How to Build an Economic Model

Let us see if we can translate my previous post on job selection into an economic model.  Start with a basic formula:

(1) AcceptOffer = a(1) + a(2)*w + a(3)*b + a(4)*oa + a(5)*t

where a is a constant, w is wages, b is benefits, oa is “opportunity for advancement” and t is treatment received in the workplace.

The first observation we make is that several of these variables are difficult to quantify—and even more difficult to objectify. So let’s start with the easy ones.

w is very identifiable: reported (on a per capita aggregate basis), subject to enforcement penalties (e.g., minimum wage laws), and used in “downstream applications” (e.g., tax filings) and therefore relatively verifiable.

b is (1) known to be non-negative and (2) often variable within, let alone between, organizations. (Vacation time, sick days, insurances offered and costs to the employee all may vary depending on level, time of service, location of office, etc.)

This could present a problem, but here we can use standard economic theory to our advantage. We do not know the amount of b, but we can assume that the employer is rational, and is offering a total compensation to the worker that s/he expects will be less than or equal to the marginal product of that person’s labor. We therefore can reasonably assume that b is related to w. If we then review the available aggregate data we can approximate that benefits offered will be approximately a certain percentage of w—and that workers will assume that assumption (and, in most cases, verify that assumption within a margin of error) before accepting the job.

We then restate the equation as

(2a) AcceptOffer = a(1) + a(2’)*w’ + a(4)*oa + a(5)*t

where w’ is the weighted combination of w and b above, and a(2’) is the restated coefficient.

If we then assume that all parties have full information of the ratio of wages to benefits, then a(2’) = a(2)=a(3), so we simplify to:

(2b) AcceptOffer = a(1) + a(2)*w’ + a(4)*oa + a(5)*t

We now have to consider opportunities for advancement and treatment. Here, we have two problems that are difficult, possibly insurmountable, for modeling.

The first is a lack of measurability. There are no public records for “didn’t get promoted.” Nor, except in extreme cases, is there a way to measure treatment by supervisors. The data that might be available&mdassh;lawsuits, official complaints, even Human Resources files (for which there are significant privacy considerations)—is all negative and, accordingly, skewed (biased). This is because (a) ninety percent or so of all workers and/or bosses will never have a complaint filed against them and (b) the ability to file a complaint may be present because the general work atmosphere is more amenable to filing one than not, so the presence of a complaint is not in itself a good or bad thing for the overall measure.

The second is that tolerances vary by person. To use an absurd example, people who use “Every Breath You Take” for their wedding may be more likely to tolerate attentions that others view as harassment. Similarly, forcing people to clock out for a “smoke break” will be viewed differently depending upon whether one is a smoker or not. General policies are just that—general.

So, if we are building an economic model, we must come up with a reasonable approximation of these last two variables. The most direct way to do this is the standard method: assume each individual has their own Utility Curve, and “prices” accordingly.

Based on their preferences and options, then, we map the compensation required to offset negative consequences from oa and t. While the variables still are not directly observable, we can make a simplifying assumption:

Assume that the compensation required to do the work is a factor of w’.

Have to work in the sewer system? Change w’ to compensate. Need to work the night shift and/or weekends? Same type of adjustment. Boss clearly favors buxom blondes and you’re a petite redhead? Adjust current salary requirements to compensate for lowered opportunity for advancement/promotion. You’re a b.b. who will have trouble getting work done because the boss will harass you? Adjust accordingly.

We assume—due to the constraint: a lack of available data—that we can reduce “a(4)*oa + a(5)*t” to some proportion of w that will compensate the worker for the environment into which they are being placed. If we further assume that the worker has complete information as to hisser preferences, the worker will not accept a job that does not offer that level of compensation.

So we can restate equation 2(b) using the Utility Curve assumption. Assume

(3a) a(6)*w” =a(4)*oa + a(5)*t

such that w” also proportionate to w(and therefore w’ as well) and a(6) is the coefficient selected by the individual that makes the offered wage compensatory to the opportunities for advancement and expected treatment on a Present Value basis.

