Inflation and the wage lag during the American Civil War

EXPLORATIONS

IN ECONOMIC

HISTORY

14, 31 l-336

(1977)

Inflation and the Wage Lag during the American Civil War* STEPHEN

J. DECANIO

Yale University

AND JOEL MOKYR Northwestern

University

This paper examines the role of inflation in financing the American Civil War, and the effects of that inflation on the level of real wages in the North. A wage determination model is specified in which the equilibrium real wage is determined by real forces and the money wage is allowed to adjust to its equilibrium value with lags. Econometric estimates of the model support Wesley Clair Mitchell’s contention that wage movements lagged price movements during the war. Comparison of the estimated equilibrium money wage and the estimated current money wage makes it possible to assess the magnitude and importance of the wartime redistribution of income attributable to inflation.

I. INTRODUCTION

The American Civil War continues to puzzle and fascinate economic historians. Over a century after the military resolution of the conflict, debates concerning the economic causes and consequences of the war are still carried on (Cochran, 1961; Engerman, 1966; Gunderson, 1974; Williamson, 1974b; Goldin and Lewis, 1975; Reid, 1976). Nevertheless, the mechanisms by which the Union and Confederate governments obtained the real resources required to conduct their operations during the war are still only imperfectly understood. The complicated budgetary details of wartime finance have been worked out as extensively as the data will allow (Trescott, 1966; Todd, 1954), but the interaction between the methods of financing and the (functional) distribution of income has never been adequately traced. * A partial list of those colleagues who have offered helpful comments on earlier versions of this paper includes Martin N. Baily, Robert Barro, Matthew Berman, William Brainard, Stanley Engerman, Claudia Goldin, Gerald Goldstein, Robert J. Gordon, Stanley Lebergott, Donald McCloskey, William Parker, Jon K. Peck, N. Eugene Savin, Peter Temin, the participants in the 1975 Cliometrics Conference in Madison, Wisconsin, and several anonymous referees. Responsibility for all remaining errors is ours. 311 Copyright 0 1977 by Academic Press. Inc. All rights of reproduction in any form reserved.

ISSN 0014-4983

312

DECANIO

AND

MOKYR

In particular, the role of inflation in financing the war effort and the effects of the inflation on wages and other factor prices remain matters of dispute. Mitchell first proposed the hypothesis that the warinduced inflation resulted in a decline in wage earners’ real incomes because money wages adjusted more slowly than prices (Mitchell, 1903, 1908). Keynes in How lo Pay fir the War (1940) gave the lag of wages behind prices a central place in his explanation of wartime finance. The Keynesian model of inflationary finance has never been empirically applied to the case of the American Civil War, and the most recent evaluations of Mitchell’s wage lag hypothesis have not been favorable (Kessel and Alchian, 1959; Engerman, 1966; Parkin and Laidler, 1975). Other research has shown that, over long periods of historical time in the United States, real wages have moved in phase with the business cycle as economic theory would predict (Long, 1960) and that cycles in money wages do not appear to have lagged cycles in the level of prices (Cargill, 1969). Nevertheless, we maintain that these tests of the wage lag are incomplete. We will show that if the separate effects of real and monetary forces on the course of real wages are properly measured, Mitchell’s insight is vindicated. This decomposition of wage movements also permits a preliminary assessment of the contribution of the Keynesian mechanism to Civil War finance. II. INFLATION,

WAR FINANCE,

AND THE WAGE

LAG

Wartime economic mobilization (in an economy previously at full or nearly full employment as the United States was in 1860) requires a transfer of real resources from individuals to the government. The resources may come from a reduction in personal consumption, a reduction in private domestic capital formation, an increase in foreign borrowing, or any combination of the three. l Governments utilize the instruments of taxation, conscription or confiscation, and the issuance of government debt (bonds and money) to command the goods and services needed for the war effort. The transfer of purchasing power from citizens to the government accomplished by taxation and confiscation is clear and direct. The transfer mechanisms involved in debt issue are less transparent, which perhaps is why these methods have traditionally been favored by democratic governments (Gordon, 1975). During the r A separate source of financing the war is through reduction of leisure consumption, that is, through a shift of the labor supply function. The often-mentioned increase in the labor participation rate of women is the most prominent example of this argument. As Engerman has shown, however, the overall dimensions of this phenomenon are ambiguous (Engerman, 1%6, p. 188). Nor is there evidence that the number of hours put in per worker rose dramatically during the war. According to Fite (1910, p. ZOO), the length of the labor day at the end of the Civil War was “decidedly reduced” compared to 1850.

INFLATION

AND WAGE LAG IN AMERICAN

CIVIL WAR

313

Civil War, the Union government2 imposed excise taxes, tariffs, and an income tax, but these direct and indirect taxes never constituted the predominant part of the total federal expenditures. For the fiscal period 1861-1865, which includes the years of major war expenditures, the ratio of total federal receipts to total federal expenditures (both measured in 1860 dollars) was 26%. According to a recent estimate, confiscation and conscription provided even fewer resources than taxes in the North (Goldin and Lewis, 1975, p. 304). All in all, these sources cannot account for the major burden of war finance to the Union. Government debt issue transfers resources away from the private sector either through its effects on capital formation and foreign lending or through inflation. The change in foreign lending during the Civil War cannot have been a large component of the transfer. The total excess of merchandise imports over exports (excluding specie flows) during the Civil War amounted to $211 million in 1860 dollars. This figure represents the maximum contribution of real resources by overseas lenders to the Northern war effort. The actual contribution from this source was undoubtedly much less, since the average five-year import surplus (again excluding specie flows) in 1860 dollars over the period 1851-1875 was $218 million (United States Bureau of the Census, 1960, pp. 537-538; Lebergott, 1964, pp. 528-529; Coelho and Shepherd, 1974). The substitution of government debt for domestic capital formation was more important than foreign lending. This substitution mechanism has recently been explored by Williamson, who argues for its importance by calling attention to the well-known fact that tangible capital accumulation in several important industries was reduced during the Civil War years (Williamson, 1974b, pp. 647-648; Cochran, 1961; see also Modigliani, 1961). Despite the observed falling off in domestic investment, however, it seems unlikely that this source by itself would have been sufficient to meet the needs of federal war finance. According to Williamson, “as a share in the 1859 non-South GNP, annual increases in the federal long term debt amount to more than 15 percent. This figure is almost equal to the non-South GDCF/GNP [Gross Domestic Capital Formation/Gross National Product] share of 19.4 percent, achieved in the 1850’s” (Williamson 1974b, p. 647).3 If aggregate Northern savings had been maintained at the 1859 level throughout the 1861-1865 period, aggregate gross capital formation would have to have been reduced from $426 * Here and throughout, our attention will be directed toward conditions in the North. Temin’s (1976) critique and downward revision of Goldin and Lewis’ (1975) estimate of the costs of the war applies only to the South and to the attempt to calculate the “indirect” war costs other than those we are considering. 3 It seems that Williamson classifies the entire issue of interest-bearing debt as “long-term debt” in this calculation (Williamson, 1974, pp. 642-643). But see our discussion below for the composition of the debt.

314

DECANIO AND MOKYR

million per annum to $108 million per annum to completely cover the $1588 million federal deficit, a reduction to 25% of the prewar level (all figures in 1860 dollars).4 If capital consumption accounted for as little as one-quarter of gross capital formation5 it is apparent that net Northern capital accumulation would have had to have been virtually extinguished in order for the Civil War deficit to have been financed from this source alone.6 The other mechanism by which government debt issue mobilizes resources is inflation. During the Civil War, inflation was both rapid and of large cumulative impact, with the consumer price level rising from an index level of 100 in 1860 to an index level of 196 in 1865. The average annual rate of increase was 13% over the five years of the war, achieving maximum rates of 25% per annum in 1863 and 1864 (computed from Lebergott, 1964, p. 528). During the war the Union government printed fiat money (greenbacks) and issued a large quantity of interest-bearing securities which were probably closer substitutes to money than to tangible capital in asset holders’ portfolios. A majority of the debt issued by the government over the period 1861-1865 was of the short-term or liquid variety, paper which according to Dewey “served in many instances the purposes of currency, expanded prices, and increased the speculation and extravagance always incident to war” (Dewey, 1934, p. 317). To the extent that bonds and money were viewed as good substitutes by the public, a government bond issue would be entirely analogous in its effects to the creation of fiat money by the government, the newly issued bonds merely replacing idle cash balances in wealth holders’ portfolios. From a quantity theory point of view, inflation would be caused by an increase in the velocity of money.7 Trescott’s breakdown of the financing of the deficit (see Table 1) shows that only 39% 4 Potential Northern capital formation was computed by applying Gallman’s 1859 total United States savings rate to the share of national income originating in the North in 1860 (Gallman, 1966, p. 34; Goldin and Lewis, 1974, pp. 323-324). 5 Gallman conjectures that capital consumption accounted for approximately one-third of gross capital formation, but this is based on Kuznets’ estimate for the period 1869-1878, an estimate which Gallman characterizes as “probably too high” (Gallman, 1966, p. 14). 6 This calculation assumes stability in both the level and distribution of Northern income over the war. In fact, total incomefell (Kessel and Alchian, 1959; Berry, 1968), which would tend to reduce potential savings. On the other hand, it is entirely possible (see later) that the share of profits increased, which might tend to increase potential savings because of differential savings rates across the scale of incomes. In this latter case, however, the mechanism by which income was redistributed would occupy a vital place in the financing operation. ’ As Studenski and Krooss put it, ‘&even if greenbacks had not been issued and bonds had been issued at whatever price they would bring in the market, inAation would have taken place once the government was forced to rely on credit, the exact form of credit expansion was not so important as assumed by some historians” (Studenski and Krooss, 1952, p. 148).

