False dichotomy (as in: both choices are false)

John Cochrane gives us a false dichotomy on slower growth:

I still suspect that slow growth is resulting from government-induced sclerosis rather than an absence of good ideas in a smoothly functioning economy.

Those really aren't the only two choices, and in fact those effects seem to be based on small effects rather than large ones. In a sense, it is like saying the energy levels of Hydrogen are mostly due to the Lamb shift rather than Coulomb's law. Let me explain. First, technology.

There are major inventions that have completely changed our lives, yet don't seem to have impacted economic growth. For example, there is the famous saying that computers (or the internet) show up everywhere except productivity. My job is entirely different from what it would have been 20 years ago. Even in the past 10 years, I've gone from needing supercomputers to doing the same work with a laptop (with the right GPU). But Robert Gordon (whom Cochrane is objecting to) doesn't think computers are important. From Krugman's review of Gordon's book:

Developments in information and communication technology, [Gordon] has insisted, just don’t measure up to past achievements. Specifically, he has argued that the I.T. revolution is less important than any one of the five Great Inventions that powered economic growth from 1870 to 1970: electricity, urban sanitation, chemicals and pharmaceuticals, the internal combustion engine and modern communication.

Gordon seems to have post hoc definitions of when inventions are great -- the ones that came before periods of high growth -- that renders the technology explanation circular. If computers and networking aren't the kind of inventions that lead to major growth, then there is something seriously wrong with the theory. 

And how these inventions lead to growth depends critically on your theory of growth. Sure productivity could be enhanced by urban sanitation (increased real output per person because people are sick less often). But urban sanitation would be critically important in my quantity theory of labor [1] where urban sanitation leads to simply more people (fewer dying). Electricity doesn't actually increase the quantity of labor like sanitation does in the QTL, but rather adds hours in the evening for some kinds of work -- likely a second order effect. 

In contrast, urban sanitation would have no direct effect in the monetary information equilibrium model where slow growth seems to arise as an entropic force (see here or the paper [2]). A large economy simply has more ways that it can be realized in terms of many slowly growth markets than a few high growth markets making the former simply the more likely state -- regardless of what products or technology exist in the economy.

Now, what about government?

The US federal government increased its size (measured in money) relative to the economy (measured in money) gradually from about the 1930s to about the 1970s (with the exception of WWII). Any person with even a modicum of math skills would see that:

NGDP(G) = NGDP(0) + c₁ (G/NGDP(0)) + c₂ (G/NGDP(0))² + ...

With G/NGDP ~ 0.2 and natural coefficients, that means it could be at most a 25% effect, not an order 1 effect. And it started as a 5% effect prior to the 1930s. Ok, so we have a scale for the effect of government as a fraction of the economy. What now?
Well, as Gordon mentions the 1970s were the end of the period of rapid growth -- meaning that growth slowed when the scale of government impact on the economy stopped growing. And since then, growth has gradually declined even when the government remained about the same size relative to the economy. So at the aggregate macro (dimensionally reduced) level, there is no obvious direct effect.
Yes, this is a back of the envelope calculation. But it means any negative impact from government would have to be unnatural (the c's are large or small or both), highly nonlinear, and/or depend critically on a serious lack of dimensional reduction in aggregating agent behavior. True to form, Cochrane does think there is a serious lack of dimensional reduction (he suggests various microeconomic policies that he thinks integrate into a macroeconomic effect). So at least he is consistent. 
But no one has ever shown this happens. No agent model has ever been aggregated and produced empirically accurate results that depended on agent micro parameters. As I've said before, if dimensional reduction doesn't occur, then economics is probably computationally intractable. And I think there is strong evidence that dimensional reduction does occur -- if only because the models [1] and [2] do pretty well with huge amounts of dimensional reduction.
Speaking of [1] and [2], neither have first order impacts from the government, and second order (at the aggregated macro scale) impacts (from immigration and equal rights/gender equality in [1] and the size of the government and/or financial sector in [2]).
So neither government nor technology seem like the the most plausible mechanisms to describe the steady decline in US growth. At least not without proposing very tedious and complex models that have no hope of being empirically rejected ... because macro data is uninformative for such tedious and complex models.

...

Update

Additional thoughts on this subject from Noah Smith. And he really gets at a good point. If we want to know how much technology has improved our lives (or government bureaucracy has made things annoying or difficult in business or our personal lives), then we should look at that subjectively. You can tell histories, but leave out the math.

I said before (paraphrasing): the greatest trick economists ever pulled was that NGDP is about our well-being. It's not. Money is an allocation algorithm, full stop and we could reach the current US NGDP without ever developing any technology.

Update, the second (30 Jan 2016)

Dietrich Vollrath as a good blog post up about the persistence of technology. Basically, all of the inventions you had at one time (1500 AD, in this case) is fairly predictive of future growth. The identity of the inventions don't matter for this prediction. But think about what else that means: all of the inventions between the 1500s and the 2000s don't matter to the prediction either. As Vollrath puts it:

In that sense, it isn't the technology in 1500AD per se that matters in the CEG regressions, this is an indicator of some kind of variation in culture or institutions (or something else?) that matters. To return to the earlier discussion, it seems likely that their results won't ultimately turn out to be causal, but the predictive power is telling us to something about how powerful those cultural/institutional [Ed.: or something else?] factors are.

I added the second something else (Vollrath included it in the first sentence, so felt it was appropriate). Maybe more inventions is a sign of a higher entropy economy? More dither?

I also changed the sentence above from "First, growth." to "First, technology." because that is what I meant.