Questions tagged [econometrics]

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

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Residuals as instrument in STATA

In paper by Coibion & Gorodnichenko authors estimate the following regression $\pi_{t+4,t+1}-F_{t}\pi_{t+4,t+1} = c+\beta(F_{t}\pi_{t+4,t+1}-F_{t-1}\pi_{t+3,t})+error_t$ by GMM, using as ...
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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-...
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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 ...
Puneet Sachdeva's user avatar
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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 ...
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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[\...
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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, \...
user346624's user avatar
3 votes
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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 ...
LJNG's user avatar
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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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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 ...
Sapna's user avatar
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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 ...
Flounderer's user avatar
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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-...
Stephanie's user avatar
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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 ...
Kevin Durant's user avatar
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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 + \...
user346624's user avatar
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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 ...
Dave's user avatar
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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: $u_i\sim i.i.d.N(0,\sigma^2)$, $x_{1i}=x_{2i}+\epsilon_i$, $\...
Katharina K's user avatar
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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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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 ...
k_c's user avatar
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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 (...
james_westfield's user avatar
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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 ...
user405402's user avatar
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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 ...
Sundown Brownbear's user avatar
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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 ...
Cola's user avatar
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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 ...
Nyashiro's user avatar
1 vote
1 answer
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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 ...
ArOk's user avatar
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OLS Forecasting Intervals

currently studying for my econometrics exam and struggling to understand the difference between these two forecasting intervals. xf are new observations added to the sample. Could someone please ...
Quack's user avatar
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dummy variable approach versus fixed effect and first difference approach

While studying Panel data analysis I came across the following reasoning. We have the following general model $$ Y_{it} = \beta_0 + \beta_1 X_{it} + v_t + \alpha_i + u_{it}$$ where $v_t$ is the fixed ...
manav's user avatar
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5 votes
1 answer
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Constants in Frisch-Waugh-Lovell / Partialling Out

If in general one wants to apply the Frisch-Waugh-Lovell "Partialling Out"-approach, should we include constants and in which of the following regressions? (1) In the first stage where we ...
Marlon Brando's user avatar
2 votes
1 answer
47 views

How do I handle outliers?

I'm calculating the beta coefficients for some stocks using a single-index linear model with the OLS method. I'm computing the betas at different return intervals to assess the interval effect on the ...
Mattia's user avatar
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1 answer
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Bias vs consistency in instrumental variable estimation

So in Mostly Harmless Econometrics, page 154, they analyse the bias of instrumental variables: They consider the case of one endogenous variable $x$, multiple instruments $Z$, and $\eta$ is the ...
clog14's user avatar
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How to interpret results from diff-in-diff binary treatment

I ran a dynamic diff-in-diff , of the form $$ y_{it} = \gamma_{i} + \lambda_{t} + \delta T_{it} + \epsilon_{it} $$ y : log(lead concentration) , log concentration of lead in drinking water. $\gamma_{...
Bridgeport BaaS's user avatar
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System GMM Estimator

Consider the dynamic linear model given by: \begin{equation} y_{it} = \rho y_{i,t-1} + \alpha_i + \nu_{it} \end{equation} where $\alpha_i$ represents individual fixed effects. The GMM two-step ...
Rebecca 's user avatar
9 votes
1 answer
92 views

Adjusted R2 and bias

Consider the population $R^2$: \begin{equation} \rho^2 = 1- \frac{\sigma^{2}_u}{\sigma^{2}_y} \end{equation} This equation describes the proportion of the variation in $y$ in the population explained ...
Dimitru's user avatar
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two fixed effect question

I was reading this journal article on two way fixed effects by Michelle M. Marcus & Pedro H. C. Sant'Anna The Role of Parallel Trends in Event Study Settings: An Application to Environmental ...
Science11's user avatar
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5 votes
1 answer
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Is zero condition mean preserved after transforming the conditioned variable?

