wages and profits

COLIN CLARK University of Queensland

Wages and Profits

Wages and profits must be regarded as simultaneously determined-profits must not be regarded as a residual. In the short period both are determined by current demand, profits fluctuating much more strongly than wages. More important is the long-period factor, which depends upon capital-labor substitution elasticity.

As seen in Figures 1 and 2, fairly good predictions of the absolute values (not merely changes) of wages and profits can be made, using only the following information: short-period factor, current aggregate real demand; long-period factors, trend (5 years moving average) of labor inputs measured in man-hours; real net capital stock at the beginning of the year; and replacement value of net capital stock at the beginning of the year. Yet many well-known econometric analyses attempt to do no more than explain changes in wages, usually by using the well-known “Phillips Curve” or some modification of it.

Phillips (1958) thought that he had shown that there was a close relationship between unemployment and the rate of increase in money wages. This idea became deeply entrenched in official and academic thinking throughout the world, with unfortunate results. In recent years administrators, who had come to believe that wage inflation would be checked if there were a moderate rise in unemployment, have found themselves confronted with high and rising unemployment combined with rapid increases in money wages and have been at a loss for an explanation or a policy.

However, the whole “Phillips Curve” rested on defective statistical foundations. Phillips formulated his theorem on British evidence only, covering a period of some eighty years. He made two basic statistical errors. First, he failed to distinguish between wage rates and earnings. The latter include piece rates, overtime, upgrading of jobs, and other factors sometimes summarized under the general heading of wage-drift; and in busy periods, earnings can rise much more rapidly than wage rates. Phillips also failed to realize that the British pre-I920 unemployment statistics which he used were not comparable with the national unemployment insurance statistics available for later years. The earlier figures

Journal of Macroeconomics, Summer 1979, Vol. 1, No. 3, pp. 245-266. 245 @ Wayne State University Press, 1979.

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were based on labor union records and very much overstated the amount of unemployment in those days, because only the unions in trades espe- cially susceptible to unemployment used to operate unemployment insurance funds.

Phillips’ conclusions could have been invalidated twenty years before he wrote from the United States evidence. In the late 1930’s unemployment in U.S.A. still stood at extreme levels. Yet this decade was a time of rapid increases in money wages. It is true that during these years American labor unions (due in part to legislative encouragement) were considerably increasing in strength, accounting for only a part of the observed wage increase. Wage increases were also marked in non- unionized industries. Therefore, if increases in money wages are not regulated by the amount of unemployment, as they clearly are not, then what does determine them?

Labor demands, union aggressiveness, and similar explanations fre- quently offered can be generalized into the term cost-push inflation. In the past it has generally been held that the cause of inflation was demand-pull, i.e., the creation of excessive demand through unduly en- larged money supply or in other ways. Now we are often told that inflation generated by cost-push factors must be directly dealt with, i.e., by legal controls on prices and wages, and that it is purposeless to attempt to control demand.

These doctrines are erroneous and dangerous. Cost-push is a truism in the sense that increased costs, with little delay, get built into prices whether they arise from increased wages, indirect taxes, import prices, or, for that matter, from increased profits. Whatever may be the case regarding the minor components of price increases (indirect taxes and import prices), the idea that wage increases arise exogenously (i.e., by some decisions made independently of demand conditions) is entirely mistaken. Rising wages are the consequence, not the cause, of inflation.

Unfortunately, about 1971, two leading economists who had great influence with their respective governments, and who had hitherto been staunch upholders of demand-pull theory (Dr. Bums in the U.S.A. and Professor Paish in Britain), suddenly changed sides and advised their governments that legal controls over prices and wages had now become necessary. Furthermore, their advice was accepted. In the U.S.A. the results were laughable, but futile attempts at price and wage control did a good deal to bring the law into disrespect. In Britain the results were far more serious, resulting in disastrous strikes and the overthrow of the Heath Government.

Those who still think that wage increases are exogenous will have to explain why they have come at this time, when they did not come in the

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past. Much is said about labor’s demands. But does one really get things just by demanding them in this world, at any rate? What must be explained is not so much labor’s demands, but why employers, complaining no doubt, are willing to make the wage payments that they do make.

A further question. So many of these theories, from the “Phillips Curve” onward, offer only to explain wage increases. What needs explain- ing is why wages, at any date, are at a particular level. It will not do to define wages merely as a random aggregation of past wage increases.

Are there not factors which explain the general level ofwages in any other terms than a cumulation of past increases? Let us put the question in another form. Suppose, in some period, there has been some quite anomalous factor causing an unusual increase (or decrease) in wages. Is this change going to be permanently embalmed in the wage level, with subsequent increases or decreases merely added to it? Or are there forces generating equilibrium levels of money wages which may be expected to modify progressively the effects of any such anomalous movement? The analysis which follows will show that what might be called the Phillips Effect is not entirely absent but is of comparatively small importance.

Eckstein and Wilson (1964) appear to have been the first to suggest that money wages might not be determined solely in the labor market but might also be influenced by the pressure of current demand on industry’s productive capacity. When the industrialist is worried about being able to maintain deliveries, he is more likely to grant wage increases and vice versa.

