# Monthly Archive for November, 2009

### Food stamps in America

Here is a NY Times article doing what the NY Times does well, this time looking at the use of food stamps across America.  Here are the basic details (emphasis is all mine):

With food stamp use at record highs and climbing every month, a program once scorned as a failed welfare scheme now helps feed one in eight Americans and one in four children.

It has grown so rapidly in places so diverse that it is becoming nearly as ordinary as the groceries it buys. More than 36 million people use inconspicuous plastic cards for staples like milk, bread and cheese
[…]
the program is now expanding at a pace of about 20,000 people a day. There are 239 counties in the United States where at least a quarter of the population receives food stamps
[…]
Nationwide, food stamps reach about two-thirds of those eligible, with rates ranging from an estimated 50 percent in California to 98 percent in Missouri. Mr. Concannon urged lagging states to do more to enroll the needy, citing a recent government report that found a sharp rise in Americans with inconsistent access to adequate food.
[…]
Unemployment insurance, despite rapid growth, reaches about only half the jobless (and replaces about half their income), making food stamps the only aid many people can get — the safety net’s safety net.

Support for the food stamp program reached a nadir in the mid-1990s when critics, likening the benefit to cash welfare, won significant restrictions and sought even more. But after use plunged for several years, President Bill Clinton began promoting the program, in part as a way to help the working poor. President George W. Bush expanded that effort, a strategy Mr. Obama has embraced.

The revival was crowned last year with an upbeat change of name. What most people still call food stamps is technically the Supplemental Nutrition Assistance Program, or SNAP.
[…]
Now nearly 12 percent of Americans receive aid — 28 percent of blacks, 15 percent of Latinos and 8 percent of whites. Benefits average about \$130 a month for each person in the household, but vary with shelter and child care costs.
[…]
Use among children is especially high. A third of the children in Louisiana, Missouri and Tennessee receive food aid. In the Bronx, the rate is 46 percent. In East Carroll Parish, La., three-quarters of the children receive food stamps.

A recent study by Mark R. Rank, a professor at Washington University in St. Louis, startled some policy makers in finding that half of Americans receive food stamps, at least briefly, by the time they turn 20. Among black children, the figure was 90 percent.

I’m not sure how I feel about food stamps.  The classically-trained economist in me wants to point out that money is fungible, so that:

• for people that, if they were given the equivalent amount of cash, would have bought the same amount of food,  the program largely serves to impose unnecessary administrative costs over a simple cash transfer and places a stigma on the recipients; and
• for people that, if they were given the equivalent amount of cash, would have bought less food, the program (arguably) willfully deprives them of welfare in addition to the administrative costs and stigma.

On the other hand, we have that:

• for the (presumed) minority of recipients that have problems with drug or alcohol abuse or have a family member that has problems, receiving aid in the form of food stamps helps ensure that there’s still food on the table (although I do assume that there is a secondary market in food stamps, not to mention in food itself);
• for the recipients living in high-crime areas, the incentive to steal food stamps is lower than that to steal cash (even if there is a secondary market, it’ll be annoying to deal with and won’t give 100 cents on the dollar), so receiving food stamps is safer;
• by giving people food stamps instead of cash, you reduce the possibility of a sense of entitlement emerging (one of the major problems in countries, like Britain, with comprehensive welfare systems is that recipients can come to consider the aid they receive as their right and not just (hopefully temporary) assistance); and
• America, for some reason that is mostly beyond me, has always had trouble facing up to the moral imperative to assist those in genuine need and presenting that assistance as food stamps seems to have granted it some political cover.

Anyway, the NY Times piece comes with some more fantastic graphics.  Here are two snapshots (click-through on either of them to get to the good stuff on the NY Times website):

Just awesome.

### On interest rates

In what Tyler Cowen calls “Critically important stuff and two of the best recent economics blog posts, in some time,” Paul Krugman and Brad DeLong have got some interesting thoughts on US interest rates.  First Krugman:

On the face of it, there’s no reason to be worried about interest rates on US debt. Despite large deficits, the Federal government is able to borrow cheaply, at rates that are up from the early post-Lehman period … but well below the pre-crisis levels:

Underlying these low rates is, in turn, the fact that overall borrowing by the nonfinancial sector hasn’t risen: the surge in government borrowing has in fact, less than offset a plunge in private borrowing.

So what’s the problem?