INFLATION

AND WAGE LAG IN AMERICAN TABLE

CIVIL WAR

315

1

United States Federal Government Deficit and Financing, 1861-1865’ Total expenditures 09

Fiscal yea

Receipts

Deficits

Price index

103 114 136 170 193

Millions of dollars, 1860 prices 1861 1862 1863 1864 1865 Total

63.4 382.1 503.6 511.9 674.6

38.0 42.4 96.1 172.9 198.2

25.4 339.7 401.5 339.0 476.4

2135.6

547.6

1588.0

Percentages of deficit financed Fiscal yew 1861 1862 1863 1864 1865 Total

Bonds m

Liquid assets

Interestbearing currency

Other currency

Change in treasury balance

Total

92.5 14.4 29.2 77.8 35.0

-1.2 51.4 28.8 -4.5 52.4

35.4 2.8

38.1 40.2 7.3 0.3

8.7 -3.8 1.8 - 16.0 9.5

100% 100 100 100 100

38.9

33.3

8.3

20.4

-0.8

100

a The table is adapted from Trescott (1966, pp. 216-218). Since Trescott’s expenditures, receipts, and funding data are presented for fiscal years, the price index was computed from Lebergott (1964, p. 528) by linear interpolation of the two calendar years included in each fiscal year. P,~~,,= 100.

of the total wartime deficit was financed by bonds, while 62% was financed by “liquid assets,” “interest-bearing currency,” and greenbacks. Dewey gives many examples of the government’s interestbearing debt performing the functions of currency (Dewey, 1934, pp. 308-314), and the National Banking Act as amended in 1864 allowed the bonds to serve as a reserve for national bank notes (Studenski and Krooss, 1952, p. 155; Dewey, 1934, p. 326). The inflation resulting from issuance of this type of government debt channels real resources to the government in three ways. First, inflation constitutes a tax on cash balances. Second, inflation may alter the distribution of income in favor of individuals with a relatively high marginal propensity to save. If wages lag behind prices, inflation redistributes income away from wage earners (and others whose incomes are fixed or slow to adjust) toward profit recipients and other

316

DECANIO AND MOKYR

“residual claimants” who save more by virtue of their position in the upper tail of the income distribution. The redistribution of income from workers to entrepreneurs, capitalists, and owners of goods allows these “profiteers” to absorb the bonds sold by the government. This type of mechanism was first proposed by Keynes (1940), and has been refined, reformulated, and modified many times since then (Koopmans, 1942; Smithies, 1942; Holzman, 1950; Maital, 1972). Third, inflation can transfer resources directly from wage earners to the government. The govemment’s power to print legal tender and to use it to purchase goods and services in the commodity markets (i.e., its right of “seigniorage”) allows it to preempt part of the consumption of anyone whose income lags behind prices or who buys goods out of resources specified in nominal terms. Determination of the magnitude and incidence of the tax on nominal balances is impossible since we do not know the wealth elasticity of consumption during the Civil War nor do we have any clear idea of the personal distribution of assets specified in nominal terms. Determination of the importance of the other two types of inflationary finance, on the other hand, is conceptually straightforward. All that is required is estimation of the extent to which wages lagged behind prices.8 The difference between actual wages and the counterfactual level of wages which would have prevailed in the absence of inflation (or, alternatively, in the presence of an inflation to which nominal wages adjusted instantaneously and fully) represents the burden of this type of inflationary war finance on wage earners. Mitchell proposed various institutional and behavioral explanations of the wage lag, such as the prevalence of contracts specified in money terms for long periods, the fact that money payments were “conventional sums,” and the unanticipated character of the inflation. In this, he was a precursor of both Keynes (1940; see also Trevithick, 1975) and modern theory (e.g., Alchian, 1970). Nevertheless, Mitchell rested his argument primarily on the empirical demonstration that money wages did not rise as much as prices during the ~ar.~ In fact, the * It is necessary here to distinguish between a short-run wage lag and a long-run wage lag or money illusion. A long-run wage lag implies that any inflationary shock will cause a permanent reduction in the real wage, since the nominal wage never fully catches up with the new higher price level. A short-run wage lag, on the other hand, is less restrictive as it allows inflationary finance to operate essentially as a disequilibrium phenomenon. B Even granting the existence of a wage lag and that total output remained constant, Mitchell’s inference that workers’ share in national product fell does not necessarily follow. The reason is that “changes in real wages and relative income shares would depend upon elasticities of substitution between factors of production in each industry, as well as effects arising from the shifting composition of output among industries” (Engerman, 1966, p. 187). This objection is logically correct, but empirically it is probably not operative. Labor’s share will move in the same direction as the real wage provided the aggregate elasticity of sub-

INFLATION

AND WAGE LAG IN AMERICAN

CIVIL WAR

317

real wage did decline rapidly during the war years. From its 1860 level of $363, the real wage (in 1860 dollars) successively fell to values of $349, $317, $304, $268, and $261 over the period 1861-1865 (computed from Lebergott, 1964). Kessel and Alchian (1959, 1960) have argued, however, that such a decline in the real wage is not sufficient evidence to establish the existence of a wage lag. They maintained that the fall in real wages observed by Mitchell could be attributed to various “real” forces set in motion by the war, and they proposed a list of such wage-depressing factors as the tax policy of the Union government, the disruption of the normal functioning of the economy due to the war, and the deterioration of the terms of trade faced by the Union states as alternative explanations. lo We agree with Kessel and Alchian that the actual money wage will be influenced by real forces, even in the short run. Yet while they recognized that both real and “monetary” (i.e., wage lag) forces may have contributed to the decline in the real wage (Kessel and Alchian, 1959, pp. 110-11 l), they did not subject their argument to a definitive statistical test. Only if both types of forces are allowed to operate simultaneously in the wage determination model can their effects be separated empirically. What is required is the specification and estimation of a model which allows the actual money wage to deviate from the equilibrium money wage, an equilibrium which in turn is determined, for any given price level, by the various real forces affecting the labor market.” III. THE MODEL AND EMPIRICAL

RESULTS

Our model of wage rate determination begins with the presumption that the equilibrium real wage is determined by real forces in the labor market. The demand and supply schedules for labor in period t are given by the equations LfD = n Yit”i( W,/zJ,)-“; I

L,s = n Z& WJZJ,)“; E

(1)

stitution is less than one. The best recent empirical estimate of the elasticity of substitution for the nineteenth century satisfies this requirement (Abramovitz and David, 1973, p. 434). lo Kessel and Alchian’s other criticism against Mitchell, that 1860 was an unrepresentative year in which wages were abnormally high, is dispelled by recent research (Coelho and Shepherd, 1976, p. 212). I1 It is interesting to note that Cargih’s (1%9) attempt to test the wage lag hypothesis by use of spectral analysis fails to distinguish the effects of real and monetary forces. Cargill has no model of real wage determination, so that his estimation of association between money wage movements and price movements may miss a significant wage lag concealed in the joint movement of wages and prices induced by real phenomena. Also, Long (1960), while showing that prices and money wages move together over the business cycle, does not distinguish between the observed money wage and the equilibrium money wage.