While there have been so many attempts by so many different methods to explain movements of wages, remarkably little has been done to explain movements of profits. Indeed the designers of many well- known econometric models treat them as no more than a residual. If they can claim that they have other equations which will explain prices and output, i.e., gross sales and labor remuneration to be deducted, namely, employment and wage rates, together with the minor cost items of import prices and indirect taxation, then we are necessarily left with an algebrai- cally determined residual for profits to which comparatively little atten- tion has been paid. In fact, the process of analysis ought to begin with an explanation of profits. Though not proportionate to profits, labor’s ability to demand wages depends upon their being earned. If an industry (temporary fluctuations apart) is not earning profits, it will soon close down, and there will be no wages paid.

Wages and profits must be regarded as being simultaneously determined, and (the other necessary information having been provided) it is prices, not profits, which must be regarded as the algebraic residual. As aggregate demand changes over the business cycle, profits, as is well

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known, are subject to violent fluctuations. Wages fluctuate considerably less, though labor has to face fluctuations in the amount of employment (to be more precise, in the number of manhours worked, taking into account changes both in employment and in the amount of overtime).

Short-period movements apart, how should we expect the long- period relation between the wages and the rate of profit to be determined? By using the elasticity of capital-labor substitution, which is surely good Hicksian theory, even though little application has been made of it. To advance the use of capital-labor substitution is not the same thing as saying that the relative shares of labor and capital in the product of industry are necessarily so determined. These relative shares will de- pend not only on relative remuneration but also on the levels and rates of growth of the quantities of capital and labor inputs.

Theoretical reasoning has so far mainly been applied to the pos- sibilities of capital-labor substitution within a firm. However, we must look more widely than this; in analyzing the macro relationship, we must take into account not only the replacement of less capitalized firms by more capitalized ones but also displacements of demand (so far as they are due to changes in relative prices) between labor-intensive and capital- intensive products, e.g., the rising importance of chemicals and engineering products relative to residential construction, clothing, and jewelry expenditure.

In searching for a substitution function, we must be careful to get our dimensions right. Wages represent a money payment for a real hour of work. So likewise we must define profits, not as the ordinary percent- age rate of return, but as the money return on the real valuation of the net capital stock (at prices of the I972 base date).

Businessmen are indeed aware that both profits and output are subject to strong fluctuations. At the same time they have to aim at a price, for a normal year, which will cover their costs and yield a gross margin sufficient to cover depreciation and profits on new investment; and their competitors will be in the same position. So such prices and profits will, in fact, eventuate. If they do not, new investment will not take place and, in a growing economy, shortages will soon supervene.

It is also intuitively clear to businessmen-whatever book entries their accountants may make, and however inadequate the depreciation allowed by the tax laws-that they will have to obtain an adequate gross profit on capital investment at its new price. A firm which earned only sufficient gross profit to service its capital assets at their old book value, in these times of persistently rising prices, would soon go out of business. So it follows that gross profits, after short-period fluctuations have been

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eliminated, will, other things being equal, have to rise almost im- mediately in proportion to any rise in the price of capital goods.

The important point, which will now be demonstrated, is that wages adapt themselves (though in a gradually changing proportion) to gross profits, i.e., to normal profits on a normal output. These gross profits vary proportionately to capital goods prices, and wages will therefore vary also. So we reach the interesting conclusion that the driving force of the in- flationary spiral is the rising price of capital goods, not consumption prices, as is generally supposed. However, this idea is not as novel as it appears. It was first propounded by that remarkable Swedish pioneer in economic thinking in the 1930’s, Erik Lindahl; and in recent times it has been developed in the United States by Lloyd Metzler.

It is true that there is considerable correlation between the movements of capital goods and consumer goods prices, and so it will not be easy to devise satisfactory statistical tests. For example, as the demand for investment goes up, engineering products may be produced with economies of scale and not rise markedly in price. But the other principal component of investment, namely construction, sometimes shows marked diseconomies of scale (mainly due to shortages of skilled labor), and large price rises occur, which more than offset engineering prices. Therefore, how are wages related to normal profits?

The process of wage bargaining can best be analyzed in the form of imaginary conversations, which do not in fact take place, but whose reasoning is thought to proceed intuitively in the minds of the participants.

“I see that you have new and expensive capital assets on which you urgently need to earn profits,” says the labor leader to the employer. “How much will you pay me not to close you down?’

“Oh, quite a lot,” replies the employer. “But I must remind you that there is now considerable unemployment, and according to the Phil- lips Curve there ought not to be any wage increase.”

“I don’t give an (expletive deleted) for the Phillips Curve and the general level of unemployment,” replies the labor leader. “Labor is all specialized nowadays. The only unemployment which concerns me is that which affects members of my own union.”

“Exactly so,” replies the employer. “If you ask for excessively high wages, I will buy still more expensive equipment and put some of you out of work.”

“So you think that there is a high coefficient of elasticity of capital- labor substitution,” replies the labor leader (not that he speaks this language-but this is his meaning). “I doubt it.”

At this point, both parties retire to consult their economic advisers.

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They have both obtained approximately similar estimates of the value of the coefficient of elasticity of capital-labor substitution, and they are now able to strike a bargain.