We can then reduce equation (2b) to

(3b) AcceptOffer = a(1) + a(2)*w’ + a(6)*w”

or, given that (a) w” is proportionate to w and w’ and (b) that the multiplier in most cases is 1, and (c) the constant (e.g., signing bonus) can be assumed without loss of generality to be 0,

(3b) AcceptOffer = clip_image002[10]

to indicate that the value varies with individuals.

To concretize the example, assume that a redhead and a blonde, as above, are both offered a job. Assume further that the redhead’s compensation requirement—lower-but-still-positive opportunity for advancement—is lower than the blonde’s for will-be-harassed-and-work-will-be-impeded. That is

clip_image002(r) < clip_image002[4](b)

There are four possibilities:

  1. The offered wage will be belowclip_image002[12](r), in which case neither will accept the job
  2. The offered wage will be below clip_image002[14](b) but above clip_image002[16](r), in which case one of the two positions will be filled
  3. The offered wage will be above clip_image002[18](b), in which case both will accept the offer and the company will have offered a higher wage than was required to fill both positions. (That the offer is what the company believes will be the employees’ s marginal product of labor [MPL] is a collateral issue.), or
  4. The company will negotiate with each, offering the redhead clip_image002[20](r) and the blonde clip_image002[22](b), and everyone will be happy—so long as initial expectations were accurate (or, if you prefer, the new employees both had full information).

Note also that there is a learning process for both the applicant and the employer. Offers and demands will be adjusted based on historic data (if both decline the offer, the next candidates of similar background will be offered more, and perceptions of growth (improvements in experience and/or education by the worker).

If we generalize this, we note that there is a distribution of clip_image002[24] (due to Individual Preferences). If we further make simplifying assumptions—e.g., a normal distribution of clip_image002[26] among the population—we come to the conceit of the “reservation wage,” and all the economic literature that is attendant upon it.

So that is how you build an economic model.  The question then becomes: how do you use it? A relatively short (though it does incorporate a micro model) discussion of that continues below the fold.

The problem—if it is one (I’m inclined to argue it is; YMMV)—is that, having built a model in which all the proxying assumptions are “simplified” into a single variable, we lose some granularity, having made a trade-off for the sake of measurement.

Accordingly, a change in the “reservation wage” may not in itself tell us whether the real wage has gone up or the work environment has become, on balance, more or less acceptable.

Again, an example, one that will be familiar to students of microeconomics. You are given two choices: (1) you can receive $100 right here and now or (2) you can travel a known distance (say, five miles)—with a finite chance of death or injury—and receive $1,000,000 on completion.

Surroundings, at this point, matter. If the five miles traveled is as an American soldier in full uniform walking outside of the Green Zone, you might well choose $100. Even when you are native to the area, the choice may vary: walking five miles through one gang’s territory is a different option than traveling that distance through different territories. Or even a pure environmental matter may have an effect: Walking five miles through a desert with no canteen, or having to swim five miles from shore in a dangerous waters, is not the same risk as walking five miles down an unpaved dirt road in the middle of the day. Even if you would be required “only” to walk down a heavily-used interstate highway with no shoulder or sidewalks, discretion may be the better part of valor.

Over time, through the “learning process” (op cit. Arrow, 1962, as all good op cits must), the dollars offered will be adjusted so that the payouts balance on a risk-adjusted basis. (Collaterally, there may be other reasons for the greater payouts; signaling by any other name.)

Now suppose the landscape changes. There is a canteen every half-mile in the desert. A gang is run out of its territory, or takes over another’s territory. The Green Zone becomes larger.

The balance has changed; the risk is different. The job is demonstrably different, and therefore requires lower (higher) compensation. But the difference has nothing directly to do with the base salary/benefits requirement and everything to do with the overall attractiveness and/or treatment received.

If we were to forget that, we would conclude that there is more demand for the job itself, and therefore people are willing to take a lower salary. If, on the other hand, we keep in mind that there are more factors to the reservation wage than just the salary itself, we realize that producing a more pleasant work atmosphere is beneficial to our firm, as it enables us both to present a good face to clients and to reduce our cost of labor.

The first type of economist probably should be avoided, as he adds very little value to the discussion of how to use the model.