I am currently considering the selection of explanatory variables in a Tobit regression model after completing efficiency scores estimation by DEA model in order to assess the factors influencing efficiency scores.
I have a question: if the explanatory variables in the Tobit model are closely related to the variables used in the DEA model, does this analysis hold any significance? For example, my DEA model analyzes the operational efficiency of the banking sector with inputs such as the total number of employees, total fixed assets, total operating expenses, total loans, and total deposits; the output variables include interest income, non-interest income, and NPLs.
If I choose explanatory variables in the Tobit model like Return on Equity (ROE), Cost to Income Ratio (CIR), NPL ratio, and Net Interest Margin (NIM), does this choice make sense?
Thank you very much for considering my question
The selection of variables such as Return on Equity (ROE), Cost to Income Ratio (CIR), NPL ratio, and Net Interest Margin (NIM), for the regression does not make sense, because multicollinearity will be introduced into the model that will make the vsriales to move together
You will need to use external factors not related to the variables you have use in the fist stage, i.e., to estimate the efficiency scores. Be careful with ratios!!, I am not convinced they are useful, they are not straightforward plus they need to be analysed with other ratios or values, items, accounts from the financial statement. On the other hand, I am unsure why will you use a tobit regression rather than for example, a truncated regression (at unitary value, i.e., removing efficiency units from the sample).
For Tobit regression, variable selection involves identifying predictors that significantly affect the censored outcome, often using statistical methods like stepwise selection or LASSO for regularization.
For a DEA (Data Envelopment Analysis) model, variable selection focuses on choosing input and output variables that accurately reflect the efficiency of decision-making units, usually through domain expertise or exploratory data analysis to ensure meaningful efficiency measurement.
I would think that the Cost to Income Ratio (CIR), NPL ratio, and Net Interest Margin (NIM) are as much determined by efficiency as the reverse. If so you have endogeneity problems. I would expect that variables such as distribution of loan and deposit size, frequency of transactions, computer systems branch network, and similar features determine efficiency (and some of your other variables.
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