We develop a macroeconomic agent-based model to study the role of demand and supply factors in determining inflation dynamics. Local interactions of heterogeneous firms and households in the labor and goods markets characterize the model. Asymmetric information implies that firm selection is imperfect and depends both on firms’ relative prices and on their size. We calibrate the model on EU data by using the method of simulated moments and show that it can generate realistic inflation dynamics and a non-linear Phillips curve in line with recent empirical evidence. We then find that the traditional demand-led explanation of inflation stemming from a tight labor market only holds when selection in the goods markets is mostly driven by relative prices in comparison to firm size. Finally, we study the response of inflation to shocks impacting consumption, labor productivity, or energy costs. The results indicate that only demand shocks lead to wage-led inflation surges. Productivity shocks are entirely passed through to prices without affecting the income distribution. Energy shocks, instead, induce sellers’ inflation after changes in both firms’ cost structure and profit margins. This is in line with the recent empirical evidence for the Euro Area.