9 takes recent household surveys from Guatemala, India, Indonesia, Kenya, Pakistan, Sri Lanka, Albania, Brazil, Mexico, and Peru. The prices of various fuels paid by each household in the first six countries were calculated by dividing the expenditure on each fuel by the quantity reported in the survey. The remaining four surveys did not report quantity data and national average prices of LPG from other sources were used to back-calculate quantities. The smaller the variation in actual prices paid, the better will be the approximation from using an average price. More details are provided in appendix 2.

Depending on the survey, there are different indicators on whether a household is an LPG user. Every survey reported expenditures on LPG during the sample period. A potential problem in equating positive expenditures on LPG with LPG use is that users who had not refilled their cylinders during the sample period would be treated as non-users.<sup>2</sup> Cross-checking was possible in eight countries in which the surveys asked additional questions related to LPG. These concerned the primary cooking fuel in six countries and other aspects of LPG use in two. Kenya had the largest number of questions specifically targeting LPG. This study takes non-zero response to the question on expenditure on LPG as the indication of LPG use, except where there are discrepancies with data from other questions on LPG, in which case alternative definitions of LPG use are examined (Kenya, Mexico, and Peru).

The approach to modeling fuel selection and fuel use for LPG follows the work of Israel (2002) and uses a Heckman-type model with two equations. The dependent variable is a 1/0 dummy for selection in the first probit (selection) equation and the logarithm of kilograms (kg) of LPG consumed or purchased per month per household in the second (consumption) equation. Heckman’s approach allows for the existence of selection bias in the second stage, in which the decision to choose LPG depends in part on unmeasured variables. A maximum likelihood approach is used except in Mexico and Peru, where a two-step estimation procedure is used (see appendix 3) because the number of LPG users in the selection equation is larger than the number of households reporting expenditures on LPG (which yield quantities consumed) in the consumption equation. Analysis for Kenya tests four different definitions of LPG using maximum likelihood or the two-step estimation procedure, depending on the number of user households entered in each stage.

The marginal effect on demand among users is termed the conditional effect, while the sum of this effect and the increased probability of use is termed the unconditional effect. Conditional and unconditional marginal effects are calculated for the first six countries covered in section 4.3 using the maximum likelihood parameter values obtained for the Heckman model.

This study uses household weights to obtain population means. For econometric analysis including Heckman-type models, unweighted estimators would be consistent and more efficient than weighted counterparts unless sample selection is endogenous to the dependent variables being investigated (Deaton 1997; Wooldridge 2002). This study examined both weighted and unweighted estimators and reports the latter except where unweighted estimators produced implausible results: Guatemala where the coefficient for household expenditure was statistically

> 2 The need to distinguish the corner solution case (households never use) from random factors leading to nonpurchase during the period, even though the household is a regular user, has been discussed in the literature (Deaton and Irish 1984; Blundell and Meghir 1987).