Well, what I hear is that officials don’t trust the demand for long-term government debt, because they see it as driven by a “carry trade”: financial players borrowing cheap money short-term, and using it to buy long-term bonds. They fear that the whole thing could evaporate if long-term rates start to rise, imposing capital losses on the people doing the carry trade; this could, they believe, drive rates way up, even though this possibility doesn’t seem to be priced in by the market.

What’s wrong with this picture?

First of all, what would things look like if the debt situation were perfectly OK? The answer, it seems to me, is that it would look just like what we’re seeing.

Bear in mind that the whole problem right now is that the private sector is hurting, it’s spooked, and it’s looking for safety. So it’s piling into “cash”, which really means short-term debt. (Treasury bill rates briefly went negative yesterday). Meanwhile, the public sector is sustaining demand with deficit spending, financed by long-term debt. So someone has to be bridging the gap between the short-term assets the public wants to hold and the long-term debt the government wants to issue; call it a carry trade if you like, but it’s a normal and necessary thing.

Now, you could and should be worried if this thing looked like a great bubble — if long-term rates looked unreasonably low given the fundamentals. But do they? Long rates fluctuated between 4.5 and 5 percent in the mid-2000s, when the economy was driven by an unsustainable housing boom. Now we face the prospect of a prolonged period of near-zero short-term rates — I don’t see any reason for the Fed funds rate to rise for at least a year, and probably two — which should mean substantially lower long rates even if you expect yields eventually to rise back to 2005 levels. And if we’re facing a Japanese-type lost decade, which seems all too possible, long rates are in fact still unreasonably high.

Still, what about the possibility of a squeeze, in which rising rates for whatever reason produce a vicious circle of collapsing balance sheets among the carry traders, higher rates, and so on? Well, we’ve seen enough of that sort of thing not to dismiss the possibility. But if it does happen, it’s a financial system problem — not a deficit problem. It would basically be saying not that the government is borrowing too much, but that the people conveying funds from savers, who want short-term assets, to the government, which borrows long, are undercapitalized.

And the remedy should be financial, not fiscal. Have the Fed buy more long-term debt; or let the government issue more short-term debt. Whatever you do, don’t undermine recovery by calling off jobs creation.

The point is that it’s crazy to let the rescue of the economy be held hostage to what is, if it’s an issue at all, a technical matter of maturity mismatch. And again, it’s not clear that it even is an issue. What the worriers seem to regard as a danger sign — that supposedly awful carry trade — is exactly what you would expect to see even if fiscal policy were on a perfectly sustainable trajectory.

Then DeLong:

I am not sure Paul is correct when he says that the possible underlying problem is merely “a technical matter of maturity mismatch.” The long Treasury market is thinner than many people think: it is not completely implausible to argue that it is giving us the wrong read on what market expectations really are because long Treasuries right now are held by (a) price-insensitive actors like the PBoC and (b) highly-leveraged risk lovers borrowing at close to zero and collecting coupons as they try to pick up nickles in front of the steamroller. And to the extent that the prices at which businesses can borrow are set by a market that keys off the Treasury market, an unwinding of this “carry trade”–if it really exists–could produce bizarre outcomes.

Bear in mind that this whole story requires that the demand curve slope the wrong way for a while–that if the prices for Treasury bonds fall carry traders lose their shirts and exit the market, and so a small fall in Treasury bond prices turns into a crash until someone else steps in to hold the stock…

For reference, here are the time paths of interest rates for a variety of term lengths and risk profiles (all taken from FRED):

To my own mind, I’m somewhat inclined to agree with Krugman.  While I do believe that the carry trade is occurring, I suspect that it’s effects are mostly elsewhere, or at least that the carry trade is not being played particularly heavily in long-dated US government debt relative to other asset markets.

Notice that the AAA and BAA 30-year corporate rates are basically back to pre-crisis levels and that the premium they pay over 30-year government debt is also back to typical levels.  If the long-dated rates are being pushed down to pre-crisis levels solely by increased supply thanks to the carry trade, then we would surely expect the quantity of credit to also be at pre-crisis levels.  But new credit issuance is down relative to the pre-crisis period.  Since the price is largely unchanged, that means that both demand and supply of credit have shrunk – the supply from fear in the financial market pushing money to the short end of the curve and the demand from the fact that there’s been a recession.

### Changing the typesetting margins in Scientific Workplace

At least half of the LSE economics department uses Scientific Workplace, but an absurdly large fraction of all PDFs they produce have two-inch margins so they end up wasting half the page.

