# Questions tagged [two-stage-least-squares]

Two-stage least squares (2SLS) is a structural equation modeling technique that is used when the IV is correlated with the DV's errors.

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### Two stage models: Difference between Heckman models (to deal with sample selection) and Instrumental variables (to deal with endogenity)

I am trying to get my head around the difference between sample selection and endogeneity and in turn how Heckman models (to deal with sample selection) differ from instrumental variable regressions (...
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### Probit two-stage least squares (2SLS)

I was told that it's possible to run a two-stage IV regression where the first stage is a probit and the second stage is an OLS. Is it possible to use 2SLS if the first stage is a probit but the ...
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### Why do you put all the exogenous variables into the first and second stage of 2SLS?

For a general MLR, let's say we have k endogenous X's, r exogenous W's, and m instruments. The first stage of the 2SLS model is regressing each of the endogenous X's on all the Z's and W's. For the ...
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### how to explain instrumental variables to a layman

I am giving a talk to a group that contains both quantitative and qualitative researchers, but most of the quants' understanding stops at crosstabs and regression. Does anyone have any ideas which ...
726 views

### Generalised Residuals - Estimated value of the density at that point for observation $j$ $i$?

I am trying to write R code for the generalised residuals as described in Vella (1993) and also mentioned by Wooldridge (2014). Wooldridge suggests to use these ...
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1 vote
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### How to do a Control Function (CF) / Two Stage Residual Inclusion (2SRI) with an ordinal dependent variable in the first stage and a glm in the second

I am trying to use a Control Function (CF) / Two Stage Residual Inclusion (2SRI) approach, because the modeled relationship that I am trying to estimate is non-linear (my dependent variable has a ...
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### Weak first stage in 2SLS

I have a simple IV model with 1D variables: $N = \alpha_z + \beta_z Z + \epsilon_z$ $S = \alpha_s + \beta_s N + \epsilon_s$ $N$ is an integer, while $S$ is dummy. $Z$ is by construction ...
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### 2SLS but second stage Probit

I am trying to use instrumental variables analysis to infer causality with observational data. I have come across a two-stage least squares (2SLS) regression which is likely to address the ...
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### Why is the functional form of the 1st stage in 2SLS not important?

In a presentation today the speaker made the above claim. He said that even if the first stage is mis-specified, the coefficient estimates of the second stage will still be valid. As a lowly graduate ...
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### 2SLS - logit/probit in the second stage?

I just have a quick question: what if I'm interested in estimating a logit/probit model in the second stage, can I follow this two-step procedure by running OLS in the first stage (endogenous variable ...
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### Definition of "optimal" instruments

The book I read (Davidson,MacKinnon - Econometric Theory and Methods) describes the definition of "optimal instrument variables" as the following: Usually, and this is seen very often in ...
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### Can there be endogeneity?

I am performing a regression in which I suspect there could be endogeneity between the main explanatory variable and the dependent. As a first step I perform an OLS regression and then, to control for ...
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### Instrumental variable with measurement error

I have a question related to measurement error bias and the use of instrumental variables. Assume I have a continuous outcome variable $Y$ which is observed with no error and an endogenous (continuous)...
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### Basic 2SLS IV Questions in Stata

(1) If I believe my instrument is exogenous conditional upon a few exogenous variables, do I include them only in the first stage? I.e. would the command be: ...
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### Why the representation in the form of $Z'X(X'X)^{-1}X'Z$ can not be simplified into $Z'Z$

Representation similar to $Z'X(X'X)^{-1}X'Z$ frequently appear to e.g. 2SLS. I think that $Z'X(X'X)^{-1}X'Z = Z'XX^{-1}X'^{-1}X'Z = Z'(XX^{-1})(X'^{-1}X')Z = Z'Z$. So why it seems that in the context ...
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### Identifiability of multivariate instrumental variable model

I'm interested in estimating the effects of $X_1$ and $X_2$ on $Y$ in the directed acyclic graph below. $U_1$ and $U_2$ are unobserved confounders. Based on Definition 7.4.1 on p. 248 of Causality ...
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### Causality studies on observational data: DID with 2SLS to compliment Rubin causal model

A study with observational data has treatment and control group but the assignment is not randomised: some chose to be in the treament, some otherwise. But the choice had been made before the ...
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### Are standard errors from a second stage with OLS always underestimated? [duplicate]

I use Stata. I build on Standard errors of a two stage least squares regression, Stata to compute manually the standard errors for my model: I cannot use standard packages (ivreg2 etc.) as the second ...
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### Non-statistically significant effect of the instrument in the reduced form of the 2SLS

I am using a 2SLS, with two endogenous variables and two instruments. I conduct the Under- and the Weak-identification tests; results from these tests suggest that my instruments are not weak. ...
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