Labor Economics

# Calculating Multifactor Productivity

### What is multifactor productivity?

Multifactor productivity (MFP) is a measure of real output per combined unit of labor and capital, reflecting the contributions of all factors of production.  A change in multifactor productivity reflects the change in output that cannot be accounted for by the change in combined inputs. As a result, multifactor productivity measures reflect the joint effects of many factors including new technologies, economies of scale, managerial skill, and changes in the organization of production.

### Who cares?

Economists care because we care how efficient different sectors of the economy are.  Healthcare workers should also care.  Why?  An August 2010 CMS memo states “the recently enacted Patient Protection and Affordable Care Act (ACA), as amended, calls for a reduction in payment rate updates equal to the increase in economy-wide multifactor productivity.”

Today, I will review how the Bureau of Labor Statistics calculates MFP.

### Calculating MFP

The following description of the Bureau of Labor Statistics’ method of calculating MFP is taken from this document.
The Tornqvist index for major sector multifactor productivity growth, A, is:

• Δ ln A = Δ ln Q – Δ ln I
• Δln I = 1/2 * [Sk(t) + Sk(t-1)] Δ ln K + 1/2 * [Sl(t) + Sl(t-1)] Δ ln L

where

• Sk(t) = capital costs(t) / total costs(t), and
• Sl(t) = labor costs(t) / total costs(t),

Of course, capital and labor are made up many different parts. BLS classifies different types of workers by their education, work experience, and gender. Capital inputs are calculated as the service flow for physical capital assets. These asset categories include: “42 types of equipment and software, 21 types of nonresidential structures, 9 types of residential capital, inventories (manufacturing available for 3 stages of fabrication), and land. BLS measures of capital stocks for equipment and structures are prepared using NIPA data on real gross investment.”  Based on these labor and capital categories (indexed by i), we can calculate the aggregate levels of capital and labor as:

• Δln K = Σi 1/2 * [Ski(t) + Ski(t-1)] Δ ln ki
• ΔlnL = Σi 1/2 * [Sli(t) + Sli(t-1)] Δ ln li

where

• Ski(t) = Cki(t) * ki(t) / total capital costs
• Cki(t) is the rental price for capital asset ki.
• Sli(t)= vli(t) * li(t)/ total labor costs
• vli(t) is the hourly compensation for worker group li.

For manufacturing and the 18 NAICS-based industries which comprise manufacturing, aggregate input has a conceptually similar definition except that there are 5 inputs rather than just the 2 used in the major sector measures.

• Δln I = 1/2*[Sk(t)+Sk(t-1)]Δln K + 1/2*[Sl(t)+Sl(t-1)]Δln L + 1/2*[Se(t)+Se(t-1)]Δln E + 1/2*[Sm(t)+Sm(t-1)]Δln M + 1/2*[Ss(t)+Ss (t-1)]Δln S

where

• L = total hours at work
• Se(t) = energy costs(t)/total costs(t)
• Sm(t) = materials costs(t) / total costs(t)
• Ss(t) = purchased business services costs(t) / total costs(t)

The data sources for selected variables can be found in this spreadsheet.