As a sneak peek here are the optimal assignments (internal structures) of 4 competing hair salons in NYC, recovered using the method outlined next! Darker cells = more time assigned. 2/17

What is activity data? I like to think of activity data as a matrix for each firm, where rows represent workers and columns represent tasks. Cells contain the fraction of total time at a firm assigned to each worker-task pair. 3/17

There are a few challenges with working with this type of data. 1) To compare matrices of different firms we need a principled way to reduce dimensions. 2) Workers with different IDs in the data may have the same skills. 3) Additional info about the worker is often missing. 4/17

Let’s start with the 1st problem. Define the org. complexity of a firm as the mutual information of its worker and tasks. It measures the distance of an observed matrix from a counterfactual matrix where workers and tasks are matched randomly. 5/17

Consider a model where firms choose their matrix and product prices based on the wages and skills of workers, own and competitor specialization costs and product market competition from other firms. Suppose for now the parameters of this model (wages and skills) are known. 6/17

Surprisingly except for a measure 0 set of wages and skills the data imply a unique, optimal assignment of worker TYPES to task TYPES and a organization cost for each firm. Given wages and skills, we can use activity data (left) to recover a firm’s internal org. (right)! 7/17

But we do not actually know the wages and skills of workers. It turns out that because an organization structure is a matrix, we can combine activity data with more traditional data on prices and market shares to identify skills and wages using a shift-share-like approach! 8/17

Let’s start with wages. If we observe prices and market shares, we can use IO-style techniques to recover a firm’s average wage bill. A firm’s wage bill is just the weighted average of the types of workers hired, which corresponds to the row sums of its internal structure! 9/17

We can identify the wages of a type of worker based on the prices and market shares of firms intense in that type of worker. The argument is not too different for skills. 10/17

If we observe market shares and prices, we can recover the quality of products within a market. Quality is determined by the matching of workers to tasks, which is again a weighted average of the skill parameters, where the weights are determined by a firm’s structure. 11/17

We can identify the skill of worker i at task k based on the market shares and prices of firms that assign a lot of a specific task k to worker i! 12/17

These arguments rely on variation in internal structures. But internal structure is endogenous! To get around this we can use variation in organization complexity and the share of tasks performed by a firm. 13/17

If a firm does a lot of task k and has a high complexity, their org. structure will use specialists in task k and assign task k to these workers! Even though complexity is theoretically endogenous, it turns out it is econometrically exogenous! 14/17

This suggests a nested GMM estimation strategy. “Inside”, for given skills/wages, we solve for all internal orgs. “Outside” we construct model-based prices and market shares to match observed prices and shares. We interact the residuals with complexities and task mixtures. 15/17

This approach is easy to program (solving the firm’s problem is 6 lines in R!) and less computationally demanding because there exists a simple algorithm to solve the firm’s organization problem by iterating on the first order conditions. 16/17