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Questions tagged [2sls]

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

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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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23 views

PCA of many weak IVs in 2SLS

"Instrumental variable estimators can be severely biased in finite samples when the degree of overidentification is high or when the instruments are weakly correlated with the endogenous regressors." ...
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5 views

Strangely identical Probit and IVProbit results

I'm currently running 3 probit regressions, each of which have IV variants. In each model the regressors and instruments are identical (the coding essentially looks exactly the same for each model, ...
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29 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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143 views

How to interpret the tests for weak instrument in R?

Stock & Yogo (2005) provide the rule-of-thumb that the first-stage F-test of an IV regression should be above 10 for the bias of the instrument to be less than 10%, and suggest to call weak an ...
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10 views

Why ivmodelFormula and ivmodel give different results in R?

I stumbled upon an issue with the ivmodel package: when exogenous covariates are included in the model, the ivmodel function ...
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22 views

Interpreting the relationship between my instrumented variable (X1), X2, and Y (IV regression)

I have run an IV regression with a dichotomous outcome (Y) and my endogenous ("instrumented") regressor (X1) is also dichotomous. I am assessing whether continuous variable (X2) is moderating the ...
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14 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
33 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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47 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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48 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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27 views

2SLS - With the same X's and Z's but 3 different Y's, Over-identification and Hausman tests give different results

Dear Stack Exchange users, Let's say that my independent variable of interest is expected to be endogenous and that I want to investigate its effect on 3 separate outcomes. I run separate 2SLS's (one ...
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1answer
52 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
84 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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27 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
67 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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80 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 ...
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1answer
74 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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637 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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807 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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141 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 ...
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1answer
37 views

mediate() vs lavaan, missing path coefficients, 2SLS does not resolve

Doing a straightforward mediation analysis, a => b => c (indirect effect) and a => c (direct effect). If I do this in mediation::mediate(), I get ...
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1answer
100 views

2sls - instrumental variables mean and variance of exogenous variable

I do not usually use two-stage-least-square regression technique and I am not a theoretic of econometrics; thus, I hope you will pardon me for this (possibly) clumsy post. Introduction Let's start ...
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1answer
340 views

why is 2SLS with dummys the same as GLS on group means?

I'm reading Mostly Harmless Econometrics (Available here), and on page 100 they say that 2SLS with dummy instruments is the same as GLS on a set of group means. I don't understand why. From the ...
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728 views

What do the assumptions for 2SLS (two-stage least squares) mean in the context of instrumental variables?

The assumptions for 2SLS are (z are the vector for instrumental variables; x are the explanatory variables in the model; u are the vector for the error term): Assumption 2SLS.1: E(z'u)=0, Assumption ...
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1answer
1k views

Endogeneity problem in OLS

I have an OLS-model with about 30 predictor variables, from which I got both big endogeneity and heteroscedasticity problems. The variables reporting these problems also pop up in the check for ...
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148 views

Significant Predictor with a Negative Adjusted R-Squared Value: Instrumental Variables Regression

I'm running an instrumental variables regression with a single predictor on a sample size of 120. When I run the regression, the predictor is significant at the 0.01 level, but the adjusted R-squared ...
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1answer
481 views

Is Sargan-Hansen J test relevant for panel data containing large number of observations?

I am working on a project that has 4680 observations (18 years, 265 regions), in which one variable is endogenous. We tried various combinations of two IVs, but always end up with a significant Sargan-...
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20 views

Why functional specification is important in RDD setting?

I'm reading Clark(2009) paper regarding the impact of education reform on school performance. The rule is that the school initiated a democratic vote at first and if 50% of students vote in favor of ...
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291 views

Simultaneous equations with interaction terms

How do you estimate the following simultaneous equation model on a panel dataset? $Y_1=\beta_1X_1Y_2 +\beta_2X_2+e_1$ $Y_2=\alpha_1X_1Y_1 +\alpha_2 X_3+e_2$ $Y_1$ and $Y_2$ are endogenous while $...
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1answer
591 views

Why use two stage least squares for the instrumental variable estimator?

Following the rationale from Econometric Methods with Applications in Business and Economics by Heij et al., the instrumental variables estimator $b_{IV}$ for the linear regression model $y = X\beta ...
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183 views

Should instruments always weakly increase standard errors?

