Hi Basil, thanks so much for this gracious response. I don’t quite buy this BOTEC though—I don’t see any theoretical reason the abstract representative agent couldn’t have a negative time preference rate. Certainly, at the individual level, people might prefer to consume during their retirement or to build up savings for high anticipated taxes/costs when they’re old. There is no mathematical problem with an individual having a negative time preference rate (e.g. Utility = log(C_young) + 2*log(C_old)). So I don’t see why rho = 0 needs to be a lower bound.
Thanks for your gracious words about my other work, and looking forward to your thoughts on the paper.
Seth Benzell
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Hi All,
I’m an economist who’s been thinking about some related issues.
I agree with the article that increases in anticipated capital productivity (or decreases in anticipated longevity) should tend to increase global interest rates. However, the blog post ignores a giant secular trend that could be driving recent (last few decade) low interest rates – a global “savings glut” due to the growth of a giant, thrifty, Asian upper and middle class. This group has a huge hunger for investment vehicles, and has been driving down global interest rates.In my recent global automation simulation paper, which models in detail demographic and productivity trends across the regions of the world, we find that interest rates will continue to decline over the next thirty years if automation (defined as capital-biased technical change) continues at its historical rate. If automation were to proceed at a rate 5x its historical rate, we calculate that world interest rates is ~still~ projected to decline, and be lower in 2050 than today. That said, if automation were to occur x10 faster than its historical rate moving forward, we would anticipate interest rates to be almost 50% higher than they are today in 2050.
In the language of the blog post, I’d argue that *rho*, the time discount rate of the representative global saver, is in essence getting smaller as more of world income is going to thrifty middle-aged Asians. A fast enough rate of automation can overcome this headwind, but there is a large headwind to be overcome.
Paper here: https://www.nber.org/papers/w29220 see section “4.3.3 Faster Rates of Automation”
I haven’t run the simulation to see what the effect would be today of a giant anticipated increase in automation in 30 years, or of everyone dying with certainty in 30 years, but those are certainly possible in our framework, and something we could try if anyone thinks it would be interesting.
Yes, I was referring to finite lived agents, which does start to get away from what the representative agent framework can handle.
To your technical point—if the real interest rate were negative, couldn’t an infinitely lived agent be able to still satisfy transversality? If there’s no productive use of additional capital at the margin, and a shitty storage technology, that would be the case. And, endogenously, a super-saving society that only wanted to throw a party at infinity might start running into that problem fast.