DATA ANALYSIS

5th Module, 2002-2003

A draft of the course to be offered at the Applied Economics Track

Professor: Stanislav Kolenikov, skolenikov@cefir.ru, skolenik@unc.edu

The purpose of the course is to equip the students of the AET with the contemporary statistical methods of data analysis not covered in the standard econometric courses. The actual coverage may differ depending on the needs of the students. It might be benefical for them to have started working on their Master Theses prior to taking this course, so that they would be able to pick the data analysis methods they would need for their research, and submit the empirical part of their theses as a term paper in the Data Analysis course.

References

Aivazian S.A., Mkhitarian V.S. Applied statistics and essentials of econometrics (in Russian). Moscow, UNITY, 1999.

T. Hastie, R. Tibshirani, J. H. Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, 2001.

K. A. Bollen. Structural Equations with Latent Variables. Wiley, 1989.

D. Huff. How to Lie With Statistics. Norton, 1993.

F. Mosteller, J. W. Tukey. Data Analysis and Regression: A Second Course in Statistics. Addison-Wesley, 1977.

StataCorp. Stata statistical software: Release 7. College Station, TX, US, 2000.

Topics (about a week per topic)

A. Statistical graphics.

Use of graphics in assessing the data is natural on the early stages of data analysis. The researcher might need to get an idea of the overall distribution of the data points, the dependencies within the data set, the presence of trends, groups of objects, outlying observations, etc, in order to either form the research hypotheses, or to describe the data. The tools to be discussed are box-whisker plots, quantile plots, smoothers for density and regression estimation, and extensions of the usual scatterplots.Uses and misuses of the graphical tools will also be discussed.

B. Factor analysis and principal components.

Principal components are used to summarize the data by constructing a single overall linear index in an efficient, in a certain sense, manner. They also arise naturally from the need for statistical graphics to embed the multivariate data set into two dimensions for plotting. The statistical properties of the principal components and a number of asymptotic results will also be mentioned.

C. Path analysis and structural equation models.

This is a more analytic extension of the factor analysis methods used when the researcher has relatively clear idea, or hypotheses, about the dependence between different variables in her data set, and a number of concepts to be related to those variables.The technique has been developed in social sciences and starts to find applications in econometrics.

D. Cluster analysis and discrimination.

Cluster analysis seeks to answer the question, Are there distinct groups of points in the data? This is an important issue, as blunt application of the standard econometric routines in the presence of clusters is highly likely to lead to biases in both point estimates and the standard errors of parameter estimates thus resulting in incorrect inferences.

E. Other dimension reduction / graphical techniques

If time permits, some other topics can be covered such as multidimensional scaling that aims at constructing the lowest dimensional space for a multivariate set of characteristics; projection pursuit, aiming at finding a direction in the data that is related to a particular “feature” such as regression or clustering; or functional data analysis that works with functions or highly dimensional objects in place of individual observations.

F. Outlier diagnostics and robust methods

Outliers are a common problem rather than something unusual in economic research. Moscow is different from the rest of Russia, and China is different from other transition countries, etc. The qualified researcher should be able to isolate the outliers, or clusters of outliers, and assess their influence on the rest of statistical analysis. If outliers still carry substantial information and should not be excluded from analysis, the need for robust and distribution free methods arises.

G. Sampling and survey data analysis

This topic is rather distant from the earlier parts of the course. One of the primary sources of statistical information in business and economics are variuos surveys of population, enetrprises, customers, etc. It is extremely important to learn not to be mislead by the numbers reported without reference to the sampling techniques and sampling problems for the popoulation of interest. The contemporary sampling schemes will be studied, and the statistical methods to obtain accurate estimates and their standard errors will be covered.

Course requirements

The grade of the course will consist of 20% homeworks, 20% midterm test, and 60% of the term paper. It may be arranged that the paper be submitted several weeks after the course is completed, and graded by the end of the next module, so that students have the full power of the methods discussed in the course at their disposal before they start working on the paper. Alternatively, the empirical part of the Master Thesis can also serve as the term paper for the course.