Just DDo It: A Depression Regression
The simplest DD calculation involves only four numbers, as in equations (5.1) and (5.2). In practice, however, the DD recipe is best cooked with regression models fit to samples of more than four data points, such as the 12 points plotted in Figure 5.2. In addition to allowing for more than two periods, regression DD neatly incorporates data on more than two cross-sectional units, as we’ll see in a multistate analysis of the MLDA in Section 5.2. Equally important, regression DD facilitates statistical inference, often a tricky matter in a DD setup (for details, see the appendix to this chapter).
The regression DD recipe associated with Figure 5.2 has three ingredients:
(i) A dummy for the treatment district, written TREATd, where the subscript d reminds us that this varies across districts; TREATd controls for fixed differences between the units being compared.
(ii) A dummy for post-treatment periods, written POSTt, where the subscript t reminds us that this varies over time; POSTt controls for the fact that conditions change over time for everyone, whether treated or not.
(iii) The interaction term, TREATd x POSTt, generated by multiplying these two dummies; the coefficient on this term is the DD causal effect.
We think of the Caldwell-era experimental treatment as provision of easy credit in the face
of a liquidity crisis, so TREATd equals one for data points from the Sixth District and zero otherwise. The bank failure rate slowed after 1931 as the Caldwell crisis subsided. In the 1930s, however, there were no zombie banks: dead banks were gone for good. The Caldwell-era failures resulted in fewer banks open in the years 1932-1934 as well, even though the St. Louis Fed had by then begun to lend freely. We therefore code POSTt to indicate all the observations from 1931 onward. Finally, the interaction term, TREATd x POSTt, indicates observations in the Sixth District in the post-treatment period. More precisely, TREATd x POSTt indicates observations from the Sixth District in periods when the Atlanta Fed’s response to Caldwell mattered for the number of active banks.
Regression DD for the Mississippi experiment puts these pieces together by estimating
Ydl = a+pTREATd + yPOSTt
+ SrDD(TREATd x POST,) + edt (5.3)
in a sample of size 12. This sample is constructed by stacking observations from both districts and all available years (6 years for each district). The coefficient on the interaction term, SrDD, is the causal effect of interest. With only two periods, as in Figure 5.1. estimates of &DD and SrDD coincide (a consequence of the properties of dummy
variable regression outlined in the appendix to Chapter 21. With more than two periods, as in Figure 5.2. estimates based on equation (5.31 should be more precise and provide a more reliable picture of policy effects than the simple four-number DD recipe.-
Fitting equation (5.31 to the 12 observations plotted in Figure 5.2 generates the following estimates (with standard errors shown in parentheses):
Ydl = 167 – 29 TREATd – 49 POST,
+ 20,5 (TREAT, x POST,) + edt.
These results suggest that roughly 21 banks were kept alive by Sixth District lending. This estimate is close to the estimate of 19 banks saved using the four-number DD recipe. The standard error for the estimated SrDD is about 11, so 21 is a marginally significant result, the best we can hope for with such a small sample.
The Atlanta Fed very likely saved many Sixth District banks from failure. But banks are not valued for their own sakes. Did the Atlanta Fed’s policy of easy money support real economic activity, that is, non-bank businesses and jobs? Statistics on business activity within states are scarce for this period. Still, the few numbers available suggest the Atlanta Fed’s bank liquidity backstopping generated real economic benefits. This is documented in Table 5.1. which lists the ingredients for a simple DD analysis of Federal Reserve liquidity effects on the number of active wholesalers and their sales.
Wholesale firm failures and sales in 1929 and 1933
Notes: This table presents a DD analysis of Federal Reserve liquidity effects on the number of wholesale firms and the dollar value of their sales, paralleling the DD analysis of liquidity effects on bank activity in Figure 5,1.
DD estimates for Mississippi wholesalers parallel those for Mississippi banks. Between 1929 and 1933, the number of wholesale firms and their sales fell in both the Sixth and Eighth Districts, with a much sharper drop in the Eighth District, where more banks failed.
In the 1920s and 1930s, wholesalers relied heavily on bank credit to finance inventories. The estimates in Table 5.1 suggest that the reduction in bank credit in the Eighth District in the wake of Caldwell brought wholesale business activity down as well, with a likely ripple effect throughout the local economy. Sixth District wholesalers were more likely to have been spared this fate. Cooked with only a four-number DD recipe, however, the evidence for a liquidity treatment effect in Table 5.1 is weaker than that produced by the larger sample for bank activity.
The Caldwell experiment offers a hard-won lesson in how to nip a banking crisis in the bud. Perhaps the governor of the St. Louis Fed, seeing a more modest collapse in the Sixth District than in the Eighth, had absorbed the Caldwell lesson by the time he reversed course in 1931. But the palliative power of monetary policy in a financial crisis was understood by national authorities only much later. In their memoirs, Milton Friedman and his wife Rose famously recounted:
Instead of using its powers to offset the Depression, [the Federal Reserve Board in Washington, D. C.] presided over a decline in the quantity of money by one-third from 1929 to 1933. If it had operated as its founders intended, it would have prevented that decline and, indeed, converted it into the rise that was called for to accommodate the normal growth in the economy.-5
Which isn’t to say that the problem of financial crisis management has since been nailed. Today’s complex financial markets run off the rails for many reasons, not all of which can be contained by the Fed and its printing presses. That hard lesson is being learned by the monetary authorities of our day.