Questions tagged [instrumental-variables]

Instrumental variables (IV) are used for causal inference with observational data in the presence of endogeneity when standard regression methods yield biased and inconsistent estimates.

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Why does the IV estimator fail to attenuate the EIV bias in a two-stage FM regression?

In Jegadeesh et al. (2019), they proposed to use the instrumental variables (IVs) estimation approach to attenuate the errors-in-variables (EIV) bias, which is inherent to a two-stage Fama-MacBeth (FM,...
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When does the Instrumental Variable (IV) method fail?

Consider the following ARMAX model: $$ y[k]=\alpha y[k-1]+\beta u[k-1]+e[k]-0.7e[k-1] $$ where $e[k]$ is a white noise. One can see that $e[k]-0.7e[k-1]$ is a filtered noise and thus using ordinary ...
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Show that the IV estimator is equal to ( ̄y1 − ̄y0)/( ̄x1 − ̄x0) [closed]

I am stuck at solving this question. Thank you and please feel free to ask any questions!
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Categorical IV with probit second stage

In a panel setting, I have a binary endogenous variable $X_{ijt}$ where $i$ indexes the individual, $j$ indexes the region, and $t$ indexes the year. I have a set of mutually exclusive binary ...
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Why not simply use your instrumental variable as your independent variable?

I'm a little confused as to why we need to go through an entire two-stage regression process to capture the effect of our instrumental variable on our independent variable, and then only use this ...
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Why is ignoring prediction error not a concern in instrumental variables?

In his book, Statistical Rethinking (2nd edition, p. 137), Richard McElreath states that including parameters with unobserved values, such as residuals, and treating them as if they were perfectly ...
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How to treat dummy variables and their interactions terms with an endogenous variable in a IV context?

I have the following regression function: # fictitious regression function Y = α1 + α2*X + α3*W + α4*D + α5*(D*X) Y is the dependent variable, X is the main ...
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In large sample, does IV fit better than OLS?

This is taken from Hansen's econometrics textbook. Take the linear model: $$Y = Z\beta + e $$ Let the residuals in an IV regression be $\tilde e$ and in an OLS regression $\hat e$. If X is indeed ...
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How to think about exclusion restriction in an over-identified IV setup?

If I have more instruments than endogenous regressors, let’s say two instruments for one endogenous regressor, my IV set up is ‘over-identified’. What does the exclusion restriction imply with more ...
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Using IV when regressor is not endogenous

Suppose I have a single regressor model and the regressor itself is uncorrelated with the error term. If I were to use IV estimation to estimate the coefficient, would the estimate be incorrect, and ...
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Fixed effect instrumental variable (IV) regression with available diagnostic tests

May I please know an R package and code to run fixed effect instrumental variable (IV) regression with available diagnostic tests (e.g., weak instrument test, exogeneity test (using Wu-Hausman), ...
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Interpretation of bias with an endogenous variable

I am running an analysis of impacts of immigration on natives' votes to anti-immigration parties, across municipalities. The concern in this type of analysis is that location decisions of immigrants ...
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Using a spatial instrument in IV regression under spatial heterogeneity

I am wondering what the implications are of using a spatial (or group-level) instrument on identification of a coefficient in a standard linear model. For convenience sake assume: $Y = \alpha + X\beta ...
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Exclusion restrictions as instrumental variables in VAR

I'd like to know if my intuition behind exclusion restrictions that we place to identify the structural vector autoregressive (VAR) models is correct. This is a question not only for econometricians ...
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Instrumental Variables - required correlation level with instrumented

I'm dealing with a regression model where my variable of interest X1 is correlated at more than 90% with one of the controls X2. X2 is also correlated at lower levels (~50% etc.) with other variables ...
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My instrument (z) only affects y through x, but y affects z directly. Is my instrument valid?

