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  • Event study approach

    EDIT: the original sample has 316 persons, the distribution of religiosity and gender is about the same in this sample here.

    Hi there,

    I am having trouble with an event study approach. It's not about finance, but about the effect of parenthood on earnings. Previous studies showed that men and women have a similar (parallel, not per se the same amount) earnings trend, but as soon as they get children the mother's earnings drop significantly while the father's stays about the same. This is the child penalty. Now, what I need to do is see if there is a significant difference in this child penalty between religious and non-religious people (considered time-invariant). I am required to do an event study approach of my professor. My sample has only parents, so everyone gets treatment at some point (the sample here is even smaller for practical reasons and confidentiality. also, it is in wide format now to take less space, i work with it in long format). The entire window is from -2 to +5, with t=0 being the year someone becomes a first time parent. i have unbalanced panel data.

    My professor made some things clear. For example, I need to make dummy variables of the eventtime, with t=-2 as reference category. This way everything is in relation to the year before birth.

    Code:
    replace eventtime = eventtime-3
    char eventtime[omit] -1
    xi. i.eventtime
    
    generate b = .
    replace b = 0 if eventtime == -1
    The basic regression that I need to do is this:

    Code:
    regress income _Ieventtime* i.age i.year, r
    predict income_p, xb
    
    foreach i in 1 3 4 5 6 7 8 {
    replace b = _[_Ieventtime_`i'] if eventtime == `i'-3
    }
    
    generate income_c = income_p - b
    generate gap = b/income_c

    This way the effect of child birth is a percentage of the counterfactual income, i.e. the expected income the parent would have had had they not become parents. This is the variable gap.

    Now, I have 5 questions.

    - Most studies about this topic regressed for each group separately. So for example, a regression for men, and a regression for women. Or in my case, one for non-religious men, one for religious men, one for non-religious women and one for religious women. Is this the best way to do it or is it better to make it one regression and maybe work with interaction effects? It is important that I can see the reaction over time. And if that would be better, which variables should interact with each other? So far I did it separately with the runby command.

    - Let's say I do the regressions separately, how do I know the effect within each regression is significant? I should be looking at the significance of gap in each time period instead of the b in each time period (or does that not really matter in this case?). My logic is that I need to do extra calculations in order to get a p value or something. In one study they calculated the mean and standard deviation of the gap variable for each time period and gender. then they said they calculated a t-value by mean/sd and they used that as a significance test. I thought it was a little more complicated than that, and the distribution etc is not right for a t value I assume. Maybe I'm just thinking too difficult.

    - In this example i used robust standard errors, but I honestly have no idea what standard errors to use. I never really understood that, and with panel data/event study I find it even harder. I read some things about vce(cluster id) and robust cluster(id), but also bootstrapping. How do I know the right standard error? Is there a specific test I can perform?

    - If I know the whether the gap variables are significant or not, I still need to know whether there is a difference between religious people and non-religious people. Many studies computed a relative child penalty per time period: (bwomen - bmen)/income_cwomen. I would do this for religous people and non-religious people separately. What test should I use to calculate if there is a significant difference (in each time period)?

    - Lastly, I have some control variables in addition to age and year. Examples are level of education (categorical variable, 3 categories) and at what age they became parents. Almost all the studies I read about this didn't include any additional control variables. I don't really understand why. What is the reason this isn't necessary? Pretty much all my control variables are time-invariant.


    I'm sorry for the extreme amount of questions. I've been puzzling with this for 2 weeks and I just don't get it. Hopefully you could help me, even if it's just a little bit.

