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.
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.