Inflation in series plot

[sastuck]

Hello all,

@ChrisBrooks helped me come up with the following code to create a series plot for average CEO salary from 2010-2017:

*series plot salary;
proc sort data=paper.Compustat_ExecuComp4 out=sorted;
	by year;
run;

proc means data=sorted;
	by year;
	var salary;
	output out=avg mean=avg_salary;
run;

proc sgplot data = avg;
series x=year y=avg_salary;
title "Average CEO salary (2010-2017)";
run;

The code runs, and everything looks good, but I had a question. Can I accurately look at the plot and say "here is the trend of average CEO salary per year from 2010-2017? Or do I need to consider inflation to the equation so that the series plot is more accurate? How can I do this?

Thanks!

[Reeza]

You need to account for inflation, because at 2% a year over 7 years thats over 14% change right there. And in CEO #'s that's a lot of $$$.

I would plot two lines - one, in light grey, that shows what it would be adjusted for inflation if nothing had changed, and the second what it actually is today, adjusted for inflation. You can build the first line by taking your 2010 numbers and applying the inflation factor. 

The Census Bureau will likely have the inflation data you need. 

[sastuck]

@Reeza Thank you for the helpful response. Would you mind being more specific as to how I will use the Census Bureau data to manipulate my compensation figures? I am just trying to see how I would do this in practice. 

Thanks!

[Reeza]

You want to know how to adjust your numbers for inflation?

Get the inflation numbers first for the years of interest. 

They usually have a base year, so pick a year to be your base year, this is why you see in texts, in 2018 dollars, in 2016 dollars etc. 

Take the inflation figures and multiply them by your values to inflate them to the 2018 dollars. 

ie to get in 2018 dollars a 2015 figure would be:

2015 $ * inflation 2016 * inflation 2017 *inflation 2018 -> number of multiplicative depends a little on your data and timing. 

But that should give you the idea. 

You can probably check an economics text for reference. Or search online for a tutorial. 

https://www.maa.org/press/periodicals/loci/joma/the-consumer-price-index-and-inflation-adjust-number...

https://www.bankofcanada.ca/rates/related/inflation-calculator/ -> can download the data from StatCan to replicate this to ensure its done correctly. 

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@sastuck wrote:

@Reeza Thank you for the helpful response. Would you mind being more specific as to how I will use the Census Bureau data to manipulate my compensation figures? I am just trying to see how I would do this in practice. 

Thanks!

---

[ballardw]

Since the data is a time series the best approach would be one of the time series analysis procedures in SAS/ETS.

To say something formally about a trend you should have something that looks at the characteristic fairly directly. Year-to-year change could be viewed as the slope of a regression line. A simple approach would involve pro reg or similar linear regression procedure and model ceo salary vs year. However to make year-to-year change more interpretable it would be better to adjust your data so that year runs from 0 to 7 instead of 2010 to 2017.

And you would want to use the raw data not the summary to include the variability.

Maybe something like:

data work.forreg;
   set paper.compustat_ExecuComp4;
   regyear = year-2010;
run;

proc reg data=work.forreg;
   model salary=regyear;
quit;

Examine the slope, the parameter estimated for regyear. The Parameter is the year-to-year change in salary fitted using ordinary least squares fitted as a straight line. The p-value of the slope is small then you could reject a null hypothesis of no change (slope=0) during the period of interest and would reflect dollars change.

Use of averages to look at such things would tend to remove the variability.

Of course you are now in the realm of having to state the question you want to have an answer for: average salary vs salaries as a whole; should I standardize the data so smaller salaries have similar affect to the whole model as the largest salaries and a whole bunch of other stuff.