Matlab Exercises

Try the exercises at Quantitative Economics.

Some of the code for these exercises is in the examples folder in my github repo.

Some of my general purpose reusable code is posted in the shared folder in my github repo.

Read the Matlab documentation on the following subjects:

Getting Started

  1. Compute the mean and standard deviation for weighted data

    Input: data and weights (matrices)

    Output: mean and standard deviation for each column

    My solution

  2. Compute the cdf for weighted data.

    Input: data and weights

    Output: cumulative percentiles and their values

    My solution

  3. Compute points at the percentile distribution for weighted data (e.g. median)

    My solution

Root finding

Write a Matlab program that numerically finds the solution of

\( f\left(x,a\right) =x^{2}-a=0 \) for \(x\geq 0 \)

  • Write the deviation function \( f(x) \)
  • Plot \( f(x) \) for \( x \in [0,4] \) .
  • Find the solution for \( a = 4 \) using fzero.
  • Find the solution for \( a = 4 \) using fsolve.

Try other algorithms, such as fminsearch for fun.

Growth Model

Consider a growth model given by the Bellman equation

\(V(k) = \max u(c) + \beta V(f(k) - c) \)

with \(f(k) = k^\alpha\).

Solve the growth model by value function iteration.

Steps:

  1. Set up a grid for \(k \).
  2. Start from an arbitrary guess \( V_{0}(k) \).
  3. Iterate over the Bellman operator until \( V \) converges.

Along the way, plot the value functions to show how they converge to the true one. Like this:

GrowthValueIter

See QuantEcon and my Matlab solution.

Useful Exercises From QuantEcon

You should also write test routines for each function.

  1. Draw discrete random numbers

    Given: probability of each state

    My solution

  2. Simulate a Markov Chain

    See QuantEcon for the setup and Julia code.

    Also compute the stationary distribution

    My solution

    Also try their Exercise 1 (illustrate the central limit theorem).

  3. Approximate an AR1 with a Markov chain from QuantEcon.

    Do this at home by simply “translating” the Julia code into Matlab.

    You will see that the syntax is very similar.

    My solution

  4. Simulate random variables to illustrate the Law of Large Numbers and the Central Limit Theorem.

    See QuantEcon for the setup and Julia code.

    My solution