318

DECANIO

AND

MOKYR

where a and b are the elasticities of labor demanded and supplied with respect to the real wage WJP,, and the Yit and Zit (with associated elasticities ei andfi) are shift terms in the labor demand and supply functions. The Yi, might include factors such as the level of total output, the phase of the business cycle, or a productivity trend; the Zit could include the size of the potential labor force or influences on the labor participation rate. Obviously, some shift variables might appear in both functions. The list of factors included in Yit and Z, could be made very long. The real wage is determined by a large number of real factors, not all of which can be treated exhaustively in the present context. The composition of the labor force, internal and external migration patterns, the accumulation of human and nonhuman capital, changes in the efficiency and competitiveness of labor markets, government intervention, and many other factors all exerted some degree of influence in the determination of the real wage. The present paper does not attempt to provide a complete analysis of the determinants of the real wage, which can be found, for instance, in Williamson (1974a, pp. 21-57, 78-83) and Lebergott (1964, pp. 154-164). Our approach is to estimate a reduced-form wage equation rather than to attempt to separately identify the labor supply and demand functions given in Eq. (1). This procedure requires fewer assumptions than would be required for structural estimation, and is adequate to isolate the effects of the wage lag. The equilibrium money wage W, is defined as that money wage which, for a given price level P,, clears the labor market by equating LtD and Lls. Transforming the equations to logarithms (with the notational convention here and throughout that lower-case letters represent the natural logarithms of the variables) yields k wt *

=

C i=l

QGit

+Pt,

(2)

where the list OfXit variables includes all the yit and zit, xgt is the constant, and the (Yi are of the form (ei - fi)l(a + 6). The equilibrium real wage in logarithms, wt* - pt, depends only on the values of the variables representing the real forces. The equilibrium money wage rate wt* is not observed, and will typically differ from the actual money wage since adjustment to the equilibrium is not instantaneous. The adjustment process may be complicated further by the influence of workers’ or employers’ inflationary expectations. Expressing the current money wage as a function of deviations of past money wages from equilibrium and of inflationary expectations based on historical rates of wage and price inflation leads to an empirical relationship in which the current money wage is a function of the real forces (the xlt), the price level, past rates of inflation, and lagged values

INFLATION

AND WAGE LAG IN AMERICAN

CIVIL WAR

of the money wage. To illustrate this, suppose the adjustment actual to the equilibrium wage is governed by the relations

319 of the

wt = vt + ycwt* - v,),

(3)

Vt = Wt-1 + pP\eTte,

(4)

*te

=

i j=l

/bLj(Wt-j

-

Wi-j-1)

+

5 j=l

Bj(p,&j

-

Pt-j-J-

(5)

In this formulation, wt adjusts to the gap between the expected money wage, vt, and the equilibrium wt* [Eq. (3)]. The expected money wage vt in turn equals the previous period’s money wage augmented by some proportion 6 (possibly unity) of the expected rate of inflation *\I [Eq. (4)]. Finally, inflationary expectations qte are a weighted average of past rates of wage and price inflation [Eq. (S)].12 Elimination of wt*, vt9 and qte from Eqs. (2)-(5) leads to the relationship Wt = i i=l

P&it + YPt + i nj(Pt-j - Pt-j-1) + i j=l

4jWt-j9

(6)

j=l

where pi = aiy and the mj and 4j coefficients are functions of y, 5, and the Bi and pi parameters. More complicated specifications of the wage adjustment and inflationary expectations parts of the model would lead to empirical relationships of the same form. Obviously, given our present state of knowledge (or ignorance) regarding the formation of expectations, it is not possible to disentangle the various influences on the rj and $j coefficients. Since both wage and price inflation terms enter (5), it is not even possible to predict a priori the signs of the individual ej and pJ. The impossibility of identifying the underlying structure of expectation formation or of placing prior restrictions on the signs and magnitudes of the individual ni and +j coefficients does not mean that any coefficients at all would be plausible. On the contrary, certain restrictions on the coefficients must hold if (6) is to be a reasonable model for nineteenth century wage movements. ‘* Although completely rational individuals would incorporate “exogenous” information other than past rates of wage and price inflation into their predictions about the future course of prices and wages (Gordon, 1973), it is not clear what information of this type besides knowing that the war was underway would have helped agents improve their forecasts during the Civil War. Our empirical models include Civil War dummy variables to partially account for this potential shift in expectations (among other things). Our unconstrained estimates (see Appendix) neither assume nor preclude rational expectations as defined by Muth (1961), though with the exception of the Civil War dummy variables mentioned above we do confine the expectational information set to the past history of wages and prices. For a discussion justifying the use of adaptive expectations (as opposed to the less ad hoc but more elusive concept of rational expectations) see Gordon (1976, pp. 203-204).

320

DECANIO AND MOKYR

Equation (6) can be rewritten difference equation:

in the form

of an (m)th-order

Wt- 5 4jwt-i = i &it + YPt + i: Tj(Pt-j -Pt-j-1). j=l

i=l

(7)

j=l

For any given and unchanging set of values of the real variables (the xii) and well-defined path of prices over time, the money wage will approach the limiting value of the solution to the difference equation as t + CQ.If the equation is stable, the limiting value or path of the money wage will depend only on the value or path of prices and on the values of the xii variables. The behavior of the “limit wage” can best be illustrated by explicitly solving the difference Eq. (7) for various price paths. The solution is composed of the sum of a particular solution of (7) and the general solution of the associated homogeneous difference equation. If the equation is stable, the solution of the associated homogeneous equation will vanish as t + ~0, so that the limit wage equals the particular solution of (7). Stability will be assumed throughout the discussion because there is no economic reason to suspect that the wage adjustment mechanism was explosive during the sample period. Simulation experiments corroborated this assumption.13 The value of the limiting money wage, given any set ofxit and a constant price level, is easy to determine from Eq. (7). Let the fixed set Of Xit be denoted by x,, (with C&x,, written simply as pxO), and let the price level be pO. Then the limiting value of the solution to (7) is given by

PXO wL=

l-c4j

Y +

j

1 - 2 f$j Po* j

(8)

This limiting value will also be the equilibrium clears the labor market at price p. provided

money wage w* which

y= 1- 1 C#Jj. j

(9)

I3 The equations derived from (7) which were estimated statistically included up to 10 lagged terms. A complete test of stability of these lOth-order difference equations under all possible types of price behavior would involve checking the Schur conditions for stability and would require evaluation of 20 x 20 determinants (Chiang, 1974, pp. 599-600). However, the econometric estimates of the 4, were always less than unity in absolute value, which is sufficient to guarantee stability with respect to once-and-for-ah price changes. In the simulation experiments, we set the equilibrium real wage equal to an arbitrary initial value. Using a structure given by Eq. (6) we either changed the price level abruptly or initiated price inflation at a constant rate. For lag parameters similar to those estimated, the money wage was either found to converge to a new long-run level (in the case of once-and-for-all price changes) or to long-run steady growth at a rate equal to the rate of inflation.

INFLATION

AND

WAGE

LAG

IN AMERICAN

CIVIL

WAR

321

This restriction on the coefficients must be satisfied if the real wage wt - pt is to approach in the limit a value wL - p0 which depends only on the values of the real variables x0. If y # 1 - C& the limiting real wage will depend on the price level as well as on x0. This would imply that participants on at least one side of the labor market suffered from long-run money illusion or, to put it another way, that mere changes in the price level could have caused a permanent shift in the labor supply or demand curve. While such an outcome is not logically impossible, to allow it would require attributing quite bizarre behavior and perceptions to either employers or employees. This constraint of neutrality of the limiting real wage with respect to the price level as expressed by (9) will therefore be assumed throughout and imposed a priori in estimation of the coefficients of the wage equation. As is usually the case with adaptive expectations, the limit wage may diverge from the equilibrium wage for price behavior more complex than a once-and-for-all price change. In order to obtain the result that the limit wage equals the equilibrium wage, certain additional constraints on the lag coefficients must be imposed. Consider the limit wage in the case of a constant rate of price change 6 beginning at t = 0. It is easy to show that if y = 1 - C$j, the limit wage is given by

Thus, if S f 0, the real wage wt - pt will approach different from the equilibrium wage, unless

an asymptotic

1 rj - C jf#3j = 0. j 1

limit (11)

If (11) is true, however, wL = wl* and the limiting real wage is invariant with respect to constant rates of inflation or deflation. This condition is thus equivalent to the existence of a long-run “natural rate” of unemployment. Since the a priori justifications for neutrality of the type expressed by equation (11) are less compelling than those for the neutrality conditions given by (9), we will report wage equations both with and without imposing (11) as a constraint prior to estimation. The constraint of neutrality with respect to the price level was imposed by substituting (9) into the basic equation (6), resulting in the following empirical equation: Wt -Pt

= C &it 1

+ C rjITj(Pt-j -Pt-j-1) j

+ C +dWt-j j

- Pt) + Ut*

(12)

In this equation, ut is the random disturbance, and the list of real forces xit includes the constant, a trend, the potential labor force, an

