Effect of legal change on innovation - figure

[Vania Stef]

Hello StataList-ers!

Help! I need somebody! I am trying to replicate the following figure.




What I am doing is simply a difference-in-difference in multiple treatment groups and multiple time periods. This figure depicts the effect of ENDAs (employment nondiscrimination acts) on innovation. Several U.S. states adopted the ENDAs in different years during the sample period. I am trying to examine the before-after effect of the legal change in affected states (treatment group) compared to the before-after effect in nonaffected states. On the y-axis: “LnPat” (ln of patent counts) and “LnCit” (ln of patent citations); the x axis shows the time relative to the adoption of the laws, ranging from 5 years prior to the adoption year (year 0) until 10 years afterwards. “Pass” is a dummy=1 if the ENDA is in place in state s in a given year, and 0 otherwise. I also have dummy variables “Year minus 5”, “Year minus 4” … “Year 0”, etc. I literally have no idea how to code it. Please, help! I’ve been reading the help files on graphs … it’s still a total mess in my mind.
Thanks heaps!

Vania

[Jorrit Gosens]

Here's a simple example of a graph that comes close:

clear
webuse grunfeld
gen yrs_since_adoption = year-1940
keep if company ==1
line mvalue yrs_since_adoption || line invest yrs_since_adoption

If you'd like better help, please provide a data example with dataex (see that FAQ on how and why: https://www.statalist.org/forums/help#stata)
One bit of confusion is whether you really have 15 dummy variables for your years, whilst a single year variable would be best here (and for most other purposes). Knowing your data layout is important in helping provide exact code for your figure.

Also make you question more specific: what code did you try so far, and what element of the graph are you still missing?

[Vania Stef]

Hello Jorrit! Thanks heaps for the help! Much appreciated!

I actually did only have dummies for the years, and after your comment and the example generated "years since adoption". I tried dataex for the first time too ... let's see if it works.
So, I am trying to see the effect of a legal change. I have a dummy for "legal" (=1 if it is legal in the country, and 0 otherwise). Also, have dummies if the policy is legalized or criminalized. I might sound confusing ... "legal"=1 if the policy is legal, so for some countries it is always 1, for some - always 0, and for others - it changes from 0 to 1. "Legalized" on the other hand is 1 only if that policy was legalized in a certain year and the years after (in a country where always legal = 0). The dependent variable is crime rate.

I have to present a plot (similar to the one above) showing the before-after crime rate in the affected states (those in which the policy was legalized compared to those with no change). In my mind there are 2 figures: 1. Crime rate on the y-aixs and years relative to the adoption of the legal change on the x-axis; There's a line depicting the crime trend in countries with legal change, and a crime rate line of the control group of countries. 2. Same figure but comparing crime rate trends in countries where the policy was criminalized vs. no-change.

