Jonathan A. Parker, et al, find a strong effect.

on average households spent about 12-30% of their stimulus payments, depending on the specification, on non-durable consumption goods and services (as defined in the CE survey) during the three-month period in which the payments were received. This response is statistically and economically significant. Although our findings do not depend on any particular theoretical model, the response is inconsistent with both Ricardian equivalence, which implies no spending response, and with the canonical life-cycle/permanent income hypothesis (LCPIH), which implies that households should consume at most the annuitized value of a transitory increase in income like that induced by the one-time stimulus payments. We also find a significant effect on the purchase of durable goods and related services, primarily the purchase of vehicles, bringing the average response of total consumption expenditures to about 50-90% of the payments during the three-month period of receipt.

Their approach uses cross-section analysis, with differences across households in the timing of receipt of stimulus payments as the identification strategy.