Interpretating coefficient on shares

[Julia Raciniewska]

Hello,
I very ensure about following interpretations, hence I would be very thankful for any advice. Let's say that my dependent variable is a percentage of managers in total employment ((managers employed in year t / total employment in year t)*100). I am estimating fixed effects model and I get the following results:

 xtreg managers using_computer  ln(RD) price_computer no_degree i.t1, fe vce(cluster industry1)

Fixed-effects (within) regression               Number of obs     =        120
Group variable: industry1                       Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.2400                                         min =         12
     between = 0.7121                                         avg =       12.0
     overall = 0.7001                                         max =         12

                                                F(4,9)            =       4.79
corr(u_i, Xb)  = 0.7263                         Prob > F          =     0.0240

                               (Std. Err. adjusted for 10 clusters in industry1)
--------------------------------------------------------------------------------
               |               Robust
       nonrout |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
using_computer |   .1085054   .0381358     2.85   0.019     .0222363    .1947746
price_computer |   .0019326   .0133758     0.14   0.888    -.0283255    .0321907
          no_d |  -.2675485   .0799442    -3.35   0.009    -.4483948   -.0867022
          1.t1 |  -.7452374   .5176425    -1.44   0.184    -1.916226    .4257513
         _cons |   56.46781   2.910799    19.40   0.000     49.88313     63.0525

(1) If using computer is the % of employees using computer, is to correct to interpret .1085054 as "for a 10% increase in the percentage of employees using computer, the share of managers increases by 1.08 percentage points?"
In general - if both dependent and independent variable is in percentages (or as an index ) , does it mean I can interpret the coefficients the same way as when variables are in logs? That is "for percentage increase in x..., y increases by .. percentage points"?

(2) In addition, if "t1" is a dummy variable = 1 for the time of the crises - does it mean that during crises share of managers decreases by 0.7 percentage points? (if it was significant )

[Clyde Schechter]

(1) If using computer is the % of employees using computer, is to correct to interpret .1085054 as "for a 10% increase in the percentage of employees using computer, the share of managers increases by 1.08 percentage points?"

Yes, this is correct. Well, almost. If you are rounding to 2 decimal places, 1.085054 rounds to 1.09.

In general - if both dependent and independent variable is in percentages (or as an index ) , does it mean I can interpret the coefficients the same way as when variables are in logs? That is "for percentage increase in x..., y increases by .. percentage points"?

Sort of. The thing is that "the same way as when variables in logs" that you are referring to is actually just an approximation, and it's only a good approximation when the elasticity is small. So you really shouldn't do that with log-transformed variables--ideally you should work your way through exponentiating the coefficient, and so forth. But the approximation you are referring to is widely used and widely (mis)understood.

(2) In addition, if "t1" is a dummy variable = 1 for the time of the crises - does it mean that during crises share of managers decreases by 0.7 percentage points? (if it was significant )

Yes, but not only that, it still means that during crises the expected share of managers decreases by 0.7 percentage points even if it isn't "significant." The American Statistical Association has adopted a new, stronger, position against the use of the concept of statistical significance, and one of the reasons for that is precisely this kind of misunderstanding. See their position statement at https://www.tandfonline.com/doi/full...5.2019.1583913. If that is too long for you to read, a shorter "pep talk" is available at https://www.nature.com/articles/d41586-019-00857-9.

[Julia Raciniewska]

Clyde Schechter Thank you for the response! I am still wondering about the interpretation of an intercept.. Does it mean that the share of managers was = 56.5 if there was no change in the % of employees using computer, no change in R&D and no change in employees without a degree?
Thank you.

[Clyde Schechter]

No. The constant term is not really a "constant term" in -xtreg, fe-. It is, instead, the average of the panel-level fixed effects. In most situations, it is of no interest.