Hi all,

I am running an OLS regression with robust clustered standard errors (due to heteroskedasticity). I am using panel data.

My dependent variable is defined as the cash share of total transactions made in a typical month, measured between 0 and 1. Out of 6,695 observations, there are 178 observations with a response of 1 and 634 observations with a response of 0.

My explanatory variables are as follows:
  • Income - this is yearly household income. It is calculated in dollars as the mean of an assigned income category. i.e. 7,500 if the respondent falls within $5-10k income category.
  • Age - measured in years
  • Education - Four categories assigned values of 1- 4.
My questions are:

(1) I have read seen previous posts indicating that other models are better than OLS when the dependent variable is a proportion like mine. For example, use logit regression? I’m not sure how to run this type of regression nor how to interpret the results. I am not sure why OLS wouldn’t work well with a dependent variable measured as a proportion between 0 and 1.

(2) How can I accurately interpret coefficients on the explanatory variables? I am a bit confused by this.

(3) Also, the coefficient on income is very small. I was thinking of dividing income/1000. Is this method okay to use to re-scale?

(4) is it appropriate to take log of my dependent variable if it is a proportion?

Any advice would be really appreciated. Thanks!


I attach below the code for conducting the OLS regression and also the sample data using -dataex-. I did not know how to insert a table of my results.

Code:
reg cashshare income age i.educat male rating holdings credit cheque i.year if sample==1, robust

