Questions tagged [econometrics]
Econometrics is a field of statistics dealing with applications to economics.
2,564
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Different estimates of conditional mean parameters from OLS vs ARCH
Consider the market model for security $i$:
$$
R_{i,t}=\alpha_i + \beta_i R_{m,t} + e_{i,t}.
$$
I estimated the parameters with the OLS method.
...
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Rubin Causal Model and Selection Bias
In the Rubin Causal Model, with a binary treatment $ T \in \{0,1\} $, the selection bias is expressed as:
\begin{equation}
E(y_0|T=1) - E(y_0|T=0)
\end{equation}
where $E(y_0|T=1) $ denotes the ...
- 257
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Autocorrelation and ARMA model
Consider the market model for security i
Ri,t=αi+βiRm,t+ei
I'm estimating the parameters of this model (alpha and beta) using OLS. However, the Breusch-Godfrey test indicates the presence of ...
- 121
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1
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How to understand why the two period Differences-in-Differences estimator is the ATT estmator?
I read in a paper here that in a two time period differences-in-differences scenario where it claims the DiD estimator is the ATT (Average Treatment on Treated). I am trying to understand why that is. ...
- 4,524
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Question Regression Heteroscedasticity
I encountered this problem while studying introductory econometrics:
Assume a LM:
$Y = X'\beta + \epsilon$
For parameter estimation we assume
$Y_{i} = X_{i}'\beta + \epsilon_{i}, i \in [n] \ (1)$
...
2
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answers
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How to specify gravity model of trade with intranational (domestic) trade flows?
Having read the literature on gravity models, I would like to estimate one myself. Focusing on cross-section only for now, they take the general form:
lnTRADEij = aXi + bXj + cZij + eij
where ...
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1
vote
1
answer
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r mixed model unstructured and ar1 covariance matrices
My goal is to specify two different covariance matrices for two different random intercepts.
Briefly, this is my dataset.
Outcome is continuous (school test scores)
13 Schools in my study. Random ...
- 537
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49
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Is a regression discontinuity with two-way fixed effects a type of Diff-in-Diff?
I recently read a paper which used a regression discontinuity design (RDD) to study the effects of a law. The key variable was = 1 for all counties following the introduction of the ban. The model ...
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Is controlling for a time period (during which an economic crisis took place) controlling for fixed effects in a Cox extended model?
I'm using a Cox extended model to measure if job contract durations changed before or after labour reform A and B were passed. So the labour reform variable is time varying (0 if no reform, 1 if ...
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why to add the interaction of two fixed effects in regression
A general question raised during my study.
For example, we are estimating the effect of X on Y at individual level. Then it is intuitive for me to add state fixed effect and year fixed effect in the ...
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Can one calculate the odds ratio from the contingency table in the multivariate case?
The odds for logistic regressions can be computed as:
$$e^{x_i^{T} w}$$
If we thus only vary one regressor by one unit (e.g. a dummy variable) while holding constant the other variables, the odds ...
- 435
2
votes
1
answer
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Fixed effects - issue
Suppose I have a longitudinal dataset in which each country $i$ is observed at different points in time $t$. Suppose that my dependent variable is a dummy variable, and I want to estimate the ...
- 257
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Regressions with different time periods
I'm trying to run a pooled OLS and fixed effects regression model using panel data but my problem is that my independent variables are measured monthly while my dependent variable is measured annually....
- 1
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Likelihood of polynomial time series
I want to model a time series process as follows:
There are a total of T periods. I want to model audience dynamics. There is an initial audience of $N_0$ that evolves over minutes indexed by $t$.
...
- 143
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13
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Two-Step GMM and Instrumental Variable
I am trying to run a regression in r using country-level panel data with female labour force participation rate as the independent variable and lnGDP, lnGDP^2, Trade (as % of GDP), Fertility, School ...
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Do I need to include confounding variables in my regression model when I use instrument variables?
Suppose I believe 'Age', 'Gender', 'Ability', and 'Motivation' are confounding variables influencing both the dependent variable and endogenous variables. I use the 'Education Level' for the treatment ...
- 3,465
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FD estimator: manual first differencing versus plm
I am working on a first-difference (FD) estimator for panel data (only two time periods).
