$[E(e|x)]^2\$ = 0 because \$E(e|x) = 0\$, and squaring 0 is still 0. So that leaves \$Var(e|x) = E(e^2|x)\$ I am confused on this part. This may be a clearer … Read more

## Solved – Understanding the homoscedasticity assumption

I can't understand how this works: \$e\$ is the error term and \$x\$ is the explanatory variable. \$\$Var(e|x) = E(e^2|x) – [E(e|x)]^2\$\$ I know that \$[E(e|x)]^2\$ = 0 because \$E(e|x) = 0\$, and squaring 0 is still 0. So that leaves \$Var(e|x) = E(e^2|x)\$ I am confused on this part. This may be a clearer … Read more

## Solved – SUTVA vs. independence

In the Wikipedia article on the Rubin causal model I stumbled upon the following quote: We require that "the [potential outcome] observation on one unit should be unaffected by the particular assignment of treatments to the other units" (Cox 1958, §2.4). This is called the Stable Unit Treatment Value Assumption (SUTVA), which goes beyond the … Read more

## Solved – SUTVA vs. independence

In the Wikipedia article on the Rubin causal model I stumbled upon the following quote: We require that "the [potential outcome] observation on one unit should be unaffected by the particular assignment of treatments to the other units" (Cox 1958, §2.4). This is called the Stable Unit Treatment Value Assumption (SUTVA), which goes beyond the … Read more

## Solved – How to determine if an instrumental variable is randomly assigned

For an IV to be valid, it must be: Randomly assigned Correlated with the endogenous variable in the model Uncorrelated with the dependent variable in the model What does the random assignment of an IV mean? How does one assess whether an IV is actually randomly assigned or not? For example, given the model: \$T_i … Read more

## Solved – Understanding the price elasticity interaction in a regression model

The question that follows is derived from a SAS User's Group paper available on the web (Price and Cross Price Elasticity Estimation Using SAS). The objective is to calculate price elasticities (own and cross). There are two products (our product and a substitute and two promotional events from us). An OLS is run from data … Read more