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# Pooling the Effects Over Time

The following is a variation on a theme that I struck in this post of March 6, 2013.

Suppose you’re standing at the edge of a ordinary-sized swimming pool – say, the sort of pool that’s common in neighborhood community centers.  The pool is outdoors, and there are people swimming in it and kids jumping into it and crawling out of it.  As all of this activity is going on you gently drop into the pool a normal-sized brick.  Using the best available measuring instrument, you likely cannot discover that the dropping of the brick into the pool raised the level of the water in the pool.

For one thing, the brick is very small relative to the volume of water in the pool – so small that the best available measurement instrument is unable to detect its effect on the water level even under the best controlled conditions.  But these conditions aren’t controlled.  All of the activity taking place simultaneously with your dropping the brick into the pool also affects the water level.  Therefore, you do not conclude from the fact that your quantitative measurement detected no increase in the pool’s water level that dropping a brick into a pool does not cause a pool’s water level to rise.

As that March 2013 post of mine argued, it would be naive empiricism of the most inexcusable sort to deny – based upon such evidence – that an object with mass added to a pool filled with water causes the water level of the pool to rise.  Likewise, it would be unscientific to conclude that the question of whether or not adding an object with mass to a pool filled with water is ‘an empirical one’ (implying that sometimes adding an object with mass to a pool filled with water does, and sometimes it does not, cause the water level of the pool to rise).

(Note that the more-precisely stated prediction about reality is that adding a object with mass to a pool filled with water causes the water level of the pool to be higher than that level would otherwise be had the object with mass not been added to the pool.  The prediction – like all predictions – is embedded in a set of ceteris paribus assumptions.)

…..

Now let’s alter the hypothetical.  Suppose that you add bricks into this pool by dropping in one brick every minute.  After each brick-drop, you measure the effect of that individual brick-drop on the pool’s water level.  Each time, the detected change in the pool’s water level is zero.  You spend a full twelve hours consistently dropping bricks into this pool in this manner (one each minute) and each time measuring the effect on the pool’s water level of your most-recent brick-drop.  Again, you detect no effect on the pool’s water level of each isolated brick-drop.  No one brick-drop causes the measurable water level of the pool to be higher.

At the end of your twelve-hour escapade, you’ve dropped into the pool a total of 720 bricks.  Do you conclude, based upon the fact that after each isolated brick drop you detected no rise in the pool’s water level, that adding 720 bricks into the pool does not cause the pool’s water level to rise?  Of course not.  You realize that if you’d dropped all 720 bricks into the pool at once, you’d have gotten as a result a measurable, and not insignificant, increase in the pool’s water level.

I believe that discussions of minimum-wage increases often involve an error similar to the one that would be made were you to conclude, after dropping a total of 720 bricks into a pool and detecting after each individual drop no rise in the pool’s water level, that adding 720 bricks into a pool doesn’t cause the pool’s water level to rise.  Not only, of course, does reason inform us that each individual brick-drop causes the pool’s water level to rise (even if a careful attempt to measure the effect of an individual brick-drop detects no effect), but the appropriate baseline for measuring the effect of 720 bricks added to the pool is the level of the water before a single brick has been added.

In the United States, national minimum-wage legislation has been around since 1938 (or, depending on how you assess such things, even earlier: 1931), and has been increased (by my count) 24 different times.  It might well be that the disemployment effect of each individual minimum-wage hike was small (perhaps even undetectable), but it does not follow from this accession of small and undetectable effects – each one the result of a measurement conducted after each isolated rise in the minimum wage – that the disemployment effect of the minimum wage is small.