I calculated manually the first difference of each variable (dependent and two regressors) and then run an OLS ...
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8
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Within transformation vs. first differencing in the over-identified case
I have the following fixed effects model:
$S_{it}=D_{it}'\gamma + \alpha_i + \epsilon_{it}$
My textbook says i can use first-differencing and derive a moment function that overidentifies $\gamma$ for ...
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8
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panel causality relationship in long run and short run
What econometrics should I use when I want to estimate the causality relationship between variables in long-run and short-run for panel data? Whether models such as panel VAR, panel VECM or panel ADRL ...
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1
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370
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How to derive the GMM estimator for the Covariate Balancing Propensity Score?
The covariate balancing propensity score (CBPS) described by Imai and Ratkovic (2014) involves fitting a logistic regression for the propensity score $\pi_\beta(\mathbf{X}) = P(T = 1\vert\mathbf{X})$ ...
- 33.4k
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Instrumental Variable with Conditional Randomization?
I am doing a study with an IV design. In my setting, the IV is only conditionally random within a year and within a cohort. In this case, do I simply include year and cohort as controls in the IV ...
- 173
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1
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Modeling quesion, linear regression or survival analysis
I am analyzing a dataset where the outcome variable is "teenagers' recreational drug use in weeks." This is continuous and highly skewed outcome variable. While the range spans from 2 weeks ...
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Bootstrapping t-statistics order of approximation error
Consider bootstrapping the $t$-statistics: $T_n = T(X_1,...,X_n) = \sqrt{n-1}\frac{\bar{X} - \mu}{\hat{\sigma}}$ for iid observations $(X_1,...X_n)$, where $\bar{X} = \frac{1}{n}\sum_{i=1}^{n}X_i$ and ...
3
votes
1
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Understanding Fixed Regressors and Conditional Expectation on Fixed Regressors $E(Y|X_i)$
I'm having trouble with the statistical idea of a fixed regressor, it seems that our $X_i's$ are not treated as random variables, but we are still able to meaningfully condition $Y$ on them in a way ...
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22
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log log model to estimate elasticities for 0 demand/dependent variable
Many of you will be familiar with the use of the log log linear regression model to estimate elasticity. I am in this situation where I can get zero demand, the dependent variable, which obviously ...
- 2,235
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13
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Analytical approach when level of self-selected treatment variable is naturally reduced during course of longitudinal study
I realized that some data I have collected may be able to make use of what I originally considered to be a nuisance issue that arose during data collection. I'm looking for input about whether I may ...
- 535
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Should I include a dummy variable for groups with few observations?
I am doing some analysis of US Senate races and in my regression I'm wondering if I should include a (party X state) indicator variable that essentially measures the average vote for the two major ...
- 1
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Choosing Regression Discontinuity or Difference in Difference?
I am interested in investigating the impact of a policy implemented in 2020 aimed at fostering sustained engagement in music-related activities. This policy involves providing a Conditional Cash ...
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Why are regression models utilizing time anachronistic while autoregressive models are preferred?
I was reading the accepted answer to this question that asked what was the difference between autoregressive models and models that directly utilize time, it states that:
Models using time or time-...
- 1,473
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How to address endogeneity concerns using a recursive bivariate probit model?
I read a paper that addresses endogeneity concerns related to a binary moderator using recursive bivariate probit models.
Their approach is:
Analyze data using a recursive bivariate probit model.
Get ...
1
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0
answers
18
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Regression when multiple observations per individual but final result is the same
I'm very new to data analysis. I'm trying to find the causal effect of seating row and laptop use on grades at a specific university. I have data from 15 introductory economics lecture sessions ...
- 11
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Inconsistency of GLS Estimator in the Presence of Predetermined Regressors and Serial Correlation
Let be the linear model:
$$y_i = x_i'\beta + \varepsilon_i$$
Using its matrix form, consider strictly exogenous assumption and spherical assumption, respectivelly:
$$E[\varepsilon | X]=0, \quad E[\...
- 79
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Advantages of GLS Estimator for OLS in the Presence of Violated Spherical Assumption
Let be the linear model given by:
$$y_i = x_i'\beta + \varepsilon_i$$
Using its matrix form, consider strictly exogenous assumption and spherical assumption, respectivelly:
$$E[\varepsilon | X]=0, \...
