Questions tagged [regression]

In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors').

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Elasticity of substitution by regression: Biased results (simulation)

I have the following simulation problem: Consumers, whose utility I know, go shopping for two goods. However, prices differ each time they visit a shop. Therefore, these consumers always purchase ...
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Diff-in-diff with two control groups: compare parallel trends

Suppose in a diff-in-diff problem, I have two control groups, but just one can be used as comparison, so I want to check which of them provides a better comparison. My idea is to compare the parallel ...
1 vote
1 answer
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Can I use negative binomial regression to estimate amount of money type data?

I know that the negative binomial regression is for count variables - can the amount of money be considered as count data? There is a paper on which I have to extend upon, where the authors are ...
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What is the common way to separate panel sample by firms' profitability?

I have panel data on firms in 3 countries (e.g., 100 firms in 3 countries in 5 years, and event happen at the 3rd year in all countries at the same time). For an example, for each firms I have 4 ...
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1 vote
1 answer
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Interpreting the regression results

This might be a basic question. The article given below checks the relationship between crime and income inequality. https://www.sciencedirect.com/science/article/pii/S0165176508001110. Both crime and ...
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Difference in Differences with panel data/repeated cross section with dummy

I have to do a public policy evaluation (on R) based on an article where the authors use a quarterly survey to study the effect of a parental leave reform in 2015(reducing the length of leave) on the ...
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1 vote
1 answer
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unobserved heterogeneity and time fixed effects

I understand that if there are correlated effects i.e. (one of) our explanatory variables are correlated with unobserved heterogeneity $\alpha_{i}$ then there will be omitted variable bias. Because ...
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Industry-specific control variables

I am writing about bank-lending to a specific industry and how that could be affected by the level of carbon intensity of a given industry within the EU. I have some thoughts on this: Trying to think ...
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2 answers
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Comparison of two AR(1) regression models (lead in dependent vs lag in dependent variable)

What is the difference between these time series AR(1) regression models (lead in the dependent vs lag in the dependent variable)? $$\begin{align}y_t = constant + \alpha y_{t-1} + error \tag{1}\label{...
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In Panel Data models, could we apply the existing Unit Root Tests (i.e. IPS) to the residuals in order to test for Cointegration?

The Engle Granger approach suggests that we check the regression residuals stationarity with ADF test and if the residuals are stationary, even if not all other model variables are, we can say there ...
2 votes
1 answer
54 views

how to use projection matrices in econometrics

We have the below expression: $$ P_{M_{1}.X_{2}} \cdot y $$ I guess its interpretation is that they are the fitted values obtained from the regression of $y$ on residuals that are obtained from the ...
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How to show SSR of the residual vector from regression of y on X1 and X2 is equal to SSR of y on X1 and X2

What I mean in the title is that when we regress $y$ on $X_1$ and by using projection matrix $M_{X1}$ how can I proceed with that: the model is $$ y = X_1 \cdot \beta_1 + X_2 \cdot \beta_2 + u $$ or ...
2 votes
1 answer
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Omitted Variable Bias with interaction terms

Suppose we have the long regression $$ y = \alpha + \beta D + \gamma X + \varepsilon $$ but instead use the short regression $$ y = \alpha + \beta D + \varepsilon $$ then one can show that the OLS ...
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Construction of F-Test

While constructing the F-test with matrix notation, For the Unrestricted model, we have: $$ y=X_{1}\cdot b_{1}+X_{2}\cdot b_{2}+e $$ For the Restricted model; $$ y=\widehat{X}_{1}.b_{1}+e_{R} $$ ...
2 votes
1 answer
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How to prove that Adjusted R^2 is less than R^2

The adjusted R^2 formula is : $$ \overline{R}^{2}=1-\left( \left( 1-R^{2}\right) \cdot > \dfrac{n-1}{n-k}\right) $$ In case of k > 1 , I continue like that; $$ \overline{R}^{2}=1-\left( \...
1 vote
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Understanding how to estimate the model of Fung and Hsieh (2001) for the hedge funds risk factors

There is an old paper about the risk of hedge fund strategies that it gathers its focus in the trend followers. This is the Fung and Hsieh (2001) paper. $\textbf{Definition of Trend Followers (TFs):}$ ...
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The dependent variable of one equation could be a regressor in another

I am estimating two different regression equations with two separate dependent variables. Each dependent variable has its own unique control variables, but they also share a similar regressor Ht. ...
1 vote
2 answers
43 views

Meaning of a statistically significant constant in a regression and more

I am running a regression the following way on stata: reg death_rate CPI HDI Where death_rate is the mortality rate of COVID-19 in 2021 (measured as a %), HDI is ...
0 votes
1 answer
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2 intercepts in a probit model about WTO/GATT concessions?