Relating the wage-profit ratio to capital-labor substitution elasticity implies an important further assumption, namely, that technical progress is Hicks-neutral (i.e., does not alter the relative marginal productivities of labor and of capital). Much further investigation is needed before we can come to a firm conclusion on this point. It must be pointed out that two recent careful analyses [David and van de Klundert (1965) and Sato (1970)] deny that technical progress is Hicks-neutral. However, their departures from it are in opposite directions. Sato concludes that technical progress raises labor efficiency by 2% per year and capital efficiency by 1%. David and van de Klundert, however, deduce figures of only 0.7% for labor and 1.5% for capital. They find a very low substitution elasticity (0.32) and, as was to be expected, labor’s share of the product rising with time. Sato places substitution elasticity somewhere between .5 and .7 but finds (apparently using different definitions) that labor’s share of the product showed little change between NO9 and 1960. He attributed this to the variability of the substitution elasticity, which, he considered, increased when capital’s share of the product declined.

Many workers in the field have a penchant for production functions. One must, of course, most strongly protest against the attempts which are sometimes made to derive production functions from annual data whose movements are dominated by short-period factors. It is only when long- run data are available, which can be averaged over business cycles, that the estimation of production functions can be seriously attempted; and the results so far have been discouraging. It would, of course, be an achievement if we could predict both wages and profits as marginal products from a production function, not using the limiting case Cobb- Douglas, but the full Arrow-Chenery-Minhas-Solow (1961) constant elasticity of substitution production function. Differentiating this function does not appear, however, to give satisfactory results. In any case, this exercise should not be attempted, because, as Solow has shown for the U. S. A., l the growth of output has been much greater (apparently because of technical progress or returns to scale) than can be explained by the marginal productivities of the capital and labor inputs. That is to say, the capital and labor factors, remunerated at their apparent marginal productivities as calculated from a production function, would fall far short of exhausting the output.

‘Aukrust (1959) is able to demonstrate this even more clearly on the data for Norway, which cover a longer period and are better defined and articulated.

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It is assumed that the unexplained residual of the supposed true production function (or in production functions as so far formulated) is distributed between capital and labor in proportion to their marginal productivities. It is also assumed that the ratio between actual wages and actual profits can be used instead of the ratio between marginal productivities required by the true substitution elasticity equation. These assumptions are theoretically questionable; but they yield understandable results.

We now see both wages and profits (short-period fluctuations apart) dependent on changes in the replacement value of the net capital stock, with the ratio between them depending, in the long run, on the relative quantities of capital and labor inputs. We need, however, one more equation before we can solve for their values. Can we expect the total of money factor incomes (temporary fluctuations again eliminated) to move proportionately to the replacement value of net capital stock? Theoretically, this expectation is questionable, but empirically, it is found to be the case. This method of analysis, however, carries the implication that there has been no long-run change in capital-output ratios. Since 1947 this does appear to have been the case, as may be seen from the Tables, though it must be borne in mind that a novel method of defining capital has been used which gives greater weight to equipment than to the same value of structures.

It is generally held that capital-output ratios had been falling before 1947. Some of this apparent fall in capital-output may have been due to overstatement of real value of net capital stock in the earlier years, due to defective price information (discussed later). But even after allowing for this inaccuracy, significant changes in capital-output ratio are still apparent for the 1929-1947 period. For this reason, though data are available back to 1929 and are given in the Table, they have not been analyzed in the same manner as the post-1947 data. An arbitrary adjustment to I929 capital productivity (described later), eliminated linearly to give post-war capital productivity by 1941, does appear to indicate for the 1930’s a substitution elasticity similar to that found for the post-1947 years, but it has a different constant in the equation.

The National Accounts figures for real gross investment in construction were subjected to serious criticism by R. J. Gordon (1988). The construction price indices used to convert money values into real investment (about which there is a great deal of confusion) mostly represented little more than the prices of labor and materials, i.e., the inputs into construction. Though some of the indices included in the general average make some (inadequate) allowance for it, most indices, in effect, assume that there has never been any change in the efficiency of the construction

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trade, i.e., in the amount of output obtained from given inputs, to say nothing of the lesser question, whether overhead costs and profits in the construction trade always move in proportion to the prices of the labor and materials inputs. By an ingenious analysis, Gordon showed that in fact there have been, at times (but not with a steady trend), important improvements in the productivity of the construction industry, particu- larly in non-residential construction. It follows that the construction price index used (at the time Gordon wrote) in the National Accounts was rising too rapidly, and, therefore, that in the early years the real values (at latter-day prices) of gross investment, and net capital stock deduced therefrom, were over-estimated.

Gordon’s and other criticisms appear to have been taken to heart in the preparation of the more recent issue of National Income and Product Accounts. Between 1946 and 1966 (the last year covered by Gordon), while the old price index for non-residential construction rose by a factor of 2.5, the new index rose by a factor of only 1.895 in comparison with Gordon’s figure of 1.825. The official index, now represented back to 1929, is therefore taken as valid.

