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Calculating Multifactor Productivity

January 12, 2011 in Labor Economics | No comments

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

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Defining a Hospital Catchment Area

November 23, 2010 in Hospitals, Labor Economics | No comments

From what areas does a hospital draw on to fill its beds?  There have been many attempts to define a hospital’s catchment area.  The Dartmouth Atlas Group uses hospital referral regions (HRRs) and hospital service areas (HSAs). One method is to determine a minimum admission rate for a given geographic unit (e.g., county, census tract, zip code).  For instance, a given zip code would be placed in a hospital’s catchment area if that zip code made up at least 0.5% of hospital admissions.  Conversely, one could include all areas where at least a certain percent of resident admissions were to the hospital in question.

A paper by Gilmour (2010) examines how to create a hospital catchment area using K-means clustering.  The goal of this process is to assign local authority districts to hospitals based on the how likely the individuals are to visit a certain hospital.  K-means clustering is used to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean. The author applies the standard K-means clustering algorithm as follows:

  1. Two cluster centers are chosen arbitrarily,
  2. Each observation is assigned into the cluster whose center it lies closest to,
  3. The center of the cluster formed by this assignment is recalculated, and
  4. The process is repeated until the cluster assignments cease to change.

Gilmour uses a multivariate approach to estimate “closeness.”  He uses principal components analysis to incorporate additional information such as the size and distribution of the hospital’s activity.

Although the K-means clustering captures a larger share of the hospital’s admissions, the catchment areas are generally much larger than is the case using the marginal methods.

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Local Labor Markets and Agglomeration Economies

November 1, 2010 in Labor Economics | No comments

If there is a boost in demand for a certain product, how will that affect wages?  This seems like a straightforward question.  However, a working paper by Enrico Moretti (2010) takes this analysis a step further by examining how labor market shocks affect the spatial component of the labor markets.

“In general equilibrium, a shock to a local labor market is partially capitalized into housing prices and partially reflected in worker wages. While marginal workers are always indifferent across locations, the utility of inframarginal workers can be affected by localized shocks. The model clarifies that the welfare consequences of localized productivity shifts depend on which of the two factors of production—labor or housing—is supplied more elastically at the local level.  A lower local elasticity of labor supply implies that a larger fraction of a shock to a city accrues to workers in that city and a smaller fraction accrues to landowners in that city. On the other hand, a more inelastic housing supply implies a larger incidence of the shock on landowners, holding constant labor supply elasticity. This makes intuitive sense: if labor is relatively less mobile, local workers are able to capture more of the economic rent generated by the shock.”

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Measuring Variation in Labor Costs for the NHS

July 6, 2010 in International Health Care Systems, Labor Economics, Medicaid/Medicare | 1 comment

The cost of running a hospital in New York City is much higher than running a hospital in Bozeman, Montana.  To take into account these cost differences, the Centers for Medicare and Medicaid Services (CMS) has created a wage index to adjust the inpatient prospective payment system (IPPS) for differences in labor costs.

However, the U.S. isn’t the only country where public health agencies adjust payments based on labor costs.  For the past 30 years, England’s Staff Market Forces Factor (MFF) adjusts National Health Service (NHS) payments for medical care.  The MFF’s origin began in a1976 report from the Resource Allocation Working Party (RAWP).  Although the goal of the MFF is to control for geographic variation in input costs, labor costs make up 65% of these input costs.  Although drug and equipment costs also make up 26% of input costs, the prices of these goods are fairly constant across all English regions.  A paper by Elliot et al. (2010) investigates the construction of the labor portion of MFF in more detail.

The MFF is calculated based on standardized spatial wage differentials (SSWDs).  These SSWDs in essence calculates the difference in labor input costs for each region compared to the national average.  The paper divides the country into regions through three different mechanisms:  a region in one of three ways: 303 primary-care trusts (PCTs), 354 local authority districts (LADs) and 207 travel-to-work areas (TTWAs). LADs and PCTs are administrative areas while TTWAs are intended to constitute largely self-contained labor markets based on commuting patterns.  Using these three definitions, the authors calculate the SSWD from the Annual Survey of Hours and Earnings (ASHE) as:

  • ln(wij)=xijβprivate + vjprivate + εij
  • ln(wij)=xijβNHS + vjNHS + εij

The first equation is used to measure wage differentials for a variety of workers whereas the last only examines NHS nurses.  The variable xij contains information on age, age-squared, gender, year dummies, industry dummies and occupational dummies.  The fixed effect variable vj measures the difference in log wages from in region j from the national mean.  In the case of the NHS regression, year and occupational dummies are removed because nurses constitute working in a single industry.