I am currently reading a research paper(Developing Countries and General Agreement on Tariffs and Trade/World Trade Organization Dispute Settlement by Marc L. BUSCH and Eric REINHARDT) and in the part ...
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1 answer
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Simultaneous Causality and Variance within a supply and demand model

Given two single-variable regression equations, one for Demand and one for Supply, both with error terms and a constant. How does one solve for equilibrium quantity, price? Obviously you can set ...
2 votes
1 answer
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How to interpret the standardized coefficients (BETA) in a mixed log-log and log-level regression

Let's say we have a model like: $$log(y) = \beta_{1} + \beta_{2} \cdot log(X_{2})+\beta_{3} \cdot X_{3} + u$$ After carrying an OLS, we are asked which independent variable has a higher impact on the ...
1 vote
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How to calculate the correlation of yield curve extrema?

The goal is to reproduce this chart: I first looked at the legend. It reads: "Correlation of Front and Back Fed Funds curve, Pivoted Around Peak Rate (Rolling 250 Day). Then I noticed that the Y-...
1 vote
1 answer
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Write equations for $E[Y_{t+k}|X_t,Y_t]$ and $E[X_{t+k}|X_t,Y_t]$

I am working with a VAR and trying to understand the dynamics of it for forecasting. Currently, I am trying to generate conditional forecasts by expressing the equations in the form of conditional ...
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1 vote
2 answers
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Why is Stata omitting some of my variables and mfx not working?

I'm trying to do a probit regression with some categorical and continuous variables but Stata keeps omitting certain variables and even claiming that some can't be used to to collinearity problems (I ...
0 votes
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39 views

log differencing and VAR model

I am working on a VAR model to forecast inflation using variables like CPI prices, oil prices, unemployment rates, PMI, inflation expectations, policy rates, and GDP. To use the VAR model for my ...
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1 vote
1 answer
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Machine learning and Inflation forecasting

Is machine learning a good tool to use in order to forecast inflation for the short term (next 2 - 3 years on a monthly or quarterly basis)? I want to be able to forecast inflation for Canada for the ...
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1 vote
1 answer
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Correlation between errors and estimates

If all assumptions hold (linear model, mean-zero error, homoskedasticity, no serial correlation and normal distribution), will the covariance between $\epsilon_{n+1}$ and $\hat{\beta}_{n}$ (the ...
1 vote
1 answer
100 views

Is this a case of perfect multicollineary?

I got two interaction terms: One is "female_minority" which is 1 if the person is a female and forms part of an ethnical minority. "Male_minority" is 1 if the person is a male and ...
1 vote
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Deriving ADF unit root test form for the time series with quadratic deterministic trend

I have the following time series process $y_t $ $$\Delta y_t = \delta + \gamma t + \epsilon_t$$ where $e_t$ is white noise process with the variance of $\sigma^2$. I guess that whereas $\Delta y_t$ is ...
3 votes
1 answer
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Derivation of sample variance of OLS estimator

Consider a Simple Linear Regression with the following assumptions: The dependent variable is related to the independent variable and the error term like: $y = \beta_0 + \beta _1 x + u$ We have a ...
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2 votes
1 answer
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Independent variables that don't vary much but are essential for the theoretical framework, what to do?

I'm working on finding out the impact of Covid.19 on commuting so income and distance will be relevant variables to include. However, these variables dont change from period to period, so it's ...
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6 votes
1 answer
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Measurement Error - Multivariate Case

I have a linear regression model, with usual assumptions holding; $E[xu] = 0$ and rank condition. $y_i = \alpha_0 + \alpha_1x_{1i} + \alpha_2x_{2i} + u_i$ I observe $\bar{x}_{2i}$, where: $\bar{x}...
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Combining a dataset of monthly observations with a dataset of annual observations for regression analysis

So i'm collecting datasets from various databases, and some of these are annual (going back 5 years), and som are monthly (same number of years). It basically says 2022, 2021, 2020, etc, for one. The ...
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0 votes
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Application of Maximum Likelihood estimation (MLE) to the Generalized Least Square (GLS) model

I have the following regression $$y = X\beta +u$$ where $y$ and $u$ are $(n\times 1)$ and $X$ is a fixed $(n \times k)$ matrix with full column rank and $\beta$ is an unknown $(k\times 1)$ vector of ...
0 votes
0 answers
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Showing the unbiased estimator of variance for GLS estimator

I have the following regression $$y = X\beta +u$$ where $y$ and $u$ are $(n\times 1)$ and $X$ is a fixed $(n \times k)$ matrix with full column rank and $\beta$ is an unknown $(k\times 1)$ vector of ...
-1 votes
1 answer
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Do Economists use Newey-West/Robust Standard Errors with GLS or GLM?

