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  • Interpret the Coefficient's Magnitude by its Standard Deviation

    Dear Members,

    I hope you are getting ready for a nice weekend.

    I am trying to analyse my regression results and I need to interpret the economic magnitude of specific independent variable in terms of its standard deviation.

    For example: Y = a + bX + u

    In general, one can say that when X increases by one unit, Y is expected to increase by 'b' value.

    Alternatively, one can say that when X increases by one standard deviation, Y is expected to increase by 'some' value.

    How to obtain this 'some' value in Stata?

    I appreciate your suggestions.

    Thank you,
    Mustafa

  • #2
    Hello Mustafa,

    Please try - listcoef - after the regression.

    Best,

    Marcos
    Best regards,

    Marcos

    Comment


    • #3
      Mustafa,

      How about something like the following:
      Code:
      sysuse auto, clear
      summarize weight
      local est1 = r(mean)
      local est2 = r(mean) + r(sd)
      
      regress mpg weight
      di (_b[_cons] + (_b[weight] * `est2')) - (_b[_cons] + (_b[weight] * `est1'))
      Best,
      Alan

      Comment


      • #4
        Marcos, the 'listcoef' did not work. I received an error. I tried "ssc install listcoef", but it didn't find it.

        Alan, your code seems to work.Yet, I will keep searching for some automatic command.

        Thank you for your suggestions

        Comment


        • #5

          Mustafa: try -findit listcoef-, the follow the instructions and/or take a look at http://www.ats.ucla.edu/stat/stata/faq/findit.htm
          Kind regards,
          Carlo
          (Stata 18.0 SE)

          Comment


          • #6
            Hi Carlo,

            Thank you for your suggestion.

            I found some useful resources.

            Comment


            • #7
              This is actually just z-standardizing the Xs before regression, e.g.

              Code:
              sysuse auto ,clear
              su weight
              g z_weight = ((weight - r(mean)) / r(sd))
              reg mpg z_weight
              or, alternatively multiply the coefficients by the standard deviation afterwards

              Code:
              reg weight mpg
              su weight
              di _b[weight] *  r(sd)
              Edit:

              Note that for both approaches the standard deviation (and mean) reported by summarize must be based on the estimation sample.

              Best
              Daniel
              Last edited by daniel klein; 29 May 2015, 08:31.

              Comment


              • #8
                Thanks Daniel,
                I think this woks as well.
                This is what Wooldridge suggests (Y)

                Comment


                • #9
                  Dear Statalisters,

                  I would like to ask something further related to Mustafa's question. If our regression involves several independent variables, do we need to standardize each indep. variable separately and then run the regression? Is there a quicker way to do it? For example, I am running the following regressions (it is the same regression but I am using 4 different specifications):

                  Code:
                  * pooled OLS regression using industry dummies
                  reg y $xlist dff_* ,cluster(id)
                  estimates store m1, title(Pooled OLS)
                  
                  
                  * Firm fixed effects
                  xtreg y $xlist, robust i(id) fe
                  estimates store m2, title(Firm Fixed Effects)
                  
                  
                  *Tobit regression
                  tobit y $xlist dff_*, ll(0) robust cluster(id)
                  estimates store m3, title(Tobit)
                  
                  
                  * Poisson fixed effects
                  xtpoisson y $xlist, robust i(id) fe
                  estimates store m4, title(Poisson Fixed Effects)
                  I would like to make some comments about the economic significance of my main coefficients x1 and x2 after the regressions (dff_* contains INDUSTRY dummies, $xlist contains several indep. variables x1, x2, ..., x10). What do I need to do to calculate the standardized coefficients and say e.g. a one standard deviation increase in x1 increases y by e.g. 0.78 standard deviation (assuming hypothetically that the standardized coefficient of x1 will be 0.78).

                  In this way (i.e. using standardized coefficients), can I make comments and compare the standardized coefficients across my 4 models? In other words, I am wondering whether it would make sense to compare the effect of the standardized x1 on y across my 4 models. Notice that $xlist contains the same indep. variables across all models. I am using balanced panel data.

                  PS. My y and x1 and x2 are count variables that take the values 0, 1, 2, 3, ..., 45.

                  Thank you in advance.

                  Best,
                  Nikos
                  Last edited by Nikos Tsileponis; 05 Jun 2015, 04:19.

                  Comment


                  • #10
                    Did not read thru the end, but regress has a beta option, that reports fully standardized coefficients.