    Thank you in advance


    Code:
    * Example generated by -dataex-. To install: ssc install dataex
    clear
    input double id float(income1 year1 age1 income2 year2 age2 income3 year3 age3 income4 year4 age4 income5 year5 age5 income6 year6 age6 income7 year7 age7 income8 year8 age8) double sex float(agebecameparent religiosity educationlevel sexrelig)
     1         . 2007 37     30000 2008 38     31000 2009 39     32400 2010 40     32400 2011 41     33800 2012 42     34800 2013 43     34800 2014 44 1 39 1 2 1
     2         . 2007 29     32400 2008 30     32400 2009 31     32400 2010 32     32400 2011 33     32400 2012 34     32400 2013 35         . 2014 36 2 31 2 3 4
     3  43573.33 2014 30     44040 2015 31     44040 2016 32     46220 2017 33     54200 2018 34     60000 2019 35         . 2020 36         . 2021 37 1 32 1 3 1
     4     24000 2014 29     24000 2015 30     24000 2016 31     26000 2017 32     36000 2018 33     36000 2019 34         . 2020 35         . 2021 36 1 31 1 2 1
     5     34560 2014 28     38880 2015 29     46710 2016 30     52370 2017 31     56256 2018 32     62280 2019 33         . 2020 34         . 2021 35 1 30 2 3 2
     6     24000 2010 34     28000 2011 35     27400 2012 36     30000 2013 37     30000 2014 38     23300 2015 39     28500 2016 40     31200 2017 41 1 36 1 3 1
     7     34800 2013 30     34800 2014 31     36800 2015 32     38600 2016 33     38400 2017 34     38700 2018 35     38500 2019 36         . 2020 37 1 32 1 3 1
     8  41353.37 2012 43  41353.37 2013 44  41353.37 2014 45  41353.37 2015 46  41353.37 2016 47  41353.37 2017 48  41353.37 2018 49  41353.37 2019 50 1 45 1 2 1
     9  21057.04 2013 29  21057.04 2014 30  21057.04 2015 31  21057.04 2016 32  21057.04 2017 33  21057.04 2018 34  21057.04 2019 35         . 2020 36 2 31 1 2 3
    10         . 2007 32 11506.375 2008 33 11506.375 2009 34 11506.375 2010 35  8818.885 2011 36  3443.904 2012 37  3443.904 2013 38  3443.904 2014 39 2 34 1 2 3
    11     30800 2012 33     35800 2013 34     24000 2014 35     15000 2015 36 12273.886 2016 37     28150 2017 38     41900 2018 39     44800 2019 40 2 35 1 3 3
    12     35550 2012 28     35487 2013 29     36000 2014 30     35200 2015 31     38400 2016 32     38400 2017 33     37600 2018 34     41390 2019 35 2 30 1 3 3
    13 20785.316 2013 30     28800 2014 31     28800 2015 32     29300 2016 33     33000 2017 34     33680 2018 35   44211.7 2019 36         . 2020 37 2 32 1 3 3
    14     19800 2010 21     19800 2011 22     20100 2012 23     21000 2013 24     23556 2014 25     24408 2015 26     28800 2016 27     31200 2017 28 2 23 1 2 3
    15     55260 2014 35     55800 2015 36     56800 2016 37     58210 2017 38     59310 2018 39     60100 2019 40         . 2020 41         . 2021 42 1 37 1 3 1
    16         . 2007 37     27600 2008 38     28100 2009 39     28800 2010 40     28800 2011 41     26994 2012 42     25704 2013 43     27024 2014 44 2 39 1 3 3
    17 17139.916 2009 25     20904 2010 26     16042 2011 27     15600 2012 28 14945.318 2013 29  11647.26 2014 30 11376.115 2015 31 11376.115 2016 32 2 27 1 2 3
    18     22800 2010 34     22800 2011 35     22800 2012 36     22800 2013 37     22800 2014 38     22800 2015 39     22800 2016 40  41038.87 2017 41 1 36 2 2 2