This is the dataex code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input long country int Year byte(Year2 Year1 Year0 Year_plus_one Year_one_plus Year_plus_two year_two_plus Year3 legal_dummy) double crime_rate byte(became_legal became_prohibited) float yrs_since_adoption
1 1990 0 0 0 0 0 0 0 0 1                7.6 0 0   0
1 1991 0 0 0 0 0 0 0 0 1                7.1 0 0   0
1 1992 0 0 0 0 0 0 0 0 1                7.8 0 0   0
1 1993 0 0 0 0 0 0 0 0 1                7.5 0 0   0
1 1994 0 0 0 0 0 0 0 0 1                7.6 0 0   0
1 1995 0 0 0 0 0 0 0 0 1                7.6 0 0   0
1 1996 0 0 0 0 0 0 0 0 1                6.4 0 0   0
1 1997 0 0 0 0 0 0 0 0 1                6.5 0 0   0
1 1998 0 0 0 0 0 0 0 0 1                7.1 0 0   0
1 1999 0 0 0 0 0 0 0 0 1                7.3 0 0   0
1 2000 0 0 0 0 0 0 0 0 1                7.2 0 0   0
1 2001 0 0 0 0 0 0 0 0 1  7.146414342629483 0 0   0
1 2002 0 0 0 0 0 0 0 0 1 7.7659045725646125 0 0   0
1 2003 0 0 0 0 0 0 0 0 1                  8 0 0   0
1 2004 0 0 0 0 0 0 0 0 1        8.392835524 0 0   0
1 2005 0 0 0 0 0 0 0 0 1        8.235955509 0 0   0
1 2006 0 0 0 0 0 0 0 0 1        8.461046791 0 0   0
1 2007 0 0 0 0 0 0 0 0 1        8.544146099 0 0   0
1 2008 0 0 0 0 0 0 0 0 1        8.307553544 0 0   0
1 2009 0 0 0 0 0 0 0 0 1        9.307450417 0 0   0
1 2010 0 0 0 0 0 0 0 0 1        10.42455458 0 0   0
1 2011 0 0 0 0 0 0 0 0 1              15.18 0 0   0
1 2012 0 0 0 0 0 0 0 0 1              14.83 0 0   0
1 2013 0 0 0 0 0 0 0 0 1              15.05 0 0   0
1 2014 0 0 0 0 0 0 0 0 1              14.13 0 0   0
1 2015 0 0 0 0 0 0 0 0 1              13.51 0 0   0
2 1990 0 0 0 0 0 0 0 0 1                  . 0 0   0
2 1991 0 0 0 0 0 0 0 0 1                  . 0 0   0
2 1992 0 0 0 0 0 0 0 0 1                  . 0 0   0
2 1993 0 0 0 0 0 0 0 0 1                8.5 0 0   0
2 1994 0 0 0 0 0 0 0 0 1                8.3 0 0   0
2 1995 0 0 0 0 0 0 0 0 1              12.63 0 0   0
2 1996 0 0 0 0 0 0 0 0 1              14.11 0 0   0
2 1997 0 0 0 0 0 0 0 0 1              16.62 0 0   0
2 1998 0 0 0 0 0 0 0 0 1                 15 0 0   0
2 1999 0 0 0 0 0 0 0 0 1               16.7 0 0   0
2 2000 0 0 0 0 0 0 0 0 1                  . 0 0   0
2 2001 0 0 0 0 0 0 0 0 1 22.504131428015942 0 0   0
2 2002 0 0 0 0 0 0 0 0 1 23.574954030775185 0 0   0
2 2003 0 0 0 0 0 0 0 0 1        27.66155611 0 0   0
2 2004 0 0 0 0 0 0 0 0 1        28.42523887 0 0   0
2 2005 0 0 0 0 0 0 0 0 1        29.08526226 0 0   0
2 2006 0 0 0 0 0 0 0 0 1        30.49166715 0 0   0
2 2007 0 0 0 0 0 0 0 0 1        30.66775041 0 0   0
2 2008 0 0 0 0 0 0 0 0 1         29.4845384 0 0   0
2 2009 0 0 0 0 0 0 0 0 1        27.69925123 0 0   0
2 2010 0 0 0 0 0 0 0 0 1        27.92178465 0 0   0
2 2011 0 0 0 0 0 0 0 0 1               30.9 0 0   0
2 2012 0 0 0 0 0 0 0 0 1               30.7 0 0   0