322

DECANIO

AND

MOKYR

adjusted price ratio measuring changes in the price of imports not attributable to domestic inflation, real GNP, an index of industrial production, and dummy variables reflecting Civil War-related disruptions of the economy not captured by the other xit variables. These variables are fully defined and discussed in the Appendix. Equation (12) was estimated by two-stage least squares because of the simultaneous determination of wt and pt. Since (12) contains what amount to lagged dependent variables, the ordinary Durbin-Watson statistic cannot be used to test for the presence of autocorrelation of the disturbance. Therefore, in addition to the ordinary TSLS estimates, (12) was estimated assuming ut to be a first-order autocorrelated process. The details of the estimators are contained in the Appendix. For purposes of exposition, all the empirical results will be discussed in terms of the parameters of the basic Eq. (12). Table A.1 in the Appendix presents the actual results of the estimation of (12) under several alternative specifications of the lag structure and for our two different assumptions concerning the absence or presence of autocorrelation. The hypotheses of Kessel and Alchian regarding the influence of the various real forces may be tested by examining the coefficients of the xit. The wartime disruption of overseas trade and the decline in domestic output would have adversely affected the real wage during the Civil War provided the coefficients of the adjusted price ratio and the output variables (GNP and the industrial production index) are positive and significant. Examination of Table A. 1 indicates that the coefficients of several of the xit are large relative to their standard errors, and have signs consistent with prior theoretical notions. The coefficient of the GNP variable is not statistically significant, although it is positive for each specification. The industrial production index, on the other hand, is a superior indicator of the effect of demand on wages, and its coefficient is positive in every specification and significant at the .05 level (two-tailed test) in seven of the eight cases. The coefficient of the adjusted price ratio is not statistically significant, although it too is positive in all specifications but one. The insignificance of this terms of trade variable corroborates, from a different point of view, Coelho and Shepherd’s conclusion that “the Kessel and Alchian hypothesis that much of the Civil War inflation was due to changes in exchange rates . . . is questionable” (Coelho and Shepherd, 1976, p. 223). The negative coefficient of the potential labor force is consistent with the presumption that this variable represents shifts in the labor supply curve. The coefficients of the trend, dummy, and product of the dummy and trend variables show that the trend of the equilibrium real wage was negative during the Civil War and positive after the war. The estimates of the lag coefficients demonstrate a substantial degree of wage stickiness throughout the sample period. A complete absence of wage

INFLATION

AND WAGE LAG IN AMERICAN

CIVIL WAR

323

rigidity and expectational effects implies that the current money wage would depend only on the current values of the real forces and the price level, and not on the past history of wages and prices. Referring to Eq. (12), this is equivalent to the requirement that $j = 0 and mj = 0 for allj. In fact, at least some of the & and 7rj are significantly different from zero in every specification of Table A. 1. This confirms Mitchell’s hypothesis that wages lagged behind prices during the Civil War period.14 Severe multicollinearity among the lagged variables makes it difficult to assess the magnitude of each individual +j> but $1 and 7r1are clearly nonzero, as are several of the later 4j and rrj when the collinearity is reduced by imposing equality restrictions on the coefficients of the later lagged terms. Since wage and price movements may have had different degrees of credibility as to the likelihood of their persistence, it is not surprising that the coefficients of past rates of price inflation tend to be negative. Indeed, dissimilarities between implicit wage and price inflation coefficients are compatible with the kinds of imperfect information and misperceptions intrinsic to the wage lag hypothesis. To assess the quantitative importance of the wage lag, we define the wage gap caused by monetary factors as the difference between the estimated equilibrium wage and the fitted wage for each year of the Civil War.15 Table 2 contains calculated values (in 1860 prices) of the wage gap for each year of the war. The estimated equilibrium real wage

@t*lpt = expN C BiXitY(1 - 1 $j>l

(13)

was computed for each of the alternative lag and disturbance specifications (i)-(viii). It is apparent that the equilibrium wage exceeded the fitted wage for all the Civil War years after 1861. The cumulative gap for those years in which the equilibrium wage exceeds the fitted wage is also given for a single nonfarm wage earner in Table 2. The total gap for a single wage earner I4 The wage lag hypothesis is also supported by data on wages earned in different occupations during the Civil War period. One important part of the explanation of a wage lag (though not the only one) is that many labor contracts extended over a relatively long period and were renegotiated infrequently. Therefore, it would be consistent with the wage lag hypothesis to observe a greater decline in the real wage earned in professions with contracts of relatively long duration than in the wages of unskilled laborers hired for short periods of time. (Assuming other things were equal of course, including comparable shifts in the demands for the different types of labor and equal perspicacity of the various groups with respect to their anticipation of inflation.) Available data on wages by occupation are consistent with this pattern. The real wage for common laborers in 1864 was 73.7% of its 1861 level, while in 1865 it was 78.1% of the 1861 level. For engineers, on the other hand, the corresponding percentages are 64.6 and 71.4%, respectively (Coelho and Shepherd, 1976, Tables 6 and 7). I5 This definition was chosen over the alternative of subtracting the actual real wage from the estimated equilibrium wage so that the calculated gap does not partly consist of the residual from the estimated equation. However, since the fit of the wage equations is very good, the difference between the two procedures is not substantial.

324

DECANIO

AND MOKYR TABLE

(et*/P,)

YEAR 1861C 1862 1863 1864 1865 Total positive gap

2

- (@JP,) Gap for a Northern Nonfarm Worker, 1860 Various Lag and Disturbance Specificationsa

6)

(ii)

(iii)

(iv)

-15.27 16.43 44.92 53.75 48.63

-6.59 23.32 66.73 77.65 70.89

- 14.74 19.14 50.37 59.19 53.50

163.73

238.59

182.20

Approximate

Dollars,

(V)

(vi)

(vii)

(viii)

(ix)’

-7.89 16.81 53.25 63.29 57.20

-1.86 31.21 66.00 78.14 85.50

-1.93 21.40 65.38 78.82 76.69

-5.99 24.26 52.81 64.15 67.97

-5.18 15.25 51.40 63.50 59.36

14.07 46.49 59.17 95.36 101.91

190.55

260.85

242.29

209.19

189.51

317.00

Calculation of Total Gap, All Northern Wage Earners, Thousands of 1860 Dollars

186lC 1862 1863 1864 1865

-31,227 32,515 88.043 107,608 99,935

- 13,477 46.150 130,791 155,455 145,679

-30,143 37,878 98,725 118.498 109,943

- 16,135 33,267 104,370 126,707 117,546

-3,804 61,765 129,360 156.436 175,703

-3.947 42.351 128,145 157,798 157,598

- 12,250 48,011 103,508 128,428 139,678

- 10,593 30,180 100,744 127,127 121,985

28,773 92,004 115,973 190,911 209,425

Total positive gap

328.101

478,075

365,044

381,890

523.264

485,892

419,625

380,036

637,086

a The total gap in each year is calculated

as

TG, =F.LFN,.(l

- r,)@~*/P,

- WdP,,,

where F = fraction of the Northern labor force effectively subject to the wage lag; LFN, = total Northern labor force; r, = fraction of the Northern labor force serving in the military; and (WC*/&‘, - l%‘JP,/p,)= the gap for a single Northern nonfarm wage earner. MN, and I~ were computed essentially by interpolations and adjustments of data contained in Lcbergott (1964) and the United States Bureau of the Census (MO). F was derived from Lebergott (1964) by interpolation between his 1850 and 1908 benchmarks, adjusting for the fact that agricultural wages (other than payments in kind which were not subject to the wage lag) were only a fraction of the nonagricultural wage. Details of these calculations are available from the authors. b Specifications (i)-(viii) correspond to those in Table A.l. Specification (ix)’ gap computed on the assumptions that lb’,*/P, = W&P,, and *,li=, = WJP,. c The negative “gaps” from the 1861 estimates were not included in the cumulative totals. The Civil War inflation did not fully get underway until 1862. sothc 1861 estimates are not important in assessing the magnitude of the wage lag. The actual wage’s exceeding the equilibrium wage in 1861 possibly suggests a small amount of excess supply in the labor market at the beginning of the war.

ranges from a minimum estimate of $164 [specification (i)] to a maximum estimate of $261 [specification (v)]. Specifications (iii), (iv), (vii), and (viii), in which long-run inflationary neutrality was imposed as a constraint prior to estimation, show a range of the estimated cumulative gap from $182 to $209. The results suggest that the wage lag mechanism was responsible for a significant portion of the decline in Northern wage earners’ incomes during the Civil War. The total decline in a single wage earner’s income from its 1860 level was $317 [column (ix)’ of Table 21. Thus at least half of the decline in a typical Northern wage earner’s income during the war is attributable to the wage lag. The average loss due to the lag over all eight specifications is 66% of the total decline in the wage earner’s income.