    19     52250 2013 32     54000 2014 33     59000 2015 34     60000 2016 35     63000 2017 36     67200 2018 37     74350 2019 38         . 2020 39 2 34 1 3 3
    20     24792 2011 28     26186 2012 29     28188 2013 30     29694 2014 31     30000 2015 32     33000 2016 33     33504 2017 34         . 2018 35 1 30 1 3 1
    21         . 2007 30  25926.84 2008 31 25695.875 2009 32  25674.83 2010 33 29208.814 2011 34 30238.377 2012 35  31439.22 2013 36         . 2014 37 2 32 1 3 3
    22  26509.09 2009 27     28800 2010 28     28800 2011 29     28800 2012 30     28800 2013 31     31200 2014 32     31200 2015 33     31200 2016 34 1 29 1 1 1
    23  35805.42 2013 23     39777 2014 24     42913 2015 25     44400 2016 26     44400 2017 27     49350 2018 28     61055 2019 29         . 2020 30 1 25 2 3 2
    24         . 2007 25     26928 2008 26     28800 2009 27     28800 2010 28     28800 2011 29     28800 2012 30     28800 2013 31     28800 2014 32 2 27 2 3 4
    25     33600 2013 33     33600 2014 34     33600 2015 35     33600 2016 36 31619.285 2017 37  7859.805 2018 38         0 2019 39         . 2020 40 2 35 2 3 4
    26     31500 2008 28     33300 2009 29     33600 2010 30     25600 2011 31     26700 2012 32     30600 2013 33     32400 2014 34     31700 2015 35 2 30 1 3 3
    27         . 2007 40     39840 2008 41     39840 2009 42     39840 2010 43   40670.5 2011 44     44796 2012 45     45576 2013 46     46258 2014 47 1 42 2 1 2
    28     35820 2014 32     36948 2015 33     37732 2016 34     41422 2017 35     41940 2018 36     41830 2019 37         . 2020 38         . 2021 39 1 34 1 3 1
    29  13309.09 2014 29     26400 2015 30     26400 2016 31     26400 2017 32     26400 2018 33     26400 2019 34         . 2020 35         . 2021 36 2 31 1 3 3
    30         . 2008 24     19800 2009 25     21300 2010 26     21600 2011 27     21600 2012 28     21600 2013 29     21600 2014 30     21600 2015 31 2 26 1 2 3
    31     32400 2010 32     32400 2011 33     34400 2012 34     35350 2013 35     34400 2014 36     36900 2015 37     39600 2016 38     42100 2017 39 1 34 1 3 1
    32     39440 2014 27     42230 2015 28     46544 2016 29     48175 2017 30     53000 2018 31     55050 2019 32         . 2020 33         . 2021 34 1 29 1 3 1
    33         . 2010 39  21057.04 2011 40  21057.04 2012 41  21057.04 2013 42  21057.04 2014 43  21057.04 2015 44  21057.04 2016 45         . 2017 46 2 41 2 1 4
    34     31200 2011 26     31356 2012 27  31409.09 2013 28  34293.86 2014 29  40694.73 2015 30  40694.73 2016 31  40694.73 2017 32  37275.27 2018 33 2 28 2 3 4
    35     30000 2008 36     30000 2009 37     30000 2010 38     30000 2011 39     30000 2012 40     30000 2013 41     30000 2014 42     30000 2015 43 1 38 2 3 2
    36  61166.52 2010 32  64581.47 2011 33  71381.16 2012 34  66503.49 2013 35   75283.3 2014 36  85332.29 2015 37  87342.09 2016 38  87342.09 2017 39 1 34 1 3 1
    37         . 2010 20      9600 2011 21      9600 2012 22      9600 2013 23      9600 2014 24      9600 2015 25      9600 2016 26      9600 2017 27 2 22 1 2 3
    38     35400 2008 28     30600 2009 29     29640 2010 30  21830.97 2011 31  24701.48 2012 32  24933.13 2013 33  24933.13 2014 34  24933.13 2015 35 2 30 1 3 3
    39     37896 2014 37     38720 2015 38     38784 2016 39     38784 2017 40     38784 2018 41     40359 2019 42         . 2020 43         . 2021 44 1 39 1 2 1