Gordon (1971) also advances considerable evidence to show that the official price deflator for producers’ durables (machinery and equipment) has an upward bias, due to inadequate allowances for improvement in quality. The following data imply

Year Official Gordon’s Figures Revision

1954 .840 .914 1958 1.000 1.000 1963 1.023 * 927

a bias of as much as 2% per year. Objections to Gordon’s results were, however, raised by Popkin and Gillingham (1971). (Gordon gave much further detail in the full text of his paper to the 1969 Conference of the International Association for Research in Income and Wealth.)

Unlike the price indices for non-residential construction, the official price indices for producers’ durables do not appear to have been altered in response to Gordon’s and other criticisms. Compromising between Gordon and his opponents, a quality bias of 1% per year is assumed throughout the period investigated (including the measurement of values for earlier years required to obtain an initial net capital stock for 1929). Slight adjustments are also needed for total real national product, to allow

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for the over-valuation in the earlier years of real output of producers’ durables contained in it.

The subject of investigation is not the manufacturing sector alone, but the whole U.S. economy with the following exclusions:

Government and government enterprises. The rate of remuneration of labor in this sector may be more or less the same as in private business, though showing a tendency to lag in times of rapid change. But, generally speaking, there is no remuneration of government capital, ex- cept perhaps the interest (often at an arbitrary rate) on that part of it financed by outstanding loans. In fact, we even lack adequate information on the stock of government capital. The charges made by governmental enterprises are generally politically determined, and their movements may differ widely from those of prices in the private market.

Farms. For many years now the income of farmers has been to a considerable extent politically determined rather than in the private market. In any case, the factor income earned by farming includes a considerable element of remuneration of land, not of capital or labor. The com- parative remuneration of land is not one of the subjects of our present study.

Rents of housing (including imputed rents for owner-occupiers). Quite apart from the question of whether these may have been politically influenced (through rent regulation, public housing, etc.) away from a market relationship, rents paid for housing represent predominantly remuneration for past, not current, production. Here also there is a sub- stantial element of remuneration of land. Expenditure on the maintenance of housing does, however, represent current production.

Household domestic service. Here we can only measure the labor input, and we have no measure of the value of the product nor of the capital stock (certain forms of household equipment) by which production has been facilitated.

The self-employed still constitute a considerable problem, even after we have excluded farmers. Official estimates are now available of the total man-hours worked by them. We make the unsatisfactory assumption that the average hourly compensation of all wage and salary employees may be applied to the man-hours worked by the self-employed to determine the labor component of their incomes, the remainder representing profit. Including this component of self-employment imputed profit, profits are defined gross, i.e., b e ore making any allowance for depreciation or f other capital consumption, taxation (corporate, personal, or property taxes), or interest.

The capital stock concept used here is net capital stock rather se- verely defined. This concept has in view much more than the expected

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ultimate scrapping of the asset. Primarily, we must consider the asset’s obsolesence, i.e., its increasing difficulty in earning profits in competition with better designed, more modem equipment.

The only way in which a true economic measure could be obtained of the combined effects of obsolescence (as defined earlier), of increasing maintenance, and of the prospective final discarding of the equipment, is from market prices of partly used capital equipment. The only case [Clark (197O)] in which this has been done on a large scale appears to have been in Norway, a country which has properly articulated current and capital accounts extending over more than a hundred years. For shipping, which is of outstanding importance in the Norwegian economy, a diminishing balance rate of depreciation of about 10% annually is indicated; a similar rate applies to other equipment. For road and motor vehicles, if considered separately, the rate would have to be higher; but 10% is probably about right for vehicles and equipment considered as an aggregate. The very detailed estimates for the U.S.A. [Goldsmith (1962)] for each kind of equipment, when aggregated, also indicate about this rate of diminishing balance depreciation. Goldsmiths more recent figures2 are as follows:

Net stocks $ billion at 1947-9 prices, end year. Business structures. (Table B122)

1945 1949 1953 1957

78.6 85.1 94.0 108.3

Non-farm producers’ durables. (Tables B119, 128)

Depreciation in following year calcu-

49.5 76.6 98.5 118.9

lated on diminishing balance %. Business structures. (Tables BlOl-104)

Non-farm producers’ durables. (Tables B113, 119)

4.9 4.7 4.5 4.4

11.5 11.2 10.8 10.2

For structures, instead of a diminishing balance depreciation, Gold- smith’s straightline depreciation of 2%% (over 40 years’ life) is used.

An important point, first made by Professor Jorgenson, now arises in the definition of capital. What matters in production, he pointed out, is not the stock of capital itself but the flow of services expected from it. A

?he Clark (1970). The original document is taken from Langtidslinjer iNorsk oekonomi 1865-1970. Oslo, Norway: Statistical Central Bureau, (1966.)

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dollar invested in equipment must be expected to give a substantially higher flow of service per year than the same dollar invested in structures; if it did not, businesses would not tolerate the high rates of depreciation and obsolescence which they have to meet on equipment. Speaking in orders of magnitude, if the rate of profit to be expected after depreciation is lo%, to which must be added depreciation at diminishing balance rates of 4% for structures and 10% for equipment, then the gross value of the flow of service from a dollar’s worth of net stock of equipment is about 1.5 times that from structures. In all capital aggregations, therefore, (both at I972 prices and at current values) the equipment component has been multiplied by a factor of 1.5, while the value of structures is entered unchanged.

