### Quantitative methods for Economists

- Course Code:
- 153400121
- Unit value:
- 1
- Year of study:
- Year 1 or Year 2
- Taught in:
- Full Year

This course is offered to first year students in 2008-09 who have at least a B in A-Level maths (or equivalent) attained. The course offers a survey of basic economic statistical techniques and applied mathematical analysis useful for intermediate and advanced economic theory. The course is an essential prerequisite for Econometrics.

**This is a core course for the BSc Economics and compulsory for BSc Development Economics and BA Economics and … (two subject degree with Economics to appear first in title). Introduction to Quantitative Methods for Economists is a prerequisite for this course if taken in year two. Students with A level mathematics or equivalent may be permitted to take this course in Year 1, subject to the year tutor’s approval. It is a pre-requisite for Econometrics.**

#### Objectives and learning outcomes of the course

On successful completion of the course, you should be able to …

- explain and use basic concepts in matrix algebra and define matrix operations including, but not restricted to, addition, subtraction, multiplication, minors, cofactors, determinants
- use the cofactor method to find inverse matrices and use Cramer’s rule to solve systems of equations
- demonstrate understanding of, derivatives, rules of differentiation, higher order derivatives, their uses and applications
- explain indefinite and definite integrals and use them to solve problems
- demonstrate understanding of first- and second-order partial derivatives and Young’s theorem
- Use the Lagrangian function to solve constraint optimisation problems
- Use the Hessian or bordered Hessian to evaluate the second order condition for relative extrema
- use the mathematical methods covered in the course to solve problems in economics.
- explain basic statistical concepts including, but not restricted to, descriptive and inferential statistics, and levels of measurement
- demonstrate understanding and ability to use basic descriptive statistic techniques including, but not restricted to, frequency tables and histogram
- use the summation operator
- demonstrate understanding of and ability to use measures of central tendency, dispersion, skewness and kurtosis
- calculate and interpret covariance and correlation coefficient
- demonstrate understanding of indices including, but not restricted to Laspeyres and Paasche indices, their uses and applications
- demonstrate understanding of and ability to use statistical techniques to analyse inequality including, but not restricted to, Lorentz curve and Gini coefficient
- explain basic concepts in probability theory including, but not restricted to, experiment, population or sample space, sample point, event, mutually exclusive, equally likely and collectively exhaustive events, random variable, discrete and continuous random variable, probability, probability distribution or probability density function (PDF), statistical independence
- use characteristics or moments of PDF including, but not restricted to expected value, variance and standard deviation, skewness and kurtosis, covariance, coefficient of correlation, conditional and unconditional expectation
- use population parameters and sample estimators including, but not restricted to sample mean, sample variance, sample standard deviation, sample covariance, sample correlation, sample skewness and sample kurtosis
- demonstrate understanding of and ability to use normal distribution, chi-square, t and F distributions
- explain the sampling distribution of an estimator (e.g. the sample mean)
- demonstrate understanding of and ability to use point and interval estimation and hypothesis testing
- explain the method of ordinary least squares (OLS) and use it to estimate regression coefficients

interpret and critically evaluate econometric results - demonstrate understanding of measures of goodness of fit including their uses and limitations
- explain the assumptions of the classical linear regression model
- use t test on regression coefficients
- use estimated regression coefficients for prediction.

#### Method of assessment

Assessment weighting: Exam 80%, weekly assessment of exercises 20% (10% each term)#### Suggested reading

**Background Reading**

Mathematics:

1. Abadir, K. M. and J. R. Magnus (2005) Matrix Algebra, Cambridge.

2. Chiang, A.C. and K. Wainwright (2005) Fundamental Methods of Mathematical Economics, Forth Edition. McGraw-Hill.

3. Jacques, I. (2009) Mathematics for Economics and Business, 5th Edition, Prentice Hall.

Statistics:

1. Barrow, M. (2009) Statistics for Economics Accounting and Business Studies, 5th Edition, Prentice-Hall.

2. Gujarati, D. and D.C. Porter (2010) Essentials of Econometrics, 4th Edition, McGraw Hill.