Friday, July 08, 2011

Government and growth: a Rorschach test

Tyler Cowen links approvingly to a new paper by Andreas Bergh and Magnus Henrekson of the Research Institute of Industrial Economics, calling the paper "useful and wise". The paper shows a negative relationship between government size and GDP growth among rich countries. The upshot:
An increase in government size by 10 percentage points is associated with a 0.5 to 1 percent lower annual growth rate. We discuss efforts to make sense of this correlation, and note several pitfalls involved in giving it a causal interpretation.
Notice that last sentence, especially the phrase "pitfalls involved in giving [the correlation] a causal interpretation." This is indeed very wise. Here are three (of the many) possible interpretations of Bergh and Henrekson's findings:

Interpretation 1: Government is good for a rich country. More government allows a country to reach a higher level of per capita GDP. Since rich countries experience conditional convergence, countries with large governments have low growth because their large governments raised per-capita GDP and hence caused growth to slow.

Interpretation 2: Government is bad for a rich country. The countries that are now rich finished converging long ago, and are now diverging, due to institutional differences. Because large governments are an inferior institution, countries with small governments are outgrowing those with large governments.

Interpretation 3: Government is neither good nor bad for a rich country within the observed levels. As countries become richer (and therefore grow slower, as in Interpretation 1), they exhibit a social preference for more government services. Hence, the causation is from GDP to government size.

Which interpretation do you believe? I predict that it will depend on your politics. Socialists will tend to favor Interpretation 1, libertarians will tend to favor Interpretation 2, American liberals will probably tend to favor Interpretation 3. It is my guess that Tyler Cowen favors Interpretation 2, but I could be wrong.

What do other scholars say? In a survey of growth economics, Xavier Sala-i-Martin of Columbia University writes:
The size of the government does not appear to matter much [for rich countries]. What is important is the “quality of government” (governments that produce hyperinflations, distortions in foreign exchange markets, extreme deficits, inefficient bureaucracies, etc., are governments that are detrimental to an economy).
This would tend to fit with my own priors, and my own politics.

So why did Tyler Cowen post the link? Did he want to give us a Rorschach test? Did he hope that we'd naturally gravitate toward Interpretation 2, and conclude that government is bad? I think that when linking to papers, it's good practice to vet the papers carefully and present them in a neutral fashion. In the case of Bergh and Henrekson's paper, the following paragraph struck me as the most telling:
Finally, while there is close to a consensus on the sign of the correlation [between government size and growth], there is also consensus on the fact that causality is very hard to establish with certainty using the method of instrumental variable estimation—or any other method currently available. In fact, it is close to conceptually meaningless to discuss a causal effect from an aggregate such as government size on economic growth. Thus, several scholars in our view have rightly concluded it is more fruitful to analyze separately the mechanisms through which different taxes and expenditure affect growth. Not all taxes are equally harmful, and some studies identify public spending on education and public investment to be positively related to growth.
To me, that seems very useful and wise indeed.


  1. Very nice post - but I think your first link is supposed to go to Tyler Cowen´s blog rather than (as now) the paper itself (which is also the second link).

  2. Thanks, good call.

  3. Hi,

    I think interpretation 1. is wrong.

    Within the neoclassical framework in which conditional convergence applies, if government is a determinant of the steady-state level of income, the coefficient should be positive if it increases the steady-state and negative if it doesn't. I think.

    You grow more slowly if you have achieved your steady-state, whatever it is, as opposed to undergoing transition dynamics (converging), but possessing a characteristic that allows a country to attain a higher steady-state (i.e. as hypothesized: a big government) does not tell you whether that steady-state has been achieved, or whether convergence is still happening.

    If you imagine something happening, like a positive shock that increases a country's steady-state (an increase in government size) then you will grow faster, but in the estimated model that's picked up because the gap between y* and initial income has just gotten bigger (y* has incresed), and it will have gotten bigger if the coefficient on govt. is positive.

    the model is a log linearisation around steady-state:

    log (yt) - log (yt-s) =
    (1 - e^lt)log y* + (e^lt-1)log (yt-s)

    variables on the RHS are proxies for y*, steady-state income (ignoring steady-state exog growth rate). Something that raises y* should have a positive coefficient, if you have "raised income up to a higher level" then yt-s = y* so both sides of equation = 0.

    But it won't mean the coefficient on one of the steady-state determinants is negative because you are growing more slowly.

    many apologies if I have misunderstoodo you and have just commited the sin of teaching grandmother to suck eggs.

  4. n.b.

    I think interpreting growth regressions is a pig, and almost nobody seems to take them seriously as log linearisations of the neoclassical model, in which you really only have 3 things to play with

    1. a) determinants of the speed of convergence and 1. b) the distance you currently are beneath SS.

    [1.a) are not estimated but are reflected in size of coefficient on lagged income 1.b) is pinned down by current income and 3.]

    2. the exogenous steady-state growth rate.

    (that's a bit like a constant interacted with a time trend)

    3. determinants of the steady-state.

    If you take that model seriously, all those variables on the RHS of growh regression are 3., and have nothing to do with how fast you'll grow, despite that being how they are universally interpreted.

    If you then think, OK screw the neoclassical model, let's say endogenous growth is what's going on, or something else, I don't have the experience to say but I think it's something of a free for all. Incidently if you like this topic, my favorite paper is Kneller Bleaney and Gemmell:

  5. Hannu Tanninen9:02 AM

    Since Joel Slemrod's excellent paper in Brookings Papers of Economic Activity 1995 there is ongong debate about this subject. I can understant why M. Henrekson is very careful in his suggestions: because his previous papers about the subject with Stefan Fölster has got quite a lot critique from other Swedish economists (see Agell et al. 2006 European economic review p. 211-218). The related question is why the Nordic countries (e.g. Denmark, Norway, Sweden and Finland) with a BIG government have been so successfull what regards to prosperity and equality?

  6. The Heritage Foundation does something similar by plotting GDP growth against its 'Index of Economic Freedom'. Its 'Index' consists of 10 separate components. It was easy to use the data and back out which components had positive or negative correlations. Freedom from high taxes actually had a negative correlation (higher taxes -> higher growth), albeit a small one. Far and away the most important factors were corruption and protection of property rights. It does not take a genius to see how corrupt societies with loose regard for individual property rights stunts growth.

    If you're looking at data and it takes mental gymnastics to prove your point, you might be lying to yourself.

    It's not a lot of government or a little government that dictates things, it's bad and good government.