    40     30000 2009 29     32010 2010 30     32400 2011 31  20721.66 2012 32 24225.246 2013 33  25504.99 2014 34  25504.99 2015 35  25504.99 2016 36 2 31 1 2 3
    41     30276 2011 33     33110 2012 34     31625 2013 35     30000 2014 36     30000 2015 37     30800 2016 38     32400 2017 39     33400 2018 40 1 35 1 1 1
    42 24746.375 2015 28 27739.406 2016 29 37192.605 2017 30 30698.467 2018 31 34002.367 2019 32         . 2020 33         . 2021 34         . 2022 35 1 30 1 3 1
    43     19120 2009 25     19224 2010 26   21378.1 2011 27 21690.943 2012 28 30166.344 2013 29  25283.68 2014 30   20523.4 2015 31   20523.4 2016 32 1 27 1 2 1
    44     31050 2011 26     38925 2012 27     39600 2013 28     39730 2014 29     41535 2015 30     44640 2016 31     52343 2017 32     56163 2018 33 1 28 1 3 1
    45     28176 2014 35     29064 2015 36     29064 2016 37     29454 2017 38     30000 2018 39     30000 2019 40         . 2020 41         . 2021 42 1 37 1 2 1
    46     28800 2010 28     28800 2011 29     28800 2012 30  26812.78 2013 31 27107.297 2014 32 27107.297 2015 33         . 2016 34         . 2017 35 2 30 1 3 3
    47     32400 2010 31     34013 2011 32     34308 2012 33     34104 2013 34     34616 2014 35     36600 2015 36     36960 2016 37 27034.254 2017 38 2 33 2 3 4
    48     19200 2008 29     19600 2009 30     20400 2010 31     20400 2011 32     22400 2012 33     22200 2013 34     22740 2014 35     22488 2015 36 1 31 1 2 1
    49     22860 2015 26     23445 2016 27     19008 2017 28  9394.252 2018 29  27905.01 2019 30         . 2020 31         . 2021 32         . 2022 33 2 28 1 3 3
    50     20400 2009 26     20400 2010 27     20400 2011 28     20900 2012 29     22790 2013 30     24058 2014 31     25108 2015 32         . 2016 33 1 28 1 2 1
    51     27600 2009 31     32550 2010 32     33850 2011 33     32400 2012 34     32400 2013 35     32400 2014 36 35158.207 2015 37  41025.45 2016 38 1 33 1 2 1
    52     30000 2009 29     31375 2010 30     31500 2011 31     33250 2012 32     35800 2013 33     36951 2014 34     35538 2015 35     35718 2016 36 1 31 1 2 1
    53         . 2007 38     39168 2008 39     33944 2009 40     31332 2010 41     35226 2011 42     38762 2012 43     47184 2013 44     47184 2014 45 1 40 1 3 1
    54         . 2007 26     22250 2008 27     18600 2009 28     16100 2010 29     16200 2011 30     16200 2012 31     16200 2013 32     16200 2014 33 2 28 1 2 3
    55     24624 2010 30     23389 2011 31     23520 2012 32     23520 2013 33     23520 2014 34     23520 2015 35     23520 2016 36 18575.336 2017 37 2 32 1 3 3
    56  7038.131 2014 23  19596.86 2015 24  4863.296 2016 25  9683.246 2017 26  4074.625 2018 27  5950.626 2019 28         . 2020 29         . 2021 30 2 25 2 3 4
    57         . 2007 30     25740 2008 31     26400 2009 32     26400 2010 33     26400 2011 34     26400 2012 35     26400 2013 36     26400 2014 37 2 32 1 2 3
    58  30928.97 2013 28  30928.97 2014 29  30928.97 2015 30  30928.97 2016 31  30928.97 2017 32  40484.67 2018 33  41353.37 2019 34         . 2020 35 1 30 1 3 1
    59         . 2010 38     31200 2011 39     31200 2012 40     31200 2013 41     21600 2014 42     21600 2015 43     21600 2016 44 22985.895 2017 45 2 40 2 2 4
