A comprehensive analysis of household transportation expenditures relative to other goods and services: an application to United States consumer expenditure data

Abstract

This paper proposes a multiple discrete continuous nested extreme value (MDCNEV) model to analyze household expenditures for transportation-related items in relation to a host of other consumption categories. The model system presented in this paper is capable of providing a comprehensive assessment of how household consumption patterns (including savings) would be impacted by increases in fuel prices or any other household expense. The MDCNEV model presented in this paper is estimated on disaggregate consumption data from the 2002 Consumer Expenditure Survey data of the United States. Model estimation results show that a host of household and personal socio-economic, demographic, and location variables affect the proportion of monetary resources that households allocate to various consumption categories. Sensitivity analysis conducted using the model demonstrates the applicability of the model for quantifying consumption adjustment patterns in response to rising fuel prices. It is found that households adjust their food consumption, vehicular purchases, and savings rates in the short run. In the long term, adjustments are also made to housing choices (expenses), calling for the need to ensure that fuel price effects are adequately reflected in integrated microsimulation models of land use and travel.

Appendix

For $r_{s} = 1,X_{rs} = \{ 1\} .$

For $r_{s} = 2,X_{rs} = \left\{ {{\frac{{\left( {q_{{s}} - 1} \right)\left( {1 - \theta_{s} } \right)}}{{\theta_{s} }}} + {\frac{{\left( {q_{s} - 2}\right)\left( {1 - \theta_{s}} \right)}}{{\theta_{s} }}} + \cdots + {\frac{{2\left( {1 - \theta_{s}} \right)}}{{\theta_{s} }}} + {\frac{{1\left( {1 - \theta_{s} } \right)}}{{\theta_{s}}}}} \right\}.$

For $r_{s} = 3, 4, \ldots ,q_{s} ,X_{rs}$ is a matrix of size $\left[ {\begin{array}{*{20}c} {q_{s} - 2} \\ {r_{s} - 2} \\ \end{array} } \right]$ which is formed as described below.

Consider the following row matrices $A_{{qs}}$ and $A_{rs}$ (with the elements arranged in the descending order, and of size $q_{s} - 1$ and $r_{s} - 2$, respectively):

$$ \begin{gathered} A_{{qs}} = \left\{ {{\frac{{\left( {q_{s} - 1} \right)\left( {1 - \theta_{s}} \right)}}{{\theta_{s} }}},{\frac{{\left( {q_{s} - 2} \right)\left( {1 - \theta_{s} } \right)}}{{\theta_{s} }}},{\frac{{\left( {q_{s} - 3} \right)\left( {1 - \theta_{s} } \right)}}{{\theta_{s}}}}, \ldots ,{\frac{{3\left( {1 - \theta_{s} } \right)}}{{\theta_{s}}}},{\frac{{2\left( {1 - \theta_{s}} \right)}}{{\theta_{s}}}},{\frac{{1\left( {1 - \theta_{s}} \right)}}{{\theta_{s} }}}} \right\} \hfill \\ A_{rs} = \left\{ {r_{s} - 2,r_{s} - 3,r_{s} - 4, \ldots ,3,2,1} \right\}. \hfill \\ \end{gathered} $$

Choose any $r_{s} - 2$ elements (other than the last element, ${\frac{{1 - \theta_{s}}}{{\theta_{s}}}}$) of the matrix $A_{qs}$ and arrange them in the descending order into another matrix $A_{{iqs}}$. Note that we can form $\left[ {\begin{array}{*{20}c} {q_{s} - 2} \\ {r_{s} - 2} \\ \end{array} } \right]$ number of such matrices. Subsequently, form another matrix $A_{{irqs }} = A_{{iqs}} + A_{rs} .$ Of the remaining elements in the $A_{{qs}}$ matrix, discard the elements that are larger than or equal to the smallest element of the $A_{{iqs}}$ matrix, and store the remaining elements into another matrix labeled $B_{{irqs }}$. Now, an element of $X_{rs}$ (i.e., $x_{{irqs}}$) is formed by performing the following operation: $x_{{irqs}} = {\text{Product}}\left( {A_{{irqs}} } \right) \times {\text{Sum}}\left( {B_{{irqs}} } \right)$; that is, by multiplying the product of all elements of the matrix $A_{{irqs}}$ with the sum of all elements of the matrix $B_{{irqs}}$. Note that the number of such elements of the matrix $X_{rs}$ is equal to $\left[ {\begin{array}{*{20}c} {q_{s} - 2} \\ {r_{s} - 2} \\ \end{array} } \right]$.