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18 votes

What is the difference between two stage least squares and instrumental variable regression?

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 ...
chan1142's user avatar
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9 votes

Why are my 2SLS estimates much larger than my OLS estimates?

Let me take an example based on the estimation of returns to education, which has been a well-studied problem. The usual result is that researchers find the 2SLS estimate to be larger than the OLS ...
emeryville's user avatar
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7 votes
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What is the difference between two stage least squares and instrumental variable regression?

IV estimators are 2SLS 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 $Z$ ...
Paul's user avatar
  • 503
5 votes

Why do we need at least as many instrumental variables as endogenous regressors to identify parameters in 2SLS?

In standard linear regression model $$y = x^\top \beta + \epsilon$$ with exogeneity $\mathbb E[x\epsilon] = \mathbf 0$ you have $K$ parameters because $\beta$ is $K \times 1$ and you have $K$ ...
Jesper Hybel's user avatar
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5 votes
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Some confusions about instrumental variable (econometrics)

Endogenous variables are correlated with the error terms and z is correlated with endogenous variable. Doesn't this imply that z is correlated with error terms? No it doesn't. For mean-...
Alecos Papadopoulos's user avatar
5 votes
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IV regression: first stage in logs, second stage in levels?

What you are describing is the so called "forbidden regression", which (in general) does not give consistent estimates. This is a summary of the notes of Ben Williams Consider a (nonlinear) ...
tdm's user avatar
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4 votes
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Can you use more than one instrumental variables in an Econometric model?

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,...
EconJohn's user avatar
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4 votes
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C-statistic when one estimation is just identified

Yes, you are correct about the conclusion that $J_{n1}=0$ and hence $C_{n}=J_{n}-J_{n1}=J_{n}$. However, despite the test statistics are the same, the asymptotical distributions and critical values ...
Q9y5's user avatar
  • 366
3 votes

What is the difference between two stage least squares and instrumental variable regression?

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 ...
Kenzie's user avatar
  • 31
3 votes

How should I regress income inequality on economic growth?

If your are interested in the statistic relationship between income inequality and economic growth, you should use GDP per capita growth since the others indicate level rather than growth. More ...
Alalalalaki's user avatar
  • 2,474
3 votes

IV estimate for entire sample is larger than IV estimates for subsets of sample?

In general regression coefficients obtained from a regression on the entire sample need not be equal to the mean of the coefficients obtained from regressions on the subgroups of the sample. I will ...
tdm's user avatar
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3 votes

Confounding versus endogenous variables. What is their relative hierarchical position?

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 ...
BB King's user avatar
  • 6,238
3 votes

Abadie's Kappa (2003) for continuous treatments / IVs

No. There is not. I tried working on deriving one for a while. I struggled for a month, failed, and then emailed some contacts at the University of Chicago to ask if they had any ideas. My buddy asked ...
Michael Gmeiner's user avatar
2 votes
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IV:Quasi-random variance V.S. 'Placebo' check

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 ...
cheesecake's user avatar
2 votes

Difference between $x$ and $X$

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 ...
Alecos Papadopoulos's user avatar
2 votes

Imbens and Angrist (1994): the $D_i(z)$ variables

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 $D_i(z)-D_i(w)$....
soccer_stats's user avatar
2 votes
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Validity condition for Instrumental Variables

Essentially, $Cov(u,W) = 0$ is implied by $E(u|W) = E(u)$ by the Law of iterated expectations
E. Sommer's user avatar
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2 votes
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What does it mean if the controls in my IV model are correlated with my instrument?

...the controls in my IV model are correlated with my instrument? The controls should be in your model precisely because they are correlated with your instrument. In the exogeneity condition $cov(z, \...
Michael's user avatar
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2 votes

What does it mean if the controls in my IV model are correlated with my instrument?

This would not make instrument necessarily invalid. For some 2SLS instrument model of form: $$y_i = \beta_0 + \beta_1 \hat{x_i} + \beta_2 k_i +\epsilon_i$$ $$x_i = \pi_0 + \pi_1 z_i + \pi_2 k_i +e_i $...
1muflon1's user avatar
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2 votes

Skepticism about the claims of instrument variable validity/exclusion through a statistical test—the Arellano-Bond Test

If yes, then how does this square with the general point that causality/exclusion cannot generally be established with statistical tests... It seems to me that "[exogeneity of IV] cannot ...
Michael's user avatar
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2 votes

Is exogeneity guaranteed for a lottery-generated instrumental variable?

The simple answer is no. Randomness does not imply exogeneity. In my opinion, the following example from Deaton: "Randomization in the tropics, and the search for the elusive keys to economic ...
tdm's user avatar
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2 votes
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Interacting covariates with the instrument in the first stage

Short answer: No. Your model is $Y=\alpha + \beta X + \varepsilon$. Even when $X$ is exogenous, if you regress $Y$ on $X$, $W_1$ and $W_2$, then the OLS estimator is inconsistent (for $\beta$) unless $...
chan1142's user avatar
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2 votes
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Can I instrument an endogenous variable and its quadratic form with the instrument and its quadratic form?

The reference given in a comment under the question by @Bertrand, of Cameron and Trivedi (2005, Section 6.5.4, page 198), is very useful, showing how linear 2SLS can be inconsistent. I just stress ...
Alecos Papadopoulos's user avatar
2 votes

IV Regression with More Observations for First Stage than Second Stage

You should completely omit the observations with missing data. The explanation takes a few lines, but the key fact of the first stage regression is that predicted values are uncorrelated with ...
Michael Gmeiner's user avatar
1 vote

The instrument in "The Colonial Origins of Comparative Development"

You should include all controls in the second stage, even if they are not instruments. The entire effect of log(mortality) should be mediated through Exprop. This does not mean there cannot be other ...
RegressForward's user avatar
1 vote
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Using dependent variable's and exogenous variables' lags as instruments in 2SLS

Is this legit and what is the rational behind this? Yes you will find this even as a recommendation in many textbooks (e.g. see Romer Advanced Macroeconomics pp 376) so it is legit although with a ...
1muflon1's user avatar
  • 57.1k
1 vote

Some confusions about instrumental variable (econometrics)

Adding to the excellent answer by @Alecos Papadopoulos, here are two simple numerical examples with $z=x^2+v$, $z^*$ is mean-centred $z$ and $v$ is independent from $u$, in which $E(xu)\neq 0$, $E(xz^*...
Adam Bailey's user avatar
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1 vote

is endogeneity a problem in the first-stage regression in a two-stage least square regression?

I'm going to assume that by "conditions for instrumental variables to work" you mean "instrumental variables is consistent." However, there are other properties to consider, like ...
jmbejara's user avatar
  • 9,355
1 vote

is endogeneity a problem in the first-stage regression in a two-stage least square regression?

Yes it is a problem. The first stage itself has to satisfy the same assumptions that standard OLS would and $cov(Z,\epsilon_1)\neq 0$ would violate them (see A Guide to Modern Econometrics by Verbeek)....
1muflon1's user avatar
  • 57.1k
1 vote

Is it reasonable, in panel data, to use past values of explanatory variables as instruments to deal with simultaneous causality?

I suggest looking into System GMM. It is a panel regression method that uses past values as instruments and is exactly what you're looking for, I think. It has a few restrictions that much be met, the ...
Brennan's user avatar
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