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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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1answer
24 views

Running a regression to avoid multicollinearity

I have the following regression (pooled OLS; panel data): Y Treated Shock Shock*Treated {with industry and year fixed effects} Y is a continuous variable, “...
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Regression estimators for an equation with three independent variables

I'm trying to find the estimators for a regression equation with three independent variables: $y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \beta_3 x_{3i} + \mu_i$ What is the betas' estimator, ...
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285 views

Proof coefficient in log-log model is equal to coefficient of elasticity

I am trying to see how we treat $\varepsilon$ in the following proof: Suppose we have a log-log single variable regression model $$ \ln(y) = \alpha + \beta \ln(x) + \varepsilon $$ then take partial ...
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Okun coefficient interpretation

I'm wondering how to interpret Okun’s coefficient. Say you have $y^c = -1*u^c$. This means that a 1% increase in the cyclical unemployment gap will produce a 1% decrease in the cyclical output gap. ...
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1answer
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Is this a valid derivation of FWL?

$Y = X\hat{\beta} + Z\hat{\gamma} + e\\ (X'X)^{-1}X'Y = (X'X)^{-1}X'X\hat{\beta} + (X'X)^{-1}X'Z\hat{\gamma} + (X'X)^{-1}X'e\\ \hat{\beta}_{short} = \hat{\beta} + \hat{\delta}\hat{\gamma} $ where $\...
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1answer
64 views

Confidence Intervals for Elasticity in Simple Linear Regression

I'm pretty sure this is a very simple question that I am missing something obvious. I have a simple linear regression with multiple independent variables. I want to calculate the elasticity (no ...
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44 views

Covariance between regression coefficient and residual

Given regression equation Y=Xβ + ε which satisfies all classical assumptions including those of homoscadasticity Estimated regression equation using OLS is the following - Y=Xb + e Where, b is ...
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How to run Panel data analysis when data on the dependent variable is on a 5 year interval basis and that on independent variable is on yearly basis?

I am reading a paper which empirically tests if primary exports affect education attainment in LAC countries over the period 1965 to 2010. It uses percentage of secondary school enrollment as ...
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Minimizing the error: Transforming dependent variable

As given in the picture, question ask us to transform dependent variable, by premultiplying with a weighting matrix W, (which will change the regression coefficient into C'β) such that the expression (...
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What are the statistical tests I need to perform before I regress GDP on multiple variables?

I'm using data over 10 countries for the period 1975 to 2010. My objective is to check if the chosen regressors have significant effect on GDP. I have very basic knowledge of econometrics which I ...
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1answer
38 views

Principal component analysis interpretation

Suppose a wealth index is computed using information on a set of 14 assets that a household possesses. The index is generated using principal components, as the 14 individual asset variables are ...
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2answers
38 views

regression method for data that contain a number of observation for several years

I have a data set about 125 companies. For each company I have the salary and some other variables about the top 5 managers in each company. One observation contains the top 5 managers in each one of ...
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2answers
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Specification bias - estimated variance is biased estimator of true variance of error term

Consider the two models $ (a) y = X\beta + u $ where $X$ is $n \times K$ and (b) $y = Z\gamma + \omega $ where $Z$ is $n \times r$. Under classical assumptions (and $Z$ and $X$ are non-stochastic) if ...
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1answer
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Transforming a matrix of explanatory variable in regression

Given the partitioned regression equation (into $X_1$ and $X_2$), I want to transform $X_1$, say $X^*_1$, such that $X_2$ and $X^*_1$ becomes orthogonal ie. $X_2^T$. $X_1^*$= 0. A matrix can be ...
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1answer
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Can I treat pooled cross-section as panel data and do regression analysis?

I work with a large survey data that is pooled cross-section, i.e, people interviewed are randomly chosen in each time period. This is not panel data. But, I aggregate the individual cells according ...
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1answer
56 views

What is the interpration of results if adding or subtracting a control variable effects the significance of explanotary variables?

