The value of panel data for micro-units in exploring aggregated relationships empirically is substantial, since such data are not only useful for estimation at both the micro- and the macro-level, but also allow comparison of properties of relationships aggregated formally from the micro-level with those resulting from aggregation by analogy in an informal way. Using panel data from manufacturing plants, we consider biases in the aggregation of the Translog production function, which does not generally satisfy the strict mathematical conditions for perfect aggregation. Linear and log-linear aggregation in the presence of random coefficients are considered. Under linear aggregation across plants, departures between geometric and arithmetic means of inputs as well as correlation between log-inputs, contribute substantially not only to biases in the output volume, but also to instability in derived input and scale elasticities and biases in total factor productivity growth. Overall, the biases under log-linear aggregation are smaller.