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There is confusion regarding the notion of "vulnerability" in the climate change scientific community. Recent research has identified a need for formalisation, which would support accurate communication and the elimination of misunderstandings that result from the use of ambiguous terminology. Moreover, a formal framework of vulnerability is a prerequisite for computational approaches to its assessment. This paper presents an attempt at developing such a formal framework. We see vulnerability as a relative concept in the sense that accurate statements about vulnerability are possible only if one clearly specifies (1) the entity that is vulnerable, (2) the stimulus to which it is vulnerable and (3) the preference criteria to evaluate the outcome of the interaction between the entity and the stimulus. This paper is dedicated to the memory of Gerhard Petschel-Held, whose pioneering work on syndromes of global change has been a source of inspiration for us and for others across various schools of thought on vulnerability.We relate the resulting framework to the Intergovernmental Panel on Climate Change conceptualisation of vulnerability and two recent vulnerability studies.

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This study explores three-way linkage between weather, agricultural performance and internal migration in India at the state and district level using census data. The estimations are based on a two-stage least squares model using panel data. The elasticity of the inter-state out-migration rate with respect to per capita net state domestic agricultural product is − 0.775, indicating that a decline in the value of agricultural output related to weather variations results in an increase in out-migration rate. The crop-wise analysis shows that a 1 per cent decline in rice (wheat) yield leads to a nearly 2 per cent (1 per cent) increase in the rate of out-migration from a state. The district-level analysis shows larger magnitudes of estimated change in in-migration rates to relative changes in crop yields. However, the district-level analysis using two-period panel data constructed from a single census provides relatively less robust results compared to the state-level analysis owing to the associated data limitations.