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.
Unless I’m missing something, an infinitely lived agent (the framework at play here) can’t have a negative time preference without violating the transversality condition, saving in every period and never consuming. An overlapping generations approach could yield something totally different, though.
Perhaps just a technicality, but: to satisfy the transversality condition, an infinitely lived agent has to have a discount rate of at least r (1-σ). So if σ >1—i.e. if the utility function is more concave than log—then the time preference rate can be at least a bit negative.
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.
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.
Unless I’m missing something, an infinitely lived agent (the framework at play here) can’t have a negative time preference without violating the transversality condition, saving in every period and never consuming. An overlapping generations approach could yield something totally different, though.
Perhaps just a technicality, but: to satisfy the transversality condition, an infinitely lived agent has to have a discount rate of at least r (1-σ). So if σ >1—i.e. if the utility function is more concave than log—then the time preference rate can be at least a bit negative.
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.