It is hard to estimate housing supply elasticities. India is a particularly useful country to study housing supply because it is large and has a variety of housing typologies. We estimate the supply elasticity of non-durable, durable, and vacant residential housing units in urban India. We use two migration-inducing exogenous events --- negative rainfall shocks and a highway upgrade program --- occurring in a distant state as demand shifters for local urban housing markets. We apply the Rosen-Roback spatial equilibrium framework to show that both the negative rainfall shocks and the highway upgrade program in a distant state increase inter-state migration. This increase leads to higher population and household growth, and therefore, higher demand for housing in local urban markets. Our findings are three-fold. First, we estimate the long-term supply elasticity of durable housing in urban India to be 1.64. This estimate is substantially lower than the long-run housing supply elasticity estimates of 6-13 for metropolitan areas in the United States seen in the literature. Second, we find that the supply elasticity of non-durable housing is -0.55. Negative supply elasticity of non-durable housing is consistent with the existence of urban gentrification through the demolition and upgrading of slums. And finally, we estimate the elasticity of vacant residential housing unit supply to be 2.63. We posit that a relatively higher vacant housing unit elasticity indicates speculative building by developers.