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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Relevance & Exogeneity of IV
I got two questions which are somehow closely related:
Let's take the famous study of Acemoglu et al. (The Colonial Origins of Comparative Development: An Empirical Investigation) as an example.
When ...
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Test an instrument's correlation with unobservable when it's redundant in structural equation
I'm working on Wooldridge's “Econometric Analysis of Cross Section and Panel Data” and I don't fully get why this test would not work.
I'll share my work with screenshots so it's clearer hope that's ...
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F-statistic Two stage least squares (2SLS) regression
In Wooldridge's advanced book, on page 105, the F-statistic for 2SLS regression is introduced. Let me illustrate the computation step by step with the following concrete example:
\begin{equation}
\...
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Does reverse causality from Z to Y violate exclusion restriction in IV?
I am estimating the effect of endogenous X on Y using 2SLS estimator with an instrument variable (Z).
X: Safety net program participation (binary), designed to increase household income
Y: Household ...
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Can I use the same regressors for Instrumental variables and the outcome variable?
I'm reading a research paper that uses an IV, they regress A, and B, to estimate C, then they use estimated C and actual B to regress on D an outcome variable. This seems to violate the only through ...
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Instrument variable analysis using randomized data
I am analyzing the effect of two randomized interventions on 1) first-time and, 2) second-time event attendance. All variables are binary (0 vs. 1). Second attendance was conditional on first ...
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Number of instruments in GMM (using pgmm in R)
Number of instruments used in GMM model (pgmm function in R)
I performed a GMM (Generalized Methods of Moments) analysis in R using the ...
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Problems with GMM (Generalized Methods of Moments) in R
I am interested in performing an analysis using a GMM model for a panel dataset.
I am conducting the analysis in R, using the pgmm package. My code is the following:...
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How to include random effect to ivreg model in R?
I have an endogenous variable X with instrumental variable Z and want to predict outcome variable Y. For this I have longitudinal data with user_id. Currently my model is:
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Serial correlation and heteroskedasticity in a first-stage regression of a 2SLS
I am about to test a Campbell-Mankiw's based model like:
$$\Delta c(t) = \mu + \lambda \Delta y(t) + \theta r(t) + e(t)$$
where $ \Delta y(t) = \ln(y(t)) - \ln(y(t-1)),~ \Delta c(t) = \ln(c(t)) - \ln(...
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Are missing variables an important factor when considering instrumental variable analysis?
I'm currently reading some papers that deal with the effects of education on health (smoking and obesity). Mostly they use an IV approach (college availability).
However in several analysis, only a ...
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What econometrics method is better for the analysis?
I need some tips and tricks to figure out what would be an appropriate econometric method to find causal relationships between $x₁$ and $Y$ in my model $Y = α + β₁x₁ + β₂x₂ + \dotsm + βᵣxᵣ + ε$
where ...
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Help understanding exact mechanics of IV under heterogenous treatment effects (LATE)
I have been reading Blundell and Costa-Dias (2009) to try and understand the exact mechanics why standard IV breaks when heterogenous treatment effects are involved. On page 62 there is an almost ...
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The magnitude of an two-stages least squares coefficient is always larger than the ordinary least squares coefficient?
I have a hard time wrapping my head around this. I know that in case of measurement errors, the OLS estimate is biased downwards zero. Omitted variables can bias the explanatory variable of interest ...
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IVs: would this rainfall specification cut it?
I need feedback to check whether rainfall is an appropriate instrumental variable. Before you boo me out, hear what I have to say.
There are two countries: A and B. A and B are 2000 miles apart.
My ...
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When analyzing causality from X to Y, is IV regression better than Propensity Matching Score
When we are analyzing the causality from X to Y, especially when literature has used extensively IV regression and PSM as a method. However, as I know PSM is matching method while IV is a regression ...
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Can I compare Fixed effect regression with IV regression.?