The value of inventories is also entered unchanged. On most inventories little depreciation is to be expected, and therefore, to make them strictly comparable with structures and equipment, their value should be slightly reduced. This refinement, however, has not been attempted.

We now face the problem of analyzing out the short-period fluctuations. The principal factor causing short-period changes in both profits and wages is the changing pressure of demand on capacity. Measuring capacity has long been a bugbear for econometricians. The method first tried-of quite deplorable crudity-was simply to draw a line through successive peaks of production, assuming that these must at the time have represented full utilization of capacity. (I used this method myself in a model constructed in 1949. It is regrettable, however, that this method is still in use.) Another method, of equally low value, has been to estimate capacity utilization from the fluctuations in the demand for electric power. This measure, of course, grossly overweights heavy industry, in comparison with light industry and services. The method used here is simply to compare real product with real net capital stock (both subject to the exclusions mentioned above). This comparison measures pressure on capacity on an arbitrary scale, without any attempt to define full capacity.

As mentioned earlier, an arbitrary estimate of capital productivity in I929 was made on the basis that the ratio of real product to real net capital stock (with redefined productivity) in that year stood at .75, comparable with the figures for years of fairly high employment in the post-1947 period.

In measuring the capital-labor input ratio, real net capital stock (at the beginning of each year) is taken as it stands. Short-period fluctuations in labor input are not analyzed. It is considered that a five-year moving average will suffice to smooth out short-period fluctuations in the labor input data. (This method carries the interesting implication that industri- alists and labor leaders, in their negotiations, both have some idea of the

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1946 1950 1954 1958 1962 1966 1970 1974 1978

Figure 1. Actual and Predicted Wages

phase of the business cycle at which they stand and that they can make reasonable estimates of the next year or two’s labor input.)

Let us now make the following definitions. The column references are to the data given in the Appendix. C = Real net capital stock in billion dollars of 1972 purchasing power

(Column 4).

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6 1950 1954 1958 1962 1966 1970 1974

Figure 2. Actual and Predicted Profits

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C* = Net current stock in billion dollars at current prices (Column 5). L = Labor input in billions of manhours, 5 year moving average (Col-

umn 11). W = Average compensation of employees in dollars per hour (Column

12).

g = Gross profits (in money) per unit of real net capital (Column lO/ Column 4).

x = Current pressure on capacity (Column G/Column 4). The capital-labor substitution elasticity relationship which we are

seeking to establish is of the form

log(wlg) = l/alog(C/L) + constant (1)

but with a supplementary allowance for the short-period capacity utilization factor x. The equation fitted (logs to base 10) is

Zog(w/g) = 1.301 + 0.758Zog(C/l) - .864x . (2)

In addition, we have the reasonably constant empirical relationship between the sum of current factor incomes and replacement value of net capital stock

Lw + cg = 0.592c* . (3)

Let y be the expected value of w/g obtained from the substitution elasticity equation. Then

WL + wCly = 0.592c* * (4)

Therefore, expected wages are

w = 0.592c*l(cly+L) . (5)

However, this equation gives the value of w before introducing the short-period demand factor (comparatively small in the case of wages). Deviations of x from its mean value of 0.676 are obtained for the current and previous year. (There appears to be a time lag in the effect of capacity utilization on wages.) The mean of these two differences multiplied by 0.5 is found to show the capacity utilization effect on the logarithm (base 10) of w, which is adjusted accordingly. Then we can estimate profits from the regression equation as it stands, in which the capacity utilization

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factor has been fully taken into account. No further adjustment for this is necessary;

g = wly . (6)

Aggregate gross profits = gC. An example of the calculation is provided in the Appendix.

The coefficient for Zog(C/L) in equation (1) is 0.758. This estimate implies a capital-labor substitution elasticity of 1.32, a value higher than is generally supposed.

Figure 1 plots actual and predicted wage; Figure 2 plots actual and predicted profits.

Appendix

Notes to Tables Unless otherwise specified, references are from National Income

and Product Accounts of the United States 1929-74 and its subsequent updatings in July issues of Survey of Current Business.

Column 1. Goldsmith (1955), Tables Ft27 and R28, gives for 1889 to 1929 the

values at current prices of all private non-farm, non-residential construction. For 1929, he gives $4.57 billion while National Accounts Table 5.4 gives $4.96 billion in all, or $4.82 billion non-farm. The difference is spread linearly over the years back to 1924.

Price data back to 1919 from Gordon (1968). See text, Column 2 in Gordon’s Appendix.

Goldsmith (Table Ft20) gives price data which are aggregated with weights-3 for industrial and commercial, 2 for public utilities, and 1 for institutions. These, however, are based on labor and materials only and need adjustment for productivity. Comparison with Gordon’s figure shows that apparently no productivity adjustment was needed between 1919 and 1929; but before that a 1% per year allowance was made. Thus, Goldsmiths price (1929 base) of 0.470 in 1889 is reexpressed as 0.626. Current values are converted to 1929 prices and thence to 1972 prices by the deflator of 0.241 (Table 7. l), which appears compatible with Gordon’s productivity estimate.

