ECON8022 - MACROECONOMIC THEORY
Assignment 2-B - Fiscal Policy in OLG and NG Models
1 Problem 1: Multi-period OLG model with inelastic labor (OLG Model of Australian economy - OLGA)
Consider a close economy lled with overlapping generations and a competitive rm. The model period is equivalent to 15 years.
The household sector consists of 4 overlapping generations. Each time period a new house- hold is born and lives for four periods (J = 4). The size of newborn generation is normalized to 1. The household is endowed with 1 unit of time and age-speci c labor productivity (hj) each period. The household works full-time for 2 periods and retires in the last 2 periods. The household preferences are given by
The household chooses a sequence of consumption and saving to maximize his discounted lifetime utility according to
subjected to period by period budgets constraints
where, j stands for agent's age at the calendar time t+j-1, cj,t+j-1 and sj,t+j-1 are consumption and saving at age j, and wt the market wage rate and rt is the market interest rate at the time t. Note that, the lifetime budget constraint has a form of
The production sector consists of a representative rm that has the following production technology where Y output, A is total factor productivity, K is capital stock, and H is e ective labor (e.g., human capital). Capital depreciation rate is δ . The rm's opti- mization problem is given by
where wt is the market wage rate and qt is the rental rate.
a) Assume that h1 = 1, h2 = 1.5, β = 0.98, σ = 2, A = 1, α = 0.33 and δ = 0.05. Find the steady state solution numerically, using two computational methods: (i) Fsolve function and (ii) Gauss-Seidle algorithm.
b) Calibration of the benchmark model: Adjust β to match the annual market interest rate of 4%. Report the life-cycle pro les of consumption and savings when r = 4%.
c) Suppose the government appears and introduces a PAYG social security program that pays pension bene ts for retirees
where Ψ is a replacement rate. We assume the government set Ψ = 30%. The household period by period budgets are given by
The social security program is self- nanced so that
where τss is a social security tax that adjusts endogenously to balance the social security program every period.
Now assume the economy is in steady state. Find the steady state solution. Explain your results.
d) Now, suppose that the government increases the pension payment for retirees to Ψ = 40%.
Study the long run e ects of the pension reform on the economy (Steady state analysis). Explain your results. Solve for the transition paths.
Remark 1 A simpple version of an OLG model was developed by Australian Treasury for scal policy analysis (OLG Model of Australian economy - OLGA) .
2 Problem 2: NGM model with fiscal policy (Treasury's Industry Model - TIM)
We consider a NG model lled with a representative household, a representative firm and a government. In this model the government taxes private consumption, capital and labor income to nance an exogenous sequenes of lump-sum transfers.
Time is discrete (t = 0, 1, ...).
Preferences. The representative household lives in nitely and has the following preference:
(1)
where β is a time discount factor, ct is consumption and lt is leisure. A typical functional form is usually used in the literature
with σ ≥ 0 and 0 < γ ≤ 1.
Technology. There is a representative rm which has access to the following CRS technol- ogy:
(2)
where, At is the total factor productivity, kt is capital input and nt is labor input. The repre- sentative rm rents inputs in competitive markets.
The law of motion for capital is
kt+1 = (1 - δ)kt + it ,
where it is investment and capital depreciates at a constant rate δ .
Government. The government collects tax revenue to nance a government spending program, Gt. There are two taxes: consumption tax (τc ), income tax (τI). The government budget constraint is given by
(3)
where qt is net rental rate, wt is market wage rate, qtkt is capital income and wtnt is labor income. In the model, we assume that the government spend all revenues on a public transfer program. Technically, the government gives Gt back to household in terms of lump-sum transfer, Tt = Gt.
Household problem. The agent is given capital k0 initially and one unit of time in each period. The agent can invest in capital market. The labor supply is nt = 1 - l1 . The houshold lifetime budget constraint is
where ct and it are consumption and investment; qt is net rental rate; and wt is wage rate; τt(c) and τt(I) are taxes on consumption, capital income and labor income, respectively. The household chooses a sequence of consumption, savings and labor supply to maximize its lifetime utility (1) subjected to the budget constraint (4).
a) Solution method: Assume that β = 0.99, γ = 0.3, σ = 2, A = 1, α = 0.33, δ = 0.025, and τt(c) = 10% and τt(I) = 15%. Assume the economy is in steady state. Solve the model numerically and report the steady state solution.
b) Calibration: Keep other parameter values unchanged and nd the value of β that is able to generate a capital-output ratio of Y/K = 3.
c) Analysis 1: We can use the model to analyse the e ects of negative technology shock. Suppose that there is a permanent decrease in TFP to A = 0.95.Analyse the e ects on output, capital, consumption, employment and welfare in long run and during the transition. Explain your results.
d) Analysis 2: We can use the model to analyse the personal income tax cuts to respond to the negative TFP shock in c). To do so we assume the government decreases the income tax rate to τI = 10% after the negative TFP shock. Analyse the e ects on output, capital, consumption, employment and welfare in long run and during the transition. To what extent the tax reform could mitigate the adverse e ects of the negative TFP shock.
Remark 2 A simple version of this NG model was recently developed by Australian Treasury to study the effects of industry policy (Treasury's Industry Model - TIM) .