Re: st: Regression Discontinuity (RD) Designs, sharp discontinuity: basic question about implementation with "rd"

[Stefano Lombardi <lombardi_stefano@fastwebnet.it>]

Hi Ariel,

thank you very much for your interest. You got the correct 
interpretation for X and the cut-off as well.

With respect to the treatment ("severance payment"), I wrote a bit 
confusingly. The "job tenure" variable is sharply discontinuos at month 
36, in the sense that if a person is laid off after having worked for 13 
or 14 or ... 35 months in the same place, he is not going to receive any 
sort of lump-sum payment. Otherwise, if one works for 36 months or more 
and is laid off, then the employer is obliged to immediately pay him a 
fixed amount of money (three months of salary of the job just lost).

Hence, every person in my dataset has been laid off, but only someone 
will receive the lump-sum severance payment (with probability 1 after 36 
moths of job tenure). The thing which probably can make some confusion 
is that I am not considering any unemployment benefit (which starts at a 
certain point and then continue to be received over time), but a 
"one-time" payment.
Also, we are interested in knowing whether this kind of treatment 
affects the duration unemployment (the "nonemployment" duration, which 
goes from the layoff to the start of the new job).

You are completely right: job position could be a very important issue. 
But the dataset is quite homogenous from this point of view. In any 
case, in the hypotheses checking part of the work I have graphically 
considered whether there is a "jump" at the threshold of this variable. 
So you are right, but I can still check if there is a violation of the 
continuity assumption at the threshold, and actually (at least from a 
graphical point of view) there is not evidence of that.

Same reasoning for the previous job salary level. Since the severance 
payment equals three months of the last job, the size of the payment is 
not the same for every one who receives it. But again, the previous 
salary range is not very wide. There are indeed some extreme cases in 
both directions, but from a graphical point of view the "previous 
salary" variable passes quite smoothly through the cut-off.

One main concern could be that employers fire more people "just on the 
left" of the 36 months cut-off (in order to elude the compulsory 
payment). But this is not the case: the number of layoffs (vs the 
previous job tenure) does not change much at the threshold. For people 
more used with the labor economics framework, my dataset is quite 
comparable with the one of the David Card's work of 2007. Of course a 
certain dose of critic is always necessary, but I consider that a very 
good work, and I wanted to start from that one.

Actually, none of the other variables that could give some problems at 
the threshold seem to be discontinuous at the threshold. Hence I would 
have liked to proceed with the "rd" command, but I really cannot 
understand what is the syntax/input problem.

Basically, on the y axis I want the mean nonemployment duration (in 
days), while on the X axis I want the job tenure in months. Hence I 
computed the mean of y conditioned to X. I did through:

egen cond_mean_y = mean(nonedur), by(ten_cat)

Now I have for each job tenure month between 13 and 52 the correspondent 
mean of the nonemployment duration (and I can easily make the plot). But 
then why "rd" does not returns the same? Where I got wrong?

I believe that "rd" should "automatically" do it by (1) including "job 
tenure" in days, and (2) choosing the correct bandwidth. The first thing 
that I tried was to include the forcing variable as continuous, but I 
couldn't manage to have a graph as I mentioned in the above paragraph..

And apart from the graph itself, I am clearly making some kind of error 
somewhere in the "rd" command, since I receive the error which i 
reported in the last post. It is also clear that the error is due to my 
ignorance, but how can I solve this problem?

Thank you very much,

Stefano











I clearly have to make Stata considers just points near to the cut-off 
in order to estimate the jump. However, without expliciting that, I 
think that Stata should do it by itself. About the bandwidth, if I am 
not wrong, Stata chooses the optimal one and also tries two others.

I do not understand

d if I hav eto insert the average


Il 11/10/2011 17:09, Ariel Linden, DrPH ha scritto:
> Hi Stefano,
>
> I am a bit confused by your variables. If I understand correctly, your X
> variable is previous job tenure which is ranges from 0-52 months and your
> cutoff is 36. However, your "treatment" is whether a person gets severance,
> which, I am assuming can be at any point along the X variable continuum?
>
> In the RD design, the cutoff is the treatment assignment, so to make it
> work, you'd have to have everyone at or above 36 months receive severance
> and everyone below 36 months not receive severance. I am not sure that is
> what you have done here?
>
> I am not an economist (I don’t even play one on television), but I am not
> sold on the premise that length of previous tenure is associated the outcome
> variable (unless it is mediated vis-à-vis the severance). I also assume that
> the size of the severance will be associated with the Y variable, and may or
> may not have a strong independent association with the X variable (the
> recent CEO of HP just got fired after a year on the job and got a
> multi-million dollar severance). Thus, the type of position (or perhaps
> salary level of previous job) will moderate the relationship.
>
> Therefore, I am not sure you have the right variables, or the right modeling
> approach here. Perhaps you should consider switching to a mediation
> (controlling for moderators) approach, or perhaps a time series approach
> with two or three variables, (a) length of previous job tenure, (b) length
> of time unemployed thereafter, (c) relative size of severance?
>
> I hope this helps
>
> Ariel
>
>
>
>
> Date: Mon, 10 Oct 2011 21:15:37 +0200
> From: Stefano Lombardi<lombardi_stefano@fastwebnet.it>
> Subject: st: Regression Discontinuity (RD) Designs, sharp discontinuity:
> basic question about implementation with "rd"
>
> Hello everybody,
>
> I have a big problem in computing a sharp regression discontinuity
> design via the "rd" function. I have read a number of papers about the
> underlying theory, but I cannot carry out even a very basic RD design..
> Unfortunately I found very little information on Statalist and on the
> whole Internet as well.. Could you please give a hand?  Every comment
> would be tremendously helpful. Here is my (labor economics) setting:
>
> "tenure_cat":    discrete forcing variable, Z = last job tenure (in
> months = 13, 14, ..., 52)
> "severance":     treatment, X_T = lump-sum severance payment
> "nonendur":     outcome, y = non-employment duration (days between the
> layoff and the start of the new job)
> The cut-off is at Z_0 = 36 months (after three years of job tenure, a
> person who is laid off is going to receive a severance payment with
> probability 1).
> Does the severance payment cause a variation in the job search?
>
> I also have "mean_nonedur" = "nonedur" mean conditioned on "tenure_cat"
> (basically the mean of y for each month between 13 to 52)
>
> My aim is to set a RD design with the mean nonemployment duration in
> days against Z in months. My first best would be to estimate the outcome
> gap through a second or higher order polynomial. All the data "far" from
> the cut-off have already been manually eliminated, hence I simply need
> to run the RD design with all the available data.
>
>
> As very first step, I simply tried to run the following command:
>
> . rd nonedur sevpay ten_cat, z0(36)
> Three variables specified; jump in treatment
> at Z=36 will be estimated. Local Wald Estimate
> is the ratio of jump in outcome to jump in treatment.
>
>    Assignment variable Z is ten_cat
>    Treatment variable X_T is sevpay
>    Outcome variable y is nonedur
>
> Estimating for bandwidth 9.826534218815946
> A predicted value of treatment at cutoff lies outside feasible range;
> switching to local mean smoothing for treatment discontinuity.
> score variables for model __00000P contain missing values
> r(322);
>
> Probably is nonsense, but I also tried to run the same command with
> "mean_nonedur" instead of "nonedur".. same result from Stata.
>
> Could you give me any suggestion about this issue? Is there something
> related to the bandwidth choice?
>
> Thank you very much,
>
> Stefano Lombardi
>
>
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