Machinery in the Residual

When William Dean Howells visited Machinery Hall at the Philadelphia Centennial of 1876, he found the engineer reading his newspaper. Around the man's chair the great Corliss engine was in motion. In Howells's account, the attendant occasionally put the paper down, climbed into the framework to apply oil, and returned to his reading. The machine seemed to have gathered the exertion into itself, leaving its keeper at leisure in the midst of the work. Howells gave its moving parts “unerring intelligence.”¹

He also gave the keeper a precarious mastery. This was a servant whose slightest movement could destroy him, and Howells allowed himself a moment's thought about the people whose industry machinery had superseded. Then he confessed that such thoughts hardly survived inside the hall. Admiration and national pride took possession again. There is more honesty in this interrupted objection than in a passage written to distribute equal credit to progress and its victims. The writer knows what he has ceased to attend to. He has not ceased to be impressed.

The same page contains a smaller resistance to the spectacle. Howells had seen more sewing machines than he wished to see. Each patent presumably had its reason, though the differences were not readily apparent to him, and he did not relish an argument with the agents and attendants who could explain them. The engine announced a great capacity in one object. The sewing machines asked him to make distinctions. His patience for the first was greater than for the second.

The visit leaves a durable image of improvement: a formidable machine, a man relieved of exertion, a multiplicity of activities proceeding around them. A moment in the installation's working life becomes a picture of the advance. It is an intelligible image, and an unusually convenient place to stop looking.

A pipe under the ground

The official report on the exhibition's grounds and buildings takes us somewhere else. South of Machinery Hall stood the boiler houses, separated from it by a railway over which fuel could be brought in. Chutes extended beneath the track into coal vaults, allowing coal to be discharged from the cars. The Corliss boiler house contained twenty upright boilers; a large steam pipe, three hundred and twenty feet long, passed underground to connect them with the engine.² The almost silent grandeur described by Howells had this other geography. Coal had to arrive, and steam had to be produced and conveyed, before the moving parts could appear so self-possessed.

The work of supplying steam was itself available to inspection. The boiler houses had viewing platforms, protected by iron railings, from which their operations could be watched. One could leave the great wheel and inspect the means of supplying it. The exhibition offered several ways of seeing its own achievement. A visitor could choose among them, or be captured by one.

Even the form of the hall belonged to the operation. According to the report, its width was determined by the distance the designers judged it desirable to convey steam from the boiler houses. Parts of the roof were kept low, with stiffened tie-beams for the shafting; other parts rose higher to admit light and ventilation. The catalogue described eight main lines of shafting extending almost the length of the building, with countershafts reaching into the aisles where required.³ Power could be offered to an exhibitor because the building had been arranged to distribute it. The hall was being designed around the routes its power would take.

There was a still less obvious connection to the landscape. Water supplied to the great fountain north of the hall helped keep the lake filled, and the lake supplied the engine's condensing apparatus. The report puts an ornamental fountain and a working condenser within the same account of water provision.⁴ A distinction between decoration and productive infrastructure would have to follow the pipes. It could not be settled by looking at the water.

The report lets admiration spread beyond the flywheel. The designers had to bring quite different requirements into an arrangement that could run: the distance over which steam would travel, the support of rotating shafts, the delivery of fuel, the movement of water, the room in which machinery and spectators were to be accommodated. Knowledge was present in those relations as well as in the central mechanism. The building was not merely an expense surrounding the achievement. Part of the achievement consisted in what the building had been made to do.

The catalogue assigned the engine fourteen hundred horsepower. That describes a capacity; it is not a record of the work delivered throughout the exhibition, still less a test of the fuel required for each unit of that work. The installation was both a source of power and an exhibit. Its successful operation does not by itself establish the cheapest way to power a factory. We can admire what was brought together without making the exhibition perform an experiment it did not report.³

What the subtraction establishes

Eighty years later, Moses Abramovitz was examining an industrial transformation in which such machinery had participated. His figures compared the American economy over the decades 1869–78 and 1944–53. Real net national product per person had approximately quadrupled. The measured increase in resources per person, combined using income weights, was much smaller. He called the importance of the productivity increase a “measure of our ignorance” about the causes of growth.⁵

Read beyond the remark and its meaning becomes more demanding. On the following pages Abramovitz considered how the growth of the market could itself support greater productivity, and how the conventional measures understated investments in people's capacities and in knowledge. His ignorance was not an empty space waiting to be occupied by one neglected substance. It concerned the causes of an improvement that the available counts of resources did not adequately explain.