In OLS, are standard error estimates using some instrument $z$, different from $x$ always weakly larger than standard errors when not using instruments? This has been discussed before: Why is the ...
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261 views

Nonlinear Two Stage Least Squares Instrumental Variable method

I am trying to figure out how this paper estimates extended Solow production function using nonlinear two stage least squares instrumental variable method (or non linear 2SLSIV). The full ...
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1answer
62 views

Continuous instrument- 2SLS estimation

I am trying to estimate the enrollment premium at high-fees schools i.e., impact of high-fee school enrollment on learning outcomes. I am instrumenting high-fee school enrollment by using a continuous ...
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547 views

Fuzzy RDD in Stata with two cutoff points

I am running a Fuzzy Regression Discontinuity Design using 2SLS. If I specified the model (and most importantly the IVs) correctly as i have never worked on a RDD before. The difference to the usual ...
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1answer
572 views

Is it possible to do a 2sls with linear regression in the 1st stage and logistic regression in the 2nd stage?

I'm working on a a bivariate logistic regression. But I have an endogeneity problem and I want solve it through 2sls with 2 instrumental variables. My thought was to regress (OLS) in first stage and ...
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117 views

2sls with lagged dependent

I have seen many papers using dynamic panel regressions when the lagged dependent is a regressor and the data has the standard panel format. so, y(t)=constant + beta1*y(t-1)+ beta2*X(t) is often ...
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1answer
654 views

Bivariate probit versus 2SLS, contradictory results (sign)

I am currently facing puzzle and I hope some of you will be able to provide me some insights. I have this model: y: binary variable, x1: binary variable (endogenous), z: binary instrument, x2: ...
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24 views

two models in 2sls procedure

I am trying to do following. bysort Country: regress bdr fam MTB lnTA this is my first stage regression for second stage I want to use another variable std as my dependent variable and use predicted ...
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265 views

Interpreting dummy variable in Heckman 2SLS

My question is regarding interpreting the output of a Heckman 2SLS. Background information: I am exploring how institutional investor presence affects investments and firm performance during ...
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1answer
277 views

Heterogeneous treatment effects with 2SLS local average treatment effect (LATE)

I am interested in a strategy to calculate heterogeneous treatment effects with an IV strategy for local average treatment effects (LATE). I am estimating the effect of postsecondary educational ...
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616 views

How to work out direction of omitted variable bias in 2sls

In OLS you can reason to the direction of omitted variable bias by using the following formula: OVB = [Omitted in long] x [Relationship between omitted and variable of interest] My question: is ...
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393 views

2SLS vs OLS Efficiency Question

I'm doing some studying for finals and I'm wondering what would happen in a case like this. With the following model $y_t = x_t * \beta + \epsilon_t$ Say you had two IV's, $a_t$ and $b_t$. In ...
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1answer
59 views

If my IV (denoted Z) equals 1, my endogenous var D always equals 1; is this a problem?

I have a binary instrumental variable Z={0,1} and a binary endogenous variable D={0,1}. By construction, D=1 necessarily holds if Z=1. There are also cases where D=1 if Z=0, but there are no cases ...
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1answer
352 views

Endogenous variable problem or why to use 2SLS?

Consider linear model $$y = \beta_0 + \beta_1x_1 + \dots + \beta_{k-1}x_{k-1} + \beta_kx_k + u $$ where $x_k$ is correlated with $u$ which results into inconsistent estimators of $\beta$. As I ...
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1answer
372 views

How does an IV regression/2SLS affect coefficient (increase/decrease) with initial simultaneity?

So let's say I want to look at how X affects Y, but there is some simultaneity going on: X ...
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1answer
535 views

Linear first stage, non-linear second stage 2SLS regression

I was wondering if it's possible to perform a 2SLS regression where I first run a regression for my endogenous variable, obtain the predicted values and then use them in my second stage regression (a ...
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570 views

Before-after analysis and selection effect

I have sales data on 200 grocery brands who add a fair trade symbol to their product packaging (6 months before they become a member, and 6 months after they become a member). I also have data on all ...
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1answer
870 views

Including several endogenous interaction terms

I would like to write you beacause of the following issue: I´m estimating an IV-model with the following common structure: $Y = constant + b1*X1 + b2*X2 + b3*Xend + b..*Xcontrols$. I´ve found also a ...
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27 views

2SLS with a discretized endogenous variable

Imagine you would like to estimate by OLS the following: $$y=\beta_0+\beta_1 med + \beta_2 high + u$$ $med$ and $high$ are dummy values with respect to some underlying variable $x \in [0,\infty)$. $$ ...