To calculate the MFF for area j, the authors impose a log-to-level wage transformation for the variable vj and normalize this differential based on the national mean.

  • MFFj=100*exp[vjprivate]/exp[J-1 (Σj vjprivate)]

The authors also conduct estimate regional variation in labor costs for doctors.  Because the ASHE sample of NHS doctors is too small to estimate robust SSWDs, the authors instead obtain data on the annual financial returns of NHS trusts through the Department of Health.

How well are these adjustments working?  To answer this question, the authors examine how the differential between private and NHS pay affect the vacancy rate for NHS positions for doctors and nurses.  When private pay is higher than NHS pay, the authors find that the nurse vacancy rate increases.  This makes sense since when the private sector pays more, nurses will be more likely to take jobs outside the NHS.  On the other hand, when private sector pay for doctors is higher, the NHS vacancy rate for physicians is lower.  This seems counterintuitive that physicians would be attracted to lower paying NHS areas.  One explanation is that areas with relatively less generous NHS pay have higher private sector pay.  Thus, these physicians can take the NHS job, but also spend part of his time working for higher private-sector pay.  Using this information, the authors conclude that “The case for additional funding in high-cost low-amenity areas to employ doctors is not supported by this analysis. The MFF adjustment in the NHS funding formula should be amended to reflect this.”

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Proposed Reforms to Medicare’s Hospital Wage Index

March 25, 2010 in Labor Economics, Medicaid/Medicare | 2 comments

A hospital in New York City faces higher labor costs than a hospital in Billings, Montana. To take into account these cost differences, Medicare adjusts hospital payments to reflect these cost differences using a hospital wage index. As currently constructed, however, many hospitals petition to be included in labor markets where they would receive a more generous wage index value.

A number of reforms to the CMS hospital wage index have been proposed. In a recent Acumen report to which I contributed, we evaluate whether some reforms proposed by MedPAC would improve the wage index’s accuracy. Below is an excerpt from the executive summary. The full report is available here.

“The Medicare statute requires that per-discharge payments to hospitals in the inpatient prospective payment system (IPPS) reflect geographic differences in the cost of labor. As a result, Medicare’s IPPS payments are adjusted by a hospital wage index that seeks to reflect the average price of labor facing each hospital. To construct the index, Medicare clusters hospitals into metropolitan statistical areas (MSAs) and residual areas (“balance-of-state” or “rest of state”). These geographical areas approximate hospital labor markets, and average wages are calculated for each using wage data from an annual survey of IPPS hospitals’ labor costs. However, accurately representing a hospital labor market is not a simple task, and inaccurately specifying a hospital labor market can create two problems.

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Does a bad economy increase blood donation?

August 25, 2009 in Labor Economics | No comments

A bad economy should increase blood donation.  As more individuals lose their job, they now have more free time to donate blood.  The opportunity cost of their time is lower, since they don’t have to miss work to donate blood.  A bad economy also creates more sympathy for those in need; thus, donor morale may increase.

Alas, Marketplace reveals that a bad economy in fact decreases blood donations:

“The Red Cross says it’s feeling a new side effect from the recession. All those job losses mean fewer people available to donate at corporate blood drives. It says up to 80 percent of donated blood comes from companies hosting those drives.“

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Obama’s Economic Case for Health Reform

July 16, 2009 in Labor Economics, Medicaid/Medicare | 1 comment

Health Reform is at the top of President Obama’s list of reform efforts. Mr. Obama claims that not only will health reform improve the physical health of the nation, it will also improve its economic health. In a Council of Economic Advisers Report, President Obama lists three reasons why slowing health care costs and expanding health care coverage will increase economic growth. Let us look at each of these arguments in turn.

