Questions tagged [2sls]
Two-stage least squares is a regression technique from econometrics used in instrumental variables analysis.
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questions
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6 views
How to interpret the coefficient from 2SLS model when the first stage outcome variable was a log transformed variable
I am estimating the following 2SLS model, and not sure how to interpret the coefficient of the second stage:
The first stage:
ln(X) = a0 + a1 IV + error
The 2nd Stage:
ln(Y) = B0 + B1 ...
1
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1answer
12 views
Why including extra instrument variables in 2SLS changes my regression coefficients?
For example, when I include $A_i$ as my first instrument variable, I got the causal parameter estimate $=0.0592$ and if I included one more IV, $B_i$, my causal parameter estimate changes to $0.0505$. ...
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5 views
Should I include interactions in the second stage of 2SLS if the 1st stage has them
I wish to estimate a standard Differences-in-differences model with a continuous treatment and a time dummy variable T:
$$ y = \beta_0 \cdot z + \beta_1 \cdot T + \beta_2 \cdot T \cdot z + \epsilon $$
...
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5 views
About post estimation test of a 2SLS
I have 2 regressors ($X_1$ and $X_2$) that I suspect be endogeneous, hence I run a 2SLS after identifying the instruments.
The Wu-Hausman test reports that only $X_2$ is endogeneous, while $X_2$ is ...
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0answers
16 views
2SLS approach using lagged dependent variable as an instrument
I was wondering if the lagged dependent variable can be a valid instrument or not.
In my data, policy intervention (x) is made depending on the outcome (y) in the past. (not depending on the effect (b)...
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8 views
IV estimation - should I report results in reduced or structural form?
I want to estimate the following model:
$$y = \alpha + \beta z + \epsilon_1$$.
$$z^* = \gamma x + \epsilon_2 \\ z = j \quad \alpha_{j-1} \leq z^* \leq \alpha_j \quad j \in \{-4, -3, \ \dots \ 3, \ 4\}...
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15 views
What is 2SLS estimator with three instruments?
Given the following model,
$$y_i = a + bx_i +e_i$$
It's known that $Cov(e, x ) \neq 0$, so we are going to use 2SLS method. We have three variables $v_1, v_2, v_3$.
What is the formula for the slope $\...
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0answers
7 views
How to decide whether to use robust errors in 2sls estimation
For my data, I have run both the OLS and IV regression to investigate the effects of health on salary. The BP test showed Heteroskedasticity for the OLS error terms so I decided to run the OLS ...
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0answers
21 views
IV Estimator or 2SLS estimator?
I am estimating the causal effect of maternal education on child health outcomes (as measured by the hight for age, weight for age z scores as well as their breastfeeding status measured by a binary ...
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31 views
What is the effect of an omitted variable in the first stage of an IV/2SLS
Background
Let me start with the fact that I read, this post, this post and this post. These questions deal with omitting exogenous variables from the main equation in the first stage. My question is ...
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19 views
2stage (instrumental variable) analysis: is reverse causality in the first stage a problem? [duplicate]
For my research I am looking into the relationship between an outcome (Y) and a predictor (X) as follows:
$$Y = X + e$$
where $e$ is the error term.
Because there might be reverse causality I am ...
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0answers
19 views
Two-stage residual inclusion or two-stage predictor substitution
I am a beginner on this site, so my apologies if I ask something incorrectly here.
I have a panel dataset that looks like this:
Ultimately, I need to estimate the predictors of patient quality of ...
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0answers
11 views
Testing for instrument validity using control function approach
Suppose we have a linear IV model with: $$ y_i=\beta x_i + \epsilon_i$$ $$x_i=\gamma z_i + u_i $$with $E(x_i \epsilon_i)\neq 0$ and $E(z_i \epsilon_i)=0$.
Then we can estimate the residuals in the ...
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1answer
16 views
Can I use same Instrumental variable for two of my endogenous variables?
I have the following model :
y= X1+x2+X1*X2+ other control
both X1 and X2 are endogenous. Can I use the same instrument for both X1 and X2?
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0answers
89 views
2SLS with a boolean regressor
So, I have the following linear model:
$$y = \alpha + \beta x + u$$
and $x \in \{0,1\}$, i.e. the variable $x$ is boolean. Moreover $x$ may be endogenous, and I have a set of instrumental variables $\...