2 2013 0 0 0 0 0 0 0 0 1                 30 0 0   0
2 2014 0 0 0 0 0 0 0 0 1               27.4 0 0   0
2 2015 0 0 0 0 0 0 0 0 1               25.4 0 0   0
3 1990 0 0 0 0 0 0 0 0 1                4.6 0 0   0
3 1991 0 0 0 0 0 0 0 0 1                8.6 0 0   0
3 1992 0 0 0 0 0 0 0 0 1                8.9 0 0   0
3 1993 0 0 0 0 0 0 0 0 1                9.5 0 0   0
3 1994 0 0 0 0 0 0 0 0 1                8.7 0 0   0
3 1995 0 0 0 0 0 0 0 0 1                  9 0 0   0
3 1996 0 0 0 0 0 0 0 0 1               9.18 0 0   0
3 1997 0 0 0 0 0 0 0 0 1               9.31 0 0   0
3 1998 0 0 0 0 0 0 0 0 1   9.33753179120746 0 0   0
3 1999 0 0 0 0 0 0 0 0 1   9.01559454191033 0 0   0
3 2000 0 0 0 0 0 0 0 0 1  7.260963687834885 0 0   0
3 2001 0 0 0 0 0 0 0 0 1                7.5 0 0   0
3 2002 0 0 0 0 0 0 0 0 1                6.9 0 0   0
3 2003 0 0 0 0 0 0 0 0 1        7.793251045 0 0   0
3 2004 0 0 0 0 0 0 0 0 1        6.791472273 0 0   0
3 2005 0 0 0 0 0 0 0 0 1        5.207313756 0 0   0
3 2006 0 0 0 0 0 0 0 0 1        4.031461001 0 0   0
3 2007 0 0 0 0 0 0 0 0 1        2.944917093 0 0   0
3 2008 0 0 0 0 0 0 0 0 1        3.451309271 0 0   0
3 2009 0 0 0 0 0 0 0 0 1        3.261442825 0 0   0
3 2010 0 0 0 0 0 0 0 0 1               3.21 0 0   0
3 2011 0 0 0 0 0 0 0 0 1               2.68 0 0   0
3 2012 0 0 0 0 0 0 0 0 1               2.81 0 0   0
3 2013 0 0 0 0 0 0 0 0 1               6.43 0 0   0
3 2014 0 0 0 0 0 0 0 0 1               7.89 0 0   0
3 2015 0 0 0 0 0 0 0 0 1               6.13 0 0   0
4 1990 0 0 0 0 0 0 0 0 1                3.4 0 0 -10
4 1991 0 0 0 0 0 0 0 0 1                2.6 0 0  -9
4 1992 0 0 0 0 0 0 0 0 1                2.3 0 0  -8
4 1993 0 0 0 0 0 0 0 0 1                3.1 0 0  -7
4 1994 0 0 0 0 0 0 0 0 1                  2 0 0  -6
4 1995 0 0 0 0 0 0 0 0 1               1.65 0 0  -5
4 1996 0 0 0 0 0 0 0 0 1               1.97 0 0  -4
4 1997 0 0 0 0 0 0 0 0 1               2.24 0 0  -3
4 1998 1 0 0 0 0 0 0 0 1   2.77489042594568 0 0  -2
4 1999 0 1 0 0 0 0 0 0 1 2.3774091269650772 0 0  -1
4 2000 0 0 1 0 0 0 0 0 0  2.557077625570776 0 1   0
4 2001 0 0 0 1 1 0 0 0 0 3.8771851187808157 0 1   1
4 2002 0 0 0 0 1 1 1 0 0 3.6954087346024638 0 1   2
4 2003 0 0 0 0 1 0 1 1 0        4.779442205 0 1   3
4 2004 0 0 0 0 1 0 1 1 0        3.708263494 0 1   4
4 2005 0 0 0 0 1 0 1 1 0        3.196768292 0 1   5
4 2006 0 0 0 0 1 0 1 1 0        4.217609716 0 1   6
4 2007 0 0 0 0 1 0 1 1 0        3.660193922 0 1   7
4 2008 0 0 0 0 1 0 1 1 0        4.254946432 0 1   8
4 2009 0 0 0 0 1 0 1 1 0        2.924597086 0 1   9
4 2010 0 0 0 0 1 0 1 1 0         3.20212203 0 1  10
4 2011 0 0 0 0 1 0 1 1 0               2.68 0 1  11
end
label values country country
label def country 1 "Austria", modify
label def country 2 "Belgium", modify
label def country 3 "Bulgaria", modify
label def country 4 "Croatia", modify

