Doubt intepreting the results of OLS using Longitudinal Datasets

[Rui Agostinho]

Hello everyone,

I have a doubt when interpreting the results obtained through OLS, when using a longitudinal dataset, that may be subtle, but I am afraid may be more impactful than I realize.

The dataset I have has information about a set of industries, for the years 2008-2019. The variables I am for now interested in are Percentage_changes_per_industry (the percentage of people that become entrepreneurs) and age_median (the median age of the workers).

The dataset looks something like this

caem2	year	Percentages_changes	Age_median
1	2008	0.10029345	43
1	2009	0.16616431	43
1	2010	0.62419285	43
1	2011	0.60629515	43
1	2012	0.57011572	43
1	2013	0.62000761	43
1	2014	0.52445023	43
1	2015	0.6367258	42
1	2016	0.65820404	42
1	2017	0.5906995	42
1	2018	0.56186026	42
1	2019	0.50835528	41
2	2008	0.4870546	39
2	2009	0.34400635	40
2	2010	0.76704545	40
2	2011	1.1684783	41
2	2012	0.65547981	41
2	2013	1.1118997	41
2	2014	1.1496571	41
2	2015	1.027984	42
2	2016	0.83689459	42
2	2017	1.3143872	43
2	2018	0.95934959	43
2	2019	1.1663697	43
3	2008	0.63722259	45

The regression and results I have now are the following:

reg Percentage_changes_per_industry age_median


      Source |       SS           df       MS      Number of obs   =       892
-------------+----------------------------------   F(1, 890)       =     90.46
       Model |  15.6591594         1  15.6591594   Prob > F        =    0.0000
    Residual |  154.065501       890  .173107305   R-squared       =    0.0923
-------------+----------------------------------   Adj R-squared   =    0.0912
       Total |  169.724661       891  .190487835   Root MSE        =    .41606

------------------------------------------------------------------------------
Percentage~y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  age_median |  -.0373358   .0039255    -9.51   0.000    -.0450402   -.0296314
       _cons |   1.908756   .1557425    12.26   0.000     1.603091    2.214422
------------------------------------------------------------------------------

My doubt then is: how exactly can we interpret the effect age_median has on Percentage_changes_per_industry? Is it:
- The value of the coefficient for Median Age is of -0.037, which indicates that when the Median Age goes up by one year, the expected Rate of New Entrepreneurs decreases by 0.037 percent, on average, everything else held constant.
or
- The value of the coefficient for Median Age is of -0.037, which indicates that when the Median Age of a given industry, in a given year, goes up by one year, the expected Rate of New Entrepreneurs decreases by 0.037 percent, on average, everything else held constant


Basically, when interpreting results that stem from longitudinal datasets, in which the data is grouped (in my case per industry and per year), do we have to be careful to analyze the results also taking that into account, or not?


Thank you,
Rui

[Jared Greathouse]

I don't understand the problem. My only comment here is that you should be using xtreg for panel data, but this aside, you appear to be interpreting your results just fine.

[Carlo Lazzaro]

Rui:
as an aside to Jared's helpful comments, it is not clear to me whether your dataset has a panel or a repeated cross-sectional structure.
These structures impliy different approaches as far as their anaysis is concerned (eg, the way standard errors should be clustered, if needed/feasible).
In addition, no matter the structure of your dataset, one predictor only is surely not enough to get any decent and informative result.