# On using empirical total population data

If you don’t have data for Civilian Non-institutional Population, can you use total population for calculating the empirical counterpart of output per worker in the model?

That is a strange question. Why would you want to use population as a proxy for workers? That being said, the difference between Civilian Non-institutional Population and total population tends to be small for pretty much all countries except for the US, because

1. most countries have a relatively small military that is usually mostly stationed at home (the “civilian” part)
2. hardly any country has as big a prison population as the US (the essence of the “non-institutional”-part)

Hi prof. Pfeifer. Thanks for the reply. I asked because I don’t have data on civilian non-institutional population for my country. But I got your answer.

Lemme also kindly ask this question. In a model with the following production function: Y_t = A_t K^{\alpha}_t L^{1- \alpha}_t, the empirical counterpart of Y_t is, for example, GDPC1, right? But in Schorfheide’s book, they divide GDPC1 by civilian non-institutional population as the empirical counterpart of Y_t. Is it a matter of preference? Like Y_t can be either GDP or GDP per capita?

It’s not really a matter of preference. GDP will grow if the population L_t grows. As perturbation techniques require modeling a stationary economy, the population growth has typically been taken out of the model before writing it down. But then the model implications are in per capita terms and the data needs to conform to this as well.

Ok…I see. So the model Y_t = A_t K^{\alpha}_t L^{1-\alpha}_t is in per capita terms, right? Like the emperical counterpart of Y_t is GDP per capita?

And after normlizing labor hours to 1 (i.e., L_t = 1), the model Y_t = A_t K^{\alpha}_t is now in per capita per labor hours terms, right? Like the emperical counterpart of Y_t is now GDP per capita per labor force?

It depends on how exactly you defined L_t. But the gist is that in the end all trends must be removed.
Also, normalizing hours to 1 is strange. You can do this for the steady state, but usually not at each point in time.

Sorry to ask (maybe a basic question). But how many ways can one define L_t? It has always been labor hours, right? In growth accounting, I know it can also be employment, but in the DSGE literature, I have not seen it been defined that way yet.

On normalizing labor hours to 1, I saw it in your paper, “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”. There, labor hours (h_t) is fixed at 1 under section 1.1, and the empirical counterpart of Y_t is \frac{(FRED: gdpc96)}{(FRED: CLF16OV)}. Is it because h_t is augmented in that model which allows it to be fixed at 1?

Also, if h_t is not normalized, what will the empirical counter of Y_t be? still \frac{(FRED: gdpc96)}{(FRED: CLF16OV)}? Thanks!!

1. The h_t in my example is a very specific model for illustrative purposes where labor is fixed. Obviously that is not true in reality.
2. DSGE models in the end almost always only model hours. But if you start with a neoclassical growth model, then you usually start with hours per person multiplied by the number of people and detrend from there.
3. Which population concept you use for per capita/per worker values again depends on the model at hand. Total population is usually appropriate if the labor force participation rate has not fluctuated too much. Otherwise, you would like a measure of workers. See e.g. the online appendix to Smets/Wouters.