Dynamic material flow analysis (dMFA) is widely used to model stock-flow dynamics. To appropriately represent material lifetimes, recycling potentials, and service provision, dMFA requires data about the allocation of economy-wide material consumption to different end-use products or sectors, that is, the different product stocks, in which material consumption accumulates. Previous estimates of this allocation only cover few years, countries, and product groups. Recently, several new methods for estimating end-use product allocation in dMFA were proposed, which so far lack systematic comparison. We review and systematize five methods for tracing material consumption into end-use products in inflow-driven dMFA and discuss their strengths and limitations. Widely used data on industry shipments in physical units have low spatio-temporal coverage, which limits their applicability across countries and years. Monetary input-output tables (MIOTs) are widely available and their economy-wide coverage makes them a valuable source to approximate material end-uses. We find four distinct MIOT-based methods: consumption-based, waste input-output MFA (WIO-MFA), Ghosh absorbing Markov chain, and partial Ghosh. We show that when applied to a given MIOT, the methods' underlying input-output models yield the same results, with the exception of the partial Ghosh method, which involves simplifications. For practical applications, the MIOT system boundary must be aligned to those of dMFA, which involves the removal of service flows, sector (dis)aggregation, and re-defining specific intermediate outputs as final demand. Theoretically, WIO-MFA, applied to a modified MIOT, produces the most accurate results as it excludes massless and waste transactions. In part 2 of this work, we compare methods empirically and suggest improvements for aligning MIOT-dMFA system boundaries.