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How can I analyze the causal effect of variable X on Y using cross-sectional data? I have employed IV regression, but now I want to test the effect of X on Y specifically for individuals belonging ...
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'Policy implementation' dummy as IV in panel data model: same across individuals?
I am using a control function approach for panel data. I have an endogenous variable in the outcome equation. I take this endogeneity into account by adding the generalised residuals of a selection ...
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Conceptual Difficult in Understanding Endogeneity
I am having a bit of trouble understanding endogeneity.
If I have a regression specification where the "true" model looks like this:
$y = \beta_1 x + \beta_2 z + \epsilon $
And we lack data ...
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2SLS with endogenous variable $X_1$ and interaction terms $X_1 \times X_2$, $X_2$ exogenous
I would like clarification on the correct way to set up the first-stage regression(s) for a hypothetical 2SLS regression. Say we have the following formula:
\begin{align}
y = x_1 + x_2 + x_1 \...
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Role of different types of variables in a linear model
In a package to write linear regression models I have found the following description:
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Does 2SLS Endogenous Interactions Use Fitted Values?
I'll try to keep this short. I am using the R fixest package. I have the following regression that I've simplified for the example:
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Confounding variables are nested with treatment, not able to be measured, how to address the influence from confounding factors?
We gathered driving data from two cohorts of drivers belonging to the same age group. The first cohort, Group A, utilized System A (treatment group), whereas Group B drove vehicles without this system ...
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Instrumental variable identifiability in a linear setting in the presence of unobserved confounders
Long story short, I'm seeing in the literature that linear instrumental variables models are identifiable, even in the presence of unobserved confounders. The unobserved confounding aspect befuddles ...
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Instrumental variable identifiability in the presence of unobserved confounders
Long story short, I'm seeing in the literature that linear instrumental variables models are identifiable, even in the presence of unobserved confounders. The unobserved confounding aspect befuddles ...
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Regression with a sum of variables and a proxy
I want to estimate the coefficient $a$ in the regression
$$ P = c + aX + bY + u $$
However, I only have the variables $T = X+Y$ and $\tilde{Y} = \mu_1 + \mu_2 Y + e$. If I had the variable $Y$, then I ...
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Fuzzy RDD and IV
I understand the close analogy between a fuzzy RDD and Instrumental Variables estimation. This is clearest in the Wald Estimator. Here is the Fuzzy RDD equation:
And here is the (manual) estimation ...
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Seeking advice on a Bayesian hierarchical model for count data with overdispersion and instrumental variable:
Dear members of the statistics forum,
I am interested in a process that selects genes from a gene pool and divides them into two groups according to the treatment. My objective is to estimate the &...
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When is an instrument too strong in the first stage?
Instrumental variable regression is estimated with ivreg in R. ivreg provides diagnostics with the ...
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Bias of Instrumental Variables Estimator
Given the IV estimator for $\beta_1$ (From $y = \beta_0 +\beta_1x + u$):
$$\beta_1 = \frac{Cov(z, y)}{Cov(z, x)}$$
And it's sample analog:
$$\hat{\beta_1} = \frac{\hat{Cov}(z, y)}{\hat{Cov}(z, x)}$$
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Impact of IV on coefficients for exogenous regressors
I am sorry if my question sounds a bit naive, but I am new to IV and have a problem. One of the variables in my regression is endogenous, and I use 2SLS to remove bias. In stage 2 I focused on the ...
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Lagging a quadratic independent variable
In the theoretical framework for my model, there is concern about reverse causality between Y and my main X variable. Additionally, I believe there's an information lag effect where economic agents ...
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Can a variable be an instrument in the first stage and an exogenous covariate in the second stage of an 2SLS regression?
I have two equations of the form:
$y = X\beta + Z\gamma + r\alpha +\epsilon_1$ (1)
$r = Z\delta +\epsilon_2$ (2)
The basic intuition here is $y$ is total cost data, $X$ is a matrix of variables ...