INFLATION

AND WAGE LAG IN AMERICAN

CIVIL WAR

325

The rest of the decline was due to the disruptive real forces outlined by Kessel and Alchian. While the impact of the wage lag on an individual wage earner was substantial, the total contribution of this mechanism to the financing of the Civil War was not as large in comparison, mainly because the total number of Northern workers subject to the lag was not a large proportion of the labor force. According to Lebergott, “as late as 1850 no less than 70 percent of the labor force were not employees. They were self-employed persons (farmers, mechanics, small tradesmen) or slaves” (Lebergott, 1964, p. 139). Furthermore, not all Northern wage earners received the same level of income as the nonfarm workers. Table 2 also contains rough estimates of the total transfer of resources away from all Northern wage earners for those Civil War years in which the gap between the estimated equilibrium wage and the fitted wage was positive. It can be seen that the total transfer of resources attributable to the wage lag ranges from $328 million to $523 million, averaging $420 million. Even though these estimates vary from only 21 to 33% of the total federal deficit of $1588 million, it must be kept in mind that less than one-third of the Northern labor force was effectively subject to the wage lag, and that these wage earners were concentrated in the lower tail of the income distribution.16 Furthermore, the resources involuntarily given up by the wage earners who were subject to the wage lag have been calculated in such a way as to exclude the war costs borne by them through payment of excise taxes, tariffs, and due to conscription. In our estimates, the reductions in the real wage brought about by the Union tax system are largely embodied in the terms of trade and Civil War dummy variables. Also, the losses of wage earners serving in the armed forces were not included in the calculation of the total gap. It is of some interest to compare the inflationary experience of the North during the Civil War with the deflationary period which followed. As one would expect, most of the annual values of the gap between the equilibrium and the predicted wage are negative for the years following 1865.17 There are good reasons to suspect, however, that inflation and deflation were not symmetric with respect to their impact on the aggregate distribution of income. Assume for simplicity that at full employment the supply of labor is perfectly inelastic. An inflationary shock reduces the real wage l6 The estimate of the proportion of the labor force subject to the wage lag was 28.1% (see footnotes to Table 2). This is a conservative estimate. Budd (1960, p. 392) puts the proportion of “hired” workers at 49%. If we had used this figure, our estimate of the amount of resources transferred would rise by approximately 70%. r’ Even though the postwar deflation was persistent, it did not occur at a uniform rate. Therefore, even if expectations were such that long-run neutrality with respect to a constant rate of inflation (or deflation) prevailed, it is not unlikely that some of the postwar deflation would have been unanticipated throughout the period.

326

D&AN10

AND MOKYR

and creates excess demand in the labor market. Since the amount of labor actually supplied is equal to the vertical labor supply curve, the wage bill declines unambiguously. A deflationary shock, on the other hand, creates excess supply in the labor market, so that the amount of labor transacted is to the left of the supply curve. While the wage rate rises, employment falls and therefore the change in total labor income depends on the elasticity of labor demand. I* Thus, the ultimate effect of the postwar deflation must have depended on the amount of unemployment generated by the negative wage gap. Since there are no annual unemployment series for this period, it is not possible to compute the total redistribution of income from profits to wage earners associated with the negative gaps. For a single employed worker, the size of the (negative) transfer from workers to capital during the period 1866-1900 averages 411 per annum over the eight specifications of Table A. 1, with very little variation in the average across specifications. This amounts to a gain of 3% of the average annual income of an employed worker, as compared to the loss of 18% of his average annual income during the war years 1862-1865. Since the deflationary period was much longer, it might be thought that the cumulative effects over the two periods of opposite price changes were comparable, but since the net postwar gain for all workers must include a deduction of indeterminate size to account for unemployment, the comparison lacks meaning. Calculation of the long-term consequences of wage rigidity on the aggregate distribution of income must await better measures of nineteenth century unemployment. IV. CONCLUSIONS

AND IMPLICATIONS

Estimation of the wage equations developed in this paper make it possible to disentangle the real and monetary influences on the course of wages during the Civil War. The real forces identified by Kessel and Alchian did indeed influence the level of the equilibrium real wage, and tended to depress that level as the economic disruptions associated with the war intenI* Asymmetries of this type can also be rationalized in terms of the microbehavior of firms (see Gordon, 1976, for a discussion of these issues). A simple example which produces the asymmetrical response is as follows: Assume that hiring and training costs are high while firing is cheap because it is expected that most furloughed workers can be rehired at will. Unanticipated inflation, perceived by individual firms as an exogenous decline in the real wage, might incline them to hire more workers, but they may not do so until they are convinced of the permanence and generality of the fall in wages. In other words, the short-run elasticity of demand for labor is smaller (in absolute value) than the long-run elasticity. During deflation, however, no such delay in response need exist. A firm may even lay off more workers than would be warranted by its long-run labor demand curve, eventually rehiring some of these workers costlessly. The short-run elasticity is thus as large or larger than the long-run elasticity for unanticipated price declines. In this simple model and in similar ones which explicitly incorporate firms’ behavior toward risk, employment responds asymmetrically to changes in the price level depending on the direction of the change.

INFLATION

AND

WAGE

LAG

IN AMERICAN

CIVIL

WAR

327

sified. At the same time, money wages lagged in the short run in adjusting to their equilibrium value. Without the operation of this wage lag, the real incomes of wage earners in the North would have declined substantially less than they actually did. Our estimates of the equilibrium real wage show that the wage lag mechanism accounted for approximately two-thirds of the decline in real income experienced by wage earners during the Civil War. A corollary implication of these findings is the rehabilitation of the ideas of Wesley Clair Mitchell, one of the first systematic quantitative economic historians. Mitchell anticipated Keynes in positing a redistribution of income brought about by inflation in the short run, and he anticipated Kessel and Alchian in the belief that, in the long run, nonmonetary forces ultimately determined the level of wages and profits. Our approach shares with modem Phillips curve models the property that the inflation process affects the economy through rigidities in the functioning of markets. These rigidities are of two types. The first are those associated with costly information. This idea is embodied in the assumption that expectations were formed adaptively, so that economic agents may have erred in their predictions of the price level and other relevant economic variables (Barr0 and Fischer, 1976, pp. 156-161). Second, adjustment was hampered by institutional constraints which prevented agents from altering existing agreements at the instant new information became available (Fischer, 1977). The difference between our analysis and the Phillips curve literature is that we do not attempt to determine whether inflation resulted in a shift in aggregate supply. The turmoil of the war makes it impossible to isolate the effect of inflation alone on output. Our model, in the spirit of Keynes and unlike the modem monetary literature, focuses on the impact of inflation on the distribution of output and the implied distribution of the burden of the war rather than on the direct effects of monetary and fiscal policy on output and employment. A complete assessment of the economic burden of the Civil War on the various classes is difficult in the absence of detailed accounts of the incomes of groups other than wage earners. The federal deficit must have been financed at the expense of some combination of wages, interest, profits, and the incomes of the self-employed, unless the government could draw on hitherto underutilized resources. As the economy was close to full employment in 1860, and since the evidence for significant shifts in labor participation is not strong, the latter was of minor importance. The resources taken for the war effort clearly imposed costs on someone. The wage lag was instrumental in shifting resources from wage earners to the government, but this transfer was not a larger share of the total deficit because only a relatively small portion of the labor force was subject to the lag. Even so, the reduction in workers’ income was on the order of three-quarters of the tax revenue. The contribution of the wage lag to financing the war effort must have been somewhat less than this amount,

328

DECANIO

AND MOKYR

since part of the transfer passed through the hands of residual claimants whose marginal propensity to save was less than unity. The bulk of the resources for the war therefore apparently was obtained through other mechanisms, namely, those discussed in Section II. More research, however, will be required before we can accurately determine “who paid for the war.” Finally, while it is difficult to rationalize a long-run wage lag, the evidence is much stronger for the existence of short-run lags, especially in periods of sharp, unanticipated inflation, typically induced by wars.le The wage lag during the American Civil War contributed to the mobilization of resources for the war effort, but its main impact was on the level of individual wage earners’ incomes. Two intriguing questions are suggested by these results: First, how, if at all, did this form of taxation affect wage earners’ support for the Union war effort? Second, to what extent did the decline in real wages during the war affect the postwar acceleration of growth and capital formation experienced by the Northern States? APPENDIX Variables and Data

The variables used in estimating Eq. (12) and their sources are the following: wt, pt. The wage and price data are from Lebergott (1964) for 1860- 1900 and Coelho and Shepherd (1974, 1976) for 1851-1859. Coelho and Shepherd’s wage and price indexes were linked to Lebergott’s at the 1860 point of overlap. For reasons discussed by Lebergott (1964, pp. 289-304, 337-352) his wage and price series are the most comprehensive and reliable for the period 1860-1900.20 I8 The same point is made for the Napoleonic wars in England by most standard texts (Deane, 1%9, p. 245; Mathias, 1%9, p. 46; Bumet, 1969, p. 245). A recent review article notes that “real wages tend to change most in periods of rapid price movement” (Flinn, 1974, p. 408). Flinn fails to find any conclusive evidence regarding the decline of real wages during the Napoleonic war period as a whole, though the data he presents are ambiguous. Moreover, ifthe short-run wage lag was largely a reflection of the fact that inflation was unanticipated, it is plausible that after more than 20 years the ability of the English government to tax the wage earners through inflation was limited. Finally, Flinn’s finding that wages and prices, by most accounts, had both increased 60-70% between 1788/1792 and 1810/1814 does not exclude the possible operation of a short-run wage lag between those dates. *OCompilations of alternative wage and price data are contained in Hansen (1925), Tucker (1933), Long (l%O), and United States Bureau of the Census (1960). Coelho and Shepherd’s wage and price data (1974, 1976) end in 1880 and therefore provide an insufficient number of data points for estimation. It should be noted that Lebergott’s wage and price Table A-19 contains an obvious typographical error. The real wage in 1864 should be $337 (1914 dolIars), the ratio of the money wage to the price index in that year (this correction is confirmed by Professor Lebergott) (Lebergott, 1%4, p. 528; the typographical error is repeated in Davis et al., 1972, p. 212).

