Thursday, February 20, 2014

You can't analyze market interventions without considering sunk costs. (Yet another minimum wage post.)

Let's consider a new batch of capital investments in a competitive market.  And, let's make some basic assumptions, that while returns are unknown for any individual investment, the required return for this capital is 10%, and the aggregate return over the lives of the investments will be 10%, with a normal distribution around that outcome.

So, here is a picture of the ROIs of these investments:

This is the basic picture of finance.  There is some normal rate of return that emerges from the supply and demand of capital, and nobody knows exactly which operations will produce it, so we diversify investment capital among projects that meet our risk profile.

But, continuing to imagine this basket of investments, the returns don't come from a static set of operations.  Over time, losses gradually are represented by discontinued operations, so that, eventually, this set of assets evolves into something like this:

If the original set of investments represented $1 billion from a single firm, under our original assumption that on average these investments provided the required return, then the remaining operations would represent, say, 2/3 of the original investment.  These assets would show a very high ROI - 20% in the hypothetical numbers that come out of my example.  But, the ROI for the entire original set of investments remains 10%.  The market value of productive assets remains $1 billion.  The original investments in the failed operations and losses incurred during their operating lives are sunk costs now.

In the context of allocating capital within these projects, those sunk costs should be discarded now.  But, in the context of understanding capital and investment more broadly, those sunk costs are still important.

Several characteristics to note:
  • The ROI of individual active projects in a competitive market will tend to be higher than the ROI for the market as a whole.
  • So, seemingly monopolistic competition can arise from competitive markets because of deviations in ex post returns.
  • The excess returns of successful operations may include excess returns from real options embedded in the operations that include follow-up investments.  But, additional other investments may continue to have an expected return of 10%, even though the existing and future pools of active investments will have returns on initial investments higher than 10%.
  • This diversity of outcomes exists throughout a market, within and among firms.  In some ways, the categorization of projects among firms when analyzing the entire market is arbitrary.  Some failed projects will have been a part of failed firms, some will have been part of active operations within firms, and some will have been discontinued within active firms.  The complete ROI on all invested capital in a given market would be difficult to ascertain, and would tend to appear higher than the aggregate experienced return, because of extensive survivorship bias, whether at the project level or the firm level.

So, why is this a post about the minimum wage?

Much of the technical discussion about minimum wage effects appears to revolve around the idea that low wage employers reflect monopolistic competition.

Using the model I outlined above, I can graphically describe four effects of minimum wage increases on a low-wage employer market.  A minimum wage hike would increase costs, creating a first-order effect of lower ROI for all firms.

Immediate effects

1) Lost or reduced operations

Research that picks up employment losses is probably largely picking up this effect.  Added costs would lead more marginal firms and operations to be discontinued or reduced.  As the graph helps to visualize, even in a competitive market with relatively free entry of new capital, this probably tends to represent a small proportion of the set of affected firms at any given time.

2) Higher prices & lower profits

Firms that weren't marginal would initially move to a new equilibrium which might mostly involve continued operations at lower ROI's.  This probably includes most existing employers.  So, research following specific firms would probably pick up this effect, which would appear to point to minimum employment effects.

Long Term effects

The initial effect on operations would be an across the board reduction in ROI.  The combination of more failed operations and lower ROI among the successful operations drops the aggregate ROI.  Remaining operations would continue to have ROI's well above the required return for the market, but without fundamental adjustments in the entrance of new capital, the expected ROI of new capital would be less than the original 10%.

3) Expanded Operations

Existing employers who were not marginal might tend to experience some expansion, first due to the exit of marginal operators, and then due to the reduction of new entrants because of the lower ROI.  This could be the source of expanded employment that some research finds.  But this particular increase in employment would come about only as the result of shifting market share within a shrinking market.

4) Reduced New Investment

The original ROI would have been the result of an endlessly complex set of financial and cultural factors that would have settled on the original expected return.  Lower ROI's would lead to some new equilibrium that would involve some combination of changing capital mixes, prices, etc. which would settle at a new reduced level of investment that could again achieve 10% expected returns.

This effect might get picked up in macro-data time series, but it is probably difficult to see clearly with any method, because it would be part of complex long term processes.

This paper from the Chicago Fed finds increased firm exits after minimum wage hikes, but it finds that, increased firm entries mostly counter the negative employment from the exits in the short run.  So, the first effect above may not lead to extensive loss of economic activity.  This result seems plausible - an initial rush of replacement capital that was previously kept out by marginally productive existing capital.  Keep in mind, however, that this result involves capital destruction from the higher level of firm failures.  The new capital that replaces the obsolete capital in the given market has had to come from somewhere.  So, while in the measured market, there is an exchange of higher wage employment for previously lower wage employment, the capital allocation required in order to create that exchange has some unmeasured cost elsewhere in the economy.  (edit:  Hmm.  Thinking about this some more, if this effect is dominant, it would mean that employment losses would largely come from outside the markets for low wage labor, because of this shift in future invested capital.  It might explain an ironic outcome where measures tracking specific minimum wage employment levels don't show diminished employment from MW hikes, but measures of the broader economy do.)

I have found employment losses associated with the period of time from slightly before an initial federal minimum wage hike to about two years after.  This seems like a quick reaction if only the 4th effect above is leading to significant net employment losses.  But, I suppose the interplay between exiting firms, entering firms, and long term changes in capital allocation could have a net effect that leads to a variety of time series patterns.

In terms of measuring long-term employment levels, a labor market with flexible wages would be expected to grow to utilize substantially all available supply.  This couldn't necessarily be said of a labor market with a price floor.  But, again, the financial and cultural processes would be so complex, that it would be difficult to measure.  I suppose that over the very long term it could be possible for a new equilibrium to lead to widespread employment opportunities for employees formerly working below the price floor.  For normal products, we would expect to see a reduction in the quantity supplied after the implementation of a price floor, but reduced supply wouldn't need to result in only an increase of unemployment.  Changes in schooling, pre-job training, and labor force participation, in general, could lead to fundamental changes in types of labor that people are capable of providing.  Opinions about results that complex are likely to fall back on priors.

Added:  Patrick Sullivan points to this research, which seems to find some of the employment declines from outcome #4, above.


  1. A very nice post! One can use your various possible outcomes to explain, for example, why firms like Walmart support raising the minimum wage.

    1. If Wal-Mart is paying slightly higher than minimum wage, and the dollar store across the street is paying minimum wage, then Wal-Mart would experience the gains of outcome #3 without the losses of outcome #2. That would explain their support.

      Depending on the design of the analysis, this sort of substitution of employment to competing firms with business models that have higher wages could mean that measures of employment within specific low wage firms would count the job losses, but might miss some of the mitigating job gains that would come out of the higher paying substitute firms, if some of the substitution goes to firms that aren't being tracked.

  2. You might want to read 'Effects of the Minimum Wage on Employment Dynamics' by Texas A&M's Jonathan Meer and Jeremy West;

    'For both theoretical and econometric reasons, we argue that the effect of the minimum wage should be more apparent in new employment growth than in employment levels. In addition, we conduct a simulation showing that the common practice of including state-specific time trends will attenuate the measured effects of the minimum wage on employment if the true effect is in fact on the rate of job growth. Using three separate state panels of administrative employment data, we find that the minimum wage reduces net job growth, primarily through its effect on job creation by expanding establishments. These effects are most pronounced for younger workers and in industries with a higher proportion of low-wage workers.'