In my econometrics class regarding multiple linear regression, we learned that one of the Gauss-Markov assumptions is the zero conditional mean, expressed as $ E(y|\boldsymbol{x}) = 0$. My question is:...
Nyashiro's user avatar
2 votes
1 answer
38 views

Time dummies - Intuition

Consider a simple two-way fixed effects model: \begin{equation} y_{it}= x_{it} \beta + \alpha_i + \delta_t + u_{it} \end{equation} where $x_{it}$ is a row vector of regressors of size $K$, and $\...
John M.'s user avatar
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2 votes
0 answers
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Stochastic order symbols - Intuition [closed]

I apologize for the following set of questions, which may seem trivial. Let $X_n$ denote a sequence of random variables. Then, $X_n = o_p(1)$ means that $\lim_{{n \to \infty}} X_n = 0$. I can use ...
Dimitru's user avatar
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0 answers
23 views

standardizing an indicator variable and coefficients to 0

I am fitting a distributed lead, lag models to understand the impact of an event that took place in 2017. My outcome y is a continuous variable. The event took place in 2017. I am interested in ...
Science11's user avatar
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2 votes
2 answers
125 views

Understanding well the concept of *ceteris paribus* in practice

The concept of ceteris paribus says that to calculate the impact of one variable on another, we need to keep everything else constant. I want to understand well how to do this in a hypothetical case. ...
user346624's user avatar
2 votes
0 answers
28 views

What is a 2-stage estimator?

I thought I would quickly find the answer to this, and maybe my capabilities of using the sites search function are very poor, but I didn't find an answer to the definition of what a 2-stage estimator ...
Lynchian's user avatar
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Understanding the Distinctions: Fixed Effects vs. Random Effects in Panel Data Analysis [duplicate]

I'm seeking clarification on the distinction between fixed effects and random effects in the context of panel data analysis. My understanding is as follows: Fixed Effects: In a fixed effects model, ...
The One's user avatar
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2 votes
1 answer
131 views

Natural log of ratios and two-way fixed-effects model bias

Bartlett and Partnoy (BP) (2020) show that OLS with natural log dependent variables that are ratios must include the $\ln(denominator)$ on the RHS in order to avoid bias (see pages 24-28) unless one ...
dcoy's user avatar
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1 vote
1 answer
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Implementing 2way Fixed Effects

My objective is to assess the impact on BMI following the establishment of a new donut shop in the neighborhood, particularly considering that the donut shop commenced operations in 2017. Researchers ...
Science11's user avatar
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0 answers
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Natural logged dependent variable and the ratio problem with two-way fixed-effects panel model

In a non-peer-reviewed (yet?) paper, Bartlett and Partnoy (BP) (2020) discuss some under-appreciated issues related to using ratios as the dependent variable. Some but not all problems are dealt with ...
dcoy's user avatar
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3 votes
1 answer
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Estimator for Dynamic Panels with Individual Specific Slopes

I'm working on some economic stuff and the objective is to conduct a panel data analysis. I assumed the following data-generating process: \begin{equation} y_{it} - y_{i,t-1} = \eta z_{i,t-1} + \...
Maximilian's user avatar
2 votes
2 answers
142 views

Building a predictive model for the Return on Investment (RoI)

I am working at a company that invests in ads for apps at different stores. I have a dataset containing the columns date, app, <...
Alberto Perez Martinez's user avatar
1 vote
0 answers
37 views

Heteroscedasticity and Serial correlation test

Let’s consider linear regression model, estimated using OLS. According to information from Hayashi (Econometrics, Chapter 2) it must be the case of no serial correlation in errors to perform White’s ...
kissmemiau's user avatar
3 votes
2 answers
72 views

Diffrence in logs vs. a % changes in econometrics: why is the dif log approvimation almost always used when the exact quantity is easily available?

I have observed that in econometrics work people almost always use the difference in logs rather than the actual percentage change. This makes no sense to me. I understand that the difference in logs ...
andrewH's user avatar
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1 vote
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Best Textbook for a Rigorous Treatment of Panel Data

I was wondering which book you recommend for a treatment of panel data that is both rigorous and intuitive. What do you recommend among Wooldridge(2010), Baltagi(2021), and Hsiao(2022)? I studied ...
John M.'s user avatar
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Difference in Difference Regression (Showing a change in independent variable coefficient for treat-post group)

I want to measure the the change in the relationship between one of my independent variables (gold price) and my dependent (conflict deaths) for my treatment post group. Any help would be greatly ...
L-Marr's user avatar
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5 votes
2 answers
132 views

Covariance matrix square root

Consider a random variable $r_t$ which represents the return of an asset at time t. In the univariate case, we just consider $r_t$ to be the return of a single security at time t. Generally, we assume ...
johnf42's user avatar
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1 vote
1 answer
61 views

Panel Data Estimation and Control Variables

My undergrad thesis has something to do with the relationship between emissions, mitigation-related official development assistance, and governance variables in chosen ASEAN countries. As such, my (...
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