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input float(year cashshare) double(age income) float(educat male) double credit float rating double(holdings cheque) float sample
2015   .1334569 31 112500 4 1 1 20 108.33333333333341 1 1
2016   .3030303 32 112500 4 1 1 21                 20 1 1
2017   .1935484 34 112500 4 1 1 24  969.6428580000008 1 1
2015  .12854996 66  27500 4 0 1 21  300.0000000000001 1 1
2016   .1992903 67  17500 4 0 1 22 180.00000000000006 1 1
2017   .1682243 68  17500 4 0 1 23                280 1 1
2016 .020833334 41 112500 3 1 1 29                  0 1 1
2017          1 42 112500 3 1 1 25                 80 1 1
2015  .05921588 25  32500 2 1 0 25               82.5 1 1
2016          0 26  37500 2 1 0 26 11.666666666666664 1 1
2017          0 27  37500 2 1 1 24  973.9285715999991 1 1
2015   .3259842 53  37500 3 0 1 21 130.44642870000004 1 1
2016  .20155144 55  32500 3 0 1 23  80.00000000000001 1 1
2017   .4016003 56  22500 3 0 1 22  60.00000000000001 1 1
2015  .06490872 26  55000 4 0 1 20                 80 1 1
2016     .09375 28  55000 4 0 1 20                 20 1 1
2015  .05271691 83 112500 3 1 1 22 1304.4642869999998 1 1
2016  .05449017 84 112500 3 1 1 18                600 1 1
2017  .24793923 85 112500 3 1 1 20                300 0 1
2015          0 38 112500 3 1 1 14  83.33333333333327 1 1
2016  .13636364 40 162500 3 1 1 17  85.73735572900041 1 1
2017          0 41 162500 3 1 1 15 199.99999999999994 1 1
2015  .53912795 57  22500 2 0 1 29                 80 1 1
2016  .12972517 58  22500 2 0 1 28 200.00000000000014 1 1
2017  .54251766 59  22500 2 0 1 29 13.333333333333336 1 1
2015 .023809524 57 162500 4 1 1 22  869.6428579999998 1 1
2016  .29116118 58  55000 4 1 1 23  710.3417382269064 1 1
2017  .13953489 59  45000 4 1 1 21  869.6428579999998 1 1
2015  .52614975 44  87500 3 1 1 23 434.82142900000036 1 1
2016   .7837778 46  87500 3 1 1 23 434.82142900000036 1 1
2017   .8249276 47  87500 3 1 1 23 500.00000000000045 1 1
2015  .12204076 54 162500 3 1 1 21  150.0000000000001 1 1
2016          0 56 162500 3 1 1 22                 40 1 1
2017   .0961064 57 162500 3 1 1 24  60.00000000000001 1 1
2015  .06973366 64  17500 3 0 1 16 100.00000000000007 1 1
2016   .1854961 66  17500 3 0 1 22   708.333333333333 1 1
2017   .0924408 67  11250 3 0 1 19                300 1 1
2015  .50914204 48   6250 3 0 0 24        2174.107145 0 1
2016   .3966907 49   8750 3 0 0 30 1779.2857159999999 0 1
2017   .8424754 50   8750 3 0 0 24  521.7857148000004 1 1
2015  .24536224 54 112500 3 0 1 24  257.4107145000001 1 1
2017          . 57 112500 3 0 1 16                  . 1 0
2015  .05657994 56 162500 3 1 1 19 200.00000000000014 1 1
2016   .2283169 58 162500 3 1 1 22 100.00000000000006 1 1
2017  .14577565 58 162500 3 1 1 20 100.00000000000007 1 1
2015   .2158688 53  67500 2 1 1 25 373.92857160000017 1 1
2016  .53102005 55  67500 2 1 0 19 240.00000000000014 1 1
2015  .03986711 47 162500 3 0 1 19  33.33333333333334 1 1
2017   .0815647 50 162500 3 0 1 14 100.00000000000007 1 1
2015  .06666667 49  67500 4 1 1 21 23.333333333333336 1 1
2016  .03590127 51  67500 4 1 1 19                 40 1 1
2017  .07803112 52  67500 4 1 1 26                 80 1 1
2015   .1700716 62  87500 2 1 1 24  280.8928574000001 1 1
2016  .17845364 64 112500 2 1 1 24 180.00000000000006 1 1
2017  .28082514 64 112500 2 1 1 23 146.96428580000003 1 1
2015  .20849185 64   8750 3 0 1 16 173.92857160000003 1 1
2016  .46384865 65   8750 3 0 1 23  95.29761913333337 1 1
2017   .3653846 66   8750 3 0 1 17                120 1 1
2016   .6631991 50  32500 2 1 1 25  782.6785722000002 1 1
2017   .6666667 51  32500 2 1 1 22  360.0000000000001 1 1
2015  .04206984 46 162500 4 1 1 19                 20 1 1
2017          0 49 162500 4 1 1 20                 80 1 1
2015   .1640541 44  87500 3 1 1 20               1600 1 1
2016   .3001541 45 112500 3 1 1 20 120.00000000000001 1 1
2017        .25 46 112500 3 1 1 16 100.00000000000007 1 1
2015        .12 28   2500 4 0 1 16                260 1 1
2016          0 29  17500 4 0 1 21                 80 1 1
2017 .069695085 30  27500 4 0 1 17 46.666666666666664 1 1
2015        .18 30  45000 4 0 1 17 100.00000000000007 1 1
2016  .06896552 32  45000 4 0 1 25                 60 1 1
2017  .14180991 32  45000 4 0 1 23 100.00000000000007 1 1
2015  .23148148 52  67500 4 1 1 20 200.00000000000014 1 1
2016   .2897196 52  67500 4 1 1 21  360.0000000000003 1 1
2017  .20763187 53  67500 4 1 1 19  340.0000000000003 1 1
2015  .09425198 46 162500 3 1 1 17  554.8214290000002 1 1
2016  .06666667 47 112500 3 1 1 22 180.00000000000006 1 1
2017   .4494983 48 112500 3 1 1 24 120.00000000000001 1 1
2015          0 31  67500 3 1 1 20                 20 1 1
2016  .12244898 33  67500 3 1 1 22                160 1 1
2017       .125 34  67500 3 1 1 20                 40 1 1
2015   .3865514 56  67500 2 1 0 29 3892.8854616688204 1 1
2016  .25685653 58  67500 2 1 0 19 126.96428580000003 1 1
2017         .2 59  87500 2 1 0 19 213.92857160000003 1 1
2015   .3388633 58  32500 2 1 0 25 195.66964305000005 1 1
2016   .4044944 60  32500 2 1 0 22 200.00000000000014 1 1
2017   .4013378 61  32500 2 1 0 22 200.00000000000003 1 1
2015   .1178344 30 112500 3 1 1 21  33.33333333333334 1 1
2016 .012800976 32 112500 3 1 1 21 25.000000000000018 1 1
2017  .01222494 33 112500 3 1 1 22   41.6666666666667 1 1
2015    .522196 59  67500 2 1 0 15 1739.2857159999999 1 1
2016  .52024233 61  67500 2 1 0 23  521.7857148000002 1 1
2015          . 69   8750 1 1 .  .                  . . 0
2016          1 69   8750 1 1 0 12 130.44642870000007 0 1
2017          1 71   8750 1 1 0 17 173.92857160000003 1 1
2015          0 53  87500 3 1 1 25  53.33333333333333 1 1
2016   .1923077 54  67500 3 1 0 21                 20 1 1
2017  .06060606 55  87500 3 1 0 26  33.33333333333333 1 1
2015   .4244186 37  13750 3 0 0 23 180.00000000000003 1 1
2016  .17261343 39   8750 3 0 0 23 213.92857160000003 1 1
2017  .15873533 40  11250 3 0 0 21 173.92857160000003 1 1
end
label values educat educat_label
label def educat_label 1 "no diploma", modify
label def educat_label 2 "high school", modify
label def educat_label 3 "graduate", modify
label def educat_label 4 "post graduate", modify
label values male male_label
label def male_label 0 "female", modify
label def male_label 1 "male", modify
label values credit credit_label
label def credit_label 0 "no credit card", modify
label def credit_label 1 "credit card owner", modify