In fact Ramsey (1928) originally formulated the problem with zero discount rate. If sigma is the parameter of the CRRA utility function u(c) = [c^(1-σ)-1]/(1-σ), I would suggest to try a Ramsey model with Cobb-Douglas production function, and also for simplicity zero exogenous efficiency growth, and the parameters of the model satisfying (delta + rho) /σ = alpha * (n+δ), where delta is the depreciation rate, rho is the time discount rate, alpha is the exponent of capital in the production function, n is the growth rate of population. rho can be set equal to zero if you like. You should obtain that in such a case obeying the Euler equation gives a constant savings rate from the beginning. This shows that a constant savings rate as an optimal solution is a special case depending on specific relations between the parameters of the model, but in general the savings rate will not be constant, optimally. Athens University of Economics and Business web: alecospapadopoulos.wordpress.com/ On 9/5/2019 01:00, gretl-users-request(a)gretlml.univpm.it wrote: > Send Gretl-users mailing list submissions to > gretl-users(a)gretlml.univpm.it > > To subscribe or unsubscribe via email, send a message with subject or > body 'help' to > gretl-users-request(a)gretlml.univpm.it > > You can reach the person managing the list at > gretl-users-owner(a)gretlml.univpm.it > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Gretl-users digest..." > > Today's Topics: > > 1. Re: Gretl-users Digest, Vol 148, Issue 7 (steady state tricks for the lazy) > (Alecos Papadopoulos) > 2. Re: Gretl-users Digest, Vol 148, Issue 7 (steady state tricks for the lazy) > (Allin Cottrell) > > > ---------------------------------------------------------------------- > > Date: Wed, 8 May 2019 22:28:37 +0300 > From: Alecos Papadopoulos <papadopalex(a)aueb.gr&gt; > Subject: [Gretl-users] Re: Gretl-users Digest, Vol 148, Issue 7 > (steady state tricks for the lazy) > To: gretl-users(a)gretlml.univpm.it > Message-ID: <6e0d0617-3e7d-b124-d6a7-f7ec466191bb(a)aueb.gr&gt; > Content-Type: text/plain; charset=iso-8859-7; format=flowed > > A clarification please Allin: are you referring to the "Ramsey" or to > the "Solow" growth model? I am confused because in the Ramsey model, we > are not heading towards the Golden Rule steady state. On the other hand > you do mention the Euler equation... > > Also what do you mean by "advantage"? In intertemporal utility terms or > something else? > > Alecos Papadopoulos PhD > Athens University of Economics and Business > web: alecospapadopoulos.wordpress.com/ > > On 8/5/2019 21:50, gretl-users-request(a)gretlml.univpm.it wrote: >> Brief word to the wise: I'd like to know, if you're heading for the >> Golden Rule steady state "from below", is there any advantage in >> respecting the Euler equation as opposed to just saving at the >> steady-state Golden Rule rate from the start (given a CRRA utility >> function with parameter sigma = 2): the answer appears to be Yes. >> >> Allin > ------------------------------ > > Date: Wed, 8 May 2019 17:35:02 -0400 (EDT) > From: Allin Cottrell <cottrell(a)wfu.edu&gt; > Subject: [Gretl-users] Re: Gretl-users Digest, Vol 148, Issue 7 > (steady state tricks for the lazy) > To: Gretl list <gretl-users(a)gretlml.univpm.it&gt; > Message-ID: > <alpine.LFD.2.20.3.1905081715370.19346(a)myrtle.attlocal.net&gt; > Content-Type: text/plain; charset=US-ASCII; format=flowed > > On Wed, 8 May 2019, Alecos Papadopoulos wrote: > >> A clarification please Allin: are you referring to the "Ramsey" or to the >> "Solow" growth model? I am confused because in the Ramsey model, we are not >> heading towards the Golden Rule steady state. On the other hand you do >> mention the Euler equation... > I'm referring to the Ramsey model, which IMO ought to be general > enough to include the case of a zero discount rate (so that the > steady state is the same as under the Golden Rule). > > In the Solow context, the usual idea of how to get to the > maximum-consumption steady state is simply to set the saving (and > investment) rate equal to its steady state value: then you're bound > to get there, regardless of your starting point. But the Ramsey > approach suggests that may not be optimal. > > Suppose we're approaching SS from below. Perhaps we should save at > above the SS rate at first, to get to SS faster? Or the opposite: > gradually increase the saving rate to its SS value? Even with a zero > discount rate this sort of choice is going to depend on the rate of > diminishing returns to consumption (e.g. the parameter in a CRRA > utility function, which I'll call sigma.). > > Dynare is able to show me that the Euler-obeying perfect foresight > path can start with saving above or below the steady-state rate > depending on the value of sigma. And I can confirm this increases > total utility over the transition to SS, relative to the constant > saving-rate case, by having gretl compute utility for the latter. > >> Also what do you mean by "advantage"? In intertemporal utility terms or >> something else? > Intertemporal utility. > > Allin > > ------------------------------ > > Subject: Digest Footer > > _______________________________________________ > Gretl-users mailing list -- gretl-users(a)gretlml.univpm.it > To unsubscribe send an email to gretl-users-leave(a)gretlml.univpm.it > Website: https://gretlml.univpm.it/postorius/lists/gretl-users.gretlml.univpm.it/ > > > ------------------------------ > > End of Gretl-users Digest, Vol 148, Issue 8 > ******************************************* >