5

It's not true that "no-one uses matching these days". It's a bit too definitive. For example, see Bilicka (2019) who recently published in the American Economic Review. I am sure it's possible to find other recent examples. It's true however that the matching estimator is much less popular than the DiD or IV. This is because the results are not ...


4

Think about a regression where you have two factors. Normally when you have a constant in the regression you would put one level of each factor to 0 as a reference level. Leaving out the constant you have two factors and put one reference level to 0 for one of these. The situation is similar here in the sense that you have firm and individual level fixed ...


3

Gale and Shapley barely make any assumptions about preferences. They don't need a functional form, simply an ordinal ranking of the options. Moreover, there are no transfers in this setting, only the discrete matching options. Even Kelso and Crawford do not use quasi-linear utility. They assume some utility function that is increasing and continuous in ...


2

I gave you an extremely vague lead in my other comment. Thinking about it a bit harder, I beieve you are right with having a look into the matching literature which I know a bit less. Here is a setting that might be of interest: Kelso & Crawford, Econometrica 1982. They study $m$ workers (=buyers in your setting) and $n$ firms (=items), where a worker ...


2

Yes, it is correct. You can (for instance) write a Taylor expansion: \begin{align*} [1-(1-\frac{x}{un})^n]^x & = [1-e^{n ln(1-\frac{x}{un})}]^x \\ & = [1-e^{n (-\frac{x}{un} + o(\frac{1}{n}))}]^x \\ & = [1-e^{-\frac{x}{u} + o(1)}]^x \\ & \sim [1-e^{-\frac{x}{u}}]^x \text{ when } n \rightarrow +\infty \end{align*}


2

An alternative approximating approach you could use as as check might be to say there are $X$ job offers in total and $u$ unemployed. So the probability that an individual does not get a particular job offer is $\left(1-\dfrac{1}{u}\right)$ and so the probability the individual does not get any job offer is $\left(1-\dfrac{1}{u}\right)^X$ which is $\left(\...


2

The matchingMarkets package in the R software now implements two constraint encoding functions to find all stable matchings in the three most common matching problems: hri: college admissions problem (including the student and college-optimal matchings) and stable marriage problem (including men and women-optimal matching) sri: stable roommates problem. ...


2

Patrick Prosser has some great java code at http://www.dcs.gla.ac.uk/~pat/roommates/distribution/ which, among other things, can compute all the stable matchings in roommate problems. The code is for roommates problems, but Patrick's code allows preferences over roommates to include unacceptable roommates. To implement a two-sided market, just make sure any ...


1

I can't suggest any research papers, but I can suggest one way of studying this problem: using an agent-based model. For example, this is a simple model of an auction on NetLogo: https://ccl.northwestern.edu/netlogo/models/BiddingMarket. Maybe you can tweak the code to make the model run a simulation of your problem. If this wasn't what you were looking for, ...


1

I found one implementation of TTC in python at http://www.dreamincode.net/forums/topic/377004-algorithmic-game-theory-top-trading-cycle-procedure/?ref=dzone. However, it does not seem to include the two additional features I was mentionning. With of without these two features : I would still love to hear about more implementation of TTC, and about ...


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