My hypothesis and I have not done any proofs, but I think Newey-West with GLS would have better estimation than OLS with Newey-West.
3 votes
2 answers
253 views

Unbiasedness and OLS Regression

I understand that we say that an estimator is unbiased if its expected value is equal to the population parameter it targets (i.e. if $\bar X _N $ is an estimator of the mean over a sample of size $N$,...
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2 votes
1 answer
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How is the standard error of the discontinuity calculated when using local regression in a discontinuous regression?

In a typical regression discontinuity design, the standard error of the discontinuity is $se(\beta_2)$ in the following model: $$Y = \beta_0 + \beta_1 X_1 + \beta_2 D + \beta_3 (D X_1) + U$$ However, ...
2 votes
0 answers
21 views

Intuition Behind Difference-in-Differences with Continuous Treatment?

It's very clear to me how a difference-in-difference model works when there is a binary treatment. If the model is $y_{i,t}=\beta_{0}+\beta_{1}P_{t}+\beta_{2}T_{i}+\beta_{3}(P_{t}*T_{t})+u_{i,t}$ ...
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Link between supply elasticity and marginal costs

I have two substitute materials (A and B) to produce a product, and I want to know the relationship between their marginal costs and the elasticity of supply of the product. Graphically I notice that ...
5 votes
1 answer
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Is program evaluation (DiD, RD) a structural estimation?

Consider program evaluation methods such as IV, Diff-in-Diff, and RD. According to Haile (2021): "Typically program evaluation requires more than descriptive analysis: one must counterfactually ...
3 votes
0 answers
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How to visualize first-stage in IV regression?

I know what matters is the F-Statistic, but for a presentation it would also be nice to add a plot that visually shows the first stage. How to best visualize that? Say you have an outcome $Y$, ...
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-3 votes
1 answer
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How to interpret the significance of estimates if it differs between regression models? [duplicate]

I am trying to analyse the impact of experiencing a certain incident on the pro-unification opinion of people. If the incident occurs, they can occur in solely 3 different types: A, B and C. We assume ...
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0 answers
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Multiregression analysis with fixed effect

I have a question about fixed effect I want to do a multivariate regression and I want to incorporate fixed effects by year and by company here is my equation: ๐ถ๐ด๐‘…=๐›ฝ +๐›ฝ๐‘€๐ด๐‘†๐ถ+๐›ฝ๐‘ƒ๐‘‚๐‘Š๐ธ๐‘…+๐›ฝ๐ผ๐‘...
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1 vote
1 answer
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How to define treatment & control groups properly?

Iโ€™m working on a project examining the effect of a 2016 cash transfer on fertility. Who is eligible for the cash? All families with: 2+ children, or 1 low-income or disabled child. The data doesnโ€™t ...
2 votes
1 answer
49 views

Difference-in-difference robust to heterogeneous treatment effect - Gendron-Carrier et al. specification

I am trying to extend the results of Gendron-Carrier et al. (2022) article published in the American Economic Journal : Applied Economics which is about the effect of subway opening on pollution. I ...
0 votes
0 answers
28 views

Fixed time and individual effects

I have the following, small question. I have panel data and have played around with it a bit. In my first estimation (1) I assumed that the coefficient of union is biased and therefore wanted to ...
0 votes
1 answer
64 views

Test for Multicolinearity

i recently ran a regression with fixed effects. As expected, STATA removed one of the dummy-variables, as well as every time-invariant variable (educ). My question is now. Why does STATA also removes ...
0 votes
0 answers
10 views

How to control an international but obmitted variable?

In my case, I deal with the firm-level data. I have a variable called X, which is an international index. I am using the standard two-way fixed effects regression. When controlling for year fixed ...
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2 votes
2 answers
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Fixed time effects or fixed individual effects?

I have the following question or problem. I am currently using panel data to predict the hourly wage. I have only used the variable "union" as an influence variable from the initial model, ...

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