0
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1answer
21 views
How do you prove that an IV estimator is (in general) inconsistent if the first stage regression does not include a constant?
Given an equation
$$
Y = \alpha + \beta X + u
$$
where $X$ is an endogenous variable and $Z$ is a valid instrument for $X$.
Then suppose that
$$
X = \gamma + \pi Z + v
$$
is the true data generating ...
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0answers
18 views
Сonfidence interval mean response and prediction interval for Instrumental Variables regression
I evaluated the regression model using the 2SLS method which is presented in the ivreg R package.
Using predict can get fitted ...
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2answers
78 views
Can I use an exogenous variable from my model as an instrumental variable?
Can I use an exogenous variable specified in my model as an instrument for an endogenous one?
It can be reasoned that there is a relationship between the two.
My conjecture is this:
Given that the ...
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0answers
114 views
Which F statistic is generated in felm (R) and why does it differ from STATA (ivreghdfe)
I'm running 2sls and making sure that my results replicate in both stata and r. In r, using felm, my code is:
...
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1answer
177 views
Non-statistically significant effect of the instrument in the reduced form of the 2SLS
I am using a 2SLS, with two endogenous variables and two instruments.
I conduct the Under- and the Weak-identification tests; results from these tests suggest that my instruments are not weak.
...
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1answer
48 views
When endogenous variable is non-normally distributed
I am trying to fit an IV probit model with my dependent variable being binary. However, my endogenous variable is a "ratio" variable, which is not normally distributed, thereby preventing me ...
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1answer
84 views
Why is the Wald Estimator equal to LATE (binary instrument)?
In Mostly Harmless Econometrics, Equation (4.1.12) states that in IV setting with binary instrument $Z$, treatment $D$, and potential outcomes $Y_1,Y_0$ for $Y$, then
$$E[Y_1-Y_0|D_1 = 1, D_{0} = 0] =...
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1answer
70 views
Test for weak instruments in Stata when using VCE robust [closed]
does anyone know how I can test for weak instruments (one instrument, just identified model) after 2SLS regression in Stata when using robust standard errors (VCE robust)?
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1answer
76 views
Using residuals in 2SLS regression to remove reverse causality
Someone suggested the following idea to me to control for reverse causality. Suppose we want to test for the effect of $X$ on $Y$ in a panel data set, but we suspect that there is reverse causality. ...
3
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1answer
582 views
A 2SLS when the instrumented variable has two interactions in the model
I am using ivreg and ivmodel in R to apply a 2SLS.
I would like to instrument one variable, ...
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0answers
15 views
How to properly use IV regression when my endogenous variable is a ratio?
I’m trying to better understand the issues relevant to the selection of an instrumental variable for a project I’m working on (and also more generally). In a recent example I ran into, my endogenous ...
2
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1answer
54 views
Inconsistency of Forbidden Regression Estimator
I am trying to prove the inconsistency of the estimator of the in the following model:
1st stage:
2nd stage:
When the population model is
and .
I know this is a forbidden regression because ...
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0answers
57 views
Instrumental variables: Fixed effects only in the second stage?
I have been under the impression that for a 2SLS FE model you got to have the fixed effects in both stages. So if you have a time invariant instrument you can forget about your FE, as they already ...
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0answers
10 views
Social-Network Peer Effect Regression
I have locally transformed model from Bramoullé 2009 to be estimated for regression estimation $\begin{equation}
( \mathrm{{I}} - {G}_{l}^{*}){y}_{l} = \beta_2( \mathrm{{I}} - {G}_{l}^{*}) {G}_{l}^...
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Addressing Near Perfect Correlations In Highly Competitive Commodity Markets
I am working on an analysis for a highly competitive agriculture market. I'm looking at county elevators in Iowa where competitors set their price for tomorrow's corn "ask" the evening before, but ...
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1answer
176 views
Missing R squared value from STATA output, what does that mean?
I ran a 2SLS regression in STATA, and there is no R squared value given in the output (only a dot where the value should be). What could this be interpreted as? Is it missing because it may be a ...
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0answers
51 views
How do I tell if my Instrument is valid?
I have the following structural model (similar) which I wish to estimate
$$
Y_t = \beta_0 + \beta_1 X_t + \epsilon_t
$$
but I'm aware that $X_t$ is endogenous or equivalently, $E[X_t\epsilon_t]\ne 0$....
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0answers
88 views
Why do estimates differ so much between Instrumental Variable (ivreg) vs 2SLS (lm)?
