Interpreting the economic significance of regression coefficients

[lal mohan kumar]

Dear Stata members,
For replicating a paper, I have chosen 2 variables, cash divided by total assets and economic policy uncertainty index (EPU).
I have the following descriptive statistics for the above 2.

 summarize  cash_ta_w epu

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
   cash_ta_w |     31696    .0545121    .0756915   .0006936   .4169685
         epu |     30566     93.8854    39.70486    49.4826    185.465

Also, I ran a panel regression with these 2 variables with firm fixed effects. My panel id indicates firms' and in every year all firms will have same EPU (EPU is macro indicator in the model). I have the following results

. xtreg cash_ta_w L.epu,fe

Fixed-effects (within) regression               Number of obs      =     25801
Group variable: id                              Number of groups   =      2868

R-sq:  within  = 0.0002                         Obs per group: min =         1
       between = 0.0015                                        avg =       9.0
       overall = 0.0000                                        max =        16

                                                F(1,22932)         =      5.31
corr(u_i, Xb)  = -0.0073                        Prob > F           =    0.0212

------------------------------------------------------------------------------
   cash_ta_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         epu |
         L1. |   .0000175   7.61e-06     2.31   0.021     2.63e-06    .0000325
             |
       _cons |   .0533294   .0007907    67.45   0.000     .0517795    .0548792
-------------+----------------------------------------------------------------
     sigma_u |  .06317561
     sigma_e |  .04796038
         rho |  .63438748   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(2867, 22932) =    14.52         Prob > F = 0.0000

Question-1: Is the economic significance of variable of interest (Lagged EPU) incredibly low since the coefficient is .0000175?
Question-2: Also can I interpret this as One standard deviation increase in Lagged EPU, on an average produces a, .0694835% (.0000175* 39.70486*100) increase independent variable?
Question-3 : Is there any transformation/change applicable to make the results more appealing to a general audience

[lal mohan kumar]

Following my previous post, https://www.statalist.org/forums/for...n-coefficients
Based on some preliminary reading, I found that alternatively, I can transform cash to total assets to a percentage, which implies the mean of cash holdings now becomes 5.45%. And then re-run the regression with cash to total assets in % and EPU.
In that case, .0000175 becomes .001754 hence one standard deviation increase in Lagged EPU on average results in a 1.2789% (.001754 *100*39.74/5.45) for the average firm.
I think I am missing something or I haven't understood this properly. In the first post, cash to total assets was a fraction(.545) and not in %. I ran the regression with those fractional variables itself.
Can someone help me in interpreting the results better?

[Phil Bromiley]

It is essentially irrelevant whether you run things as a decimal fraction or a percentage. You're just moving the decimal point. When you look at the effect of a one standard deviation change, it should be the same.

You can't interpret economic significance simply from the parameter – it depends on the units in which you measure something. If you changed the dependent variable from the ratio with a mean of.05 to a percentage with the mean of 5, the coefficients on the rhs variable should increase by 100x.

If you want the coefficient to look larger, just rescale the right-hand side variable or the left-hand side variable. Note that this should not substantively change anything – it's strictly cosmetic.

You are doing the right thing – the easiest way to interpret economic significance is to take a standard change in the right-hand side variable and look at the change in predicted value. Where the variables have a meaningful metric, sometimes just looking at a one unit change, or a move from the 25th percentile to the 75th percentile is fine, but folks often use a one standard deviation change. Note, you don't need to do this manually. The margin statement will do it for you quite easily.

[lal mohan kumar]

As usual, I am very thankful to you Phil. I think I can continue with my models and results

[Jeff Wooldridge]

You might also try using log(epu), and then when you change this variable by .10 it’s an increase in epu of about 10%. It may fit better and be more resilient to outliers.

[lal mohan kumar]

Dear Jeff
First,thanks for your expert opinion. From your textbooks, we were taught such transformations. However, when it comes to some published articles, half of them use Raw EPU & a few of them use log EPU even though in some cases sample firms are same. In some cases, results hold under both(raw EPU and Log(EPU) but most of them didn't report why they chose a particular way. In econometrics texts, I have seen that authors like you show separate tables for each with reasons(like the one suggested where log reduces the impact of influential observations).

I have an added query and if someone could answer it, it will be helpful. My question,- is it necessary to show that results should hold in a simple linear regression framework?
Taking my example, when I did the following code, the variable of interest, EPU( lagged value of the natural log of the arithmetic average of the BBD index in the 12 months of fiscal year t)
is not significantly associated with my dependent variable(cash scaled by total assets).

xtreg cash_ta L.log_epu

However, with controls and firm fixed effects, I could get significance(could be due to better model fit of multiple regression vis-a-vis with simple regression). Now my issue is if I put simple regression results, EPU is not a significant predictor of cash to total assets. I have seen papers which proceed in a similar fashion where they first regress dep var on variable of interest-report its significance and finally do a kitchen sink regression where all predictors are used to make sure still the significance of variable interest lies unflinchingly. Is it necessary that there should exist a significant relationship between dep var and variable of interest even without any controls,before proceeding to a developed model?

Once again thanks to all!