------------------ copy up to and including the previous line ------------------


Would really appreciate your help! I'm a newbie and struggling but really want to learn! Greetings!

Vania

[Jorrit Gosens]

First, I make some changes to your data example, because there is only one country that legalizes in your example

*** This is just a few changes to the data so the example makes more sense
replace became_legal= 1990 if country==1
replace became_legal= 1995 if country==2
replace became_legal= 2006 if country==3
replace became_legal= 2000 if country==4

gen yrs_since_legalization=Year-became_legal

I think its easier to specify an exact year in 'became_legal', rather than having dummies. This also helps with countries that legalized before the year 1990. If you know those years, you can still calculate yrs_since_legalization, even if legalization was done outside of the period in your data on crime rates.
I also guess you probably don't really need all the Year0 Year1 etc dummies, but I can't say for sure.

In any case, once we have years since legalization, we can graph crime rates averaged over all countries:

egen mean_crime_rate = mean(crime_rate), by(yrs_since_legalization)
sort yrs_since_legalization
line mean_crime_rate yrs_since_legalization
sort country Year

Or alternatively:

line mean_crime_rate yrs_since_adoption, by(country)

Or:

twoway (line crime_rate yrs_since_adoption if country==1)(line crime_rate yrs_since_adoption if country==2)(line crime_rate yrs_since_adoption if country==3)(line crime_rate yrs_since_adoption if country==4)

Give these a try and see which one fits your desired result best.


Edit:
Also note that your currently have a problem with your definition of 'yrs_since_adoption' as it is set to zero when no adoption was recorded in the entire time period. That means Stata will take it as the crime_rate in 0 years since adoption, and will not produce the graphs that you want. If no legalization or crimilization was observed, this variable should be set to missing instead of to zero.

[Vania Stef]

Jorrit, thank You so much for the help! It's invaluable to me! Really appreciating it!

First, I got your point about my definition of "yrs_since_adoption" ...it didn't come to my mind but I understand now.

Second, a question: why do you generate the mean by (yrs_since_legalization)? Why not by "year"? I'm confused here ... what about those countries where no legalization or criminalization occurred?

Also, should I generate "yrs_since_legalization" and "yrs_since_criminalization" instead of "yrs_since_adoption"? Or is this unnecessary?

Believe it or not, I am still unable to make the plot ... take a look at my first post - this is the graph in my mind! Crime rate on the y-axis, years_since_adoption on the x-axis, and two lines (to visually see the difference) - one line is crime rate of the countries that legalized, the other line - crime rate of those with no-change. Same thing but with countries that criminalized vs. no-change. But then how to do this ... and especially if when no legalization/criminalization is observed, the "yrs_since_adoption" is set to mv-s. A third graph could be countries that legalized vs. those that criminalized.

Including a better example:

