# **b. Expenditure estimates**<sup>12</sup>

In addition to estimating the proportion of entrants, it is necessary to estimate expenditures on the relevant product among new consumers or users. The estimation of consumption expenditure among new entrants is conditioned on the probability or likelihood of consumption and is modeled as , where denotes expenditure. The unobserved expenditures of entrants are treated similarly to missing values, where these missing values are the unobserved expenditures of entrants. EE[uu |uu> 0] uu To address the non-randomness of the decision to consume, the analysis assumes that, at the margin, the new consumers of the product share observable characteristics with current consumers.<sup>13</sup>

The suggested approach relies on the first-order Taylor approximation to measure the welfare of current users.<sup>14</sup> The Taylor approximation allows an assessment of the impact of price changes on well-being under the assumption of a given basket of goods. Following a first-order Taylor approximation, the impact of price changes on well-being can be approximated as follows: , (9) ii ii ddww= −uu ∗ddpp , where denotes the change in well-being, the expenditures on the good , and the observed proportional change in the price of good i. For instance, if the price increases by 1 percent, well-being ii ii decreases by ddww 0.01 ∗e . uu ii ddpp ii In addition to measuring the impact of price changes on the welfare of current consumers, the analysis must also include the changes in the well-being of entrants to measure adequately the welfare impacts of competition. The average expected expenditures on good among new consumers in group (for example, decile 2) is denoted by ∂ , and the average expected expenditures of current consumers in the same group is denoted by gg,ii ww ∂ .15 If the estimated proportion of entrants in group ii gg is uu ∂∂cc∂ cc denoted by (estimated using a probabilistic model), then the following is true: gg,ii uu gg gg,ii ππ ∂ ∂ (10) ww ∂∂ccnn∂ nn gg,ii gg,ii gg,ii uu = ππ uu

> 12 See the mcema user manual for more information (Rodríguez-Castelán et al. 2021). A detailed discussion on the implications of the availability of price data on the items of interest is also presented in the manual.

> 13 The mcema module for Stata allows a selection among six methods to estimate the expenditure of new entrants: (a) imputation using average expenditures (unconditional mean imputation), (b) random imputation using the expenditures of current users, (c) imputation based on expenditure models and linear regressions (regression, conditional mean imputation), (d) imputation using an expenditure model and the random imputation of residuals (stochastic regression imputation), (e) imputation based on an expenditure model and quantile regressions, and (f) imputation using a quantile regression model and a random imputation of residuals.

> 14 Jackson (1984) introduces the foundations of the hierarchic demand system whereby the change in a bundle of goods can be modeled. In what follows, a selective demand model is introduced to link the selection of goods with real income. There are two hot deck approaches. The first is the distance function approach, and the second is the pattern matching approach. The first imputes the missing value based on the smallest squared distance statistic to the case with the missing value. The matching pattern method used here assumes that the sample can be stratified into separate homogenous groups and that imputation can be performed randomly within each group (Fox-Wasylyshyn and El-Masri 2005). See also Ahmad and Stern (1984, 1991); Araar (1998); Araar and Paolo (2016); Creedy (1998); Newbery (1995); Yitzhaki and Lewis (1996).

> 15 Current users are users with positive expenditure under a concentrated market (status quo). Nonusers would then be the remaining users who do not exhibit positive expenditures under a concentrated market (status quo).

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