Questions tagged [econometrics]

Econometrics is a field of statistics dealing with applications to economics.

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7 views

A GLS estimator, that is also an FGLS estimator

In the slides i'm studying, i found something interesting: In many situations, we can use a linear regression model of the form "y(i) = x(i)beta + epsilon(i)" , where epsilon(i) ~ (0, sigma²,...
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Linear probability model difference in difference?

I see frequently people opposed to linear probability models for binary outcomes, and I know there are related questions to this on this forum, but I want to make sure my understanding is correct. ...
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Interpreting Impulse Response Function

I am trying to estimate a forward guidance shock on the expected path of the future federal funds rates and industrial production of manufacturing and construction. I built my SVAR model using Smith ...
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1answer
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What is the difference between Consistency and Identification?

Dear experienced friends, I start to learn Econometrics recently and there is a question really confuses me. Suppose we have a sample linear model $$ y = \beta*X. $$ From the definition, we know the ...
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Diff-in-Diff: Time-varying treatment and Treatment affects Outcome

I would like help with the following question. I have searched the internet and I can't come to a definite DiD setup. I appreciate any help or thoughts that you might want to share. My setting/dataset ...
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1answer
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Why are the standardised residuals of a GARCH process a white noise process

Suppose I have a GARCH process: $$X_t = \mu_t+\varepsilon_t$$ $$\varepsilon_t=\sigma_tz_t$$ where $z_t$ is some iid zero mean, unit variance random variable, and: $$\sigma_t^2=α_1 \varepsilon_{t−1}^2 +...
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Generalized DiD with non-binary treatment variable? How to proceed?

I have a certain law as my (non-binary) treatment variable (range: 0-2) at the state level which takes on different values based on whether it prohibits altogether (2), limits (1), or allows the ...
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54 views

GLS estimator - derivation

I'm stuck with the following question: Given the model $$Y_t=\alpha+\beta X_t+u_t\,,$$ where the standard assumptions hold but $Eu_t^2=\sigma^2 X_t^2$, derive the GLS estimator. Basically, all Gauss ...
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Level of Aggregation for Event Study (Staggered DiD) Analysis

This might be a bit basic, but I'm struggling to determine the ideal level of aggregation of the data for an Event Study analysis. I wish to study if a specific policy affected fertility in certain ...
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Creating Proxy variable to minimise estimation error

As part of my econometrics project, I am investigating wage structures for female workers. The econometric model I am using follows the Mincer earnings function. The dataset available includes ...
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Some simplified equations to reflect structural equations mediation analysis

In panel data: Yi = [Yi1, ..., YiT]', Xi = [Xi1, ..., XiT]', (i=1, ..., n), I estimate a linear fixed-effects regression of mental health scores Yi as influenced by an unemployment shock (USit) as ...
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Resources for mediation analysis

I am looking for resources to study mediation analysis. But to be specific, What I am instrusted in is something like the following. Say we have an outcome y, and some treatment (or shock x) which ...
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1answer
37 views

Interpreting Kernel density Plot

Below I am showing the kernel density with the size of the informal economy, and would appreciate support on interpreting this. For instance, what does the of the Kdensity line around .017 represent ...
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Interaction with endogenous variables in the first stage

I am working with industry level data and trying to solve an issue with omitted variables bias, by using an instrument. The problem with my instrument is that it only varies relatively little. I.e. ...
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Diff vs xtreg different results in Stata

I am trying to perform a DiD with three different methods. Here is an example of my dataset (the complete data is here), where "regime" is the treatment that starts in 2007 and goes until ...
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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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Poisson Regression assumption of constant rate in a fixed interval

My understanding of the Poisson distribution is that the probability of an occurrence is the same for any two intervals of equal length, or of equal space if not in a time dimension. My confusion is ...
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Concentration method

In one of my lectures, we were dealing with non-linearity and concentration method applicability. We are given the threshold model: $$g(x,\beta)=(\beta_1+\beta_2x_1)\coprod[x_2\leq\beta_5]+(\beta_3+\...
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Random sampling and independence in a real world problem

In the book "Introduction to Econometrics" by Stock and Watson It is used this example to illustrate the relation between random sampling and independence of the random variables : My ...
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1answer
15 views

Interpreting Correlation and Scatter Plot Results

I tested for correlation between average unemployment rate and log average real GDP (U.S. 2017 dollars) for 163 countries, and created the scatter plot below: Based on the correlation coefficient and ...
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1answer
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Clarification on the assumptions $E[u|x]=0$ and the $x_i$ being fixed in repeated samples in Wooldridge Introductory Econometrics

The author is writing on the assumption $E[u|x]=0$. The part of the text which is not clear to me is this (the red lines emphasize where the critical portions are located) : In the first piece I don'...
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1answer
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Moderation (interaction) - Cannot use moderation if a moderator has an effect on independent variable?

I have a following simple moderation model: $$ y = b_0 + b_1x + b_2m + b_3(x \times m) + e $$ However, previous studies have also found that $x$ has a effect on $m$: $$ m = a_0 + a_1x + u $$ If $x$ ...
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Difference between leverage plot, partial regression plot/added-variable plot, and component-plus-residual plot?

What is the difference between leverage plot, partial regression plot/added-variable plot, and component-plus-residual plot? In my intro stats course, I was only taught leverage plots, and not the ...
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1answer
29 views

How does diff-in-diff work for multiple datapoints?

