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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17 views

How do 'econometric' explanations differ from 'economic' ones?

I am interpreting some coefficients of a regression model and have been asked to, first, give an 'economic' explanation and then an 'econometric' explanation as to why coefficients differ as more ...
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68 views

How do I obtain a correlation between two variables?

Can I differentiate a quadratic regression model formula with the form $$Y_i=\beta_0+\beta_1 X_{1i} +\beta_2 X_{1i}^2+\epsilon_i$$ (added to this formula would be other control variables e.g dummy ...
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29 views

Interpretation of Difference-in-Differences Regression Results when Only the DID Coefficient is Significant

I have a standard DID regression of the form: Y= β0 + β1*[Time] + β2*[Treatment] + β3*[Time*Treatment] + ε where Time is a dummy equal to 1 for period after policy change and Treatment is a dummy for ...
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Difference-in-Difference (DID) Regression with Non-Stationary (but Cointegrated) Treatment and Control Groups

I would like to run a DID regression between two periods where each period spans multiple years. For example: Period 1: 1970Q1-1990Q4 Period 2: 1991Q1-2010Q4. My treatment and control variables are ...
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How can you find all parameter estimates are statistically significant but without performing any sophisticated calculations?

I have a question that contains a list of parameter estimates and their related standard errors. It then goes on to ask that I explain how I know all parameter estimates are statistically significant ...
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28 views

How to properly interpret logged interaction variables

I have the following regression to interpret elasticity of demand: Ln(demand) = const - 0.6*ln(fare) I understand that a 1% increase in fare results in a 0.6% decrease in demand I want to add dummy ...
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1answer
46 views

How to interpret this regression coefficient?

I am performing a simple single variate regression on the variables crime rate (denoted by crrate) and the probability of getting arrested (denoted by prarrest). To be precise, the variables are ...
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31 views

Analytical approach to estimate equilibrium price for Real Estate Property

I am looking to calculate the equilibrium price, i.e an optimal price that I can set without affecting demand and maximize revenue. I've gathered historical data: occupancy rates, asking rents for ...
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Using margins after probit estimation to equal probabilities between almost identical individuals

I'm considering a Probit model for the probability that a student will finish the course based on their hours of study, age, sex, origin, how they passed the previous course and labor market situation ...
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18 views

Linear Regressions: When to expect the residuals to NOT have conditional mean 0?

Suppose that $Y, X,$ and $U$ are random variables such that the regression $$Y=\beta_0+\beta_1X+U$$ is the best linear predictor of $Y$ given $X$. My question is, when can we expect $E(U|X)=0$? I ...
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Controls for a GDP per capita model

I'm constructing a model to test the relationship of some different factors on GDP per capita in a single year using simple OLS regression. Most studies I've found on economic growth simply use the ...
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Demand-side effects meaning

I found the term of demand-side effects in the abstract of the following paper: journals-sagepub-com/ DOI/abs/10.1177/0974930619872083 . What does that mean? Can you explain it to me please? I need ...
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Social-Network Peer Effect Regression Analysis

I have locally transformed model from Bramoullé 2009 to be estimated for regression estimation $\begin{equation} ( \mathrm{{I}} - {G}_{l}^{*}){y}_{l} = \beta_2( \mathrm{{I}} - {G}_{l}^{*}) {G}_{l}^...
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diff and diff with multiple time periods - test parallel trend assumption

I am performing this resgression: $$ y_{it} = \beta_{0} + \beta_{1}\text{Treat}_{i} + \sum_{j \neq k} \lambda_{j} \text{Year}_{t=j} + \sum_{j \neq k} \delta_j \left( \text{Treat}_i \cdot \text{Year}_{...
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Negative elasticity of substitution in a CES production function

I have empirically estimated the elasticity of substitution parameter in the following model: $$Y_t=[(A_1L_tK_{t})^{\rho} +(A_2M_{t})^{\rho}]^\frac{1}{\rho} $$ here, $Y_t$ is output, $A_i$ is a ...
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model design - fixed effects model for paired differences

I have two panels. One panel that consists of an economic indicator variable across firms and years. The second panel consists of the same economic indicator variable across the same firms and years. ...
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How to determine intergenerational income elasticity over more than two generations?

