### Abstract

Partial linear models provide an intuitively appealing way to examine gasoline demand because one can examine how response to price varies according to the price level and people's income. However, despite their intuitive appeal, partial linear models have tended to produce implausible and/or erratic price effects. Blundell et al. (2012) propose a solution to this problem that involves using Slutsky shape restrictions to improve the precision of the nonparametric estimate of the demand function. They propose estimating a constrained partially linear model through three steps, where the weights are optimized by minimizing an objective function under the Slutsky constraint, bandwidths are selected through least squares cross-validation, and linear coefficients are estimated using profile least squares. A limitation of their three-step estimation method is that bandwidths are selected based on pre-estimated parameters. We improve on the Blundell et al. (2012) solution in that we derive a posterior and develop a posterior simulation algorithm to simultaneously estimate the linear coefficients, bandwidths in the kernel estimator and the weights imposed by the Slutsky condition. With our proposed sampling algorithm, we estimate a constrained partially linear model of household gasoline demand employing household survey data for the United States for 1991 and 2001 and for Canada for 2006–2009 and find plausible price effects.

Original language | English |
---|---|

Pages (from-to) | 346-354 |

Number of pages | 9 |

Journal | Energy Economics |

Volume | 67 |

DOIs | |

Publication status | Published - 1 Sep 2017 |

### Keywords

- Kernel estimator
- Markov chain Monte Carlo
- Price elasticity
- Slutsky condition
- Smoothness

### Cite this

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**A Bayesian sampling approach to measuring the price responsiveness of gasoline demand using a constrained partially linear model.** / Chen, Haotian; Smyth, Russell; Zhang, Xibin.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - A Bayesian sampling approach to measuring the price responsiveness of gasoline demand using a constrained partially linear model

AU - Chen, Haotian

AU - Smyth, Russell

AU - Zhang, Xibin

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Partial linear models provide an intuitively appealing way to examine gasoline demand because one can examine how response to price varies according to the price level and people's income. However, despite their intuitive appeal, partial linear models have tended to produce implausible and/or erratic price effects. Blundell et al. (2012) propose a solution to this problem that involves using Slutsky shape restrictions to improve the precision of the nonparametric estimate of the demand function. They propose estimating a constrained partially linear model through three steps, where the weights are optimized by minimizing an objective function under the Slutsky constraint, bandwidths are selected through least squares cross-validation, and linear coefficients are estimated using profile least squares. A limitation of their three-step estimation method is that bandwidths are selected based on pre-estimated parameters. We improve on the Blundell et al. (2012) solution in that we derive a posterior and develop a posterior simulation algorithm to simultaneously estimate the linear coefficients, bandwidths in the kernel estimator and the weights imposed by the Slutsky condition. With our proposed sampling algorithm, we estimate a constrained partially linear model of household gasoline demand employing household survey data for the United States for 1991 and 2001 and for Canada for 2006–2009 and find plausible price effects.

AB - Partial linear models provide an intuitively appealing way to examine gasoline demand because one can examine how response to price varies according to the price level and people's income. However, despite their intuitive appeal, partial linear models have tended to produce implausible and/or erratic price effects. Blundell et al. (2012) propose a solution to this problem that involves using Slutsky shape restrictions to improve the precision of the nonparametric estimate of the demand function. They propose estimating a constrained partially linear model through three steps, where the weights are optimized by minimizing an objective function under the Slutsky constraint, bandwidths are selected through least squares cross-validation, and linear coefficients are estimated using profile least squares. A limitation of their three-step estimation method is that bandwidths are selected based on pre-estimated parameters. We improve on the Blundell et al. (2012) solution in that we derive a posterior and develop a posterior simulation algorithm to simultaneously estimate the linear coefficients, bandwidths in the kernel estimator and the weights imposed by the Slutsky condition. With our proposed sampling algorithm, we estimate a constrained partially linear model of household gasoline demand employing household survey data for the United States for 1991 and 2001 and for Canada for 2006–2009 and find plausible price effects.

KW - Kernel estimator

KW - Markov chain Monte Carlo

KW - Price elasticity

KW - Slutsky condition

KW - Smoothness

UR - http://www.scopus.com/inward/record.url?scp=85031743138&partnerID=8YFLogxK

U2 - 10.1016/j.eneco.2017.08.029

DO - 10.1016/j.eneco.2017.08.029

M3 - Article

VL - 67

SP - 346

EP - 354

JO - Energy Economics

JF - Energy Economics

SN - 0140-9883

ER -