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I am working with some real estate data on housing units. For a given market, I have data on occupied units, rents, and control variables such as population, demographics, income levels etc.

I'd like to obtain the diminishing marginal effect and the elasticity estimate. i.e the point at which rents have a diminishing effect on occupied units.

I attempted to do this using ols - log-log regression, I need non-linear model to fit the data.

import statsmodels.formula.api as sm

model1 = sm.ols(formula = 'np.log(Occupied_units) ~ np.log(Rent) + np.log(Income) + np.log(unemployment)', data=df).fit()

My question is, what non-linear models can I use to estimate this diminishing effect? and how do I interpret the results? i.e the point at which the effect starts to diminish.

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