How to compute the standardized coefficient of a dummy interaction term slope?

[Jaap van Duivenboden]

Hello,

For my research, I am performing a linear regression on panel data. The dependent variable is 'percentage fund flow', the independent variables are the level of economic uncertainty (as represented by 'OverallEPU') and a dummy variable for the type of fund (D_SRI), where D_SRI takes the value of 1 for socially responsible investment (SRI) funds, and zero otherwise.

The problem that I have is that I want to interpret my results in the following way: A one standard deviation change in OverallEPU results in a ... standard deviation change in percentage fund flows (the dependent variable). The regression results including the standardized coefficients (beta) are presented below:

. reg PercFlow_fund_w i.D_SRI##c.OverallEPU, beta

      Source |       SS           df       MS      Number of obs   =    12,839
-------------+----------------------------------   F(3, 12835)     =     33.11
       Model |  584.281809         3  194.760603   Prob > F        =    0.0000
    Residual |  75500.3803    12,835  5.88238257   R-squared       =    0.0077
-------------+----------------------------------   Adj R-squared   =    0.0074
       Total |  76084.6621    12,838  5.92651987   Root MSE        =    2.4254

------------------------------------------------------------------------------------
   PercFlow_fund_w | Coefficient  Std. err.      t    P>|t|                     Beta
-------------------+----------------------------------------------------------------
           1.D_SRI |  -.0789553   .1166603    -0.68   0.499                -.0162169
        OverallEPU |  -.0024575   .0004171    -5.89   0.000                -.0732526
                   |
D_SRI#c.OverallEPU |
                1  |   .0022981     .00059     3.90   0.000                 .0994249
                   |
             _cons |   .5209132   .0824665     6.32   0.000                        .
------------------------------------------------------------------------------------

For every single coefficient estimate, the standardized coefficients are easy to see. However, the problem is that the slope coefficient between OverallEPU and the dependent variable for SRI funds is the sum of OverallEPU and D_SRI#c.OverallEPU. Adding the standardized coefficients the same way seems like the right thing to do. Nevertheless, the standardized coefficient of the interaction term is larger than that of OverallEPU, which seems wrong, since the magnitude of the coefficient (0.0022981) is lower than that of OverallEPU (-0.0024575). Does anybody know whether the calculated standardized coefficient (beta) of interaction variables in Stata are useful or may be wrong? Any alternative ways to interpret the economic significance of my relation for SRI funds?

Kind regards,

Jaap

[Clyde Schechter]

I think doing a standardized regression here is a mistake and will only result in incomprehensible results. On the assumption that your EPU variable has no natural metric, or its natural metric is unfamiliar to your target audience, it is reasonable standardize that variable. It is less clear whether it is reasonable to standardize your outcome variable, percentage flow fund. As I do not work in finance, I don't know what flow fund means, but if your variable is a percentage of something called flow fund, that seems like a very natural metric that everybody should be able to understand. By contrast, what on earth will 1 standard deviation difference in percentage flow fund mean to anybody? Sounds like obfuscation rather than explanation to me. So if I were you, I would probably do something like this:

egen EPU_standardized = sd(Overall_EPU)
reg PercFlow_fund_w i.D_SRI##c.standardized_EPU

Then to see the association between standardized_EPU and PercFlow_fund_w in funds with and without socially responsible investments:

margins D_SRI, dydx(standardized_EPU)

The units of these marginal effects will be percentage points of flow fund per standard deviation difference in EPU. That strikes me as the most understandable way to interpret these results.