For total consumption, food and non-food consumption, respectively. The imputation process requires not only these shares but also the consumption of comparable items ( ) of those in previous rounds. ii2022 Second, the two-step random hot deck imputation methodology is implemented following Fernandez, yy Olivieri, and Sanchez (2023), whose analysis is based on the approach proposed by Lucchetti et al. (2020). This method utilizes PMM (Predictive Mean Matching), LASSO regression, and resampling techniques to predict the 2010 and 2016 consumption aggregates comparable to the data collected in the 2022 HIES. This methodology aims to accurately rebuild the poverty and inequality trends that Bangladesh has experienced over the last 12 years while avoiding some assumptions behind parametrical alternatives. The implicit approach behind PMM-like methods (Little and Rubin 2002) does not require defining an explicit model for the distribution of the missing values. Because of this, predictive mean matching is less vulnerable to model misspecification than traditional parametric methods (Van Buuren, 2018).

Morris, White, and Royston (2014) conducted simulation studies to contrast the results of PMM versus a parametrical approach under different data missingness scenarios (entirely at random, at random, and not at random). They demonstrated that PMM-like methods are effective when the underlying imputation model is accurately specified. Furthermore, this approach offers an enhancement compared to parametric imputation in scenarios where the imputation model is not correctly specified. These findings are consistent with Schenker and Taylor (1996), who compared partially parametric (PMM-like) and fully parametric regression-based multiple-imputation methods. They found that a fully parametric approach yields marginally more efficient estimates of the outcome's marginal distribution function than the partially parametric methods. However, when there is a misspecification in the mean structure, all methods remain effective in estimating the marginal mean. However, the fully parametric approach exhibits a slight rise in bias and variance. In estimating the marginal distribution function, the fully parametric method encounters difficulties in various scenarios, while the PMM-like methods continue to perform well. In addition, when empirical data diverge from their assumed distributions, PMM typically excels at maintaining the original distribution of the data more effectively than fully parametric Multiple Imputation (MI) methods.

The random hot deck PMM imputation method, enhanced with statistical learning techniques and resampling, significantly improves the estimation of a comparable 2010 or 2016 consumption aggregate, thereby refining poverty and inequality measurements. This method incorporates regularization to prevent overfitting and employs cross-validation to reduce the mean square error (MSE) of predictions. Consequently, it offers more precise welfare predictions for data outside the estimation sample than traditional regression models. This increased accuracy is achieved through automatic variable and model selection, which involves penalizing coefficients and using cross-validation, as Tibshirani (1996) described. These advancements are particularly crucial in the context of the proposed approach and represent a significant improvement over traditional PMM methods.

However, despite these advantages over fully parametric approaches, the effectiveness of these methods still heavily relies on the correct specification of the imputation model. Morris, White, and Royston (2014) advised that researchers should focus on accurately specifying the imputation model 5