* Example generated by -dataex-. To install: ssc install dataex
clear
input long country int year byte(legal_dummy became_legal became_prohibited alwaysLegal alwaysIllegal) double crime_rate float(yrs_since_adoption yrs_since_legalization yrs_since_criminalization)
4 1990 1 0 0 0 0                3.4 -10  . -10
4 1991 1 0 0 0 0                2.6  -9  .  -9
4 1992 1 0 0 0 0                2.3  -8  .  -8
4 1993 1 0 0 0 0                3.1  -7  .  -7
4 1994 1 0 0 0 0                  2  -6  .  -6
4 1995 1 0 0 0 0               1.65  -5  .  -5
4 1996 1 0 0 0 0               1.97  -4  .  -4
4 1997 1 0 0 0 0               2.24  -3  .  -3
4 1998 1 0 0 0 0   2.77489042594568  -2  .  -2
4 1999 1 0 0 0 0 2.3774091269650772  -1  .  -1
4 2000 0 0 1 0 0  2.557077625570776   0  .   0
4 2001 0 0 1 0 0 3.8771851187808157   1  .   1
4 2002 0 0 1 0 0 3.6954087346024638   2  .   2
4 2003 0 0 1 0 0        4.779442205   3  .   3
4 2004 0 0 1 0 0        3.708263494   4  .   4
4 2005 0 0 1 0 0        3.196768292   5  .   5
4 2006 0 0 1 0 0        4.217609716   6  .   6
4 2007 0 0 1 0 0        3.660193922   7  .   7
4 2008 0 0 1 0 0        4.254946432   8  .   8
4 2009 0 0 1 0 0        2.924597086   9  .   9
4 2010 0 0 1 0 0         3.20212203  10  .  10
4 2011 0 0 1 0 0               2.68  11  .  11
4 2012 0 0 1 0 0               2.81  12  .  12
4 2013 0 0 1 0 0               6.43  13  .  13
4 2014 0 0 1 0 0               7.89  14  .  14
4 2015 0 0 1 0 0               6.13  15  .  15
5 1990 1 0 0 1 0                 .4   .  .   .
5 1991 1 0 0 1 0                1.2   .  .   .
5 1992 1 0 0 1 0                1.4   .  .   .
5 1993 1 0 0 1 0                1.1   .  .   .
5 1994 1 0 0 1 0                2.1   .  .   .
5 1995 1 0 0 1 0                .82   .  .   .
5 1996 1 0 0 1 0               1.08   .  .   .
5 1997 1 0 0 1 0               1.61   .  .   .
5 1998 1 0 0 1 0   .801068090787717   .  .   .
5 1999 1 0 0 1 0  .7957559681697612   .  .   .
5 2000 1 0 0 1 0                 .8   .  .   .
5 2001 1 0 0 1 0 2.3653088042049935   .  .   .
5 2002 1 0 0 1 0 1.6993464052287581   .  .   .
5 2003 1 0 0 1 0        1.787348769   .  .   .
5 2004 1 0 0 1 0        3.156914432   .  .   .
5 2005 1 0 0 1 0        2.475989777   .  .   .
5 2006 1 0 0 1 0                  0   .  .   .
5 2007 1 0 0 1 0        2.475989777   .  .   .
5 2008 1 0 0 1 0                  0   .  .   .
5 2009 1 0 0 1 0                  0   .  .   .
5 2010 1 0 0 1 0                3.3   .  .   .
5 2011 1 0 0 1 0                3.4   .  .   .
5 2012 1 0 0 1 0                2.2   .  .   .
5 2013 1 0 0 1 0                1.6   .  .   .
5 2014 1 0 0 1 0                1.2   .  .   .
5 2015 1 0 0 1 0                1.7   .  .   .
6 1990 1 0 0 1 0                8.6   .  .   .
6 1991 1 0 0 1 0                7.4   .  .   .
6 1992 1 0 0 1 0                6.9   .  .   .
6 1993 1 0 0 1 0                7.4   .  .   .
6 1994 1 0 0 1 0                7.1   .  .   .
6 1995 1 0 0 1 0               7.03   .  .   .
6 1996 1 0 0 1 0               6.57   .  .   .
6 1997 1 0 0 1 0               6.36   .  .   .
6 1998 1 0 0 1 0  6.553398058252427   .  .   .
6 1999 1 0 0 1 0  6.155339805825243   .  .   .
6 2000 1 0 0 1 0 4.8543689320388355   .  .   .
6 2001 1 0 0 1 0  5.496870109546166   .  .   .
6 2002 1 0 0 1 0  6.401333202627194   .  .   .
6 2003 1 0 0 1 0        6.333751237   .  .   .
6 2004 1 0 0 1 0        6.734194859   .  .   .
6 2005 1 0 0 1 0        5.831338513   .  .   .
6 2006 1 0 0 1 0        5.166298267   .  .   .
6 2007 1 0 0 1 0        6.176355805   .  .   .
6 2008 1 0 0 1 0        5.097636113   .  .   .
6 2009 1 0 0 1 0        4.597817856   .  .   .
6 2010 1 0 0 1 0                5.3   .  .   .
6 2011 1 0 0 1 0               6.09   .  .   .
6 2012 1 0 0 1 0               6.06   .  .   .
6 2013 1 0 0 1 0               5.67   .  .   .
6 2014 1 0 0 1 0               6.43   .  .   .
6 2015 1 0 0 1 0               5.56   .  .   .
7 1990 0 0 0 0 0                9.5  -9 -9   .
7 1991 0 0 0 0 0               10.3  -8 -8   .
7 1992 0 0 0 0 0               10.8  -7 -7   .
7 1993 0 0 0 0 0                9.6  -6 -6   .
7 1994 0 0 0 0 0                9.2  -5 -5   .
7 1995 0 0 0 0 0               8.42  -4 -4   .
7 1996 0 0 0 0 0               7.37  -3 -3   .
7 1997 0 0 0 0 0               8.23  -2 -2   .
7 1998 0 0 0 0 0  7.885304659498208  -1 -1   .
7 1999 1 0 0 0 0  8.967851099830796   0  0   .
7 2000 1 0 0 0 0   9.31409295352324   1  1   .
7 2001 1 0 0 0 0  9.199477514461654   2  2   .
7 2002 1 0 0 0 0  9.304056568663938   3  3   .
7 2003 1 0 0 0 0         8.76592329   4  4   .
7 2004 1 0 0 0 0        10.40686779   5  5   .
7 2005 1 0 0 0 0        8.764736752   6  6   .
7 2006 1 0 0 0 0        9.682793877   7  7   .
7 2007 1 0 0 0 0        8.995946339   8  8   .
7 2008 1 0 0 0 0        7.203520557   9  9   .
7 2009 1 0 0 0 0        6.371186022  10 10   .
7 2010 1 0 0 0 0              16.37  11 11   .
7 2011 1 0 0 0 0              15.09  12 12   .
end
label values country country
label def country 4 "Croatia", modify
label def country 5 "Cyprus", modify
label def country 6 "Czech Republic", modify
label def country 7 "Denmark", modify

Thank you in advance!

