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


From   Stefano Lombardi <lombardi_stefano@fastwebnet.it>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Regression Discontinuity (RD) Designs, sharp discontinuity: basic question about implementation with "rd"
Date   Wed, 12 Oct 2011 02:13:56 +0200

Dear Austin,

Thank you very much for the reply. Here there are some additional information about the dataset.

About the forcing variable:
"ten_cat" is measured in months (12 - 58). The last 5 categories are full of missing values. alternatively, "tenure" is the same variable measured in days. I would want to use this one choosing the correct bandwidth.

Just to have a rough idea of the data, here it is the the table of the frequencies of "ten_cat":

. tabdisp ten_cat, cell(freq cumfreq)

----------------------------------
job       |
tenure    |
categorie |
s         |       freq     cumfreq
----------+-----------------------
       13 |      14296       14296
       14 |      13989       28285
       15 |      13564       41849
       16 |      12595       54444
       17 |      11629       66073
       18 |      11269       77342
       19 |       9735       87077
       20 |       9441       96518
       21 |       8897      105415
       22 |       8426      113841
       23 |       7735      121576
       24 |       7407      128983
       25 |       5672      134655
       26 |       5451      140106
       27 |       5486      145592
       28 |       5224      150816
       29 |       5041      155857
       30 |       4631      160488
       31 |       4516      165004
       32 |       4277      169281
       33 |       4049      173330
       34 |       4059      177389
       35 |       4190      181579
       36 |       3601      185180
       37 |       2938      188118
       38 |       2937      191055
       39 |       3006      194061
       40 |       2790      196851
       41 |       2680      199531
       42 |       2609      202140
       43 |       2417      204557
       44 |       2414      206971
       45 |       2257      209228
       46 |       2221      211449
       47 |       2300      213749
       48 |       1725      215474
       49 |       1682      217156
       50 |       1809      218965
       51 |       1730      220695
       52 |       1602      222297
       53 |       1579      223876
       54 |       1464      225340
       55 |       1486      226826
       56 |       1458      228284
       57 |       1384      229668
       58 |       1375      231043
----------------------------------

Severance pay takes two possible values: people are treated at tenure = 1094 (days) or at ten_cat = 36 (months). What I expect is that after the cut-off the mean of nonemployment duration (y_bar, in days) raises. Notice however that severance pay is generally delivered within one month of job termination, but I have not information about the exact moment in wich the sum of money is paid.

Since I have the forcing variable both in months and in days, I have plotted the following graphs: - y_bar VS tenure: the scatterplot is quite dispersed around the threshold but it is clearly evident a decreasing trend before the cut off, then an increasing trend starting from the right of the cutoff. By including a straight interpolating line to the left and one to the right of the cut-off, the average treatment effect is of about 9.5 days. - y_bar VS ten_cat: there is a clear jump between 36 and 37 (y_bar is respectively 148 and 161). After the jump the observations stay steadily higher than the ones to the left of the cut-off.

From the regression you told me to do (using either ten_cat or tenure) comes out a R^2 = 1, with the dummy that explains the entire variation of severance payment.

Using Z in days and running rd nonedur Z, bdep the problem seems overcame (I don't know why, anyway)! I get:

Two variables specified; treatment is
assumed to jump from zero to one at Z=0.

 Assignment variable Z is Z
 Treatment variable X_T unspecified
 Outcome variable y is nonedur

Estimating for bandwidth 14.14255035704279
Estimating for bandwidth 7.071275178521395
Estimating for bandwidth 28.28510071408558
------------------------------------------------------------------------------
nonedur | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwald | 30.76441 8.9709 3.43 0.001 13.18177 48.34705 lwald50 | 34.90172 14.25218 2.45 0.014 6.967965 62.83548 lwald200 | 23.17764 6.553702 3.54 0.000 10.33262 36.02265
------------------------------------------------------------------------------

With bandwidth 7.1 and 14 the estmated effect is not precise, I would go for the third one. However, since I have many observations close to the cut-off, probably I could also restrict the window of the observations considered through the "n(real)" option. Is that sensible?

Also, if I plot the graph though the option "gr" it is not informative: all the oservations are plotted (basically the entire graph is completely full of dots) and not the means of nonendur. Also, the X-axis range is the entire forcing variable range, but I just want a "zoom" near the cut-off (let's say, between 950 and 1150). I probably have to work with "scopt", but how exactly?

Thank you very much!!

Stefano










Il 11/10/2011 19:43, Austin Nichols ha scritto:
Stefano Lombardi<lombardi_stefano@fastwebnet.it>:
Apparently there is a problem in your data; if you give us information
about the actual data, maybe we can diagnose it.
Is ten_cat measured in days, so that it takes on a larger number of
discrete values, many of which are close to the threshold, or does it
take on a small number of discrete values?
Does sevpay take on one of two possible values, or is it more continuous?
What happens when you regress sevpay on z=(ten_cat-36) and a dummy for
z>=0 (ten_cat>=36), and their interaction?
What happens when you type
g z=ten_cat-36
rd nonedur z, bdep
?
The bandwidth calculations assume the data far from the cutoff have
NOT "already been manually eliminated" as you have done, so you may
want to clarify how you want to estimate the optimal bandwidth.

On Tue, Oct 11, 2011 at 1:12 PM, Stefano Lombardi
<lombardi_stefano@fastwebnet.it>  wrote:
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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