Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.

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

 From Stefano Lombardi To statalist@hsphsun2.harvard.edu Subject Re: st: Regression Discontinuity (RD) Designs, sharp discontinuity: basic question about implementation with "rd" Date Tue, 11 Oct 2011 19:12:12 +0200

```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.

related to the bandwidth choice?

Thank you very much,

Stefano Lombardi

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```
```
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```