I'm running a regression model to test whether unionisation rates have an impact on wages. I've introduced an instrumental variable: public support for unions. As far as I can tell, this instrument ...
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Choosing between a set of potential instruments

I have a question regarding instrumental variable analysis/2SLS. I would like to estimate the following IV regression: $$Y_{ht} = 𝛼_{h} +𝛿_{𝑡} + 𝜷_𝟏(MM_{ht})+ 𝜷_𝟐(Shock_{ht−1})+𝝉(MM_{ht}∗...
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Instrument variables for Hausman Taylor estimator

According to the manual, it looks like Hausman Taylor is using time invariant exogeneous variables as instrument variables (IV) for time invariant endogeneous variables. Is it possible that I only use ...
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Orthogonality conditions in system-GMM

It is not very clear to me a detail about the orthogonality conditions in system-GMM estimation. Suppose x is our endogenous variable. We instrument x with its lagged differences. The inference is ...
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Two-stage least squares with no instruments

I'm reading a paper that estimates a model that resembles two-stage least squares, but they include the same controls in both stages and no instruments. What does this achieve? For example, we want to ...
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Instrumental Variables: satisfying exclusion criterion with Covariates

I have encountered a situation wherein I am trying to ascertain the causal effect of X on Y through an IV approach in a cross-country panel study, but the exclusion restriction is not entirely valid. ...
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Can I use pooled ols and IV_ols estimation techniques for panel data?

I want to regress the econometric model about the impact of household poverty on children's education. I used two waves of surveys of micro panel data in 2007 and 2014. When using the pooled ols ...
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Accounting for time effects with time covariates vs. instrumental variables or other alternatives

I have sales data where I expect some structure in time due to inflation, market changes, etc. I am not a statistician by training, but I am aware of the issues that this presents and the technique of ...
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Different standard errors in Stata and R for instrumental variables (ivreg)

Working with instrumental variables (IV), I noticed differences between reported standard errors in Stata (e.g., using ivreg2) and R (e.g., using AER:ivreg2). In R I found ways to replicate Stata's ...
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Instrumental variable approach to account for self-selection in some experimental groups

I have conducted an experiment in which participants were randomly assigned to six groups: Control group Control group with additional information about problem Pre-set treatment group Pre-set ...
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Validity of instruments: Hausman test

When doing a Hausman test for validity of the instruments there is a requirement for the amount of instruments (m) to be larger than the amount of potentially endogenous regressors (k) (m>k) why is ...
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Using standard deviation to interpret regression results

The paper by Bhalotra and Clots-Figueras (2014) on women's political agency and health interpret their Instrumental variable regression results in the following way. Raising the share of seats held ...
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Comparing treatments when there is imperfect compliance

Imagine a situation where we have a 2x2 cross-randomized program with imperfect compliance to the treatment arms. Thus, units are assigned to treatment A, treatment B, or both treatments. Once they ...
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What is an applicable instrument for my regression of demand for credit on interest rate?

I have a OLS regression for panel data with demand for credit as dependent and interest rate as independent. I'm worried about simultaneous causality and have decided on using an instrumental variable ...
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Instrumental variable estimator - why is the projection matrix not the identity matrix?

the instrumental variable estimtor using GLS or 2SLS is: ß=(𝑋′P𝑋)^(-1)∗𝑋′P𝑌 with P = Z(𝑍′Z)^(−1) Z' But if we solve the brackets of P, we would get: P = ZZ^(-1) Z'^(-1)Z' which gives the identity ...
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Instrumental variables - OLS - estimation

I have a question regarding the OLS estimation, in the case of an estimation with instrumental variables: We assume the linear model $𝒚= 𝑿\beta+𝒖$ with $Z$ = instrumental variables. Multiplying the ...
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Instrumental variable requirement for endogenous variable and its transformation

I've been trying to find an answer to my question for a while now but I just cant find one. The question is: if I have an endogenous variable and its transformation in one regression equation, does ...
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OLS Estimator for ARMA(1,1)

