Intergenerational Equity and the Discount Rate for Policy Analysis

Mertens, Jean–François; Rubinchik, Anna

doi:10.1017/s1365100510000386

Cited by 4 publications

(15 citation statements)

References 30 publications

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“…Assume that this set of acceptable policies is shift‐invariant (cf. Assumption 3 in Mertens and Rubinchik (), so that any policy, when shifted in time, remains feasible and just; and that each individual utility is bounded on this set. It is shown in Mertens and Rubinchik () that the normalization in this case amounts to choosing welfare weights

θ_{τ, x} = e^{- (1 - ρ^{τ}) γ x}

.…”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

“…Definition (Mertens & Rubinchik, , definition 1) (i)Let

t_{h} : t \mapsto t + h

be the translation by h on

double-struckR

; and

{double-struckS}_{h} : ξ \mapsto ξ \circ t_{- h}

be the time‐shift on functions of time. (ii)Fix a Banach space E .

K_{E}

is the set of infinitely differentiable functions

ϕ : R \to E

with compact support …”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

“…Definition (Mertens & Rubinchik, , definition 2). (i)

(B, \bar{π})

is the set B of basic policies , open in the Banach space E , together with some point

\bar{π} \in B

, called the status‐quo policy. (ii) P is the set of policy reforms

π : R \to B

s.t.…”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

“…Definition (Mertens & Rubinchik, , definition 3). For

g \in E^{★}

, the dual of a topological vector space E ,

false⟨ g, e false⟩ \overset{def}{=} g false(e false)

.…”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

“…The first one combines Corollaries 2 and 3 of the main result there. Proposition (Mertens & Rubinchik, ). Assume that

ν - β + false(1 - ρ^{τ} false) γ \in Z_{scriptF} \forall τ

and assume that the traditional welfare function is Gâteaux‐differentiable on P at

\overset{π}{true}

, then for some collection

{false{q^{τ} \in E^{★} false}}_{τ \in normalΘ}

, its differential equals

\sum_{τ \in Θ} \int_{- \infty}^{\infty} e^{(ν - β + false(1 - ρ^{τ} false) γ) t} false⟨ q^{τ}, δ π (t) false⟩ d t .

…”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

See 4 more Smart Citations

Discounting and welfare evaluation of policies

Mertens

Rubinchik²

2017

J Public Economic Theory

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We start with the premise that if policy discounting is to have any welfare relevance, one has to accept it being a derivative of a social welfare function (SWF). We show that if that derivative is to have a net present value (NPV) form, then the baseline allocation must be stationary. In addition, we show that at a stationary baseline in an overlapping generations growth economy, the intergenerationally fair discount rate equals the growth rate of per‐capita consumption, which is, roughly, 2% for the United States. This differs from the interest rate, even in the golden rule equilibrium, unless population growth is null. The last result is based on the main theorem in Mertens and Rubinchik (2012) and is demonstrated for a policy space that might naturally arise in applications.

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θ_{τ, x} = e^{- (1 - ρ^{τ}) γ x}

.…”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

“…Definition (Mertens & Rubinchik, , definition 1) (i)Let

t_{h} : t \mapsto t + h

be the translation by h on

double-struckR

; and

{double-struckS}_{h} : ξ \mapsto ξ \circ t_{- h}

be the time‐shift on functions of time. (ii)Fix a Banach space E .

K_{E}

is the set of infinitely differentiable functions

ϕ : R \to E

with compact support …”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

“…Definition (Mertens & Rubinchik, , definition 2). (i)

(B, \bar{π})

is the set B of basic policies , open in the Banach space E , together with some point

\bar{π} \in B

, called the status‐quo policy. (ii) P is the set of policy reforms

π : R \to B

s.t.…”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

“…Definition (Mertens & Rubinchik, , definition 3). For

g \in E^{★}

, the dual of a topological vector space E ,

false⟨ g, e false⟩ \overset{def}{=} g false(e false)

.…”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

“…The first one combines Corollaries 2 and 3 of the main result there. Proposition (Mertens & Rubinchik, ). Assume that

ν - β + false(1 - ρ^{τ} false) γ \in Z_{scriptF} \forall τ

and assume that the traditional welfare function is Gâteaux‐differentiable on P at

\overset{π}{true}

, then for some collection

{false{q^{τ} \in E^{★} false}}_{τ \in normalΘ}

, its differential equals

\sum_{τ \in Θ} \int_{- \infty}^{\infty} e^{(ν - β + false(1 - ρ^{τ} false) γ) t} false⟨ q^{τ}, δ π (t) false⟩ d t .

…”

Section: Discounting In An Og Model With Exogenous Growthmentioning

confidence: 99%

See 3 more Smart Citations

Discounting and welfare evaluation of policies

Mertens

Rubinchik²

2017

J Public Economic Theory

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Equilibria in an overlapping generations model with transfer policies and exogenous growth

Mertens

Rubinchik

2012

Econ Theory

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For an overlapping generations economy with varying life-cycle productivity, non-stationary endowments, continuous time starting at −∞ (hence allowing for full anticipation), constant-returns-to-scale production and ces utility we fully characterise equilibria where output is higher than investment, which is strictly positive. Net assets (aggregate savings minus the value of the capital stock) are constant in any equilibrium, and, for balanced growth equilibria (bge, defined for an economy with stationary endowments), net assets are non-zero only in the golden rule equilibrium, in accord with [12]. The number of bge is finite. Their parity, however, depends on the life-cycle productivity, in particular, on the relation between the intertemporal elasticity of substitution, the minimal working age and the minimal tax age.

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Regularity and Stability of Equilibria in an Overlapping Generations Growth Model

Mertens¹,

Rubinchik

2017

Macroecon. Dynam.

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In an exogenous-growth economy with overlapping generations, the Cobb–Douglas production, any positive life-cycle productivity, and time-separable constant elasticity of substitution (CES) utility, we analyze local stability of a balanced growth equilibrium (BGE) with respect to changes in consumption endowments, which could be interpreted as a transfer policy. We show that generically, in the space of parameters, equilibria around a BGE are locally unique and are locally differentiable functions of endowments, with derivatives given by kernels. Furthermore, those equilibria are stable in the sense that the effects of temporary changes decay exponentially toward ±∞.

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Intergenerational Equity and the Discount Rate for Policy Analysis

Cited by 4 publications

References 30 publications

Discounting and welfare evaluation of policies

Discounting and welfare evaluation of policies

Equilibria in an overlapping generations model with transfer policies and exogenous growth

Regularity and Stability of Equilibria in an Overlapping Generations Growth Model

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