Indirect Least Squares
- Estimates parameters of models when the relationship between inputs and outputs is non-linear and not directly measurable.
- Common in econometrics and finance: first estimate the dependent variable at different input levels, then fit a parametric curve to those estimates.
- Fits can use mathematical models such as quadratic, polynomial, linear, or exponential curves.
Definition
Section titled “Definition”Indirect least squares (ILS) is a statistical method used to estimate the parameters of a model when there is a non-linear relationship between the dependent and independent variables.
Explanation
Section titled “Explanation”ILS is applied when the true relationship between variables is unknown or difficult to measure directly. The typical approach is to estimate the dependent variable at a set of values of the independent variable, then use those estimates to calculate the parameters of a chosen mathematical model (for example, quadratic, polynomial, linear, or exponential) that describes the relationship.
The method is commonly used in fields like econometrics and finance where non-linear relationships arise and direct measurement of the functional form is challenging.
Examples
Section titled “Examples”Estimating product demand
Section titled “Estimating product demand”The dependent variable is the quantity of the product demanded and the independent variable is the price. The true relationship is non-linear, with a negative relationship between price and quantity demanded. Using ILS, the analyst first estimates demand at different prices, then uses those estimates to calculate the parameters of the demand curve, for example with a quadratic or polynomial model.
Estimating investment return
Section titled “Estimating investment return”The dependent variable is the return on an investment and the independent variable is the risk associated with the investment. The true relationship is non-linear, with a positive relationship between risk and return. Using ILS, the analyst first estimates returns at different levels of risk, then uses those estimates to calculate the parameters of the return curve, for example with a linear or exponential model.
Use cases
Section titled “Use cases”- Econometric applications where the functional form between variables is unknown or hard to observe directly.
- Finance applications for estimating relationships such as risk versus return when the relationship is non-linear.
Related terms
Section titled “Related terms”- Dependent variable
- Independent variable
- Parameters
- Model
- Demand curve
- Return curve
- Quadratic model
- Polynomial model
- Linear model
- Exponential model
- Econometrics
- Finance