Recent work has revived two intertwined challenges to aggregate production functions (the 'identity' and 'aggregation' problems). This paper examines both problems in the context of aggregate industry-by-country analysis, first demonstrating the relevance of the identity problem for industry-level analysis and tracing its origin in the System of National Accounts. Using a case study of materials quality in global forestry and logging, the paper then compares estimates from fully physical versus conventional (monetary) production functions to isolate the aggregation problem and show that credible inference depends on appropriately modelling heterogeneity in production processes. Materials quality is measured via finite mixture modelling applied to global satellite data. Attempting to estimate the parameters of a common production technology yields poor results, because of differences in production processes between countries. The paper offers a practical approach for dealing with heterogeneity via Data Envelopment Analysis and heterogeneous coefficient panel estimators, and concludes with guidance to help applied industry-level analysis recognize and avoid both the identity and aggregation problems. [ABSTRACT FROM AUTHOR]

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