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## 24.1 Modeling Reality

### Learning Objective

1. Why are structural models generally superior to reduced-form models?

We’ve learned in the last few chapters that monetary policy is not the end-all and be-all of the economy or even of policymakers’ attempts to manipulate it. But we knew that before. The question before us is, Given what we know of IS-LM and AS-AD, just how important is monetary policy? And how do we know? We’ve got theories galore—notions about how changes in sundry variables, like interest rates, create certain outcomes, like changes in prices and aggregate output. But how well do those theories describe reality? To answer those questions, we need empirical evidence, good hard numbers. We also need to know how scientists and social scientists evaluate such evidence.

Structural models explicitly link variables from initial cause all the way to final effect via every intermediate step along the causal chain. Reduced-form evidence makes assertions only about initial causes and ultimate effects, treating the links in between as an impenetrable black box. The quantity theory makes just such a reduced-form claim when it asserts that, as the money supply increases, so too does output. In other words, the quantity theory is not explicit about the transmission mechanismsHow A leads to B in a causal chain; how A is transmitted, so to speak, to B. of monetary policy. On the other hand, the assertion that increasing the money supply decreases interest rates, which spurs investment, which leads to higher output, ceteris paribus, is a structural model. Such a model can be assessed at every link in the chain: MS up, i down, I up, Y up. If the relationship between MS and Y begins to break down, economists with a structural model can try to figure out specifically why. Those touting only a reduced-form model will be flummoxed. Structural models also strengthen our confidence that changes in MS cause changes in Y.

Because they leave so much out, reduced-form models may point only to variables that are correlated, that rise and fall in tandem over time. Correlation, alas, is not causation; the link between variables that are only correlated can be easily broken. All sorts of superstitions are based on mere correlation, as their practitioners eventually discover to their chagrin and loss,http://www.dallasobserver.com/2005-09-08/dining/tryst-of-fate/ like those who wear goofy-looking rally caps to win baseball games.http://en.wikipedia.org/wiki/Rally_cap Reverse causation is also rampant. People who see a high correlation between X and Y often think that X causes Y when in fact Y causes X. For example, there is a high correlation between fan attendance levels and home team victories. Some superfanshttp://en.wikipedia.org/wiki/Bill_Swerski's_Superfans take this to “prove” that high attendance causes the home team to win by acting as a sixth, tenth, or twelfth player, depending on the sport. Fans have swayed the outcome of a few games, usually by touching baseballs still in play,http://www.usatoday.com/sports/columnist/lopresti/2003-10-15-lopresti_x.htm but the causation mostly runs in the other direction—teams that win many games tend to attract more fans.

Omitted variables can also cloud the connections made by reduced-form models. “Caffeine drinkers have higher rates of coronary heart disease (CHD) than people who don’t consume caffeine” is a reduced-form model that probably suffers from omitted variables in the form of selection biases. In other words, caffeine drinkers drink caffeine because they don’t get enough sleep; have hectic, stressful lives; and so forth. It may be that those other factors give them heart attacks, not the caffeine per se. Or the caffeine interacts with those other variables in complex ways that are difficult to unravel without growing human beings in test tubes (even more alarming!).

### Stop and Think Box

A recent reduced-form study shows a high degree of correlation between smoking marijuana and bad life outcomes: long stints of unemployment, criminal arrests, higher chance of disability, lower lifetime income, and early death. Does that study effectively condemn pot smoking?

Not nearly as much as it would if it presented a structural model that carefully laid out and tested the precise chain by which marijuana smoking causes those bad outcomes. Omitted variables and even reverse causation can be at play in the reduced-form version. For example, some people smoke pot because they have cancer. Some cancer treatments require nasty doses of chemotherapy, the effect of which is to cause pain and reduce appetite. Taking a toke reduces the pain and restores appetite. Needless to say, such people have lower life expectancies than people without cancer. Therefore, they have lower lifetime income and a higher chance of disability and unemployment. Because not all states have medical marijuana exceptions, they are also more liable to criminal arrest. Similarly, unemployed people might be more likely to take a little Mary Jane after lunch or perhaps down a couple of cannabis brownies for dessert, again reversing the direction of causation. A possible omitted variable is selection bias: people who smoke pot might be less educated than those who abstain from the weed, and it is the dearth of education that leads to high unemployment, more arrests, and so forth. Unfortunately, bad science like this study pervades public discourse. Of course, this does not mean that you should go get yourself a blunt. Study instead. Correlation studies show that studying . . . .

### Key Takeaways

• Structural models trace the entire causal chain, step by step, allowing researchers to be pretty confident about the direction of causation and to trace any breakdowns in the model to specific relationships.
• Reduced-form models link initial variables to supposed outcomes via an impenetrable black box.
• The problem is that correlation does not always indicate causation. X may increase and decrease with Y, although X does not cause Y because Y may cause X (reverse causation), or Z (an omitted variable) may cause X and Y.
• Reduced-form models can and have led to all sorts of goofy conclusions, like doctors kill people (they seem to be ubiquitous during plagues, accidents, and the like) and police officers cause crime (the number on the streets goes up during crime waves, and they are always at crime scenes—very suspicious). In case you can’t tell, I’m being sarcastic.
• On the other hand, reduced-form models are inexpensive compared to structural ones.