Consistency Criteria for Budgetary Datasets

For every subject whose choices are in the dataset, Prest v0.9.11 can find and count the total number of violations (resp. score) for each of the axioms/criteria (resp. choice consistency index) listed below.

Note: much of the terminology and notation that follows is introduced and explained in the Datasets and Revealed Preference Relations sections.

Weak Axiom of Revealed Preference - WARP

Strict:

\[x^i\succsim^R x^j\;\; \Longrightarrow\;\; x^j\not\succsim^R x^i\]

Non-strict:

\[x^i\succsim^R x^j\;\; \Longrightarrow\;\; x^j\not\succ^R x^i\]

Strong Axiom of Revealed Preference - SARP

\[x^i\succsim^{\widehat{R}}x^j\;\; \Longrightarrow\;\; x^j\not\succsim^R x^i\]

Generalized Axiom of Revealed Preference - GARP

\[x^i\succsim^{\widehat{R}}x^j\;\; \Longrightarrow\;\; x^j\not\succ^R x^i\]

Note

SARP implies WARP strict.

GARP implies WARP non-strict.

Houtman-Maks index - HM

This corresponds to the smallest number of observations that need to be removed from a given subject’s data in order for the remaining choices to satisfy GARP, SARP, WARP (strict) or WARP (non-strict).

Prest v0.9.11 computes each of these four HM indices for budgetary data by finding both their upper and lower bounds.

If the two bounds coincide, Prest reports the exact HM index for the axiom in question. If they differ, Prest v0.9.11 reports the range \(m\leq HM \leq n\) of possible values.

Tip

To use the consistency-analysis feature: right-click on the dataset of interest [e.g. “DatasetX.csv”] in the workspace and select “Analysis -> Consistency analysis”.

To view the consistency-analysis output: right-click on the Prest-generated dataset [e.g. “DatasetX.csv (consistency)”] in the workspace and then click on “View”.

To export the consistency-analysis output (in .xslx or .csv format): right-click on the Prest-generated dataset [e.g. “DatasetX.csv (consistency)”] in the workspace, click on “Export”, and then select one of the following options:

An example of a budgetary dataset that can be analysed in this way can be found here.