this is a topic that i feel is very implicit in a lot of economics, but is some times brushed over in interest of getting strait to the model or the maths. But often i realise i don't actually know exactly what i'm doing/modelling.
So I would love people's thoughts, truly understanding these terms and differentiating between them in context:
Example:
Let's take the following constrained optimisation problem (I'm assuming i can think of this as a "model" e.g. of consumption choice, under resource constraint?
- $U(x_1, x_2) = (x_1x_2)^{1/2} s.t. G(x_1, x_2, p_1, p_2, m) = p_1x_1 + p_2x_2 - m = 0$
Where normally i understand we may not explicitly write the constraint as a function of m, but i wan't to in this case to help develop the fullest understanding:
Paramater vs Decision Variable:
- $p$ & $m$ are our parameters of the model, and specifically they are parameters of the function $G$ and, $x_i$ are our decision variables in the model and of both functions?
Endogenous Vs Exogenous:
I'm using the following as a definition of endogenous variable, is this correct and appropriate?
An endogenous variable is a variable that depends on other variables in a statistical and/or economic model. If the value changes for an endogenous variable, it is because there are changes to its relationships with other variables in the same model. Therefore, it is similar to a dependent variable because both are influenced by one or more independent variables.
In this model i would assume that $p$ and $m$ are Exogenous? As they do not depend on other variables in the model, they are set externally?
I assume $x_i$ is Endogenous, because the amount we set for $x_1$ depends on the value of $p$ and $m$ e.g. this is made explicitly in the compensated demand function:
$x_i^* = \frac{m}{2p_i}$
Is this correct? Because we are choosing our optimal level of $x_i$ based on our model assumptions (e.g. preference assumptions), and the specific values of the parameters, $p$ and $m$.
Independent vs Dependent:
In layman's terms, I'm seeing Independent variable's as the one's we change e.g. the x axis, and dependent variable is the variable we measure e.g. the y axis.
- So in this case would our independent variable be the $x_i's$ and the dependent variable actually be the functions $U$ and $G$.
- Or would our dependent variable the optimal value of $x$ that we determine, our $x_i^* = \frac{m}{2p_i}$
Further Complications: I also want to discuss when the state of these variables may change, i.e. when looking at the maximum value function, exogenous parameters can become endogenous i believe. But i will save this for a separate question, thanks!
Questions:
- Am i correct?
- Is there a simple way to think of this going forward
- What are the important implications of getting this right and wrong (for example understanding dependencies when taking derivatives etc.)