Modern Stochastic Approach to Index Numbers

There are three foundational approaches to the construction of index numbers: the axiomatic, the economic, and the stochastic approaches. This page is devoted to the development of a modernized stochastic approach to index numbers (SAIN), one that systematically addresses earlier criticisms and brings out its full potential. The material presented here is not a review of established results; each topic contains a novel contribution. 

The Modern Stochastic Approach to Index Numbers: A Review [Paper, Perliminary]

1-      Common vs Differing Mean Assumption

2-      Weighted Estimation

3-      The two approaches and the equivalence

4-      Arbitrariness

5-      Estimation Methods

6-      Testing Indexes

7-      Reliability Measures

8-      The real strength

The Modern Stochastic Approach to Bilateral Index Numbers 

Reliability of Ideal Bilateral Indexes [Paper, about to submit]

1-      Notation

2-      Formulas of Variances

3-      Specification

4-      Interpretations

5-      Price Dissimilarities

Equivalence of two Stochastic Approaches to Index Numbers [Paper, about to submit]

Influence Functions for Bilateral Price Indexes

The Modern Stochastic Approach to Multilateral Index Numbers

Multiperiod Indexes  [Paper, Perliminary]

1-      Fixed Base

2-      Chained Base

3-      GEKS

4-      CPD

5-      Recursive GEKS and TPD

Generalization of CPD  [Slides]

1-      Generalization-I

2-      Generalization-II

3-      Generalization-III

4-      Generalization-IV

The Stochastic Approach to Multilateral Index Numbers for ICP  [Published, Paper2, Perliminary]

1-      CPD

2-      IKLE

3-      GK

4-      GEKS

5-      Specification of the error term

6-      Interpretations

Reliability Measure using Resampling Methods [Slide]

Generalized Indexes and Quality Change [Slide]

Dealing with Dissimilarity

Minimum Distance Shortest Path [Paper-1 and Paper2, both submitted]

Multilateral Price Dissimilarity [Paper]

Weighted GEKS

1)      Defining Weighted GEKS

                Rao version

            Balk version

2)      Properties of Weighted GEKS

3)      Minimum Variance weighted GEKS

Balk Version

Rao Version

4)      Minimum Variance 0-1 Weighted GEKS

5)      Reduced-Biased Weighted GEKS

Influence Function

6)      LASSO Weighted GEKS

7)      Below Basic Heading Weighted GEKS

Quantile TPD and CPD and Robust Indexes  [Paper-1, submitted]

Fixity

Interpolation

Missing Prices, Scanner\ Web Scraped Data and Hedonics

Imputation of Missing Prices

Application of Hedonics

Scanner Data

Application of Machine Learning to Web-scraped Data

Housing Price Indexes

Quantity Indexes and their Reliability

Theory of Weighted Estimation [Slides]

1-      Linear Regression

2-      Nonlinear Regression

3-      System of Equations

4-      Nonlinear-Non-additive

5-      QMLE

Bayesian Approach to Index Numbers

Nonparametric Index Numbers

Existence and Uniqueness of Solutions to Multilateral Indexes [Paper Published]

Software to Estimate Index Numbers