    60 12315.123 2011 29 12223.875 2012 30 12223.875 2013 31 12223.875 2014 32 12223.875 2015 33 12223.875 2016 34 12223.875 2017 35 12223.875 2018 36 2 31 1 2 3
    61     46800 2014 35     46800 2015 36     50800 2016 37     51600 2017 38     62600 2018 39     78000 2019 40         . 2020 41         . 2021 42 2 37 1 3 3
    62     23832 2010 29     23832 2011 30     23832 2012 31     23832 2013 32     23832 2014 33     28758 2015 34     39799 2016 35     45084 2017 36 1 31 2 1 2
    63     26400 2011 27 25061.744 2012 28 25748.496 2013 29  24209.04 2014 30 19588.096 2015 31  22292.38 2016 32         . 2017 33         . 2018 34 2 29 1 3 3
    64     26400 2012 27     26400 2013 28     26400 2014 29     27800 2015 30     28800 2016 31     28800 2017 32     28800 2018 33     35400 2019 34 1 29 2 2 2
    65     26400 2012 24     28800 2013 25     33600 2014 26     33600 2015 27     33600 2016 28     33600 2017 29     33600 2018 30     33600 2019 31 1 26 2 3 2
    66 29316.504 2009 30 30263.637 2010 31 26987.645 2011 32   23954.6 2012 33   23954.6 2013 34   23954.6 2014 35  24036.14 2015 36  24933.13 2016 37 2 32 1 3 3
    67  8578.897 2015 31 30076.564 2016 32  29665.03 2017 33  29665.03 2018 34  29705.04 2019 35         . 2020 36         . 2021 37         . 2022 38 2 33 1 3 3
    68         . 2013 34     33600 2014 35     34800 2015 36     38100 2016 37     39600 2017 38     39600 2018 39     39600 2019 40         . 2020 41 2 36 1 3 3
    69   5564.03 2009 21  5543.034 2010 22  5811.877 2011 23         0 2012 24         0 2013 25         0 2014 26         0 2015 27         . 2016 28 2 23 2 2 4
    70         0 2014 36         0 2015 37         0 2016 38         0 2017 39         0 2018 40         0 2019 41         . 2020 42         . 2021 43 2 38 2 2 4
    71 28201.734 2011 32 28562.035 2012 33  29461.14 2013 34  30810.85 2014 35  30928.97 2015 36  30928.97 2016 37  30928.97 2017 38  30928.97 2018 39 2 34 1 2 3
    72 13142.248 2015 22  20196.52 2016 23  23959.89 2017 24  30218.18 2018 25     30000 2019 26         . 2020 27         . 2021 28         . 2022 29 2 24 1 2 3
    73     25200 2010 28     26200 2011 29     26400 2012 30     26400 2013 31     26400 2014 32     26400 2015 33     26400 2016 34     26400 2017 35 2 30 1 3 3
    74         . 2007 34     27075 2008 35     28200 2009 36     29950 2010 37     33900 2011 38     34800 2012 39     34800 2013 40         . 2014 41 1 36 2 2 2
    75         . 2007 30     31250 2008 31     32940 2009 32     23466 2010 33     21900 2011 34     21900 2012 35     21900 2013 36     21900 2014 37 2 32 2 1 4
    76         . 2013 30 15948.936 2014 31 23098.846 2015 32 14169.602 2016 33 14094.375 2017 34  13943.92 2018 35 16047.946 2019 36         . 2020 37 1 32 1 1 1
    77     49200 2009 47     50100 2010 48     50400 2011 49     50400 2012 50     50400 2013 51     50400 2014 52     52480 2015 53     53670 2016 54 1 49 1 2 1
    78  17766.03 2011 26  22078.83 2012 27     28423 2013 28 28507.736 2014 29     31803 2015 30     34362 2016 31     34776 2017 32         . 2018 33 2 28 1 3 3
    79     25200 2011 26     26400 2012 27  24511.15 2013 28 19282.754 2014 29 19282.754 2015 30  6427.584 2016 31         0 2017 32         0 2018 33 2 28 2 2 4