INFLATION

AND

WAGE

LAG

IN AMERICAN

CIVIL

WAR

329

C. Constant term. T. Pure trend. IZ~. The potential labor force is represented by total population reduced during the Civil War by a fraction obtained by calculating the proportion of the Northern labor force serving in the armed forces. The basic population variable used was total United States population rather than an estimate of the Northern population. This is acceptable since the non-South population remained a fairly constant fraction of total United States population over the sample period, ranging from 72% in 1860 to 75% in 1900 and never moving outside that narrow range. The armed forces reduction factor for 1860- 1865 was calculated as the ratio of above-trend armed forces to the non-Southern labor force (United States Bureau of the Census, 1960, pp. 9, 12-13, 736-737; Lebergott, 1964, p. 510). a,. The adjusted price ratio as used here is defined as At = (ZtUs/ZtUK)I Gf, where Ztus = the United States wholesale price index (Warren and Pearson, 1933, pp. 12-13); ZtUK = the United Kingdom wholesale price index (Mitchell and Deane, 1962, pp. 474-475); and G, = an index of the price of gold in dollars (Mitchell, 1908, p. 4). The value of G, was taken to be 1.0 after resumption of specie convertibility in 1879. [See Kindahl (1961).] The adjusted price ratio represents the deviation of the price of gold from the value which would be implied by the purchasing power parity theory. (Since most United States trade during this period was with the United Kingdom, the price level in the United Kingdom may be taken as a proxy for the price level of the United States’ trading partners.) The variable A, therefore measures changes in the domestic price of imports not attributable to changes in the United States price level. y,. Annual real GNP (Berry, 1968, p. 32). qt. Industrial production index (United States Bureau of the Census 1966, pp. 168-169). D,. A Civil War dummy variable taking on the value 1 over 1860-1865 and 0 over 1866-1900. D, . T. Product of the trend and the Civil War dummy. The variables rtl, a,,~~, and qt are in natural logarithms (lower-case notation), while T and Df are not. The trend is included to allow for disembodied productivity growth and to permit trended variables such as the industrial production index to capture business cycle influences. Inclusion of the adjusted price ratio, GNP, and industrial production variables is required to test the Kessel and Alchian hypotheses that the disruption in trade and decline in domestic output adversely affected real wages. The dummy variables on the constant and trend during the Civil War are necessary both to provide a fair test of the Kessel-Alchian hypotheses and to fit the wage equation accurately. The Civil War dummy variables will capture the effects of real forces inadequately represented by the other xit. Examples of such real

330

DECANIO AND MOKYR

forces include the federal wartime taxes and the drawing of soldiers from the prime working age groups [which could have decreased the quality as well as the size of the labor force (Engerman, 1965, p. 188)]. The dummies may also partially reflect wage lag or expectational effects as well as the effects of these real forces. To the extent that this takes place, however, our estimates will understate the importance of the lag mechanism, since we attribute all of the influence of the dummy variables to real forces. This is appropriate since the Kessel and Alchian explanation is the “null hypothesis” being formally tested. Speci’cation

of Lag Structure and Disturbance

Table A. 1 contains two-stage least squares estimates of the coefficients of (12) under alternative assumptions regarding the structure of the lags and disturbance terms. Specifications (i)-(iv) were estimated by TSLS assuming that the disturbance was not autocorrelated. The TSLS procedure with current wt andp, endogenous was to treat the ( w~-~ - pt) variables as endogenous, and to include all the wI+ as instruments. Identification was secured by inclusion of the nominal money stock mt,21 the nominal stock of federal interest-bearing debt b, (United States Bureau of the Census, 1960, p. 721), and pt-l as instruments. All past rates of inflation and lagged wages were treated as predetermined. Thus the complete set of instruments consisted of all the exogenous xit and the predetermined or exogenous wt-j, (p,-j -pt-j-l), m,, bt, and pt-1. Specifications (v)-(viii) were estimated assuming a first-order autocorrelated disturbance. The estimation procedure in this case is outlined in Fair (1970). The (wt..+ - pt) were again treated as endogenous, and the instrument list of the nonautocorrelated case was augmented by the endogenous, exogenous, and predetermined variables of Eq. (12) lagged one year (eliminating linearly dependent variables from the instrument list). The estimation procedure iterated over the autocorrelation parameter p until the minimum sum of squared residuals was found. Four alternative specifications of the lag structure are reported. Equations (i) and (v) allow all the 4j to be different. Equations (ii) and (vi) constrain all the #+ beginning with & to be equal. All specifications allow n1 through 7r4 to be different, but constrain the mj to be equal beginning with TV. Specifications (iii), (iv), (vii), and (viii) are the same as specifications (i), (ii), (v), and (vi), respectively, except that the constraint of longrun neutrality - 2 = 0) was imposed prior to estimation. (See notes to Table A. 1.) (C?Tj

j$j

*I The nominal money stock for 1867-1900 was taken as money supply plus time deposits from United States Bureau of the Census, 1966, pp. 208-209, Series B-l 11 (Friedman and Schwartz). For 1860-1866, the money stock estimates were constructed by working backwards from 1867 using successive annual money supply ratios computed from Friedman and Schwartz (1970, pp. 224-225).

INFLATION

AND WAGE LAG IN AMERICAN

331

CIVIL WAR

TABLE A. 1 TSLS Coefficient Estimates and Associated t Ratios for the Wage Determination Equation, 1861- 1900, wI -PI = C Ax*t + 1 Tj(Pt-j - PI-j-11 + IL djtwt-j -PO + Ut 1 1 , Lag and disturbance specification’

Variable c

(0

T

D.T

”

(1 0.0730 IO.4561

-29.984 [-1.7721

0.0288 Il.8451

-0.0534 [-2.1621

-1.314 I- 1.6201

(ii)

- 19.347 [-1.509]

0.0220 [I.7231

-0.0346 [-1.8881

- 1.222 [-1.7611

(iii)

-29.797 [-1.8301

0.0293 [1.980]

-0.0515 [-2.3291

-1.387 [-l.%lI

0.0835 [0.569]

(iv)

-17.455 [-1.404]

0.0191 [I.6151

-0.0363 [-xm]

-1.029 j-1.6711

0.0102 (0.09831

(-4

-18.519 1-1.4941

0.0184 [1.523]

-0.0330 [-1.7631

-0.858 [-1.3431

(vi)

-7.994 [-0.7031

0.0102 IO.8821

-0.0195 (-1.1511

-0.616 [-0.9701

(vii)

- 19.308 [-1.5671

0.0180 [l.S221

-0.0381 [-2.2811

-0.771 [-1.3161

(viii)

-6.912 [-OS991

0.00850 [0.762]

-0.0232 [-1.3561

-0.507 [-0.8661

4

D

0.172 [1.607]

99.535 12. la]

0.222 [2.690]

64.579 [1.893]

0.187 [2.530]

95.946 [2.334]

0.194

67.651

Y 0.0615 [0.453]

0.0552 [0.432]

I=3401 ~2.0071 0.00424 [0.0417]

0.213 [2.7701

61.675 [1.770]

0.00319 [O.O2S6]

0.0531 CO.4821

0.226 [3.082]

36.497 [1.158]

0.0728 [0.639]

0.0180 [0.179]

0.192 [2.986]

71.192 [2.289]

0.0855 [0.780]

0.202 L3.0231

43.293 L1.3631

(i)

-0.733 [-2.0901

-0.220 [-0.7941

-0.492 [-2.4101

-0.220 [-1.0331

-0.603 [-1.5581

0.505 [2.210]