Most textbooks and texts in blogs like to provide example of diff-in-diff using 4 datapoints. It's almost always an example with two cities, an intervention in one of them and then the calculation of ...
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1answer
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Question about Instrumental variables, endogeneity, and correlated errors

I have seen his notation to describe the Instrumental Variable framework, and I wish to make sure I understand it. Y is the dependent variable, x is treatment, and z is the instrument: $y = f(x,\...
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Asymptotic distribution of $S_n$

I am reviewing some exams from Hansen's webpage and came across this question that unfortunately doesn't have a suggested solution. In the regression/projection model $$y_i=x_i'\beta+e_i$$ $$E(x_ie_i)=...
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Panel Data anaysis with fixed effect model

I'm analysing a panel data including European banks through a certain time interval (2015-2019). I want to measure the effects of certain financial characteristics (size, leverage etc.) on the amount ...
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Joint Hypothesis testing

Take the model $$y_i = x'_{1i}β_1 + x'_{2i}β_2 + e_i$$ and $$E(x_ie_i)=0$$ where $β_1$ and $β_2$ are each k × 1. How would you test the joint hypothesis that the ratio of each element of $β_1$ and $...
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Regression for unbalanced panel with mostly unique observations (RE, FE, Pooled OLS?)

I have a firm-level dataset comprising 3 time periods and about 10,000 observations, 9,000 of which are unique firms that appear only once. The other 1,000 appear either twice or in all 3 waves. I do ...
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How would a Bayesian answer this question from Jeffrey Wooldridge

Jeffrey Wooldridge, a famous econometrician, posed the following question to Bayesians on twitter: I think frequentists and Bayesians are not yet on the same page, and it has little to do with ...
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Intuitive explanation behind conditional mean independence?

From what I understand from $E(U|X) = 0$ is that: for every slice of X (i.e. if we fix X, we can get a (normal) distribution of Y values that tend (as the definition of normal distribution) to cluster ...
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41 views

Conley Standard Errors in Logit and Probit

I am looking for an implementation of Conley (1999, 2008) standard errors in logit and probit regressions. There is code targeting OLS regressions (1, 2, 3, 4), but I did not find anything adequate ...
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Logit vs probit model [duplicate]

I am planning to do a study that uses binary dependent variable, such as a person is either in the labour force or not in the labour force. The function will have independent variables, for example ...
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20 views

Sign of simultaneous causality bias?

suppose I have the following simultaneous causality relation: $Y_i = \alpha_0 + \alpha_1X_i + V_i;$ $X_i = \beta_0 + \beta_1Y_i +U_i$ Where both of the equations are positively related. I want to find ...
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1answer
27 views

R: difference in interpreting estimates of plm and LSDV model?

What is the difference in the estimates of plm and least squares dummy variable (LSDV) models? And how does the interpretation of the variables differ in general? Imagine the following ...
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27 views

HAC variance to construct standard errors

I am facing some difficulties understanding this question. It hasn't been long since I started with econometrics, so I'm new to all of this. Suppose we have a function $$E[c_t|y_t,c_{t-1},y_{t-1},c_{t-...
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20 views

Multilevel Ordered Logistic Regression (meologit)

I have data on individual outcomes where the individual is a member of a subgroup (e.g. department) and a group (e.g. firm). I have analysed this (cross-sectional) data in Stata using an ordered logit ...
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1answer
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Is choosing only significant coefficients (based on t stats) from a multiple linear regression model a good idea, provided the F stats is significant?

I doubt if this topic has already been discussed here. I did search the forum before posting this question and read similar posts, however unable to find my answer, perhaps due to my limited ...
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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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How to calculate the interest rate risk of a portfolio in Eviews

I am having difficulties in obtaining Eviews data for a portfolio, that is completely made up from insurance companies and I would like to show that it should point that interest rate changes are ...
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Fourier Transform and ESTAR model

Please , I need a Monte-carlo Simulation code in R, Using Fourier transform and ESTAR model(KSS_203 model) as Data generating process in other form me to compute their critical value, finite sample ...
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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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What are the good and bad properties of the restricted GLS estimator as compared to a regular GLS estimator, an OLS estimator, and a RLS estimator?

I'm trying to figure out the major differences and advantages of these 4 types of estimators (RGLS, GLS, OLS, RLS). In what ways would say RGLS be better/worse than GLS, or OLS, or RLS?
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1answer
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Gauss Markov Theorem and zero conditional mean/mean independent assumption

So I read online that one of the assumptions of Gauss Markov Theorem is: $$E[\epsilon_i]=0$$However, we also know that one of the assumptions for linear regression is the zero conditional mean: $$E[\...
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2answers
102 views

Expectation of structural equation

I am trying to learn about structural equations, and in this post here Correlation, regression and causal modeling I am having difficulties trying to prove the answer. The problem is, given structural ...
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Joint asymptotic distribution and measures of fit

I have been looking for something similar but couldn't find any, unfortunately. Some help would be much appreciated. Consider a simple bivariate linear mean regression $$y=\beta x + e$$ where $E[e|x]=...
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20 views

Difference-in-discontinuity when the running variable is time

I am trying to implement a difference-in-discontinuity design for a research project I am working on. The idea would be to estimate a discontinuity at a cutoff both before and after the program ...
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33 views

Consistency and asymptotic distribution

This problem is from Hansen's econometrics textbook, chapter 7. The model is $Y = X'\beta+e$ with $E[e|X] = 0.$ An econometrician is worried about the impact of some unusually large values of the ...
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2answers
35 views

Overlapping confidence interval

If we had two confidence intervals overlap for two parameters, can we say that these two parameters are equal to each other? I read in some articles that this doesn't always hold, so what would be the ...
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Strict Exogeneity vs Weak Exogeneity Assumptions

I am getting confused trying to intuitively understand the difference between the strict exogeneity assumption and the weak exogeneity assumption (in the case of multivariate linear regression model). ...

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