    80         . 2008 28     22800 2009 29     24104 2010 30      9400 2011 31     11210 2012 32 10473.327 2013 33      9900 2014 34      9900 2015 35 2 30 1 2 3
    81  24647.86 2011 31 24536.016 2012 32 24536.016 2013 33 24536.016 2014 34 24536.016 2015 35 24536.016 2016 36 22219.195 2017 37  19784.13 2018 38 2 33 2 1 4
    82 17616.922 2009 28 18587.043 2010 29 19988.994 2011 30  20289.57 2012 31 21357.615 2013 32  23094.98 2014 33 23573.066 2015 34 23573.066 2016 35 2 30 1 2 3
    83         . 2007 29 18902.143 2008 30  20808.07 2009 31  22326.44 2010 32     24000 2011 33     24000 2012 34     24000 2013 35     24000 2014 36 1 31 1 1 1
    84  2944.542 2015 25         0 2016 26         0 2017 27         0 2018 28 2917.9775 2019 29         . 2020 30         . 2021 31         . 2022 32 2 27 1 2 3
    85  39267.46 2012 42  39267.46 2013 43  39267.46 2014 44  39267.46 2015 45  39267.46 2016 46         . 2017 47         . 2018 48         . 2019 49 2 44 2 3 4
    86     31590 2013 27     34945 2014 28     38220 2015 29     42493 2016 30     44300 2017 31     51600 2018 32     53800 2019 33         . 2020 34 1 29 2 3 2
    87     40800 2008 37     43800 2009 38     45600 2010 39     45600 2011 40     45600 2012 41     41920 2013 42     48000 2014 43     48000 2015 44 1 39 1 3 1
    88         0 2009 29         0 2010 30         0 2011 31         0 2012 32  9753.571 2013 33 17561.824 2014 34 17487.648 2015 35 17116.766 2016 36 2 31 1 3 3
    89     45604 2009 37     47987 2010 38     52200 2011 39     52200 2012 40     59750 2013 41     50400 2014 42     50400 2015 43     50400 2016 44 1 39 1 3 1
    90  50929.49 2014 27  50523.91 2015 28  50118.33 2016 29  50118.33 2017 30  40353.05 2018 31     38400 2019 32         . 2020 33         . 2021 34 2 29 2 3 4
    91 28100.164 2011 32 27793.895 2012 33 26740.113 2013 34  29464.42 2014 35     30100 2015 36     40000 2016 37     41700 2017 38     44400 2018 39 1 34 1 2 1
    92  31948.06 2015 28 32119.256 2016 29 34002.367 2017 30 38212.684 2018 31  36016.25 2019 32         . 2020 33         . 2021 34         . 2022 35 2 30 1 3 3
    93     30000 2009 32     31640 2010 33     30904 2011 34     29984 2012 35     32588 2013 36     33648 2014 37     34675 2015 38     35235 2016 39 2 34 1 3 3
    94      7492 2013 26         0 2014 27 11376.115 2015 28 11573.312 2016 29 10993.705 2017 30  3533.451 2018 31  3533.451 2019 32         . 2020 33 2 28 2 3 4
    95     52500 2008 31     57000 2009 32     57000 2010 33     57000 2011 34     60000 2012 35     61000 2013 36     61200 2014 37     61400 2015 38 1 33 1 3 1
    end
    label values sex gender
    label def gender 1 "Male", modify
    label def gender 2 "Female", modify
    label values religiosity religiosity
    label def religiosity 1 "Non-Religious", modify
    label def religiosity 2 "Religious", modify
    label values educationlevel educcat
    label def educcat 1 "Low educated", modify
    label def educcat 2 "Average educated", modify
    label def educcat 3 "High educated", modify
    label values sexrelig sexreligious
    label def sexreligious 1 "mn", modify
    label def sexreligious 2 "mr", modify
    label def sexreligious 3 "fn", modify
    label def sexreligious 4 "fr", modify
    Last edited by Sandra Bloem; 08 Jul 2020, 17:22.
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