1:49 a.m.
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:
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> 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>
> 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>
> 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>
> 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>
> Message-ID:
> <alpine.LFD.2.20.3.1905081715370.19346(a)myrtle.attlocal.net>
> 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
>
> ------------------------------
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> ------------------------------
>
> End of Gretl-users Digest, Vol 148, Issue 8
> *******************************************
>