- 79
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votes
1
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Multicollinearity and control variables dilemma
I had some superficial understanding of multicollinearity, that two highly correlated variables in the regression model are not what we want, as the estimated coefficient would be biased.
Control ...
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1
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What is the difference between pointwise confidence interval and uniform confidence interval in econometrics?
I'm reading Callaway, Bacon, Sant'Anna (2021) paper on continuous treatment. In section 6 they show their result of applying their proposed method to Acemoglu and Finkelstein (2008) medicare example. ...
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36
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Log transformation uses
I am trying to understand how the migration of a male member affects the number of hours spent by left-behind women in various agricultural and non-agricultural activities. I used a simple OLS model ...
- 1
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0
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Interpretation of coefficients in panel data
A colleague asked me a question about the interpretation of coefficients in a panel data regression. I'm not familiar with this field but I want to help. The question is this:
In our project, we ...
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Difference-in-differences when treatment status is revoked
I am trying to analyze the effect of receiving "elite" status on a university's number of international first-year students. I have a perfectly balanced panel of 17 universities over an 18-...
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General Expression for the $t$-th difference of conditional means
In econometrics, it is common to work with the difference-in-differences of conditional means. For example, let $Y$ denote a variable of interest and $X_{1}$ and $X_{2}$ denote binary regressors. The ...
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Independence of Shocks in ARCH(1): A Doubt from Hayashi’s Book
I am reading Hayashi's Econometrics book, and on pages 104 and 105 he defines the ARCH(1) model for a time series $g_i$ as:
\begin{aligned}
g_i &= \sqrt{h_i} \varepsilon_i, \\
h_i &= \zeta + \...
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2
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Why can the method of moments be expressed as a minimization problem?
Generalized method of moments (GMM) estimation seems to be called generalized method of moments because the standard method of moments (MoM) is a special case, following the following logic.
MoM is ...
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Undergraduate econometrics - linear model
I have the following model which I am trying to understand:
$y_i=\beta_0+\beta_1 x_{1i} + \beta_2 x_{2i}+ u_i \sqrt{x_{2i}}_i$
where:
$u_i\sim i.i.d.N(0,\sigma^2)$,
$x_{1i}=x_{2i}+\epsilon_i$,
$\...
- 11
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votes
1
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Test serial correlation for panel data
I have a set of panel data (including variables X1, X2, X3. and N=193; T=22) these variables are used as independent variables in the model. I want to check the autocorrelation of each of these ...
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0
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9
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Linear regression with pglm: factor effect and country
For my thesis I try to run a linear regression on a gravity trade model. The goal is to analyze the influence of investments on exports between several country pairs over time. For this purpose I have ...
- 1
1
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0
answers
26
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Width of Confidence Intervals for Variance Estimates in Contrast to Point Estimates
We are conducting a variance decomposition using a hierarchical linear random effects Bayesian model to investigate the variance in a DV that is affected by three nested layers. We estimate credible (...
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1
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Detrending and data transformation to logarithm can be done together?
I want to get the effect of bitcoin price changes on foreign currency price. The third variable is inflation, which is an explanatory variable.
Should variables be detrended before regressing? Is it ...
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0
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44
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Staggered DiD: Single Treatment
Consider a study involving subjects from 30 cohorts. The key event is a law passed by the Federal Government in 2017, which banned the use of certain vaping products.
Among the 30 cohorts, individuals ...
0
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1
answer
17
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How to interpret a regression with years on the LHS
I would like to know how I can interpret the coefficients in a regression when the dependent variable is years.
For example, suppose I am interested in the year different cities received a new Apple ...
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58
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Deriving the Exact Percentage Change Formula in Logarithmic Models
I have been studying the relationship between logarithmic changes and percentage changes in the context of regression analysis. I understand that when working with small changes, the change in the ...
- 83
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101
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Conditional expectation function and causal inference
!For the question itself skip to the last paragraph!
It is my understanding that iff we have a model of the form $$Y = m(X) + e$$ and $E[e|X] = 0$ we know that $m(X)$ is the conditional expectation ...
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