Gross stock represents the cumulated construction of the past 40

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years (assumed life under 2Yz% straight line depreciation). This datum is needed for calculating depreciation in Column 2. (For certain adjustments to construction data after 1939 see Note to Column 2.)

Column 2. Initial figure from real value of construction since 1889 (see note to

Column l), with each year depreciated to show net value remaining at the beginning of I929 on 2M% per year straight line depreciation. Sub- sequent figures by adding private non-farm non-residential construction at 1972 prices (Table 5.5) less depreciation at 2Yz% on outstanding gross stock. New construction data have to be slightly modified [see Gordon (I969)] for government structures released to private ownership, mostly between 1940 and 1966, but a few also in latter years, not adequately shown in National income and Product Accounts.

Column 3. In the light of Gordon’s criticisms (see text) which appear to have

been met in the pricing of structures, but not of producers’ durables, a quality improvement factor of 1% per year (base 1972) has been applied both to National Accounts data and to Goldsmith’s earlier figures. Thus, the deflator given for 1929 of 0.337 (Table 7.14) becomes 0.516.

Goldsmith (Table P6) gives gross investment data back to 1897 at I929 prices excluding business cars, which are recorded in Tables PI3 and P14. National Accounts (Table 5.6) show business car sales at $1105 million in 1929, of which $399 million were on farms (Goldsmith’s figure assumed correct), leaving some $700 million non-farm; but Goldsmith shows only $365 million non-farm. Goldsmiths non-farm business car sales are therefore doubled throughout. To this revised aggregate are applied the 1% per year quality improvement factor and 10% per year diminishing balance depreciation to find the 1929 initial net stock (with a small arbitrary allowance for pre-1897 equipment surviving to 1929). Sub- sequent years from gross investment (Table 5.6) less 10% per year diminishing balance depreciation. Small adjustment for release to private ownership of government equipment (see note to Column 2). Farm investment (to be excluded) assumed to be farm machinery plus half tractor sales, together with farm cars. These are estimated by Goldsmith up to 1941, for which year they were $0.74 billion (at 1972 prices). This figure is arbitrarily interpolated up to $1.9 billion (1972 prices) for 1948-1963, after which date they are assumed to be 1.15 times the sales of farm machinery.

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Column 4. Net stock of structures plus 1.5 times net stock of equipment plus 5

year moving average of non-farm inventories at 1972 prices (from Table 5.10; pre-1947 data is taken from Suroey of Current Business, December 1972).

Column 5. Net stock of structures and equipment multiplied by prices of 4th

quarter of previous year (Table 7.1), before 1946 by interpolation of annual data. Current value of inventories from Table 5.9 and Survey of Current Business, December 1972.

Column 6. The starting point is real Gross Domestic Product at 1972 prices

(Tables 1.8 and 6.2) from which are deducted: Gross Housing Product (Table 1.21); Gross Farm Product (Table 1.19), less value of farm housing, plus

rent paid to non-farmers; Domestic service (Table 6.2: earlier data from Table 2.6 in the 1965

edition of National Accounts). Government and government enterprises (Table 6.2; for earlier years Table 1.8 for government, with supplementation for government enterprises in accordance with the ratio which they show to government in Table 6.3). Allowance for overstatement before 1972 (and understatement after 1972) of total real product through absence of quality improvement factor in prices of producer durables. Deductions for this quality factor range from $5.7 billion (at 1972 prices) for 1929 and $7.0 billion for 1947 to $4.2 billion for 1960 and zero for 1972, to an increment of $3.2 billion for 1976.

Column 7. Total indirect tax less subsidies (Table 1.9), less farm (Table 1.19),

less housing (Table 1.20).

Column 8. All compensation of employees less farm domestic government and

government enterprises (Table 6.5), also less a small allowance for employees engaged in housing administration (not construction) based on Table 1.20, and very small allowances for foreign employment.

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Cohn Clark

TABLE 1. Data and CaZcuZations

PAate Non-fm Non-resident&l Capital Stock, Beal $ Billion at 1972 Rices, Beginning of Year Product

Yew Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7

Bed cross AU capital 08 AU capital Domestic Deduct&n for

Producers’ dej?ned (equipment x as dej?ned, Product indirect taxation Struchrres %tWCtWeS dwables 1 S, including inventortes), net stock, at 1972 pticea leaa subaidtes

gross stock net stock net stock net stock cuwent LmbJe $ bul&n $ billion

1923 377 220.7 55.7 374.6 125.1 228.3 4.7 1930 393 231.3 60.5 392.2 127.3 lQQ.8 4.7 1931 403 238.6 62.0 399.6 122.1 178.2 4.4 l!a32 408 239.4 60.9 395.7 112.8 145.5 4.4 1933 406 235.5 57.8 383.2 101.5 140.7 5.2 1934 404 230.2 55.5 371.1 98.5 154.7 6.0 1935 403 225.2 54.3 363.3 100.8 172.5 6.2 1836 402 220.7 54.7 360.7 102.2 2023 6.8 1837 404 218.2 57.3 364.2 107.6 212.7 7.3 l&33 407 218.0 61.3 371.8 115.6 198.7 7.2 1939 408 215.7 61.8 373.0 115.9 219.1 7.5 KM0 410 213.6 63.3 377.0 116.6 239.2 8.0 1841 411 213.3 67.6 386.4 127.3 277.7 9.4