[Jorrit Gosens]

Second, a question: why do you generate the mean by (yrs_since_legalization)? Why not by "year"? I'm confused here ... what about those countries where no legalization or criminalization occurred?

Simple answer: because the example graph you provide in post #1 has 'years since adoption of the policy' on the y axis. This is also the way to do it. Suppose you have countries X Y Z that legalize in 1990, 2000, and 2010, respectively. If we want to see development of crime rates since adoption, then we have to shift the y axis so that the year of adoption becomes year 0 for all countries.

Also, should I generate "yrs_since_legalization" and "yrs_since_criminalization" instead of "yrs_since_adoption"? Or is this unnecessary?

Yes, this would be my idea: create variables year of legalization & years since legalization, and the equivalent for criminalization. Then you can put both lines in one grpah, where the value 0 on the y axis is the moment of either legalization or the moment of criminalization.

Believe it or not, I am still unable to make the plot ... take a look at my first post - this is the graph in my mind! Crime rate on the y-axis, years_since_adoption on the x-axis, and two lines (to visually see the difference) - one line is crime rate of the countries that legalized, the other line - crime rate of those with no-change.

This is not possible. Think about this again when you read the answer to your first question. The graph is meant to show developments in countries X Y Z that legalize in 1990, 2000, and 2010, with developments plotted since the year they legalized. Not the actual year, years since legalization. We cannot add a line for countries that never legalized in this graph, because there is no year when they legalized.

[Vania Stef]

Dear Jorrit! Thank You tons!

Your help was really invaluable! I am done with the graph - wouldn't have made it without you! Thanks for your patient comments and explanations! All the very best!

[Vania Stef]

Dear Jorrit, it’s me again!

I have a clarifying question, please help!



As you already know I am looking at the effect of a policy change on crime rate. I have a dummy “Legal”, which equals 1 if the policy is legal (in a particular year and country), and 0 otherwise. In some of the countries it’s always been legal, so “Legal” is always 1. In other countries it’s never been legal, therefore, the dummy is always 0. On the other hand, some countries legalize (criminalize) the policy, thus the variable changes from 0 to 1 (1 to 0).

Apart from the “Legal” variable, I have generated two additional ones: “Legalized” and “Criminalized”. “Legalized” (or “Became_Legal”, not sure about the most appropriate name) is 1 only for a country that legalized in a given year and the following years: say, country “X” legalized in 1991, so the dummy for this country is 0 in 1990, and 1 in 1991, 1992, etc. For those countries where no change occurred (it’s always been legal/illegal), the dummy is 0. The logic is exactly the same with the variable “Criminalized”: changes from 0 to 1 if the policy was criminalized in a country in a given year, otherwise 0.

I am running a regression with “Legal” and separate ones with “Legalized” and “Criminalized”. My supervisor told me to get rid of the last two variables and just stick to one dummy – “Legal”, and whenever I want to analyze the effect of legalization, just to drop the observations with criminalization, and vice versa. Whenever I am interested in the impact of criminalization, drop the subsample with countries that legalized. Is this correct?

When I follow this instruction, when dropping the legalized-subsample and looking only at the countries that criminalized vs. the no-change countries, the coefficient (“Legal” on crime) has the opposite sign of what it should have (criminalizing should increase crime, instead it has a negative sign … my understanding is that this is because of the “Legal” dummy – it changes from 1 to 0 in the criminalizing countries). I think I having the two separate variables for legalization and criminalization makes sense (at least to me)! What should I do? What is your advice? What is the right way to do it?
Thank You heaps!!!

[Jorrit Gosens]

This is quite a tough question. I would say this should probably be discussed a lot in your subject matter journals, best approach is to read some articles there probably.
I see the difficulty with having overlapping dummies for 'status' and for 'status change', essentially, but I'm really unsure as to the best approach with these.