0.111 [OAOO]

(ii)

-0.692 [-2.3801

-0.250 [-1.3051

-0.320 [-2.0351

-0.147 l-O.9991

-0.429 [-2.1971

0.548 [2.986]

0.0613 [0.256]

(iii)

-0.715 [-2.1811

-0.218 (-0.817)

-0.477 I-2.5861

-0.1% [-1.1461

-

0.529 12.7781

0.0905 [0.361]

-0.0558 I-0.2011

(iv)

-0.717 [-2.4951

-0.249 [-1.2991

-0.330 [-2.1061

-0.189 [-I.4641

-

0.501 (3.0141

0.104 [0.456]

-0.00363 [-0.01441

-0.0507 [-0.2581

-

w

-0.933 [-2.9871

-0.344 [-1.5571

-0.309 [-1.6101

-0.0620 [-0.3071

-0.633 [-2.609]

0.805 [4.040]

-0.305 [-I.0451

0.170 10.5121

-0.110 [-0.3421

-0.194 [-0.7051

(vi)

-0.809 [-2.7441

-0.243 [-1.2241

-0.219 I-l.3281

-0.207 [-1.3441

-0.289 [-Z.OSS]

0.627 13.4321

-0.0773 [-0.2951

0.0760 [0.265]

-0.0521 [-0.2541

-

(vii)

-0.957 [-3.1931

-0.317 [-1.5201

-0.343 I-l.9631

-0.128 I-O.8231

-

0.718 [4.143]

-0.188 [-0.7281

0.0486 IO.1731

-0.0184 [-0.0651]

-0.231 [-0.9291

(viii)

-0.801 [-2.7901

-0.231 I-l.1871

-0.254 [-1.6161

-0.238 [-1.8201

-

0.534 [3.183]

-0.00640 [-0.0244)

-0.0170 [-0.08431

-

0.0381 10.1611

-0.0770 [-0.2521 0.0400 [0.153]

Variable

(9

0.00237 [0.009371

-0.125 C-O.4571

0.197 [0.664]

-0.251 [-0.9241

0.152 [0.484] -0.0640 [-0.3231 0.140 (0.4681

-0.285 [-1.1971 -

-0.273 [-1.2261

Statistic

-0.0568 [-0.3041

-

0.991

0.827

0.161

0

332

DECANIO

AND

TABLE

MOKYR

A. 1 -Continued

Variable

Statistic

-

-

-

-

-

-0.0454 L-2.4571

0.990

0.688

(iii)

0.00435 10.01781

-0.107 f-O.4271

0.179 LO.6541

-0.248 [-0.9491

-0.0412 [-0.2491

-

0.991

0.783

0

0

(iv)

-

-

-

-

-

-0.0532 [-4.0201

0.989

0.768

0

0

-0.101 (-0.3301

0.0407 [0.1461

-0.238 L-1.362)

-

-

0.998

0.725

-0.302

-0.525

-

-

-

-

-

-0.0550 [-2.5291

0.995

0.702

-0.332

-0.288

(vii)

0.186 (0.6991

-0.145 [-0.530)

0.103 CO.4251

-0.28d (-I.8921

-

-

0.998

0.811

0

-0.466

(viii)

-

-

-

-

-

-0.0664 (-4.124)

0.993

0.784

0

-0.185

(ii)

w

(vi)

0.209 [0.726]

-0.329

0

a For each specification (i)-(viii). the estimated value of the coefficient of each variable is listed in the column headed by the variable. The number in brackets below each estimated coefficient is the t ratio, the coefficient divided by its standard error. Blanks (-) indicate that the variable did not appear in the specification. The “real” variables C through D (with time subscripts omitted) are defined in the Appndii. The sample pmiod is Ml-I900 (with lagged variables extending back to 1851). The lag variables are defined (for each observation) as follows. Specifications (i)-(ii): j = 1, , 10, m, = wt-, - PI, 10 4 = Z +L -PA I-S j=l,...,4, *, = Pt-J -PI-H.

!h = (PI-1 -pt-l-1)

m, = (w-,

-PO

- w5i

+iW5)

k-6

(PM

j=l,...,4,

-PI-k-l),

i (P,-* -PI-k-l

).

j = 1,

, IO,

Thus the coefficients of the ml are the r$, and the coefficients of the $, are the w, of Eq. (12). The restriction & = 4. = +, = & = 6 = QIP is imposed in specifications (ii) and (iv), and the coefficient of m, is the common value of these parameters. The restriction ?rs = ?ra = r, = n. = ws is imposed in all four specifications, and the coefficient of $ in (i) and (ii) equals E: Ls r,. The definitions of m,. m,, and & in (iii) and (iv) amount to imposing the neutrality restriction 1 n, - 1 j+, = 0 in those specifications. Specifications (v)-(viii): In these specifications, the variables are defined similarly to the variable definitions in specifications (i)-(iv), except that one fewer legged wage and one fewer lagged inflation rate are included. Thus $ is the average of only the tifth through eighth lagged intlation rates, and m, includes only lagIted wage terms through (wIws - pl). The variables in tbc specifications in which inflationary neutrality is imposed [(vii)-(viii)] are adjusted accordingly. Omission of the terms involving IV-,~ and p,-lois dictated by the necessity of including all endownous and predetermined variables lagged once in the instrument list for the TSLS autocorrelated disturbance estimator. together with the fact that the data extends only 10 periods back from the initial sample date of 1861. Interpretation of the coefficients is entirely analogous to the interpretations of the coetlicicnts of specifications (i)-(iv).

INFLATION

AND

WAGE

LAG

IN AMERICAN

CIVIL

WAR

333

The possibility of structural change during the sample period always threatens the validity of time series results, but we have attempted to minimize the risk by restricting our interval of observation to one in which (except for the Civil War) the main institutional outlines of the American economy (and in particular, of the labor market) remained relatively unchanged. Statistically, Eq. (12) including the dummy variables appears adequate to embody the economic changes which occurred during the Civil War. F tests of the null hypothesis that the structure of the model was the same during the Civil War years as during the postwar period do not lead to rejection of that hypothesis even at high probabilities of Type I error. The appropriate F statistics (Johnston, 1972, p. 207) for the nonautocorrelated specifications (i)-(iv) were not significant at the 25% level. All the specifications contain a large number of lagged wage and price change terms. Inclusion of these long lags is justified on both theoretical and empirical grounds. In the nineteenth century, government monetary policy either was directed at an objective other than explicit control of the rate of price change (as in the announced plan to resume specie payments after the Civil War) or was largely passive (as under the gold standard after 1879). Thus it is likely, whatever model of expectations is preferred, that a fairly long period of experience would be required for a prolonged inflation or deflation to be completely assimilated and full neutrality [restrictions (9) and (ll)] to be embodied in the lag coefficients. This theoretical and historical presumption is supported by the statistical evidence. When multicolhnearity is reduced by imposing equality constraints on the more distant lagged price inflation and wage rate coefficients, the later price inflation (4) coefficients are usually more than twice their standard errors and the later wage rate (m,) coefficients are all significantly different from zero. The estimates certainly provide no evidence against the hypothesis of long-run inflationary neutrality. Estimated values of 1~~ - Cj+j are close to zero in those specifications in which this restriction is not imposed. For example, in specification (ii), the coefficient estimates imply that a sustained inflation rate of 13% per annum (the average Civil War rate) would lead to a limit wage of 94% of the equilibrium wage; in specification (i) the limit wage overshoots the equilibrium and settles at 103% of the equilibrium wage. In these two specifications, F tests of the linear restriction (11) do not lead to rejection of the null hypothesis of long-run neutrality [F values of .0438( 1,17) and .364( 1,22) for (i) and (ii), respectively], but these tests are of very low power because of the lack of precision of the individual coefficient estimates. Experiments were performed with various lag structure specifications other than the ones reported in Table A.l. All these experiments confirmed the main outlines of our results, although there was some variation in the computed magnitude of the gap ( @,*/P3 - ( *JPt) from specification

