Mastodon Cancel Infinity: Identities
Showing posts with label Identities. Show all posts
Showing posts with label Identities. Show all posts

Wednesday, September 10, 2014

On Congressional snack accounting

K. William Watson wrote an amusing little piece yesterday over at Cato. Riffing off a POLITICO article about Congressional staff bartering gifts of snack food, Watson highlighted the natural impetus to trade. In his own words he writes “[i]n order to be insufferably pedantic.”

On the contrary, Watson is insufficiently so. He writes
I think it’s worth pointing out how crazy it would be to restrict this trade. Should offices worry that they’re running a snack trade deficit? Are some snacks being unfairly traded at too low a price? Are other offices inadequately inspecting their exports for safety?
Obviously, the trade is highly regulated. Only certain gifts may be exchanged, and production of these snacks presumably fall under common regulatory schemes before entering into the staff barter system. Ultimately, though, I would like to focus on the question of the “snack trade deficit.” Offices should worry about the existence of such deficits– not because trade deficits do not matter; rather it is unclear what a legal snack-trade deficit might look like.

A trade deficit results from drawing down on currency or other capital stores to finance an excess of imports over exports. To a first approximation, then a snack trade deficit involves paying more cash for snacks obtained than the cash received for snacks given up. But the Congressional snack trade is regulated so no cash may change hands and everyone winds up with exactly the cash they started with. There can be no snack trade deficit so long as staffers merely barter snacks.

But snacks are not the only medium circulating in the Congressional snack trade. According to the POLITICO article, snacks have been exchanged for use of a cell phone charger. This is probably no big deal. Use of snacks for rewarding unpaid interns is probably a but more sketchy, but pales in comparison to the fact that there are unpaid interns. Ultimately, the critical question is what else might be exchanged for snacks?
Alabama Republican Rep. Robert Aderholt’s chief of staff, Brian Rell, said in an email that he doesn’t see a lot of trading going on; “it is more like a tailgate where food is readily available.”
To the extent this is true, great. Share and share alike. Perhaps there are offices which are snack-rich and others snack-poor and so there may be net transfers of snacks from rich to poor showing up in the snack accounts even if there are no snack trade deficits. But to the extent that there are any expectations for non-snack compensation offices should very much worry about large snack account imbalances.

Wednesday, February 19, 2014

Multiple Identities Can Deceive Even More

Consider a closed economy (no international transactions) so that \begin{equation} Y=C+I+G \end{equation} Savings is defined as unconsumed income, so national savings ($S$)-- which counts both private and government consumption-- is given by \begin{equation} S=Y-\left(C+G\right)=I \end{equation} Thus, the mystical “savings-investment identity” is born. In a closed economy, savings must equal investment. You like investment, don’t you? You believe that increasing the capital stock makes us more productive, right? So we should strive to increase national savings, don’t you think? And since we only can consume or save our income, we ought to consume less.

Not necessarily. It depends on the model. Suppose I gotta install microwave ovens. Custom kitchen deliveries!1 If you unexpectedly fail to buy a new oven then very likely I am stuck with a larger inventory and the immediate effect is to increase $I$ by the same amount as the fall in $C$, leaving $Y$ unchanged. Or maybe I will then fail to buy from the manufacturer who then slows production, lowering both $C$ and $Y$. These are not the only possible results, but the point is it matters because equation (2) says that lowering your consumption increased savings only in the former case.

And even then the increased investment came as an inventory increase-- which is nice because it allows for additional future consumption, but it doesn't actually increase productivity.

The bottom line is that while it is tempting to argue from an accounting identity, it is the story that matters. The identity just helps keep the story straight.

1 Back in 1984, someone totally could have kept his issues to himself instead of calling a guitarist on your MTV a “f****t”.

Identities Can Be Deceiving

Many an economist may be heard complaining that accounting identities are not models. And about this, many an economist is correct. Unfortunately, this sad refrain bears repeating. Accounting identities are not models. In fact, they can be downright misleading. Take for example, the basic national accounting identity defining GDP: \begin{equation}Y=C+I+G+X-M\end{equation} Clearly, imports $M$ count against GDP. But does an increase in imports lower GDP? It looks like imports reduce GDP, but the equation does not tell us this. To see why this might be so, let us divide expenditures into domestic production and foreign imports. That is, $C=C_d+C_m$, $I=I_d+I_m$, $G=G_d+G_m$, $X=X_d+X_m$, and finally $M=C_m+I_m+G_m+X_m$. Then \begin{equation}Y=C_d+I_d+G_d+X_d\end{equation} It appears that imports do not enter into GDP at all. Yet it is no less correct to write \begin{equation}Y=\left(C-C_m\right)+\left(I-I_m\right)+\left(G-G_m\right)+\left(X-X_m\right)\end{equation} which again suggests that imports reduce GDP one-for-one. Which equation is correct? They all are. They all provide exactly the same information, yet invite the reader to different interpretations. Equation (2) invites the reader to believe that $C_d$ is independent of $C_m$ (which may or may not be true.) Equation (3) invites the reader to believe that $C$ is independent of $C_m$ (which also may or may not be true.)

Rather, we require a model to tell us how the various parts move. For example, we might say $G$ and $X$ are fixed, but an additional dollar of $M$ increases $C$ by \$1.50 and reduces investment by \$1.00. The accounting identity would then tell us GDP falls by 50 cents for every dollar of additional imports. Is it true? The result depends on the model, and the model need not be reasonable. Suppose instead that an additional dollar of imports leads to a million dollars of additional consumption. Garbage in, garbage out. But the identity must hold.

As we will see in a future post, identities get more deceptive when used in combination with other identities.