I do have income data for individuals from different families over three generations (y, yparents, ygrandparents). To determine the two-generational social mobility, I run a simple linear regression: ...
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Higher interest rates and default probabilities for longer loan term

I am analyzing LendingClub data with two available loan terms: 36 and 60 months. In the course of my analysis I have spotted that both the interest rates associated with each loan and the default ...
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1answer
21 views

Understanding General Least Squares

From what I understand, we have our OLS estimator in matrix form which is, $$\beta_{OLS} = (X'X)^{-1}X'Y$$ What we want to do is transform this, as the assumption that we have constant variance is ...
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How do I convert change over a ten-year period into annual growth rate?

I am working on an econometrics project where I need to find the impact of climate change on agriculture in India. The project requires me to use an existing econometric model from some peer reviewed ...
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51 views

Difference between a multiple regression and several linear regressions?

Context: I'm an undergrad who took Intermediate Econometrics more than a year ago and I'm trying to brush up on some of the skills. As I was reviewing multiple regression, I realized I didn't quite ...
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Does anyone recognize the shape of this residuals vs. fitted plot?

Hello Stack Exchange community, I'm running a regression on a survey dataset which consists of 45,381 individuals in 36 countries using Stata. My model is specified as: ...
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1answer
51 views

Hedonic regression and attribute-shares in house prices

Given a house with price $P$ and attributes $h_1,\dots,h_n$, I want to estimate how much each attribute costs as a percentage of house price $P$. In other words, if we express house price as the sum ...
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Value relevance, informative information, Financial statements, IFRS 9

What are the theories that say that the disclosures in the annexes of the report and accounts are less relevant than the figures in the financial statements, is there anything? I've been looking for ...
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35 views

Meaning of regression coefficients

I am having some trouble understanding exactly what is meant by the "true" Regression coefficients. Let's say it is stated that "the true regression coefficients are given as $y=a+bx+e$ where the ...
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1answer
32 views

Logistic regression: Equation for marginal effect at the mean

I am estimating the following logistic regression (binomial family) by maximum likelihood: $$ \ln\left(\frac{Y}{1-Y}\right) = \beta_{0} + \beta_{1}D + \beta_{2}X + \epsilon$$ where D is a dummy. ...
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1answer
33 views

Forecasting quarterly EUR/USD exchange rate

My aim is to forecast the one-quarter ahead EUR/USD exchange rate. I have constructed a regression model with the following as explanatory variables: exchange rate in the previous quarter, EUR/USD ...
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Measuring time discount in scheduled services: is there a literature in empirical economics?

Prices might be different, for the same service at some date, if you try to acquire the service two weeks in advance and again at a closer date (e.g. two days prior to the scheduled date), such as ...
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Can you take the moving average of quarterly data of an explanatory variable in a regression to smoothen noise and get more accurate coefficients?

I'm trying to use acceleration of quarterly data on household debt (the difference in the difference in debt) in a regression on unemployment (only concerned with correlation) but quarterly data is ...
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How to use schooling years information to better identify the returns to education

Assume that you have the dates of birth of the individuals in the dataset. Imagine that in 1985, the Ghanaian government has decided to raise the school leaving age from 10 to 15 years old. How would ...
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35 views

Detecting Multicolinearity

Are high R square and low t-stats a signal for multicollinearity? What is the nature of this problem and correction? Also, how do you generally decide if the problem is high enough to be corrected?
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How do I run a regression with the restriction that one set of parameters are proportional to another?

I'm running a regression with a set of 3 dummy variables (for four categories of a variable) and these 3 dummies interacted with a continuous variable. I want to impose the restriction that the vector ...
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33 views

Moderation effect of a variable [closed]

Should we include some control variables in regressions when we test a moderation effect of a variable?
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104 views

Econometrics: why the i.i.d assumption and weak exogeneity assumption imply strict exogeneity?

The proposition is from lecture notes of advanced econometrics of Yongmiao Hong: A1: $\{Y_t,X_t'\}_{t=1}^n$ is an i.i.d. random sample. A2: $E(\varepsilon_t|X_t)=0$ almost surely with $E(\...
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1answer
40 views

Is conditional mean independence, $E(e_i | x_i)=0$, a different assumption from $E(x e) = 0$? (from Hansen)

This question comes out of Hansen's Econometrics ((https://www.ssc.wisc.edu/~bhansen/econometrics/Econometrics.pdf)) In section 2.18, we only impose the assumptions of finite variance and $Q_{xx}$ ...
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19 views

Effect of Agricultural products on GDP/capita

What is the best way to regress this effect. I would like to show the effect of the production of different agricultural products (Rice, maize, wheat etc..) have on the gdp of a country (India in this ...
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47 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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19 views

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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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
183 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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59 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
57 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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55 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
59 views

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 ...