1947 428 218.8 91.7 444.2 220.8 1948 432 223.7 105.7 472.7 259.8 1949 440 229.7 117.9 502.1 299.6 1959 447 2.X5.1 125.1 523.0 313.5 1951 455 241.5 134.1 547.8 345.8 1952 466 249.3 143.9 577.7 361.5 KS3 475 257.0 153.2 691.1 404.0 1954 484 266.9 164.3 632.4 629.2 1955 488 278.0 172.8 658.7 451.1 1956 515 290.4 183.5 689.9 484.0 1957 533 304.6 144.3 722.6 539.9 1958 551 318.2 204.9 755.3 583.0 1959 569 329.7 209.7 776.8 594.7 1860 586 340.8 217.3 801.3 613.4 1961 606 353.7 225.9 830.8 634.1 1962 624 366.5 233.2 859.9 653.0 1963 643 381.6 243.8 695.4 680.4 1964 660 396.4 255.3 933.3 710.6 1965 680 410.7 271.1 983.1 75252.2 1966 704 433.9 291.9 1047 813.5 1967 727 457.1 317.0 1120 895.5 1968 747 478.1 338.9 1135 974.3 1969 768 4Q9.7 353.5 1239 la57 1970 7Q0 522.9 381.1 1311 1173 1971 814 544.2 403.0 1373 12a7 1972 843 563.9 422.8 1431 1407 1873 878 583.9 449.1 1500 1536 1974 917 605.5 482.9 1575 1710 1975 952 623.9 516.2 1650 2076 1976 981 634.7 535.2 1696 2321 1977 1009 645.5 556.6 1747 2559

339.7 16.1 355.7 17.4 354.0 18.3 399.4 19.9 418.3 21.6 m.5 23.7 451.7 25.6 442.9 25.1 478.8 26.7 488.9 28.6 496.9 31.5 490.5 31.3 527.7 34.3 536.2 37.0 547.4 38.2 583.0 41.1 607.9 43.8 644.1 43.9 685.7 50.0 730.8 51.5 745.1 55.7 782.1 63.1 802.4 68.7 795.1 72.9 620.6 80.2 878.7 86.5 935.6 92.2 914.3 100.2 891.6 107.3 957.5 118.0

Wages and Profits

Column 8

Labm Input and AppNcat&n Factor Income8 Remuneratton of Equntbn

Cohnn 9 Column 10 Column 11 Column 12 Column 13 Column 14

Imputed Man-hm,rs worked AOWoge Cmnpen8atton lnbor income (inchftng compensation Predicted Redicted gx.ss ofemproyees of self employed Gross profIts df employed) of empkyees cum~ationof P-oPb

$ billion $ billion $ billion billion S/hour employees $ihmu $ billion

42.8 6.0 23.1 79.6 ,613 36.7 6.1 16.9 72.7 ,616 32.0 5.9 11.9 64.3 .590 24.2 5.4 6.0 54.9 .539 22.7 5.1 5.3 54.4 ,511 26.3 5.9 8.7 55.0 36 28.7 6.1 10.3 58.3 ,597 32.7 6.2 14.8 65.1 ,597 37.8 6.7 14.6 68.7 3548 34.3 6.9 13.1 62.5 ,659 37.3 7.1 15.5 66.5 ,667 40.8 7.3 20.5 70.5 .682 51.6 8.4 23.2 80.1 .I49

105.0 19.7 37.3 89.5 1.339 1.209 36.1 115.9 21.9 43.7 90.7 1.519 1.402 41.5 113.7 21.0 45.8 85.9 1.568 1.571 43.3 12.53 22.5 54.6 89.4 1.653 1.614 49.7 144.6 22.5 65.4 93.6 1.785 1.778 57.7 155.2 25.4 61.0 95.9 1.883 1.925 62.0 168.1 27.3 61.7 98.1 2.004 1.996 66.2 166.7 27.1 61.8 93.8 2.066 2.066 63.3 180.8 28.2 74.9 97.2 2.150 2.137 70.3 196.7 30.1 72.3 99.7 2.277 2.307 73.5 206.6 31.7 74.6 99.2 2.402 2.514 78.3 204.4 32.0 74.5 95.2 2.484 2.651 78.6 223.5 33.2 84.7 96.9 2.596 2.705 84.3 234.8 34.5 81.2 99.8 2.699 2.784 86.3 239.6 35.5 84.9 99.1 2.776 2.815 87.3 256.7 36.3 96.0 101.6 2.884 2.872 94.1 270.0 37.0 102.3 103.0 2.980 2.836 99.1 239.4 36.8 112.1 105.5 3.112 2.w 106.4 312.4 40.2 123.5 109.6 3.217 3.101 115.2 345.4 40.9 139.3 114.2 3.383 3.263 125.6 367.9 42.8 139.8 115.1 3.568 3.479 128.8 403.6 45.5 150.5 117.4 3.826 3.702 145.7 445.8 50.1 147.1 12Q.8 4.105 3.945 148.6 470.1 52.7 143.7 116.6 4.410 4.259 151.0 499.1 57.9 160.8 118.4 4.707 4.491 160.4 550.1 60.5 181.6 122.2 4.996 4.894 182.5 619.7 66.5 193.1 127.9 5.365 5.26 206.4 680.4 73.7 196.0 127.8 9.901 5.74 208.9 714.9 77.5 237.7 122.7 6.458 6.73 232.0 8a3.8 86.5 274.2 121.6 6.977 1.45 272.0

