("The Causes of the 1929-33 Great Collapse: A Marxian Interpretation," by James Devine in Research in Political Economy. vol. 14: pp. 119-194, with annotation added.)

[introduction] [section I] [section II] [section III] [section IV]

[appendix B] [end of this section] [references] [notes] [short version]

[[p. 177]]

Appendices

 

Appendix A: Data Sources and Methods.

Tables I and II: Column (1) comes from USDC [1975: 126], series D-4. Subtracting those employed in agriculture (series D-6, p. 127) gives column (2). Multiplying by M. Reich's [1986: 125, table 4-C] nonfarm proletarianization rate (interpolated between 1900, 1910, 1920, and 1930) gives column (3). An index of weekly hours in manufacturing was used as a proxy for hours of work in the non-farm sector: it was an average of three similarly-moving series (D-831, D-803, and D-765) with overlapping time periods. (Other indices of working hours showed similar trends: see series D-796 (p. 169) and D-846,847 (p. 172).) This was multiplied by column (3) to get column (4). Finally, to get column (5), column (4) was multiplied by nonfarm output per labor-hour (series D-684). All are converted to index numbers.

Column (6) is the growth rate of column (1), while the sources of all the data is explained above. Column (7) is growth of column (5) due to the subtraction of the farm sector. Column (8) is that due to changes in the proletarization rate. Column (9) is that due to changes in hours per week, while column (11) is due to changes in productivity. Column (13) is from USDC [1975: 232], series F-128. Except for 1929, average data was used.

Table III: Column (14) is from USDC [1975: 126], series D-10, adjusted so that it measures unemployment as a percentage of the nonfarm labor force rather than employment. Column (15) is Romer's [1986] total-economy unemployment rate, multiplied by the ratio of the Lebergott nonfarm unemployment rate to the Lebergott total-economy unemployment rate. Column (16) is from Douglas [1930: 445]. Extrapolations for 1928 and 1929 are based on a simple regression equation for 1900-27:

D = a + bAS + uT + E,

where D is the Douglas series, AS is the alternative series (Lebergott non-farm or estimated Romer), T is a time trend, and E is random error.

AS:

Lebergott

Estimated Romer

Constant

6.08412

-15.8802

Std. Error of Est.

2.403506

2.782648

R squared

0.721435

0.626619

Coefficient of AS:

1.045191

2.015525

t-stat:

7.73506

6.1878192

coefficient of T:

0.264988

0.285005

t-stat:

4.484839

4.06749

Regressions using the natural log of time had similar results. [[p. 178]]

Diagrams 1 & 2: Martin [1939], tables 4, 7, 10, 16.

Symbols: W = total wages and salaries, E = Entrepreneurial Income, Y = realized private production income. Subscripts: A = agriculture, M = manufacturing.

Diagram 1: Non-Farm entrepreneurs = (E - EA)/Y; Agriculture = YA/Y;

Non-Entrepreneurial Manufacturing = (YM - EM)/Y; Other = 1 - (all of the above)

Diagram 2 (before conversion to index numbers): Unadjusted = (Y - W)/Y ;Non-Entrepreneurial = (Y - E - W)/(Y - E)

Non-Agricultural = (Y - YA - W + WA)/(Y - YA) ;

Non-Ent., Non-Agr. = (Y - YA - W + WA - E + EA)/(Y - YA - E + EA); Unadjusted Manuf. = (YM - WM)/YM

Non-Ent. Manuf. = (YM - EM - WM)/(YM - EM) .

Diagram 3-A: Duménil et al. [1987: appendix] and Duménil and Lévy [1993].

Diagram 3-B: Total Economy: Duménil and Lévy [1993].

Non-farm: Mage [1963: 174, 256-7]: total pre-tax gross surplus value minus capital consumption divided by capital stock.

Merged Corporate: a merged series, calculated from Epstein and Gordon [1939], Goldsmith [1955: 925], and merged NBER data [USDC, 1975: 941, series V304, V292].