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GMM efficiency vs IV efficiency condition
Let the true model be
$$
Y = X_1\beta_1 + X_2\beta_2 + u
$$
but $X_2$ is omitted, so we estimate
$$
Y = X_1\gamma_1 + e
$$
by a valid instrument $Z$, so $\gamma_1$ is the 2SLS estimator.
Assume now, $...
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Should instrumental variables abide by the effect hierarchy principle?
People sometimes include the interactions between their instruments and region/year or the interactions between different instruments in the first stage of a 2SLS regression. I wonder if the effect ...
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Is this a case of simultaneous equations?
My model estimates the percentage of living-in agricultural workers (that is, the ones provided with board & accommodation) in labor force. The unit is the % of those workers in a district:
Y = a0 ...
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Can I have an interaction-term between the predicted endogenous variable and other exogenous variables in the second stage Modell of a 2SLS?
I have a question regarding 2SLS and interaction-terms between the predicted endogenous variable and a set of exogenous variables (second stage).
I want to calculate the effect of an endogenous ...
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2-stage least squares (2SLS) with 0th-stage Probit correction: Additional fixed effects in 2SLS
I am dealing with a binary endogenous variable and thus trying to use a 2SLS model with Probit correction in the preliminary ("0th") stage, a procedure described in Wooldridge (2002; p.623, ...
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Time series regression with instrument variable
I want to know what model I should use to make causal inferences with time series variables with the instrument variable method.
For instance, I want to estimate the effect of price on sales. I have ...
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What kind of tests should I run for my master's thesis?
I am analyzing the effect of covid rates and covid lockdown levels on murder and suicide rates for the 50 most populous counties in the U.S. I am not sure what to do to analyze the question in ...
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Can an explanatory variable be both endogenous and exogenous?
I have two dependent variables that I will use in two separate models (namely math_score & language_score) and one independent variable (relative_power) that I will use in both models using Stata ...
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Can an instrument be correlated with 2 endogeneous variables in instrumental variables regression?
Given that I have a dependent variable $Y_i$, two endogeneous variables $W_i \text{ and } X_i$ and an instrument correlated with both $W_i \text{ and } X_i$, can we still perform two stage least ...
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instrument variable for bins of endogenous variable
In my research, for example, trunk is the endogenous independent variable of interest and headroom is the instrument variable for trunk. Both headroom and trunk is continuous variable.
Let’s assume ...
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Instrument fails when I cluster standard errors
I am replicating the Bhalotra-Figueras paper on women's political agency and health (Paper Here) an IV model where $x$ is measured at the district-level and have an instrument $z$ measured at the ...
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Why add control variables in the second stage of an IV regression?
I am reading an article on the effect of income on energy choice (e.g., choice between traditional sources such as charcoal and modern ones such as electricity).
The authors instrument income with ...
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Why would an instrumental variable have its strength measured by an F-statistic?
A typical "rule of thumb" for instrumental variables is that an F-statistic of ten or higher indicates a strong instrument. This is mentioned in this Cross Validated post, which contains a ...
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IV Regression - Instrumenting for Interaction Terms
So I have four variables: y, x1,x2 and z. I also have a vector of controls. x1 is a dummy variable, and I have reason to believe x2 is endogenous, so I want to run an IV regression. The problem is my ...
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IV Regression - First Stage Observations Higher than Second Stage
This is a very basic question, but I need help. Imagine I have a dataset for variables y, x, and z. I am running an instrumental variable regression such that y is my main outcome variable. So I am ...
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IV Regression Instrumenting for two variables
Imagine I want to estimate the following main regression:
$$
y = \beta_{1} x_{1} + \beta_{2} x_{2} + controls + \varepsilon
$$
But I am worried about endogeneity of x1 and x2 and so I try to use the ...
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Instrumental Variables will not pass the F test
I am doing a 2SLS to work out the relationship between crime and real wages across different regions, with time and unit dummies included for fixed effects.
I have tried several different variables as ...
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