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The meaning of the words first Some people use the word "IV estimator" to refer to any estimator that uses instrumental variables. To them, IV estimators contain 2SLS, LIML, k-class estimators, and others, so 2SLS is a special case of IV. For example, the title of Bekker's (1994, Econometrica) paper is "Alternative approximations to the distribution of ...


7

Actual availability of regressors may be an issue here, but if all four mentioned variables are available, the situation is as @Michael mentioned in a comment: Since $X_2$ is correlated with $Y$, it should be included in the regression specification as a "control". $$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + u$$ This is intuitive, but it also takes care ...


5

2SLS estimators are IV estimators. An IV estimator is the sample analog of the form: $\beta = \frac{Cov(Y, Z)}{Cov(X, Z)}$, where $Y$ is the outcome variable, $X$ is the endogenous variable, and $Z$ is the instrumental variable. It can be shown that the 2SLS is of the above form. The advantage of 2SLS estimators over other IV estimators is that 2SLS can ...


3

Check out Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems by David Card (2001) ECA I know distance from school has been used in the past as an IV..although it has been criticized.


3

There's no magic. What you have to realize is that the result is conditional on the validity of the assumptions: A) Under the assumption that there is measurement error, then yes, the average of two measurements will be on average closer to the truth than a single opinion. This is very believable. We all do this kind of thing all the time. For example, when ...


2

Generally 2SLS is referred to as IV estimation for models with more than one instrument and with only one endogenous explanatory variable. You can also use two stage least squares estimation for a model with one instrumental variable. It can be shown that IV estimation equals 2SLS estimation when there is one endogenous and one instrumental variable. ...


2

There is no contradiction in two approaches. Baum-Snow (2007) looks at the effect of the Interstate Highway construction on those MSAs which happened to lie on its way. The randomness comes from the fact that when the plan for the Interstate Highway project was considered, the aim was to connect distant areas. Through which MSAs the highway would go was ...


2

Instruments are used as a replacement for an independent variable if we think that independent variable is endogenous. That means, we think it may be correlated with our error term. So in the case of estimating money made by a twin, we have a model: $$\text{salary} = \beta_0 + \beta_1 \cdot \text{guess} + u$$ Where $u$ has standard properties mean zero and ...


2

I hope this meets your idea for intuition, but equation 1 comes from using the Law of Total Expectation with the independence condition (Condition 1). There are four possible values of $D_i(z)-D_i(w)$. $$D_i(z)=D_i(w)=1$$ $$D_i(z)=D_i(w)=0$$ $$D_i(z)>D_i(w)$$ $$D_i(z)<D_i(w)$$. Consider the LHS of (1). $$E[(D_i(z)-D_i(w))*(Y_i(1)-Y_i(0))]$$ From the ...


2

Essentially, $Cov(u,W) = 0$ is implied by $E(u|W) = E(u)$ by the Law of iterated expectations


2

The question is not totally clear, but I will attempt to give you some guidance. To answer your first questions, confounding variables are not a type of endogenous variable. We do not observe nor are we interested in the confounding variables, which means they are not endogenous variables in our model. You later give the correct definition of an ...


1

Neumark and Wascher did a lot of work on the minimum wage in the 90s and 00s, including their 1992 piece "Employment Effects of Minimum and Subminimum Wages: Panel Data on State Minimum Wage Laws". A non-paywalled version of the article can be found here. It includes use of panel data (cross sectional data that you are interested in can be considered a ...


1

Formulas can be checked against infinite online resources, not here. The most widespread use of $x$ and $X$ to distinguish something, is when it is needed to emphasize what is treated in theoretical derivations as a realized value (a fixed number, $x$), and what as a random variable, $X$. When using matrix algebra though bold uppercase denotes a matrix (...


1

I looked a bit more into this and I think I found the confirmation of my suspicion into this article, which describes the command ivreg2 in STATA. I am not a super-techy econometrician but from my understanding it can apparently be done using the orthog() option, and under certain conditions it is equivalent to a Hausman test. http://www.stata-journal.com/...


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(i) I think your idea makes sense. Under the null, $[X,Z]$ is orthogonal to $\varepsilon$. Under the alternative, $X$ is correlated with $\varepsilon$. (ii) Your statement that it's "basically a test of whether the OLS residual are orthogonal to $Z$" is exactly what I think. (iii) Your thought about the power depending on the relevance of $Z$ also makes ...


1

If you have endogeneity between a dependent variable and error term the use of Instrument variables are the way to go. as long as $\mathbf{COV}(x_1,z_1)\ne0,\mathbf{COV}(x_2,z_2)\ne0,\mathbf{COV}(z_2,e)=0$ and $\mathbf{COV}(z_1,e)=0$ you can do so.


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For the benefit of readers I note that, as the authors write at the bottom of p.2557 "We define trust as the subjective probability individuals attribute to the possibility of being cheated." So they actually measure "lack of trust" (the higher the value of the variable, the lower the trust), in order to see whether it co-varies positively with risk ...


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