I am conducting some regressions on economic growth determinants and I am disillusioned. Essentially by choosing what groups of variable to regress I can get the desired significance. What does this ...
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Regression analysis with interaction and decomposed main effect

I'm trying to figure out if I need to include the main effect in a regression analysis with an interaction if I am already including a decomposed version of the main effect. For example, let: ...
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Interpreting regressions results: different scales and variables interaction

I want kindly ask if someone can help me interpreting the results of regression that I need for my master thesis. The model is this : countries are indexed by i and time by t. Dependent variable ...
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35 views

Should a Price Elasticity of Demand model exclude items that sold out or marked down from the original price

Consider a Price Elasticity of Demand model built with linear regression to estimate the Percent Change in Quantity Demanded given a Percent Change in Price specifically for specialty items which have ...
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1answer
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How to determine correct fixed effects in linear regression model using unbalanced paneldata

I am currently working on a research project regarding the introduction of mandatory earnings guidance regulation in multiple countries within a time span of 10 years (staggered adoption). As I can ...
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2answers
58 views

Should coefficient on interaction term be positive or negative?

I have the following model for housing prices price = $\beta_0$ + $\beta_1$ sqrft + $\beta_2$ bedrooms + $\beta_3$ sqrft $\times$ bedrooms + $\beta_4$ bathroom, where sqrft is square feet. I am ...
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1answer
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Possible regression biases with GDP [x] vs Health expenditure [y] (both per capita)

I am regressing per capita health expenditure on per capita GDP. I have 3 data columns (health expenditure, gdp, population) So my regression function is healthexpenditure/population = b0 + b1.(gdp/...
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Generating Variable frequency

I three variables, zipcode, date (month_year) and name of an installer. I need to generate: 1- a new var that is equal to the number of repetitions the installer name is repeated in month_year and in ...
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1answer
671 views

What is a good proxy for government quality?

Is it ok to use corruption as a proxy for government quality?
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1answer
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When using OLS is it always necessary to drop the weak and insignificant variable? [closed]

Some of my variable shows weak collinear relationship on my dependent variable.. how should I address this?
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1answer
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Can a complex interaction term mean more than what it's composed of?

I'm cross-posting this question on both Economics and Cross Validated to get answers from a different perspective on each field. It is generally accepted to cross-post if the question is tailored to ...
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28 views

How should I rebase my GDP?

I have a constant GDP data from 1988 to 2009 in constant 1985 prices and GDP data from 2009 to 2017 in constant 2000 prices. My question is how should I rebase my GDP? Upon searching the web, i don'...
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2answers
46 views

What is the tolerable level for multicollinearity? and possible remedial measures for it?

My data has issues of multicollinearity. Upon estimating, I found out that my data have high levels of VIF In however I was confused as to what level of VIF can I possibly ignore the issue of ...
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10 views

Transformation of cutpoints in Ordinal Probit/Logit regression

The likelihood for an ordinal probit/logit regression model is given as - $f(y|\beta ,\gamma ,z ) = \prod_{1}^{n} \left [ \Phi (\gamma _{j} - x_{i}'\beta ) - \Phi (\gamma _{j-1} - x_{i}'\beta ) \...
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1answer
37 views

How do I fill gaps in my data?

In my study, I have 5 independent variables which contains 21 observation each. However one of my independent variables have 3 gaps. What should I do? e,g I would need to know the effect of ...
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1answer
42 views

Are unit root tests necessary or useful on small samples of time series data?

I have a 16 year time series (annual frequency with 16 observations). I will conduct an OLS regression. In this setting do I need a unit root test? Do you have additional suggestions for things that ...
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1answer
43 views

Should the control variables in an econometric regression be correlated with both the dependent and the primary independent variables?

If, for instance, my dependent variable is some happiness index, and my independent variable is a dummy for whether they experienced some randomly occurred natural disaster. I am trying to analyze the ...
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1answer
34 views

Correct Equation for Pooled OLS Regression (with Time Dummies and Interaction Terms)

I have a question regarding a pooled OLS regression. Basically, I’m not sure I’m writing out the equation properly. The data is on feature films released between 2006 and 2016 (11 years); box office ...
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2answers
176 views

What's the use of '% to GDP' type of variables?