                    Best
                    Daniel

                    Comment


                    • #11
                      Nikos: You only have to standardize the variables x1 and x2; see Daniel's code above. You'll want to use the -margins- command for the tobit model; the coefficients will not give you the marginal effects, standardized or otherwise.

                      I trust you realize that the four methods you propose will naturally have different coefficients because they assume very different functional forms. You will have to obtain average partial effects for the Tobit and Poisson models to make them comparable to the linear models. Also, you might want to use the Tobit Correlated Random Effects approach. JW

                      Comment


                      • #12
                        Originally posted by Jeff Wooldridge View Post
                        Nikos: You only have to standardize the variables x1 and x2; see Daniel's code above. You'll want to use the -margins- command for the tobit model; the coefficients will not give you the marginal effects, standardized or otherwise.

                        I trust you realize that the four methods you propose will naturally have different coefficients because they assume very different functional forms. You will have to obtain average partial effects for the Tobit and Poisson models to make them comparable to the linear models. Also, you might want to use the Tobit Correlated Random Effects approach. JW
                        Daniel thanks for code! It was very helpful.

                        Dear Prof. Wooldridge,

                        Thank you very much for your help and suggestion. I was wondering whether I could ask you something related to the interpretation of the coefficients when using the 4 models I describe above:

                        1) In the pooled OLS regression, the coefficient of x1 is 0.718: So, I will say that 1 unit increase in x1 leads to 0.718 units increase in y.
                        2) In the Firm FE model, the coefficient of x1 is 0.720. Can I say again that 1 unit increase in x1 leads to 0.720 units increase in y ? Would this be correct? Is it suspicious that the coefficient of x1 is very similar? In other words, is it something that is not uncommon?
                        3) In the tobit model, as you suggest, I need to run marginal effects. So, I type in Stata "mfx" after the regression. The coefficient of x1 now becomes 0.760. Can I interpret it in the same way?
                        4) After the Poisson Firm FE, I also run "mfx" and the coefficient of x1 now becomes 1.056. Again, can I interpret it in the same way? e.g. 1 unit increase in x1 leads to 1.056 units increase in y?

                        The reason why I am employing these 4 different models is that I need to show that my results and conclusions remain the same when using different model specifications that assume different functional forms. The dependent variable (y) is a count variable that takes values 0, 1, 2, 3, ..., 45. My main independent variable (x1) takes values 0, 1, 2, ..., 5. Based on Cameron & Trivedi, I think the most "correct" model is Poisson Firm FE. Please let me know if you have the same opinion.

                        I really appreciate your help once again!

                        PS. These are my models again for convenience:

                        Code:
                        * pooled OLS regression using Industry dummies
                        reg y $xlist ind_dummies, cluster(id)
                        estimates store m1, title(Pooled OLS)
                        
                        * Firm fixed effects
                        xtreg y $xlist, robust i(id) fe
                        estimates store m2, title(Firm Fixed Effects)
                        
                        *Tobit regression
                        tobit y $xlist ind_dummies, ll(0) robust cluster(id)
                        estimates store m3, title(Tobit)
                        
                        * Poisson firm fixed effects
                        xtpoisson y $xlist, robust i(id) fe
                        estimates store m4, title(Poisson Fixed Effects)
                        Best regards,
                        Nikos

                        Comment


                        • #13
                          Hi All,

                          Just running -reg y x1 x2... xk, beta- will give the standardized beta coefficients (interpreted as increases in standard deviations, rather than units) in place of the confidence interval. (EDIT: I did not see Daniel's post above. Consider this as supporting his assertion!)

                          Josh

                          Comment


                          • #14
                            Hi Joshua,

                            Thanks for your reply. Yes, this is what Daniel also suggests. And it works fine! In my last post above, I now asked Prof. Wooldridge and everyone else of course how I should interpret the coefficients (not the standardized ones this time) of the 4 models mentioned above.

                            Thanks.

                            Nikos

                            Comment


                            • #15
                              Dear Statalist,

                              I have a question, I am working with rainfall and child health ((WHO) weight height z score.., etc) data. I defined positive and negative rainfall shocks as +/- 1 SD with respect to historical mean for a given region. My question is, do I need to further apply Daniel's codes in no.7 to determine the standardised coefficients?

                              For instance, do I need to do:
                              sum pos_rain
                              gen z_pos_rain = ((pos_rain - r(mean))/r(sd))
                              reg wh_zscore z_pos_rain
                              Would this be the correct way to interpret the increase in standard deviations?

                              Thanks for your help with this.

                              Regards

                              Comment

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