OLS Linear Regression

Overview

This class allows you to OLS linear regression estimation with the ability to control for fixed effects according to some choice variables. Moreover, you can use robust methods (heteroscedasticity and cluster robust std. errors) to estimate the variance-covariance matrix.

Inputs

The OLS linear regression model can be called by using the class ols in the main file. To call this class, you need the following inputs:

• dataset is the dataset where you store the data you want to pass into the ols model.
• regressors is the list of strings of all explanatory variables you want to use to explain y. It is very important that you pass a list of strings even if your explanatory variable is just one variable.
• dependent is the list of the string of the column that stores your dependent variable in your dataframe. It is very important that you pass a list of strings even if your explanatory variable is just one variable.
• cons is True by default, but if you want to regress without intercept, just declare cons = False .
• fixed_effects by default is an empty list. However, you can pass a list with the string of all variables you want to use for fixed effects. For example, if you have a panel dataset of countries years, you can pass a list of string of the variable that stores countries and a string for the variable that stores years.
• method is "standard" by default, but if you want to a heteroscedasticity robust variance covariance matrix, just declare method = 'heter' Moreover, if you want to estimate the variance covariance matrix with clustered method, you have to pass method = 'cluster'.
• cluster by default is an empty list. However, if you decided to use a clusterd estimation, you have to pass a list containeingn the string for the variable you want to use as clusters.

Features

• To summarize the results, just call "your object name" . summary(). It will print just the table with betas, std, t, p value, and confidence interval.

• Use coefficients() if you want to obtain beta coefficients.

• Use standard_dev() if you want to obtain standard deviation for betas.

• Use fitted() if you want fitted values.

• Use residuals() if you want residuals.

• Use summary() if you want a table form summary of the estimation.

Example

To initialize the model (suppose the module is imported as reg:

model  = reg.ols(dataset = df, regressors=['exper','expersq','kidslt6','kidsge6'],dependent = ['lwage'])

To call the informative summary:

model.summary()

And here is the output:

Linear regression
---------------------------------------------------------------
lwage      coefficient           se          t    p_value       low 95       high 95
-------  -------------  -----------  ---------  ---------  -----------  ------------
exper       0.0456439   0.0141809     3.21869        0      0.0178494    0.0734385
expersq    -0.00101304  0.000417998  -2.42356        0.02  -0.00183232  -0.000193768
kidslt6     0.0314494   0.0892375     0.352424       0.72  -0.143456     0.206355
kidsge6    -0.0345768   0.0283234    -1.22079        0.22  -0.0900906    0.020937
cons        0.875164    0.120301      7.27478        0      0.639374     1.11095
---------------------------------------------------------------