Something from Nothing: Estimating Consumption Rates Using Propensity Scores, with Application to Emissions Reduction Policies

Nicholas Bardsley,Milena Büchs,Sylke V Schnepf

doi:10.2139/ssrn.2731970

Abstract

Consumption surveys often record zero purchases of a good because of a short observation window. Only mean consumption rates can then be inferred. We show that propensity scores can be used to estimate each unit's consumption rate, revealing the distribution. We demonstrate the method using the UK National Travel Survey, in which c.40% of motorist households purchase no fuel. Estimated consumption rates are plausible judging by households' annual mileages, and highly skewed. We apply the same approach to estimate CO2 emissions and direct outcomes of a carbon cap or tax. Analysis of such policies based solely on means appears to have a negative bias, because of skewness of the underlying distributions. The regressiveness of a simple tax or cap is overstated, and redistributive features of a revenue-neutral policy are understated.

Highlights

A potential problem in survey sampling is that a phenomenon of interest occurs infrequently relative to the period in which data is collected, leading to zero-inflated data
Gibson and Kim [13] test several of the infrequent purchase models, using a dataset containing both stock use and purchasing decisions, arguing that they exhibit substantial biases. Whether or not these models are inherently biased, we find it plausible that they can be mis-specified for the data to hand, so there is a need for credible specification checks
Covariates that are included in the regression have very low standardised biases. (Austin [24], for example, reports that standardised bias of less than 10% are regarded as low in applied work.) mileage, the coefficient at the bottom, shows the highest bias, exceeding 20%

Summary

Introduction

A potential problem in survey sampling is that a phenomenon of interest occurs infrequently relative to the period in which data is collected, leading to zero-inflated data. If a wildlife survey runs camera traps for a short time, negative results may obtain even where a target species is known to reside [1]. In the social sciences a key example is purchase infrequency. This occurs when a consumption diary is used to record buying over a relatively short duration, typically 1–2 weeks. Sampled households often record no purchase, even if they are known to consume the good in question. But many will not make purchases in a given two weeks, which is the period in the UK’s Living Costs and Food Survey for example

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