The recent minimum wage debates among the various campaigns are pretty disconnected from a model of how the damn thing actually works in the real world. In part, that’s a function of campaigns not doing nuance, but it’s also because there is no model that economists agree on as per why the empirical results on minimum wage increases are so different from the predictions of the classical model.

As I’ll show in a moment, that model predicts a lot of unemployment and you just don’t see that following moderate minimum wage increases. To be clear, I’m not arguing you don’t see any job loss. But you don’t see anything like the predictions of minimum-wage opponents: the number of beneficiaries of the increases virtually always far surpasses anyone hurt by them.

Start with the classical, textbook model. Now, as you’ve heard me say before, “all models are wrong; some models are useful.” But when it comes to the minimum wage, this model is both wrong and useless. If you’re in an econ class and your professor presents this model of the minimum wage and nothing more, she is guilty of malpractice.

The X-axis measures employment (N) and wages (W) are on the Y-axis. Demand curves generally slope down, a negative function of the wage rate, and vice-versa for supply curves. The equilibrium wage and employment levels are at the intersection of D and S. Impose a minimum wage above the equilibrium level and workers want to supply more labor than employers demand, so the wage mandate generates unemployment.

Why is this model so off? Staying within the competitive framework, the first variation adds dynamics, showing how a positive demand shock can absorb the wage increase. D_0 is the original demand curve, but Paul Krugman gets elected president and introduces a massive infrastructure program, such that the demand curve moves out to D_1, absorbing the wage increase with no unemployment.

This is, of course, fanciful, but to the extent that higher minimum wages get spent in places where consumer demand is constrained by working poverty, the model may be telling us something about why moderate increases have their intended impact. The same dynamic is likely operative when immigration raises labor supply: the demand the immigrants generate helps to offset their added supply.

Of course, a negative demand shock would have the opposite impact. Yet even when wage increases have been introduced in down economies (e.g., 1991), we’ve not seen large disemployment effects, so this model too is surely incomplete. Also, demand increases can be accompanied by supply increases (I’m holding supply constant in this second figure), and that too will just get you back to the similar, doleful dynamics seen in Figure 1.

[During the 1990s, the minimum wage and the EITC were increased, and welfare reform was introduced. In the context of these first two figures, that might lead you to expect a large supply shock, lowering wages and boosting employment. Except what actually occurred was both low wages and low-wage employment went up significantly. Thus, in the context of these models, supply expanded but demand expanded further. Or, as we say around here: full employment solves a lot of problems.]

Still sticking with the model, we can introduce some ideas into the diagram that comport a bit more with reality. In the low-wage labor market, demand has consistently been found to be highly inelastic, meaning workers/employers are not that responsive in terms of employment to changes in wages (dlog(emp)/dlog(wage)=small number like -0.1 to -0.3, or something…). Let’s assume supply is pretty inelastic too, which at least from the perspective of low-income workers (versus kids of wealthier families) seems plausible, since they’ve gotta work as opposed to choosing whether or not to work.

When you draw inelastic supply and demand curves, you end up predicting a lot less unemployment. Given the confidence intervals (statistical uncertainty) around our econometric estimates, you can see how if this model is more accurate, significant estimates of job loss effects are hard to pull out of the data. Which they are, suggesting this version may well be trying to tell us something about low-wage workers and their employers’ tempered responsiveness to increases in the wage floor.

In some cases, it has been observed that employment increases after the minimum wage is raised. There’s a model for that too, called a monopsony labor market, meaning a job market with one employer (details here; figure shown below). Compared to the models shown thus far, where wages are set at the level of the macroeconomy (vs. the level of the firm), in monopsony, the big employer sets the wage. If she sets it too low, employment and output can be inefficiently low. Since the employer faces an upward-sloping supply curve, when she raises the wage, she pulls more people into work (see the link for the meaning of the other labels in the model).

The monopsony model may sound arcane—the classic example is the one-company coal town—but it may not be too much of a reach to conclude that the low-wage labor market in a given town or city works kind of like this. As the link concludes, “the minimum wage is increasingly effective in improving efficiency, the more the market is controlled by buyers. A minimum wage is increasingly problematic, the more the market is competitive.” The fact that employment has not responded to wage increases as in the competitive market (Figure 1) might confirm your suspicion, as it does mine, that the low-wage labor market is typically not in equilibrium and is dominated by buyers (of labor), like fast-food restaurants, who may well operate in ways that mimic monopsony.

In a Republican debate the other night, Donald Trump, when asked whether the minimum wage should be raised, answered “no” because, he asserted, our problem is that wages are too high. His colleagues generally seemed to agree with him.

The next figure plots this (cockamamie) idea. W_0–the current minimum wage–is too damn high, and is thus restricting job growth. Take it down to the intersection of supply and demand, and you end up with more jobs. But here’s a fun wrinkle: deport 11 million unauthorized immigrants—7 percent of your workforce—and build a wall, thus whacking the heck out of your labor supply (as seen by the inward shift of S_0 to S_1) and the competitive model predicts higher wages but fewer jobs. If the negative supply shock is strong enough, it can fully offset the initial wage loss such that the post-wall wage of W_2 equals the original minimum wage.

This part of the exercise proves that much as you shouldn’t look directly at a solar eclipse, thinking through Trumponomics is ill-advised.

Otherwise, do we learn anything from all this modeling? Most importantly, the competitive model as conventionally drawn is misleading. Economic models vastly simplify the economy, which can yield some insights, such as the dynamic, inelasticity, and monopsony points above. But at end of the day, you really don’t want to push any of these too far. In economics, when the theory doesn’t match the evidence, trust the evidence.

(h/t, Ben S for help with figures.)