Unadjusted Manufacturing: (1 - share of total payroll in manufacturing value-added) [USDC, 1975: 666, series P10 and P7] divided by the ratio of total capital to value-added in manufacturing, in 1929 dollars [Creamer, Dobrovolsky, and Borenstein, 1960: 40, column 4]. Data years are marked by the "X" and the curve was linearly interpolated between those dates. The share of payroll for 1900 was extrapolated between 1899 and 1900.

Diagram 3-C: Unadjusted manufacturing: see diagram 3-B. Adjusted manuf.: this is the unadjusted rate, times (RM - EM)*YM/(YM - EM)*RM, where data come from Martin [1939]. See diagram 1 for definitions. This equals the actual non-entrepreneurial profit rate if the output-capital ratio for non-entrepreneurial manufacturing equals that of the manufacturing sector as a whole.

Diagram 3-D: Adjusted profit rate: see diagram 3-C. Merged corporate, see diagram 3-B. Taitel is from Taitel [1941], profit rate on net worth of the corporate system, before taxes, using 1923 valuation of net worth.

Diagram 4-A: Duménil-Lévy [1991], exponentiated. Merged manufacturing series: USDC [1975: 667, series 13, 15, 17]. The Federal Reserve's index of manufacturing output was merged with Frickey's index, using the NBER's values for 1914 and 1919. Capacity utilization is measured [[p. 179]] as a ratio between the actual production index and the exponential trend (between 1860 and 1970). Data points based on the FRB are marked with an "X," while those based on Frickey are marked with an "O." The section of the line based on interpolation has no marking.

Diagram 4-B: See diagram 4-A.

S-C-H is Spenser, Clark, and Hoguet [1961]; Hickman-Coen is Hickman and Coen [1976].

Bassie-Foster is from Foster [1984], averaging year-end figures to give a yearly figure.

Diagram 5: Investment/Industrial Production: Manufacturing investment in plant and equipment from Chawner [1941], deflated with a wholesale price index and divided by manufacturing industrial production. Both annual and quarterly numbers presented for 1923-29.

I/(C+H): calculated from Balke and Gordon [1986], where I is business investment, C is personal consumption, and H is residential construction.

Diagram 6: Total Economy (1): Duménil & Lévy [1993].

Total Economy (2): Capital-Output ratio (smoothed series), La Tourette [1965].

Manuf. (1): Gillman [1958: appendix 3, lines 3, 5]. 1920 dropped, since it reflects severe recession conditions.

Manuf. (2): Creamer et al. [1960: 40, column 4].

[introduction] [section I] [section II] [section III] [section IV ]

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Appendix B: Mathematical Models.

  1. Conditions for Stable Growth.

In the leading sector, net income (Y) is distributed between surplus (R) and wages (W), according to a distributive factor s and the rate of capacity utilization (u). The former variable reflects class conflict, which in turn primarily depends on the progress of accumulation and the degree and type of organization of the classes. The latter variable reflects the fact that as capacity use rises, overhead labor is used more fully so that a greater surplus is realized relative to output.

R/Y = s u^b ; 1 > s > 0 ; b > 0W/Y = 1 - s u^b

(B-2)

where b is a coefficient of elasticity of the surplus share with respect to capacity utilization. On the other hand, u = Y/Z, where Z equals full-capacity output.

For simplicity, assume that the economy operates at or below full utilization (u < 1) so that there is no squeeze on surplus due to excessively high utilization and the resulting bottlenecks. Any squeeze on profits due to high demand for labor and high wages [cf. Devine, 1987] would be reflected not in u, but in s. Though [[p. 180]] the possibility of this latter type of squeeze cannot be ruled out a priori, it seems not to fit the labor-abundant 1920s and thus will be ignored below.

Note that if u = 1, then Y = Z and R/Y = R/Z = s. So the profit rate with u = 1, that is, the full-capacity profit rate, equals: 

r* = (R/Z)/(K/Z) = s/k

(B-3)

where k is the capital-capacity ratio (K/Z). The variable r* will be taken as given and presumed to rise (as in section III.C).

