Questions tagged [2sls]

Two-stage least squares is a regression technique from econometrics used in instrumental variables analysis.

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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 ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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 $\...
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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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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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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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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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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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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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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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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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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. ...
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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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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 ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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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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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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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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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 ...