263

Cohn Clark

Column 9. Since 1948 manhours worked by self-employed from differences

between Tables 6.10 and 6.11, from which farmers can be excluded. Earlier years estimated approximately from Census data. Hourly labor earnings imputed at the rate of all employee compensation (see Column 12).

Column 10. Current value Gross Domestic Product (Tables 6.1 and 1.7) less

government and government enterprises (for estimation for earlier years see note to Column 6) less household domestic wages, less housing gross product (Table 1.20), less farm gross product (Table 1.19, but see note to Column 6), less sum of Columns 7, 8 and 9.

Column 11. Since 1948 (from Table 6.11) excluding farm, government and gov-

ernment enterprises, and household domestic (from Table 6.10). Earlier years approximated from Kendrick’s Productivity Trends in the United States (Kendrick’s data include self-employed and exclude farm and government workers). A small deduction was made for housing (see note to Column 8).

Column 12. Column 8/Column 11.

Example: Calculation of expected wages and profits in 1976. 1. Real net capital stock at 1972 prices at beginning of year,

$ billions (C) 2. Smoothed (S-year moving average*) Labor input includ-

ing self-employed billions of manhours (L). 3. Equation relating log(wlg) to log(CIL) with capacity

utilization factor standardized to its mean value of 0.676 gives expected value of w/g at average capacity utilization (y).

4. Column 1 + Column 3 (C/y). 5. Column 4 + Column 2 (C/y+ L).

1696.

127.5

37.19 45.6

173.1

*To calculate the moving average, values have to be assumed for 1977 and 1978 of 129.0 and 130.5, respectively.

264

Wages and Profits

6. Replacement value of net capital stock at beginning of year, $ billion (C*).

7. 0.592 Column 6 (expected factor income at average capacity utilization).

8. Column 7 + Column 5 (expected hourly wage at average capacity utilization), $.

9. Real gross domestic product at 1972 prices, $ billion. 10. Column 9 f Column 1 (measure of capacity utilization)

(4. 11. Similar measure for previous year. 12. Difference between mean of Columns 10 and 11 and

average 0.676 capacity utilization. 13. 1 + 0.5 (Column 12). 14. Column 8 x Column 13 (expected wage at current

capacity utilization). 15. Equation relating log(wlg) to log(CIL) with actual capac-

ity utilization factor gives expected value of w/g 16. Column 14 + Column 15 (expected value of g). 17. Column 16 x Column 1 (expected gross profits, $ bil-

lion).

2321.

1374.

7.94 957.5

0.564 0.540

0.124 0.938

7.45

46.45 0.1604

272.0

Received: June, 1978

References Arrow, K. J., H.B. Chenery, B.S. Minhas, and R.M. Solow. “Capital-

Labor Substitution and Economic Efficiency.” Review of Economics and Statistics 43 (August 1961): 22550.

Aukrust, 0. “Investment and Economic Growth.” Productivity Measure- ment Review 16 (February 1959): 3554.

Clark, C. “Net Capital Stock.” Economic Record 46 (December 1970): 449-66.

David, P.A. and T.H. van de Klundert. “Biased Efficiency Growth and Capital-Labor Substitution in the U.S.” American Economic Review 55 (June 1965): 357-94.

Eckstein, 0. and T.A. Wilson. “Short-Run Productivity Behavior in U.S. Manufacturing.” Review ofEconomics and Statistics 46 (February 1964): 41-54.

Goldsmith, R.W. A Study of Saving in the United States. Princeton: Princeton University Press, 1955.

-. The National Wealth of the United States in the Postwar Period. Princeton: Princeton University Press, 1962.

Gordon, R.J. “A New View of Real Investment in Structures, 1919-

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Colin Clark

1966.” Review of Economics and Statistics 50 (November 1968): 417- 28.

-. “$45 Billion of U.S. Private Investment have been Mislaid.” University of Chicago, Center for Mathematical Studies in Business and Economics, Report 6901, 1969.

-. “Measurement Bias in Price Indexes for Capital Goods.” Review of Income and Wealth 17 (June 1971): 121-174.

Phillips, A.W. “The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957.” Economica 25 (November 1958): 283-99.

Popkin, J, and R. Gillingham. “Comments on ‘Recent Developments in the Measurement of Price Indexes for Fixed Capital Goods.“’ Review of Income and Wealth 17 (September 1971): 307-09.

Sato, R. “The Estimation of Biased Technical Progress and the Production Function.” International Economic Review 11 (June 1970): 179-208.

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