I need help specifying my economic model given United States Lithium Renewable D

Question

I need help specifying my economic model given

United States Lithium Renewable Demand = _1 Real GDP+ _2 CPI+ _3 CPI Energy+_4 Federal Funds Rate+ _5 Unemployment Rate+_6 Total Renewable Energy Production+_7 Solar Energy Consumption+ _8 Wind Energy Consumption+_9 Total Renewable Energy Consumption+_10 Utility-Scale Solar Energy Consumption for Electricity:Electric Power Sector + _11 Solar Electricity Net Generation+_12 Lithium Imports+_13 Lithium Exports+_14 Estimated Lithium Consumption+ _15 World Production (Gross Weight)

This model breaks every assumption of the classical linear regression model. Firstly this model suffers from omitted variable bias. Secondly, the model suffers from multicollinearity of certain variables. Thirdly the model suffers from heteroscedasticity after running a variance inflation factor test on certain variables. Lastly, I know the model is incorrectly specified after attempting to perform a Mackinnon Davidson- White Test(MWD) because there are undefinable points in the data ie.”0”; making it impossible to find the linear specification because it can’t be defined as linear nor log-linear. My question is where do I go from here? How would I re-specify the model not only to solve these issues but also fix certain assumptions. Thank You

Explanation / Answer

Firstly,To remove omitted variable bias, you should include those variables that are significant in predicting the outcome but have been omitted, no need to add unnecessary predictors, that will lead to overfitting.

to remove multicollinearity, you may perform a Principal Components Analysis (PCA), which cuts down the variables to a subset of the original variables, and also these are uncorellated.

This can be done in R using the command prcomp()

for heteroscedasticity, one way to deal it is by using Weighted Least Square, you need to weight the variables with inverse of its variance, this is a common method.

As far as I know MWD test is to check whether linear or log linear model fits the data. but you cannot use log on 0,thus you have to stick to linear model,unless otherwise specified.

Or you can check the residual plot, if the plots hows a non linear pattern, then you should fit some polynomial.

This is all I can Say without the data.

hope it helps.

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