THE ECONOMIC IMPACT OF SLOWING HEALTH CARE COST GROWTH

  1. It would raise standards of living by improving efficiency. Decreasing health care costs while maintaining the same quality of health care would certainly improve efficiency. However, simply decreasing costs will not necessarily improve efficiency since the quality of medical care could deteriorate. Many researchers believe that Americans receive too much specialist care and not enough primary care. Cutting costs in the primary care sector may actually decrease efficiency. Further, decreasing reimbursement for groundbreaking technologies may slow the growth of longevity rates. Thus, cutting cost by reducing reimbursement for inefficient medical care would improve efficiency, but cutting cost by reducing payment for cost-effective method would actually decrease efficiency.
  2. It would prevent disastrous budgetary consequences and raise national saving. The first part is certainly true while the second is not. The Medicare Trust Fund is will run out of funds in less than ten years. As the baby boomers continue to progress into retirement, the promised health care benefits will need to be financed by a higher tax rate on workers. Thus, the government must take some action to bolster its fiscal solvency. Cutting health care costs, however, may not increase national savings. Let us assume overall spending on medical care health care spending is too high right now. This may be the case because employers–not employees–choose the set of health plans offered and the moral hazard problem has lead to overconsumption. In this case, decreasing spending would increase savings, because individuals are spending too much on health insurance. But why are people spending “too much”? It could be the case that they are spending (on average) exactly what they want to given the expensive nature of medical care. If this were the case, reducing government health care expenses would be offset by an increase in private health expenditures. For instance, a government cut in reimbursement rates to doctors would decrease spending and increase savings. Patients faced with the possibility of lower quality care may opt to spend more money on more personalize health care (e.g., flat-rate no limit primary care doctors) which would decrease savings. The net effect on savings is ambiguous.
  3. It would lower unemployment and raise employment in the short and medium runs. The most important point to mention here is “Who cares about the short/medium runs?” If you are going to implement new huge government program to reduce unemployment in the next 3 year, this is a huge mistake. Any large health reform effort should be made not for it’s short run impact, but for its long run impact. Nevertheless, cutting costs may create a small short-run increase in employment. The reason is that firms can will pay less for health insurance (or pay lower taxes for Medicare) and can hire more employees. However in the medium to long run, total worker compensation is set in a competitive market. Thus, a drop in health insurance premiums will likely be offset by higher wages and employment will remain at the same level as if no cost-cutting occurred. As evidence of this, the cost of health care has increased monotonically for the last 30 years. On the other hand, unemployment looks like a sine wave, displaying no strong long-term trend.  If medical costs caused unemployment, one would expect unemployment to be increasing over the long run just as medical costs have done.

THE ECONOMIC IMPACT OF EXPANDING COVERAGE

  1. It would increase the economic well-being of the uninsured by substantially more than the costs of insuring them. It is likely that the economic of the uninsured would increase. It is likely that the economic well-being of the currently insured would decrease (through higher taxes). The net effect in the short run is likely to positive. To restate, in the short run, expanding coverage is almost certainly worthwhile. The question is whether or not expanding coverage be detrimental in the long run. Would an increase in the proportion of individuals with government-run health care lead to a stifling of innovation? Would lobbying by interest groups (e.g., PhARMA, AMA) lead to distorted reimbursement patterns? Would costs cutting measures lead to longer wait times to see doctors? While the short run benefits of expanding health insurance coverage are clear, the long run effects on both economic and health sector efficiency is ambiguous.
  2. It would likely increase labor supply. The CEA claims that “reducing disability and absenteeism in the work place” will increase the labor supply. This is true, but may be offset by a reduced number of people who are employed in the first place. Many people take second jobs just for the health insurance. If individuals can get health insurance without working, this could decrease the labor supply. Overall, I believe the net effect will be small. The more important economic impact is (3) below.
  3. It would improve the functioning of the labor market. This is definitely true. Individuals often keep job below their skill level simply because they fear losing health insurance. Other high-skilled individuals will take low-paying second jobs (e.g., Starbucks) just to have some insurance coverage. These two problems are named Job Lock and Job Stretch. If workers can choose employers based on wages, their own skills, and the overall work environment, this will lead to more efficiency labor market than if individuals would need to choose jobs based on the health plans offered. Further, it would increase small business innovation. Workers would be more attracted to small business if they knew they could receive insurance from the government.

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Job Stretch

July 10, 2009 in Health Insurance, Labor Economics | 3 comments

In this blog, I have frequently discussed the concept of Job Lock.  Job Lock occurs when you don’t leave a job that you wish to leave (either because it is low paying or you do not like the work) simply because you do not want to lose your health insurance.  Leaving your current job for one that is more lucrative may not be worthwhile if you lose health insurance.  Even if a new job’s potential salary is more than your salary+benefits at your old job, you may still not leave since the price of group health insurance is much less than the price of non-group health insurance, especially for those with pre-existing conditions.

Yesterday, Reuters reported on another phenonmenon: Job Stretch.  Take a look at the following excerpt from the article:

Real estate agent Lisa DeWaal serves coffee at a Starbucks outlet for four hours every morning before she goes to the office to start her “day job.”  The reason has little to do with the state of the housing market and everything to do with the one big perk that 20 hours a week at the coffee counter provides: affordable health insurance for her and her three children.

