Business Cycle Dynamics of a New Keynesian Overlapping Generations Model with Progressive Income Taxation

2.1 Households

Households live T + T^R = 240 periods (corresponding to 60 years). Each generation is
of measure 1/(T +T^R). The first T =160 (=40 years) periods, they are working, the last
T^R = 80 periods (=20 years), they are retired and receive pensions. Agents are also
heterogeneous with regard to their productivity level e(s, j). The productivity e(s, j)
depends on the age s and the idiosyncratic productivity type j ∈ {1, . . . , ne}. Individ-
ual productivity is non-stochastic, and an individual will not change his productivity
type j over his life time. The mass of type-j agents in each generations is constant and
denoted by μ (j ). The s-year old household with productivity type j holds real money
holdings M_t^s,j /P_t and capital k_t^s,j in period t. He maximizes expected life-time utility
at age 1 in period t with regard to consumption c_t^s,j , labor supply n_t^s,j , and next-period
s, s,

money balances M_t₊₁ , and real capital k_t₊₁ :

T+T^R

Et β^s-¹u ct^s+^,js-1

s=1

Mj 1 1

Pt+s-1 ’

s,j
t+s-1

(1)

where β is a discount factor and expectations are conditioned on the information set
of the household at time t. Instantaneous utility u (ct, Mt, 1 — n_t^ is assumed to be:

∣^^c,P^,¹^{— n})

γ^ln c ^{+ (1}^— γ)^ln M ⁺ η0⁽¹ 1-)η ^-C^γjΓ^ +_rl (1 -n)1 -η

1 -σ ⁺^η⁰ 1 -η

if σ = 1

if σ 6= 1,

(2)

where σ > 0 denotes the coefficient of relative risk aversion.³ The agent is born
without capital k_t¹^,j = 0, j ∈ {1, . . . , ne}, but receives an initial cash endowment from
the government M_t¹^j that is fixed in terms of the beginning of period price level Pt-1
and equal for the different productivity types, i.e., M_t¹^j /Pt-1 =: m¹ > 0 for all t and j .

The s-year old working agent with productivity type j faces the following nominal
budget constraint in period t:

P (s+⁺¹^{3 s}jʌ ( ^s⁺¹³ M^s3ʌ I P j

Pt k_t₊₁ — (1 — δ)k_t + M_t₊₁ — M_t + Ptc_t

Pt yt^,3

Pt-1 π

(3)

= Ptrtkt³ + Ptwte ( s,j ) n^s_t^,3 + Pttrt + Pt Ω t — PtT

s = 1, . . . , T, j = 1 . . . , ne.

³We follow Castaneda, Dlaz-Giminenez, and Rlos-Rull (2004) in our choice of the functional form for
the utility from leisure. In particular, this additive functional form implies a relatively low variability
of working hours across individuals that is in good accordance with empirical evidence.

More intriguing information

1. The voluntary welfare associations in Germany: An overview
2. Draft of paper published in:
3. Group cooperation, inclusion and disaffected pupils: some responses to informal learning in the music classroom
4. TLRP: academic challenges for moral purposes
5. CGE modelling of the resources boom in Indonesia and Australia using TERM
6. ALTERNATIVE TRADE POLICIES
7. Gender and headship in the twenty-first century
8. Voting by Committees under Constraints
9. Innovation Trajectories in Honduras’ Coffee Value Chain. Public and Private Influence on the Use of New Knowledge and Technology among Coffee Growers
10. El Mercosur y la integración económica global