## Friday, August 26, 2005

### Explaining the Statistical Discrepancy Between GDP and GDI with Non-Defense Related Government Consumption

This is one you may want to skip.  I'm not sure if anyone is following the questions about the statistical discrepancy between GDP (gross domestic product) and GDI (gross domestic income), but I have more progress to report for anyone who is.

The reason this is important is that measures of economic growth can differ by as much as .5% depending upon which measure is used and there is evidence the Fed is looking at both income based (derived from GDI) and product based (derived from GDP) measures in assessing productivity.  Because of this, understanding why the two measures differ is important.  The BEA assumes GDP is the more accurate measure and the statistical discrepancy is assigned to GDI, but not everyone shares that view.

Some may be here for the first time, so let me briefly recall the puzzle.  In trying to determine why the GGP/GDI ratio varies, I decomposed GDP into C, I , G, and NX and discovered G appeared more correlated with the discrepancy than the other components of GDP.

Here are the pictures.  The statistical discrepancy has a fairly persistent pattern over time.  Dividing the discrepancy by GDI (which doesn't alter the pattern much, it just makes the series more homoskedastic so the pattern is easy to identify) gives:

The other series in the graph, government spending divided by GDI, G/GDI, duplicates the pattern in the discrepancy fairly well and that is what surprised me and others I’ve shown this to.  Why are the two series so correlated?  Is it spurious (Klein found a similar result so I’m less inclined to believe this), or is there information that can be used to both understand the source of the discrepancy and perhaps even reduce it as a consequence?

The patterns seem fairly close, though the association may not be quite as strong for a longer sample:

Still, it does appear that the two series move together for the most part.

After digging up a few papers the last few days on this topic, most notably these (here and here), I decided to graph the components in G divided by GDI.  By looking at each component individually perhaps the source of the correlation can be better identified. There are two fundamental components in G, federal expenditures and state and local expenditures.  Within each of these, spending is broken down according to consumption and investment.  Finally, federal expenditures are divided into defense and non-defense spending.

The first graph shows state and local government expenditures and the discrepancy since 1980, and the second shows federal government expenditures since 1980.  Both series, as in all graphs in this post, are divided by GDI:

Neither graph seems very revealing, though states and local does fit well up until around 1998.  Here are the same two graphs for the full sample:

Let’s try another cut.  Instead of dividing government expenditures into state and local versus federal, let’s divide them into defense and non-defense spending.  Here are the graphs from 1980:

That appears to be a more fruitful cut.  Non-defense spending is much more correlated with the discrepancy than defense related spending.  Here’s the full sample:

Not a perfect correlation, but enough to wonder what is driving it.  Let’s try yet another cut, this time separating into government consumption and government investment expenditures (all categories, e.g. state and local, federal, defense, and non-defense are included):

and, as usual, for the full sample:

Consumption to GDI moves closer to the discrepancy to GDI series than does the investment to GDI series.  Overall the suggestion is that non-defense consumption exhibits the discrepancy pattern more clearly than the other series.  Let’s graph that series to see if this conjecture holds:

And, for the full sample:

This does appear to provide a closer association.

So, what I’ve learned is that a good place to look for the source of the discrepancy is in non-defense government consumption expenditures. Now I need to determine why this particular series is correlated with the discrepancy.

Posted by on Friday, August 26, 2005 at 12:33 AM in Economics, Methodology | Permalink  TrackBack (0)  Comments (2)