In my study I will look for the relationship between the Gini coefficient and trade, FDI and other variables. However, as I was regressing it... the result turn out to be insignificant. My data that I ...
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0answers
44 views

How do we calculate Beta in a OLS regression of the mean of y on the mean of lag of y?

In a simple OLS regression we calculate the estimator Beta by dividing the covariance of x and y by the variance of x. How do we calculate the estimator Beta if we regress the mean of a variable (at ...
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1answer
50 views

What R-squared is a low R-squared?

I keep hearing that R-squared does not really matter in economics research and that due to the unpredictable human nature, economics research regressions tend to have low R-squared. But how much is ...
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2answers
129 views

OLS estimator derivation: second-order condition to prove global minimum?

In deriving our ordinary least squares estimates, we can partially differentiate the sum of squared errors $\sum_{i=1}^{n} {e_i^2} = \sum_{i=1}^{n} {(Y_i- \hat{\alpha}-\hat{\beta}X_i )^2}$ with ...
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1answer
41 views

Multivariate linear regression: how to test for whether the slopes are the same?

If I regress wages on education and the dummy variable gender using a linear conditional expectation function (wage = a + b(education) + c(gender)), how can I test that the slope b is the same for ...
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17 views

Estimation of investment adjustment costs

Hi I am working on a problem set in my macroeconomics course. I have a hard time figuring out how to get started on one of the problems. The set-up is the following. A price-taking firm maximizes: $\...
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16 views

How to do elasticity modeling for products where there is slab pricing like electricity?

I have few product categories eg prod1 prod2. Each category have similar products. So prod1 has 3 similar products with slight difference in features and prod2 has 5 products with slight differences. ...
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32 views

Demand equation with demographics

I am trying to reconcile the derivation of a demand equation with what I actually run in an OLS model. After solving $$max_{x_1,x_2}U(x_1,x_2)= \alpha ln(x_1) + \beta ln(x_2)$$ subject to $$p_1x_1+...
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2answers
118 views

Unbiased but inconsistent estimator [closed]

Assume a random sample X1, ..., Xn with a normal distribution with mean μ and variance σ2. How do we know the following estimator is unbiased, but inconsistent?
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1answer
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Justification for my Random Effects estimation

I need to defend my use of the Random Effects (RE) estimator in my economics project. I've been told in cross validated that the proper place for the question is here. The causal effect of the ...
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Controlling for a variable in OLS - Stratification and Reaggregation. Simple Example

In his engrossing book "Naked Statistics" Charles Wheelan begins to explain how controlling for variables works by stratifying the sample. However, he stops short of explaining the reaggregation, ...
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92 views

Profit maximization problem using linear regression (pooled OLS)

I'm currently on a university assignment where I'm stuck more or less in the middle. I have to answer the following problem: Suppose you are interested in estimating the production function for ...
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How do I measure effects over years in panel data with individuals?

I'm working with a longitudinal panel dataset that surveys the same few thousand individuals biennially and I have six years of this data. My dependent variable would be how much individuals spend on ...
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Can A/B be a better variable than separate A, B in linear regression?

While learning Econometrics, I got curious to know whether A/B can make a better variable than separate A and ...
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1answer
81 views

Linear Regression Assumptions of Homoskedasticity

When I studied linear regression analysis, one of the assumptions taught was that of homoskedatiscity. I understood that homoskedasticity was required for significance testing on the coefficients. ...
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1answer
83 views

Why does instrument exogeneity imply conditional mean zero?

In the following slide ECON4150 - Introductory Econometrics Lecture 16: Instrumental variables, Monique de Haan it says that "instrument exogeneity implies $E[u_i \mid Z_i]=0$" where instrument ...
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1answer
50 views

Dummy variable regressor OLS coefficient formula

Consider the standard linear regression model: $y_i = \alpha + \beta D_i + e_i$ where the coefficients are defined by linear projections and $D_i$ is a dummy variable. In the population, the ...