I am working with some messy pilot data to figure out whether Instrumental Variable analysis will help interpret the results of a randomized controlled trial I am preparing. Treatment compliance in ...
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0answers
394 views
Instrumental variables with interactions between endogenous variables
I have two endogenous variables $x_1$ and $x_2$ and am trying to estimate the following model:
$$y = \theta_0 + \theta_1 x_1 + \theta_2 x_2 + \theta_{12} x_{12}$$
where $x_{12} = x_1\times x_2$. I'm ...
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1answer
1k views
What control variables do we need for IV regression?
I am running and IV regression and I need help on what control variables to include in the IV regression. I believe that I have to control for potential variable that are correlated with both the ...
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0answers
21 views
Implementation of 2SLS in regression with AR errors?
Consider the following simple example:
$Y_t=\beta X_{t-1}+\varepsilon_t$
$X_t=\gamma Y_t + Z_t +u$,
where
$\varepsilon_t=\alpha\varepsilon_{t-1}+\eta$,
and $E[Z_t\varepsilon_t']=E[uu']=E[\eta\...
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0answers
227 views
Meaning of centred and uncentered r square [closed]
I'm not sure I understand fully the meaning of centred/uncentered r2.
Is uncentered r2 is same as adjusted r2? and if not, how can I know the adjusted r2?
That result estimated by IV analysis.
the ...
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0answers
48 views
Instrumental variables and GARCH
Can you use the predicted value from the first stage (as estimated using 2SLS) to replace the endogenous variable in a GARCH model? Or, what would be a different way of using instrumental variables in ...
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1answer
84 views
Is the IV approach applicable to endogenous count variable in a linear regression?
In a linear regression setting, one of the regressors (independent variables) is endogeneous. However, strictly speaking it is not continouus, but a count variable. A continouus instrumental variable ...
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0answers
159 views
Overidentified vs just identified models
Why go with overidentified models as opposed to just-identified?
If you can go with over-identified models, how many instrumental variables can you have at max in a 2SLS model?
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0answers
71 views
2sls asssumptions vs IV assumptions
Silly question but I was confused about the independence assumption for instrumental variables when they are used in 2SLS. Is it the case that the instrumental variable used in 2SLS only has to be as ...
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1answer
85 views
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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1answer
241 views
Standard errors of *partial* two stage least squares coefficients
Here partial 2SLS (I coined this term and found it descriptive) is the approach that SAS uses for 2SLS. Compared to "ordinary" 2SLS which in the first stage projects all explanatory variables $X$ onto ...
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0answers
39 views
Interpretation of correlation in endogenous regression model
Suppose you have a linear regression with an endogenous regressor $x$ that can be represented as follows:
$x = z'\delta + \epsilon_1$
$y = \beta x + w'\gamma + \epsilon_2$
where
$\begin{pmatrix}\...
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1answer
195 views
Instrumental variables with non-normal endogenous
Does it make sense to conduct an instrumental variables model where the endogenous variable of interest is continuous but not normally distributed? I know for normal regression purposes, there is no ...
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0answers
116 views
Role of rank condition in identification of 2SLS - matrix algebra
I could write down all the steps for identification of the 2SLS estimator but my question is really a matrix algebra question which is required in the last step for finding out what the beta vector is ...
2
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1answer
115 views
How should an author convince readers that weak instruments are not a problem?
I see in a lot of instrumental variables papers that authors will often discuss first stage $R^2$ values or $F$ statistics to assuage concerns that they are working with a weak instrument. This seems ...
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2answers
1k views
How does IV 2SLS obtain a causal coefficient?
Despite reading and conducting several practical examples with IV 2SLS, I am still uncertain how, specifically and mathematically, 2SLS is able to obtain a causal coefficient, β, of an assumed ...
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0answers
2k views
2SLS Estimation for a Fuzzy Regression Discontinuity Design
I am using a Fuzzy Regression Discontinuity Design for the first time and this maybe a very basic question to some. I am estimating the Fuzzy RD with 2SLS.
Suppose, my data is of the following form:
...
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0answers
190 views
2SLS (IV) with fractional outcome variable and spatially autocorrelated error terms
I face the challenge of estimating a 2SLS (IV) model with a fractional (ranging between 0 and 1) outcome variable and spatially autocorrelated error terms (the data is spatially explicit, i.e. for ...
