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We use a latent class production function approach to consider the existence of differences in household income functions to observe whether this is a key determinant to livelihood outcomes between households in rural India. Empirical analysis is valuable in understanding the levels of poverty, observed poverty dynamics, and the mechanisms behind why households have alternative livelihood dynamics. However, survey measures of income and consumption are often prone to large volatility and measurement error. To account for this, many papers adopt a livelihood regression index which describes a relationship between a measured livelihood of a household and the value of the assets owned. The fitted values from this regression can generate predicted livelihoods of households given a set of assets, avoiding the previously discussed volatility. However, previous studies have estimated the livelihood index as an average across the entire sample population, only allowing for homogeneous differences in how livelihoods are generated between households and across time. This assumes all households share the same marginal elasticises from assets. However, this is inconsistent with the livelihood literature where structural differences in livelihoods is often argued to be driven by differences in the levels and contributions assets provide in generating a livelihood. This paper presents a latent grouping strategy that allocates households into the sub-groups that best represents their average observed livelihoods, using the ICRISAT data of agrarian households in rural India. The algorithm estimates the livelihood index given an initial clustering on outcomes, and then reallocates households if the log-likelihood of being represented by another group is higher. The algorithm is repeated until there are no movements between groups in the sample. A latent estimation allows for estimations to not be based on assumptions of homogeneity or subjective a-priori grouping of households. The resulting fitted values of the estimated livelihood indexes is used in a first-order auto-regressive process to consider the existence of possible unstable thresholds in livelihood dynamics. This shows whether subgroups converge to a single livelihood equilibrium or diverge to separate equilibrium contingent on their starting livelihood endowment. A divergence would indicate the existence of a poverty trap where households converge to persistently low livelihood outcomes and do not have the assets or capabilities to overcome structural obstacles. The latent estimation shows there is significant heterogeneity in how households utilise asset holdings to generate a livelihood which cannot be observed through a homogeneous livelihood estimations. The sub-technologies also allow for a discussion on the qualitative differences between technologies and groups, where the results indicates households derive greater livelihoods from diversification in income, insurance against macroeconomic shocks and access to collective technology. The corresponding fitted values from the sub-group livelihoods find conditional convergence of livelihoods but at different levels and rates between the sub-groups. These differences in trajectory functions cannot be observed with homogeneous estimations and emphasises that a latent estimation is crucial in analysing poverty through livelihood trajectories when there is significant household heterogeneity.


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