Next assume a Kaleckian consumption function where all wages are consumed but only part of surplus:

C = W + (1 - a) R ; 0 < a < 1= (1 - a s u^b) Y

(B-5)

 where (B-5) is derived from (B-4), (B-2), and (B-1).

 Total demand (which in equilibrium equals net income, Y) depends not only on C but on planned net investment (I) in the leading sector and external demand (E). E is "net exports" to other (non-leading) sectors, including the demand-side benefits of fiscal stimulus received by the leading sector. Thus, from (B-5):

Y = E + I + C = E + I + (1 - a s u^b) Y

(B-6)

 Solving for Y:

Y = (E + I)/(a s u^B)

(B-7)

By definition, capacity utilization is

u = Y/Z = k Y/K

(B-8)

Therefore, from (B-7) and (B-8),  

u = (E + I) k/(a s u^b K)

(B-9)

Simplifying using v = u^(1+b) and equation (B-3),

v = (E + I)/(a r* K) = (e + g)/(a r*)

(B-10)

[[p. 181]] where g and e are defined in section III.C. Condition (2) in the text is derived from this.

Using v as a proxy for u,  

dv/dr* = - (e + g)/(a r*) = -v/r*

(B-11)

This is negative since both v and r* are positive. Capacity utilization (and thus v) cannot be negative, while a "leading sector" will have a positive potential profit rate. Therefore, v and capacity use fall as the full-capacity profit rate rises, ceteris paribus. As seen from (B-3), this happens if either the capital-capacity ratio (k) falls or the surplus-capacity ratio (s) rises.  

2. A Simple Model of Investment.

In the stock-adjustment model, desired net investment is

Id = (Kd - Kold) = (kd Yex - k Zold)

(B-12)

In the first part of this equation, Kd is the desired stock of means of production, Kold is the stock of these goods left over from the previous period, and is the stock-adjustment coefficient. In the second part, kd is the desired capital-output ratio at full capacity utilization, Yex is the expected level of demand, k is the actual capital-output ratio at full capacity utilization, and Zold is full-capacity output in the previous period. This equation can be restated as the desired rate of growth of the capital stock:

gd = Id/Kold = (kd/k)(Yex/Zold) -

(B-13)

The and kd/k = ratios are partly determined by expected profit rates (and indirectly by actual profit rates): investment plans should be sped up (rising ) and desired capital stocks boosted (rising ) as profit rates r rise. But supposing that these ratios are constant, this implies that if expected capacity utilization (closely related to Yex/Zold) falls, gd also falls.

3. Interaction.

The interaction of the conditions for stable growth (part 1) and the actual determination of the growth rate (part 2) is relatively complex. Only a simple version is considered here. Assume that b = 1, so that u = v. Also assume that u = Yex/Zold and g = gd (a sort of short-term equilibrium). Then, it can be shown that [[p. 182]]

du/dr* = (dg/dr* - a u)/(a r* - )

(B-14)

where dg/dr* = ( u - 1)r + r u and r and r are the partial derivatives of and with respect to r*.

The denominator of (B14) must be positive for the product market equilibrium to stable (investment responds less than does saving to changes in capacity utilization). So 

du/dr* > 0 iff dg/dr* > a u

(B-15)

A rise in r* can hurt capacity utilization if g is relatively unresponsive to r*. The extreme case is that of part 1 of this appendix: if g does not change at all, then a rise in r* lowers u. On the other hand, if g is highly responsive to r*, then capacity utilization can rise with r*. This seems unlikely since it is not r* but the actual profit rate (r) that determines investment. But if we assume that u is constant as r* rises, so that the actual profit rate rises with r, it is more likely that dg/dr* > a u. But this condition is less likely to be met if u is high. This implies that we could have r* rising, stimulating g and u to rise. But when u rises, the validity of condition (B-15) could be negated, so that the continued rise in r* causes u to fall.

[introduction] [section I] [section II] [section III] [section IV ]

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