334

DECANIO

AND MOKYR

to specification. For example, equations similar to (12) were estimated including only lagged wage rates (i.e., the rj were all set equal to zero). The results were similar to those reported here, although the largest and smallest of the calculated cumulative gaps in these wages-only models were more extreme than the largest and smallest cumulative gaps shown in Table 2. It is possible (though not very likely) that only past wage rates influenced the inflationary expectations of workers, but in any event the wages-only specifications are clearly inferior to Eq. (12) on statistical grounds, in light of the significance of the estimated Tj. In addition, variants of Eq. (12) were estimated including only a small number of lagged terms. These specifications too are inferior to the reported results on statistical grounds (because of the significance of the coefficients of $I and m,), and also lead to implausible conclusions regarding inflationary neutrality. For example, if only four lagged wage and four price inflation terms are included, the estimated cumulative gap is $390 in the nonautocorrelated specification and $419 in the autocorrelated specification. However, the limit wage resulting from sustained inflation at the Civil War rate of 13% is only approximately 75% of the equilibrium value in these two cases. On the other hand, if inflationary neutrality is imposed in these few-lag specifications, the estimated cumulative gap is $118 in the nonautocorrelated case and $170 in the autocorrelated case. For the reasons discussed above, we believe the requirement that an inflationary or deflationary experience be fully incorporated into expectations in five years or less to be implausible, but even the smallest of these gap estimates ($118) is 37% of a single nonfarm worker’s cumulative Civil War income loss. While all these alternative specifications confirm the existence of the wage lag effect, we believe that the estimates presented in Table 2 constitute the best estimates of the magnitude of the effect. REFERENCES Abramovitz, M., and David, P. A. (1973), “Reinterpreting Economic Growth: Parables and Realities.” American Economic Review LXIII, 428-39. Alchian, A. A. (1970), “Information Costs, Pricing, and Resource Unemployment.” In E. S. Phelps et al. (Ed.), Microeconomic Foundations of Employment and Inflation Theory. New York: W. W. Norton. Pages 27-52. Barro, R. J., and Fischer, S. (1976), “Recent Developments in Monetary Theory.” Journal of Monetary Economics 2, 133- 167. Berry, T. S. (l%S), Estimated Annual Variations in Gross National Product, 1789 to 1909. Richmond: The Bostwick Press. Budd, E. C. (l%O), “Factor Shares, 1850-1910.” In Conference on Research in Income and Wealth, Vol. 24: Trends in the American Economy in the Nineteenth Cenfury. Princeton: Princeton University Press for the National Bureau of Economic Research. Burnett, J. (1969), A History of the Cost ofLiving. Harmondsworth: Penguin Books. Cargill, T. F. (1%9), “An Empirical Investigation of the Wage-Lag Hypothesis.” American Economic Review LIX, 806-816.

INFLATION

AND WAGE LAG IN AMERICAN

CIVIL WAR

335

Chiang, A. C. (1974), Fundamental Methods of Mathematical Economics. New York: McGraw-Hill. Cochran, T. C. (l%l), “Did the Civil War Retard Industrialization?” Mississippi Valley Historical Review XLVII, 197-210. Coelho, P. R. P., and Shepherd, .I. F. (1974), “Differences in Regional Prices: The United States, 1851-1880.” Journal of Economic History XXXIV, 551-591. Coelho, P. R. P., and Shepherd, J. F. (1976), “Regional Differences in Real Wages: The United States, 1851-1880.” Explorations in Economic History 13, 203-230. Davis, L., Easterlin, R., Parker, W., et al. (1972), American Economic Growth: An Economist’s History of the United States. New York: Harper and Row. Deane, P. (1969), The First Industrial Revolution. Cambridge: Cambridge University Press. Dewey, D. R. (1934), Financial History ofthe United States. New York: Longmans, Green. Engerman, S. (1966), “The Economic Impact of the Civil War.” Explorations in Entrepreneurial History 3, (second series), 178- 199. Fair, R. (1970). “The Estimation of Simultaneous Equation Models With Lagged Endogenous Variables and First Order Serially Correlated Errors.” Econometrica 38, 507-516. Fischer, S. (1977), “Long-term Contracts, Rational Expectations, and the Optimal Money Supply.” Journal of Political Economy 85, 191-205. Fite, E. D. (1910), Social and Industrial Conditions in the North During the Civil War. New York: Macmillan. Flinn, M. W. (1974), “Trends in Real Wages, 1750-1850.” Economic History Review XXVII, 395-413. Friedman, M., and Schwartz, A. J. (1970), Monetary Statistics of the United States. New York: National Bureau of Economic Research. Gallman, R. E. (1966), “Gross National Product in the United States, 1834-1909.” In Conference on Research in Income and Wealth, Studies in Income and Wealth, Vol. SO: Output, Employment, and Productivity in the United States after 1800. New York: National Bureau of Economic Research. Goldin, C. D., and Lewis, F. D. (1975), “The Economic Cost of the American Civil War: Estimates and Implications.” Journal of Economic History XXXV, 299-326. Gordon, R. J. (1973), “Interest Rates and Prices in the Long Run: A Comment.” Journal of Money, Credit and Banking V, 460-463. Gordon, R. J. (1975), “The Supply of and Demand for Inflation.” Paper presented to N.B.E.R. Conference on the Economic Analysis of Political Behavior, April. Gordon, R. J. (1976), “Recent Developments in the Theory of Inflation and Unemployment.” Journal of Monetary Economics 2, 185-219. Gunderson, G. (1974), “The Origin of the American Civil War.” Journal of Economic History XXXIV, 915-950. Hansen, A. H. (1925), “Factors Affecting the Trend of Real Wages.” American Economic Review XV, 27-42. Holzman, F. D. (1950), “Income Determination in Open Inflation.” Review of Economics and Statistics XxX11, 150-158. Johnston, J. (1972), Econometric Merhods, second ed. New York: McGraw-Hill. Kessel, R. A., and Alchian, A. A. (1959), “Real Wages in the North During the Civil War: Mitchell’s Data Reinterpreted.” Journal of Law and Economics II, 95-113. Kessel, R. A., and Alchian, A. A. (1960), “The Inflation-Induced Lag of Wages.” American Economic Review L, 43-66. Keynes, J. M. (1940), How to Pay for the War. New York: Harcourt, Brace, Jovanovich. Kindahl, J. K. (1961). “Economic Factors in Specie Resumption: The United States, 18651879.” Journal of Political Economy 59, 30-48. Koopmans, T. (1942), “The Dynamics of Inflation.” Review of Economics and Statistics XXIV, 53-65.

DECANIO AND MOKYR

336

Lebergott, S. (1964), Manpower in Economic Growth: The American Record Since 1800. New York: McGraw-Hill. Long, C. D. (1960), “The Illusion of Wage Rigidity: Long and Short Cycles in Wages and Labor.” Review of Economics and Statistics XLII, 140-151. Maital, S. (1972), “Inflation, Taxation and Equity: How to Pay for fhe War Revisited.” Economic Journal 82, 158- 169. Mathias, P. (1%9), The First Industrial Nation. London: Methuen. Mitchell, B. R., and Deane, P. (1962), Abstract of&fish Historical Statistics. Cambridge: Cambridge University Press. Mitchell, W. C. (1903), A History ofrhe Greenbacks. Chicago: University of Chicago Press. Mitchell, W. C. (1908), Gold, Prices, and Wages under the Greenback Standard. Berkeley: University of California Press. Modigliani, F. (l%l), “Long-Run Implications of Alternative Fiscal Policies and the Burden of the National Debt.” Economic Journal LXXI, 730-755. Muth, J. F. (l%l), “Rational Expectations and the Theory of Price Movements.” Econometrica 29, 315-335. Parkin, J. M., and Laidler, D. E. W. (1975), “Inflation: A Survey.” Economic Journal 85, 741-809. Reid, J. D., Jr. (1976), “Understanding Political Events in the New Economic History.” University of Chicago, Center for Mathematical Studies in Business and Economics, Report 7616 (April). Smithies, A. (1942), “The Behavior of Money National Income Under Inflationary Conditions.” Quarterly Journal of Economics LVII, 113- 128. Studenski, P., and Krooss, H. E. (1952), Financial History ofthe United States. New York: McGraw-Hill. Temin, P. (1976), “The Post-BeIlum Recovery of the South and the Cost of the Civil War.” Journal

of Economic

History

36, 898-907.

Todd, R. C. (1954), Confederate Finance. Athens, Ga.: University of Georgia Press. Trescott, P. B. (1966), “Federal Government Receipts and Expenditures.” Journal of Economic History XXVI, 206-222. Trevithick, J. A. (1975), “Keynes, Inflation, and Money Illusion.” Economic Journal 85,337 101-113. Tucker, R. S. (1933), “Real Wages Under Laissez-Faire.” Barron’s XIII, (October 23), 6-7. United States Bureau of the Census (1960), Historical Statistics of the United States, Colonial Times to 1957. Washington: Government Printing Office. United States Bureau of the Census (1966), Long Term Economic Growth, 1860-1965. Washington: Government Printing Office. Warren, G. F., and Pearson, F. A. (1933), Prices. New York: John Wiley. Williamson, J. G. (1974a), Late Nineteenth-Century American Development. Cambridge: Cambridge University Press. Williamson, J. G. (1974b), “Watersheds and Turning Points: Conjectures on the Long-Term Impact of Civil War Financing.” Journal of Economic History XXXIV, 636-661.