Job Stretch is a term (that I just invented) where individuals take a second (or third) job in order to get health insurance.  Taking a second job in and of itself is not evidence of Job Stretch; many people prefer additional income over additional leisure time. However, when high-skilled workers take low-skill jobs just for health insurance benefits, this is an example of a labor market inefficiency.  The inefficiency is caused by a system of health insurance provided at the employer level.

Now we have two labor market inefficiencies to worry about: Job Lock and Job Stretch.



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Trust your employees, Increase Productivity

May 29, 2009 in Experimental, Labor Economics | No comments

At least that is what a study by Falk and Kosfeld (2006) found.  

The research question they tested was if the principal can set a minimum level of x, should they?  An economist would say, of course.  The agent has an incentive to not work at all.  Setting a minimum level of work would guarantee a return for the principal.  To test this, they set up the following experiment.  

  • An agent (worker) must decide on a level of x, which is seen as a proxy for work.  The cost function is simply c(x)=x.  They have an initial salary of 120.  Thus, their payoff is 120-x.
  • The principal (boss) wants the agent to choose a large x (aka to work as much as possible.  Their payoff is 2x.
    • If the agent decides x=20, then the worker gets 100 and the principal gets 40.

However, it turns out that setting a minimum level of x is counterproductive.  By setting the minimum level of x, this shows that the principal does not trust the agent.  This leads the agent to choose a lower level of x chosen by the worker.  For instance, if the principal chooses a minimum x of 5, the agents chose x=12.2 on average.  However, if the principal does not choose a minimum x, then the agent chose an average x of 25.1.Further, principals knew this would happen.  About two-thirds of principals decided not to dictate a minimum level of x.  

The best interpretation of these results can be shown by an excerpt from the memoirs of David Packard, the founder of Hewlett-Packard (HP):

“In the late 1930s, when I was working for General Electric…, the company was making a big thing of plant security. … GE was especially zealous about guarding its tool and parts bins to make sure employees didn’t steal anything. Faced with this obvious display of distrust, many employees set out to prove it justified, walking off with tools and parts whenever they could. … When HP got under way, the GE memories were still strong and I determined that our parts bins and storerooms should always be open. … Keeping storerooms and parts bins open was advantageous to HP in two important ways.  From a practical standpoint, the easy access to parts and tools helped product designers and others who wanted to work out new ideas at home or on weekends. A second reason, less tangible but important, is that the open bins and store- rooms were a symbol of trust, a trust that is central to the way HP does business” (David Packard, 1995, p. 135). 

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Are all the good men married?

December 9, 2008 in Labor Economics | No comments

Does marriage cause men’s wages to rise?  This is the question addressed by UCSD professor Kate Antonovics and Robert Town in their 2004 paper in AER cleverly titled “Are all the good men married?”

It has been shown that married men earn more money than non-married men with similar characteristics.  Why is this?  A few explanations are:

  1. Married men are more productive since they specialize in non-household production,
  2. Employers could discriminate in favor of married men, or
  3. the unobservable characteristics that make men more productive in the labor market also make them more attractive in the marriage market.
A simple way to figure out the marriage wage premium is to run an OLS regression.
  • wij = βMij + γXij + μij + fj + uij   (1).
  • M: married, X: other variables, μ: individual fixed effect, f: family fixed effect, u: error term 
  • For OLS, the residual is equal to μij + fj + uij   (1).

Using OLS, the authors find that married men earn a 19% wage premium over non married men.  However, this specification does not solve the selection problem.  If it is true that unobservable factors affect wages and marriage eligibility, then the marriage dummy variable will be correlated with the residual and β may be biased upwards.  

How do the authors solve the endogeneity problem?  They use data from the Socioeconomic Survey of Twins.  For a pair of monozygotic twins, we can rewrite equation (1) as follows:

  • w1j= βM1j + γX1j + μ1j + fj + u1j  (2)
  • w2j = βM2j + γX2j + μ2j + fj + u2j  (3)

Since twins are in the same family, we know that fj in both equation is the same.  Further, we assume that the genetically determined, individual specific earnings endowment is the same across twins (i.e., μ1j = μ2j). Thus we can difference out the two equations so that we are left with:

  • w1j – w2j = β(M1j – M2j) + γ (X1j – X2j) + (u1j – u2j)  (4)
Using this specification on the twin data, the authors find that marriage confers a 26% wage increase.  Because of the similarity between the OLS and twin data, the authors claim that “men are not selecting into marriage based on unobserved heterogeneity in earnings capacity.”

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