I finally got sufficiently annoyed to discover how to change it:

1. Open a SW tex file
2. Under the ‘Typeset’ menu, choose ‘Options and Packages…’
3. Under the ‘Packages’ tab, add the ‘geometry’ package
4. Under the ‘Typeset’ menu, choose ‘Preamble…’
5. Add a line at the end specifying the margins.

For example:

\geometry{left=1in,right=1in,top=1in,bottom=1in}

Units of measurement available are listed on the webpage where I got this:  http://www.mackichan.com/index.html?techtalk/370.htm

### Approximating a demand function with shocks to the elasticity of demand

Entirely for my own reference …

A demand function commonly used in macroeconomics is the following, derived from a Dixit-Stiglitz aggregator and exhibiting a constant own-price elasticity of demand ($$\gamma$$):

$$!Q_{it}=\left(\frac{P_{it}}{P_{t}}\right)^{-\gamma}Q_{t}$$

A demand-side shock can then be modelled as a change in the elasticity of demand:

$$!Q_{it}=\left(\frac{P_{it}}{P_{t}}\right)^{-\gamma D_{t}}Q_{t}$$

Where $$\ln\left(D_{t}\right)$$ is, say, Normally distributed and plausibly autocorrelated.  We can rewrite this as a function of (natural) log deviations from long-run trends:

$$!Q_{it}=\overline{Q_{t}}e^{q_{t}-\gamma e^{d_{t}}\left(p_{it}-p_{t}\right)}$$

Where:

• Variables with a bar above them are long-run trends:  $$\overline{X_{it}}$$
• Lower-case variables are natural log deviations from their long run trends (so that for small deviations, they may be thought of as the percentage difference from trend):  $$x_{it}=\ln\left(X_{it}\right)-\ln\left(\overline{X_{it}}\right)$$
• The long-run trend of all prices is to equal the aggregate price:  $$\overline{P_{it}}=\overline{P_{t}}$$
• The long-run trend of $$D_{t}$$ is unity

We’ll construct a quadratic approximation around $$q_{t}=p_{it}=p_{t}=d_{t}=0$$ but, first, a table of partial derivatives for a more general function:

 Function Value at $$x=y=z=0$$ $$f\left(x,y,z\right)=ae^{x+bye^{z}}$$ $$a$$ $$f_{x}\left(x,y,z\right)=ae^{x+bye^{z}}$$ $$a$$ $$f_{y}\left(x,y,z\right)=abe^{x+bye^{z}+z}$$ $$ab$$ $$f_{z}\left(x,y,z\right)=abye^{x+bye^{z}+z}$$ $$0$$ $$f_{xx}\left(x,y,z\right)=ae^{x+bye^{z}}$$ $$a$$ $$f_{yy}\left(x,y,z\right)=ab^{2}e^{x+bye^{z}+2z}$$ $$ab^{2}$$ $$f_{zz}\left(x,y,z\right)=abye^{x+bye^{z}+z}+ab^{2}y^{2}e^{x+bye^{z}+2z}$$ $$0$$ $$f_{xy}\left(x,y,z\right)=abe^{x+bye^{z}+z}$$ $$ab$$ $$f_{xz}\left(x,y,z\right)=abye^{x+bye^{z}+z}$$ $$0$$ $$f_{yz}\left(x,y,z\right)=abe^{x+bye^{z}+z}+ab^{2}ye^{x+bye^{z}+2z}$$ $$ab$$

So that in the vicinity of $$x=y=z=0$$, the function $$f\left(x,y,z\right)$$ is approximated by:

$$!f\left(x,y,z\right)\simeq a + a\left(x+by\right) + a\left[\frac{1}{2}\left(x+by\right)^{2}+byz\right]$$

From which we can infer that:

$$!Q_{it}\simeq \overline{Q_{t}}\left[1+\left(q_{t}-\gamma\left(p_{it}-p_{t}\right)\right) + \frac{1}{2}\left(q_{t}-\gamma\left(p_{it}-p_{t}\right)\right)^{2}-\gamma\left(p_{it}-p_{t}\right)d_{t}\right]$$

If introduced to a profit function, the first-order components ($$q_{t}-\gamma\left(p_{it}-p_{t}\right)$$) would vanish as individual prices will be optimal in the long run.

Update (20 Jan 2010): Added the half in each of the last equations.