In OLS on a census, should statistical significance be ignored? Let's say I'm trying to tell whether my company's sales have had a downward trend over the last 10 years.  Let's also say I have available to me the last 10 years of quarterly sales.  If I run a bivariate regression with time as the independent variable and sales as the dependent variable, and if the regression coefficient for time is negative, do I need to examine the regression coefficient's t-statistic?  I mean, aren't these data based on a census of my population of interest?  If they're a census, why would I need statistical testing?
Basically I'm wondering how often my knee-jerk reaction to apply statistical testing has been wrong-headed. 
 A: I think the correct answer depends on the question.  If your question is, "On average have the observed sales of my company decreased over time?" there is no reason for statistical inference.  Suppose on the other hand you think that the data generating process is:
observed_sales = constant + fundamental_trend * year + white_noise 
You are interested in testing the hypothesis "fundamental_trend = 0".  In this case, you can think of the observed sales of your company as a finite sample of an infinite data generating process, and employing statistical inference makes sense. 
A: I believe you're correct. Confidence bounds are needed when we are sampling from a random process. If you assume that the data you have exactly represents the companies true financials and there is no measurement error  then you can accurately say the regression coefficient is the true coefficient. 
However, if the data might be subject to measurement error (the data may not reflect true financials) or there is huge 'jitter' (like your companies financials change on a daily basis) then I think you would need confidence bounds...
