Homework I
Moyu Liao
USyd
2024 S1
1 LP estimation with additional moments
1.1 The Model
Consider the production function estimation using LP method. We consider an CES production
function
Qit = e
ωit
(
βkK
κ−1
κ
it + βlL
κ−1
κ
it + (1− βk − βl)M
κ−1
κ
it
) κν
κ−1
Price are fixed at Pit = 1 for all firms. The productivity follows an second order polynomial process:
ωit = ρ0 + ρ1ωit−1 + ρ2ω2it−1 + it
You can find the data in "CES_data.mat". Note that for simplicity, I omit the ex-post quantity
shock (ζit) from the model.
The columns of data matrix are organized in the follow order [Q1,K1, L1,M1, v1, Q2,K2, L2,M2, v2],
that is the first column is the first period quantity, second column is the first period capital, etc.
You can also find the data
We illustrate in class how to estimate the LP model using Cobb-Douglas production function.
You are asked to estimate the production function using the CES model above with some slight
modification:
• When you do non-parametric estimation of Φ, also add the third order polynomial of capital,
material and labor into the regression.
• In class and the sample code, we use construct ωit−1 by Φit−1− f(kit−1, lit−1,mit−1). We will
keep this, but simply change the f to the CES function.
• We will add some additional moments by using an alternative way to construct evolution
process residual, call it eps_alt. Let ω_altt−1 = log(Qit−1) − f(kit−1, lit−1,mit−1) (and
similarly for ω_altt), and let
eps_alt = ω_altt − ρ0 − ρ1ω_altt−1 − ρ2ω_alt2t−1
1
• Then, construct additional moments using eps_alt and its interaction with the instruments.
• As a result, you should have 14 moments in the GMM estimation.
You can modify the sample code we discussed in class to construct your own code.
1.2 Requirements.
When you estimate the parameters, impose the following constraints:
• 0 < βk < 1, 0 < βl < 1, 0 < ν < 1, κ > 0.001. You can use upper and lower bound command
to impose this constraints
• 0 < 1− βk − βl. You should use a Aineq matrix to impose this condition.
Your homework should consist of two parts: 1. A simple pdf file containing your estimation
result (i.e. what is the point estimate), and your name. 2. The Matlab files (you should have 3)
that can be used to estimate the parameters.
Also, you should have correct comment on your code for it to be readable, including the input
and output headers of your .m files.