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Econ 311: Advanced Macroeconomics
Problem Set 1
Due: 15 August 2024
1 Solow Model (10 points)
Instructions. Use Table 1.11 from Stats NZ National Accounts (Accumulation Accounts) to find the closing balance for “total non-financial assets” for the year ending 31 March 2018 (i.e., t=2018). Let this be your baseline aggregate capital stock. Assume production is governed by a Cobb-Douglas function using capital and labour as inputs. You are going to workout the per capita capital stock and output level in steady state, as well as the first year in which it is obtained. Start by “calibrating” (assigning a real-life value to) the following parameters:
δ,s,n,α, L.
1. Provide an academic reference and short written motivation for the source of your choice for each parameter. Example: I set the rate of depreciation to 6.6% drawing on comparable estimates for the United States, published by the Bureau of Economic Analysis (BEA, 2023) . I compute the depreciation measure by taking the depreciation estimate for fixed assets and consumer durable goods in 2018, $5,238.5, and dividing it by the estimate for average capital stock over the 2017-2018 period, (84, 439.2 + 74, 284.82)/2 = $79, 362. I consider the U.S. estimate to be comparable to New Zealand because...). [3 points]
2. Complete the table below:
|
Parameter |
Assigned value |
Reference |
|
Example:
x δ s n α L |
0.7 |
Hicks & Fairly (2010) |
[1 point]
3. Derive mathematically using your calibrations (a) the per capita capital stock in steady state; (b) output per capita in steady state; (c) your forecast for the capital stock in 2021. [3 points]
4. How does this forecast compare with the actual Stats NZ estimate for 2021? [1 point]
5. Use Excel, R, Matlab or equivalent to plot the evolution of capital from 2018-2100 using your calibrations. Provide a labelled figure of your plot. [2 points]
2 Intertemporal Optimisation (5 points)
Suppose a household solves the following two-period consumption-savings problem:
c1(m)
u(c1 ) + βu(c2 )
s.t. (1)
a = a0 + y1 − c1
c2 = y2 + (1 + r)a
where u(ct ) = ln(ct ) for t = 1, 2.
1. Set up a Lagrangian for the household. [1 point]
2. Solve for the household’s choice of c1 , c2 and a in closed form, providing a written interpretation of each step. [3 points]
3. What happens to savings, a, if y2 increases? [1 point]