Vector Autoregression in Stata When the Dependent Variable is Binary Logit Model

[Vince Williams]

Dear Stata Users:
I am interested in estimating impulse response function in stata (VAR). Basically I am trying to estimate the marginal probability of rain in a county changes in response to the occurence of rain in the same county at some point in time (one, two, three or four quarters ago).
I have a county-year-quarter panel and I am trying to estimate the probability of rain (binary 0 and 1 variable).
Here is the Model I am Interested in:
Dependent variable Rain (0 or 1 for the county)
Independent Variable Rain_lag1- is a dummy equal to one if the county was rain one quarter ago
Independent Variable Rain_lag2- is a dummy equal to one if the county was rain two quarter ago
Independent Variable Rain_lag3- is a dummy equal to one if in the county was rain three quarter ago
Independent Variable Rain_lag4 - is a dummy equal to one if in the county was rain four quarter ago
I am aware that there are VAR in stata.

https://blog.stata.com/2016/08/09/vector-autoregressions-in-stata/

However I am curious what happens if I have a binary independent variable. Should't logit VAR be applied in this case.
Also do I need time fixed effects and county-quarter fixed effects?

* Example generated by -dataex-. To install: ssc install dataex
clear
input double(county year qtr qn rain)
46119 2006 3 200603 0
22053 2010 3 201003 0
51105 2003 4 200304 0
51165 2012 1 201201 0
31133 2005 4 200504 0
48009 2002 2 200202 0
20061 2016 1 201601 0
30083 2006 2 200602 0
12125 2015 1 201501 0
21033 2014 3 201403 0
21151 2008 4 200804 0
46053 2017 3 201703 0
47121 2007 4 200704 0
48207 2017 1 201701 0
42101 2017 2 201702 0
29021 2012 1 201201 0
13237 2014 3 201403 0
13021 2014 1 201401 0
55005 2007 2 200702 0
40011 2004 3 200403 0
51595 2013 3 201303 0
46127 2004 3 200403 0
38037 2017 1 201701 0
31129 2004 4 200404 0
18025 2010 1 201001 0
13173 2017 1 201701 0
12121 2011 2 201102 0
18121 2012 4 201204 0
39069 2009 4 200904 0
36081 2013 3 201303 0
51620 2004 2 200402 0
12011 2016 3 201603 0
26003 2002 1 200201 0
17197 2017 2 201702 0
54045 2010 4 201004 0
38067 2011 4 201104 0
37117 2008 2 200802 0
22037 2016 4 201604 0
 2150 2012 2 201202 0
47049 2017 3 201703 0
31057 2011 3 201103 0
39127 2006 4 200604 0
48137 2012 3 201203 0
72061 2005 3 200503 0
21007 2008 1 200801 0
40131 2011 2 201102 0
26113 2016 2 201602 0
18007 2017 4 201704 0
24510 2002 1 200201 0
48123 2013 4 201304 0
17181 2005 3 200503 0
18151 2002 3 200203 0
27063 2009 2 200902 0
23021 2003 4 200304 0
20037 2013 4 201304 0
48395 2005 4 200504 0
48155 2004 3 200403 0
 4007 2017 3 201703 0
19127 2014 4 201404 0
36091 2015 3 201503 0
20093 2012 2 201202 0
17019 2002 3 200203 0
37141 2009 1 200901 0
46085 2015 4 201504 0
55109 2012 3 201203 0
19027 2012 3 201203 0
21061 2014 4 201404 0
47051 2003 4 200304 0
 1075 2008 3 200803 0
19169 2008 4 200804 0
 6079 2009 4 200904 0
47185 2010 2 201002 0
72137 2015 4 201504 0
31077 2007 3 200703 0
38001 2011 3 201103 0
37197 2011 1 201101 0
 5021 2010 2 201002 0
55087 2011 1 201101 0
54087 2006 1 200601 0
47099 2010 4 201004 0
40137 2007 4 200704 0
29017 2008 4 200804 0
29101 2005 2 200502 0
29041 2013 1 201301 0
48055 2016 4 201604 0
72111 2013 2 201302 0
21147 2008 3 200803 1
12047 2006 1 200601 0
51720 2006 2 200602 0
29049 2002 1 200201 0
13223 2012 2 201202 0
47013 2012 4 201204 0
21061 2002 4 200204 0
42009 2002 1 200201 0
49023 2009 4 200904 0
 5081 2004 4 200404 0
26037 2007 1 200701 0
51770 2012 2 201202 0
48209 2014 4 201404 0
37141 2006 1 200601 0
end