Public Lectures on Structural Econometrics - CEMMAP masterclass - Shared screen with speaker view
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Are there any good reference texts that would capture most of the topics for this course?
I can't access the lecture slides of today's lecture, is this an issue for everybody?
You mean from the website?
Yes, me neither :(
@Dante: they are up here
Thank you, I was getting a 404 error from the website
Yes: if you refresh the page all should work now
How do we choose theta1 and theta2?
Note that this is given by the structure of the problema to estimate
The function f1 only depends on theta_1, whereas the function f2 depends on both
@Irina: it is for sake argument. Bob is saying: suppose you have a model that separates the way he is describing i.e. suppose you have a modular structure
how should you proceed then?
I see. Thank you!
But we know the distribution of epsilon_n?
Otherwise, we wouldn’t be able to simulate
@Irina: the point Bob was making is general. To simulate your model, yes, you need to know the DGP it implies
Can someone give me a sense of what the function Psi is? I am still a bit lost as to what it concretely represents
“The behavioural equations of the model”, what does that refer to concretely?
It's a summary of all the functional and distributional assumptions of the model.
@Lisa: it is like a first order condition, an equilibrium condition, etc
@Lisa as concrete example think of labor demand = labor supply in equilibrium => labor demand - labor supply = 0
With labor demand and supply given by some functional form
@Lisa&Milena: yes! Think about a budget constraint, a resource constraint, a first-order condition for the choice of a continuous action, and similar. They can all be written in Psi(.)=0 form
thanks everyone! I get it now
Another question: how do you “simulate” x and y? Do you draw them?
Or do you simply simulate epsilon
That depends. Are they exogenous or endogenous?
@Lisa, yes, you will assume a distribution for epsilon, and draw from there. Then get the draw of y and x based on the model and the draw of the epsilon.
If they are exogenous, then you need to draw them the same way that you draw epsilon
If they are endogenous, then they are defined by the model
mmh ok I see, thank you
Could I say that in Simulated Method, we simulated the integral, rather than have the analytic form of the integral (like in previous lectures)?
@Pengzhan yes, you use simulated method to compute the integral if there is no analytical solution to the integral.
For an example, think multiple choice probit model where you need to compute triple integrals of normal densities .
@Xiaoxia Thanks. My feeling is that to get the analytical solution we need more assumptions, especially on the error terms.
or different assumptions that leads to simpler integrand.
I mean, it seems that with enough assumptions, we could always get the aggregation expression. Simulated methods is another way to do it.
Hmm... I'm not sure I see what you mean. Would you like to ask the professor?
@Pengzhan: in rich structural models you may not be able to derive the analytical form of the integral so you may end up reverting to simulation in this case too
In many cases due to non-linearities, the dimentionality and the distribution of epsilon it is impossible to compute the integrals analytically. Simulation methods help us get around this.
@Elena, thanks! It kind of answering my puzzles. My feeling is that there were many paper with anaytic results in Rust times. But nowadays more paper without anaytic solution but SMM.
How do we choose A_N in slide 28?
@Penghzan: yes, many interesting models are simply very difficult (or impossible) to solve analytically -- they involve multidimensional functional equations to solve for Psi(.)=0, many dimensions of unobservable to integrate over, etc
Thank you Elena and Xiaoxia!
Miguel Angel Cabello
What is the difference between system and difference gmm? When is it appropriate to use one vs the other?
Have to leave now. See you next weekend!
@Handy, some people use this terminology to refer to different ways of dealing with dynamic panel data methods (Arellano-Bond would be the difference gmm and Arellano-Bover refers to the system gmm). If that is the case, there is a long answer about one versus the other, but the short answer is more assumptions (Arellano-Bover assumes the process is stationary) vs more robustness (Arellano-Bond is not very robust when the autoregressive coefficient is close to 1).
Ok thank you Joan