Benchmark different algorithms for least squares and instrumental variable estimators.

The goal of this project is to benchmark different ols and iv implementations. There are two aspects to the project, one is to see how different implementations perform when the number of observations, variables and instruments increase and the other aspect is to see how accurate the estimator of different implementations become when there exists data issues like collinearity and weak instruments and efficiency issues like how many instruments to include to effectively tackle endogeneity in the data (just identified or over-identified iv). Perfomance is defined as the time it takes for the implementation(s) to be executed.

The goal of this project is to demonstrate how different observations, variables and instrument sizes affect the the perfomance of the ols/iv implementations as well as the accuracy of the estimator in relation o the true beta. The main challenges faced during this project is the difficulty in constructing valid covariance matrices for the cases of instrumental variables - especially to demonstrate the weak instrument case. As discovered in the proccess of completing the project, it is challenging to construct positive definite matrices with simulated data that will have all the properties required to check the accuracy of the implementations under weak instruments. Further improvement is required in this aspect so as to make it possible to generate valid covariance matrices for the case of weak instruments.

The resulting output of this project contains:

• perfomance plots for ols that display an increase in runtime as observations and variables increase.
• perfonance plots for iv that display an increase in runtime as observations, variables, and number of instruments increases.
• accuracy plots for ols that show that as colliniarity increases, the accuracy of the estimator in relation to the true beta decreases using the root mean squared error approach.
• accuracy plots for ols that show that as colliniarity and number of instruments increases, the accuracy of the estimator in relation to the true beta decreases using the root mean squared error approach.
• accuracy plots for iv showing that as the strength of the instruments decreases, the accuarcy of the estimator should also decrease (**to revert back to in the future).

There are four main steps involved in the project:

1. Ols and iv implementations
2. Generating the data
3. Timing and perfomance plots
4. Accuracy plots

In the first step, l write functions for all the ols and iv implementations in two seperate modules. This follows from the standard textbook ols and iv formulae (please see benchmark.ipynb for formulae). After this l implement a data generating function (in a seperate module) that generates the different datasets required for the project. To generate the perfomance plots, l implement timing functions to get runtimes for each implementation over different observations, variables and instruments and lastly, l implement the root mean squared error method to check the accuracy of all ols and iv implementations.

The file directory is organised into a code folder that contains all the modules you need to generate the benchmark plots. All plots will be generated and saved in a seperate bld folder that will be created as a result of invoking code embeded in the benchmark modules.

To reproduce the results mentioned above you will need to:

1. Clone/download my repository to your local pc/machine
2. run the benchmark_ols.py and benchmark_iv.py modules contained in the code folder via anaconda using the comand 'python benchmark_ols.py' and 'python benchmark_iv.py'.
3. The resulting .png files will be stored in the bld folder.

The modules above depend on the following modules (also contained in the code folder)

• timing.py
• generate_data.py
• iv.py
• ols.py

This project as alluded to earlier requires:

• anaconda or any terminal from which you can execute python scripts
• your preffered python version installed