John Cochrane's recent blog post on the differences between New Keynesians and Old Keynesians prompted some good responses. I particularly liked that of Simon Wren-Lewis.
There are two assumptions in the simple NK model that I find particularly troublesome. The first is that agents have an infinite time horizon. The second is that agents are homogenous, or that capital markets are perfect, so that everyone can borrow at the risk-free rate. There are certainly versions of the model where these assumptions are relaxed, but I'm not convinced how well the whole NK architecture copes with this.
I was thinking about this, whilst reading some recent posts on Brian Romanchuk's excellent blog, where he talks about interest rate effects (especially here).
The NK assumptions described above are quite important to the impact of interest rates in that world. Taking a very simple model, where GDP (y) is made up of only consumer spending (c) and government spending (g), we have:
y = c + g
all in real terms.
In the long run, there is assumed to be no output gap, so GDP is at its natural level (y*), so we can determine equilibrium consumption (c*) as:
c* = y* - g*
The assumption of consumers maximising utility over an infinite time period, then implies that the relationship between consumption today and consumption tomorrow is a function of the interest rate. The exact form depends on the assumed utility function, but might be something like this:
ct = ct+1 - α . log [(1+r)/(1+β)]
where r is the real interest rate and α and β are preference parameters. Current consumption is then given by working backwards from the long run equilibrium level using expected future interest rates. Higher interest rates will imply less consumption today.
In this model, therefore, interest rates have a substitution effect but no income effect. Changes in interest rates change how households allocate spending between periods, but don't make households feel any better off overall. This is because households look at long run income and long run income is simply determined by equilibrium output less what the government spends.
This conclusion on interest rates however stands in sharp contrast with that of many Post Keynesians, who see an important income effect from rate changes . In PK models, this arises as a result of the additional interest income of households due to higher interest paid on government debt. For most, PK economists, this effect tends to override any substitution effect.
In the basic NK model, it's basically Ricardian Equivalence that is eliminating this income effect. Interest paid on government debt is just a form of transfer income, comparable to a negative tax, so an increase has no effect because agents know they will just pick up the cost later.
And this is really where the assumption about time horizons matters. Agents maximising over infinite lives might indeed be Ricardian (perhaps given other conditions as well). But this is a strong assumption, and not in my opinion a very realistic one. Once we assume agents with a shorter time perspective, the dynamics become somewhat different.
Rather than consider a world with infinitely lived agents, a good way of looking at this is to think of a world with agents who live and die, with agents at all different stages of the lifecycle. Now, a rise in interest rates redistributes future purchasing power from those without assets to those that do. To a significant extent, this actually means a redistribution away from agents that have not yet been born, or at least are not yet active consumers. The potential negative impact on their spending does not therefore materialise currently.
In effect, we are inducing today's consumers to spend more by promising them a bigger share of tomorrow's resources at the expense of people who have no impact on current demand.
The impact of interest rate changes is a complicated one. There are different effects working in different directions. To my mind, the simple NK model assumes away some of the more interesting aspects of what might be going on.