We consider the ARMA(1,1) model: $$ y_t = \beta y_{t−1} + \varepsilon_t + \theta \varepsilon_{t−1}. $$ I would like to demonstrate that $y_{t-2}$ provides an instrumental variable estimator for $\beta$...
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Questions on Instrumental Variable Analysis in Stata

I am new to IV regression and have a few basic questions for implementing this in Stata. I have panel data from 1980 to 2020 at the country-level. My instrumental variable (IV) is an interaction term ...
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Explain in layperson's terms why predictive models aren't causally interpretable

Imagine that you are asked to infer some causal effect -- a change in an outcome $y$ in response to some variable $x$. But, the person asking for this directs you to use a predictive model to do so. ...
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2 stage least squares, summing the first stage

I have a situation where the behavior of 1 group affects the welfare of another. (smokers affecting non-smokers through second-hand smoke). The 1st group is affected by a treatment (a tax is imposed ...
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Struggling to find a good Instrumental Variable for Housing Tenure (Social housing)

As part of some research, i am examining the impact of living in social housing on youth violence at a borough level (London). The explanatory variable (social housing) clearly exhibits endogeneity ...
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When should one use Propensity Score Matching instead of Instrumental Variables to judge the impact?

I have a dataset with a lot of covariates and we need to judge the impact of one variable on the other. Initially, I was supposed to use Propensity Score Matching, but I started wondering as to when ...
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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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What control variables should be included back in a second stage regression?

Suppose you want to estimate the average effect of $X_1$ on $Y$ using the model: $E(Y_i|X_i) = \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \beta_3 X_{3i}$ If I understand correctly, there is an ...
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Are two weak instruments better than one weak instrument?

From my understanding, when using IV regression to eliminate confounding effects, we prefer to have a single strong instrument, over multiple weak instruments which can lead to bias. My question is, ...
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Should we use an instrument when the independent variable is exogenous?

Suppose I'm trying to estimate $Y_i = \beta_0 + \beta_1 X_i + u_i$ with $E[u_i \mid X_i] = 0$. I don't need an instrument. However, what if I have $Z_i$ such that $\operatorname{Cov}(X_i,Z_i) > 0$ ...
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How to simulate a confounding variable?

Suppose we have $X_{true}$ and $Y_{true}$ with a given correlation coefficient $\rho$ between them. We also have a third variable $W$. The three variables may have any distribution you like. Now we ...
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Efficiency of IV vs GMM

I am trying to understand how IV/just identified GMM and overidentified GMM compare when it comes to efficiency. The way I understand it, we are able to identify the vector of coefficients in IV and ...
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Is this an ARMA(2, 1) process?

I am puzzled by an equation, $$ y_t = \phi_1 y_{t-1} + \phi_2 y_{t-2} + u_t + \varepsilon_t - \varepsilon_{t-1}, $$ where $u_t$ and $\varepsilon_t$ are independent white-noise processes. Is this an ...
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Instrument validity: does a positive and significant coefficient on Z in a regression of Y on X and Z pose a problem?

I have an initial regression of Y on X and Z. Both of my coefficients on X and Z are non-zero and strongly statistically significant. X and Z are correlated but I am told collinearity shouldn't be an ...
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Difference-in-differences on compliers

I'm trying to estimate a generalized DID (two periods three groups)'s local average treatment effect on Stata. The DID code used was: ...
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Which type of correlation is used when IV has four categories?

I am working on parenting styles (IV) that is a categorical variable with 4 categories. My DVs are personality traits and quality of life. I have created dummy variables (IV) for regression analysis. ...
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How does Basmann’s 2SLS differ from Theil's 2SLS?

I am reading Diagnostics for 2SLS Regression. In the paragraph "Review of 2SLS Estimation", the 2SLS regression is reviewed. It says that the 2SLS regression was developed by Theil and ...
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What is the difference between GMM-style instruments and IV-style instruments in GMM estimation via xtabond2 or plm?

My question refers to the implementation of GMM estimators, e.g., in the package xtabond2 for Stata or package plm in ...
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