Statistics for Economics 2025

BA II Year Course at MSE

Logistics

Timings: Monday at 9:30 AM, Wednesday at 11:00 AM

Venue: G2

Teaching Assistants: Sriram R., Anagha R., Hariharasudhan S. (BA 2023)

Syllabus

Basics of probability theory: Intro to school probability theory, sample spaces, events, Kolmogorov axioms and independence of events.

Random variables and their distributions: Discrete and continuous random variables, cumulative density functions, probability mass functions and density functions, joint densities, independent variables. Expectation, variance, covariance and moment generating functions. Properties of moment generating functions and sums of random variables. Order statistics.

Special distributions: Bernoulli, Binomial, Poisson, Geometric, Uniform, Exponential, Normal, Gamma, Beta, Chi-square, T-distribution. Multivariate normal and connections to linear algebra.

Limit laws: Almost sure convergence, convergence in probability, convergence in expectation and convergence in distribution. Weak law of large numbers and Central limit theorems.

Estimation: Likelihood, Sufficient statistics, Maximum Likelihood estimation, Method of moments, Bias, efficiency, MVUE, Cramer-Rao Bound, Rao-Blackwell improvement, Consistency of an estimator, Bayesian estimation. Confidence intervals.

Hypothesis testing: Introduction to hypothesis testing, simple vs composite hypothesis, power, p-value, randomised tests, Neyman-Pearson lemma. Goodness of fit.

Course Objectives

This course provides a rigorous foundation for reasoning and decision-making under uncertainty — a central challenge in economics and data analysis. It introduces the mathematical structure of probability theory, emphasizing the formulation of random phenomena through sample spaces, events, and the axioms of probability. Students will learn to describe and analyze random variables, compute and interpret expectations, variances, and covariances, and use moment-generating functions to characterize distributions and sums of random variables.

The course further develops familiarity with standard probability models such as the Binomial, Poisson, Normal, and Gamma distributions, including their interrelationships and multivariate extensions. Students will study asymptotic results such as the Law of Large Numbers and the Central Limit Theorem, which provide approximations for complex random behavior.

Building on these probabilistic foundations, the course introduces statistical inference, including point estimation, properties of estimators such as bias and efficiency, and methods such as maximum likelihood and the method of moments. Finally, students will learn the principles of hypothesis testing, developing a systematic framework for comparing competing models and drawing reliable conclusions from data.

At the end of the course, we solved problems from India’s famous competitive exams like ISI M.Stat, MSQE, JAM M.Stat and Econ, IES/ISS exams and MSEET.

References

Assignments

Main Tests

  • Internal I: Probability theory (discrete and continuous), random variables, special distributions, order statistics, Moment generating functions, Law of large numbers. Supplementary paper
  • Internal II: Central limit theorem, Multivariate normal distribution, point estimators, maximum likelihood estimator, method of moments estimator, bias, consistency, sufficiency, efficient estimator and Cramer-Rao bound, Rao-Blackwell improvement, Bayesian statistics. t-statistic, z-statistic, $\chi^2$ -statistic, confidence intervals. Supplementary paper
  • Finals: All the syllabus in internals 1 and 2. Additionally, hypothesis testing were included. The entire class found it time consuming.

Results

My course was modelled on the MIT course on statistics for economists.. The assessment included weekly tests and a final exam with ambitious breadth. Student performance was strong overall. This result is unusual for this course and indicates the cohort’s sustained effort across the semester.