In this paper, a dynamic general equilibrium (DGE) model of growth–inequality relationships, with missing credit markets, knowledge spillover and self-employed agents, is calibrated to New Zealand data. The model explains how two distinct policy shocks involving redistribution and immigration imply, subsequently, two completely opposite outcomes. Agents’ inability to borrow aggravates a negative macroeconomic effect of heterogeneity on growth. Redistribution mitigates that effect but creates microeconomic disincentives on saving and work-effort. Consequently, immigration shocks that perturb variance of efficiency induce a negative growth–inequality relationship, while redistribution shocks, in New Zealand’s case, produce larger fluctuations in incentives than in macro benefits, implying a positive growth–inequality relationship.