The counting had nevertheless accomplished something. A country can produce more because it employs more people, because those people work longer, because they have more productive equipment, or because the work is organized and performed differently. These changes can occur together. Comparing the growth of output with the growth of specified inputs prevents an increase in scale from being mistaken, without further inquiry, for an increase in productivity. It also makes an apparent improvement answerable to a comparison: output relative to which inputs, measured how? The number gives the question a place to begin.

Robert Solow's 1957 contribution connected such a comparison to a production function. Under his assumptions, including payment of factors at their marginal products, the observed shares of income could be used to weight the growth of inputs. The portion of output growth left after subtracting those weighted contributions measured a shift of the function. He used technical change broadly, to include changes that were not inventions. In his application to the private nonfarm American economy from 1909 to 1949, he attributed roughly seven-eighths of the increase in output per hour to that broadly interpreted change.⁶

The calculation deliberately left a residual. Measurement errors could enter it, but so could improvements the inputs had not separately captured. Calling the whole result an error would confuse the unfinished explanation with a failed calculation. Conversely, giving the remainder the name technology would not identify the alterations by which the economy had become more productive. The subtraction and its interpretation are different accomplishments.

Solow was particularly candid about capital. What he wanted was the flow of services supplied by productive assets; what he possessed was an estimate of the assets in existence. He illustrated the difference with machines replaced by more durable successors of the same annual capacity. The measured stock could grow without a corresponding increase in the maximum annual services it could supply. He also attempted an admittedly rough adjustment for idle capital.⁷ The engineer and the economist were not divided by the latter's indifference to whether a machine was working. That difficulty was already inside the economist's paper.

A turbine and an office building are both physical arrangements, and each can change what people are able to do. Their appearance under a capital aggregate does not require an analyst to believe that they perform the same service. The pertinent question is which differences survive the construction of that aggregate. It is possible to collect unlike things into a useful measure while remaining responsible for the purposes for which their differences matter.

Charles Hulten's history of productivity measurement defends precisely the work that broad attacks on the residual tend to pass over. He describes how Jorgenson and Griliches distinguished types of capital and labor, and how capital-service measures could address changes in the composition of investment. A movement from long-lived structures toward shorter-lived equipment need not disappear unnoticed into a single stock. The resulting dispute over the size of the residual concerned the inputs and their measurement, not just rival names for the remainder.⁸

Hulten also follows the problem across industries. Fuel can appear explicitly in an industry's gross-output account while intermediate transactions cancel in aggregation to the whole economy. The resulting absence of a separate line in an aggregate is not evidence that the physical input was forgotten. Following productivity through those connections is established economic work.⁸ It leaves a further question when an accounted change becomes the basis for proposing a change in production. What would have to be done to obtain the improvement?

Buying the engine

Suppose someone hoped to obtain a service comparable to that of the hall's installation elsewhere. Buying an engine of the stated capacity would settle only part of the matter. The buyer would need to know what the connected equipment demanded, how motion was to reach it, and what could be supplied at the chosen site. Those questions could alter the building, the transmission, the provision of steam, or the choice of engine itself. A successful installation is evidence that a particular arrangement worked. It is not a promise made by its most conspicuous component to every future owner.

The official report's treatment of the roof is revealing here. The desired transmission system had consequences for the building before the machinery was running. To describe the final outcome as a quantity of capital is legitimate for some inquiries. To use that quantity as though it specified an arrangement that could be bought and made productive anywhere is a further inference, and a costly one. No defect in the arithmetic is required for the inference to fail. The information needed to reproduce a service exceeds the information needed to count the assets associated with it.

Nor does a detailed inventory finish the work. A list of boilers, pipes and shafts would tell another undertaking more than a photograph of the flywheel, but the parts still have to be related to a purpose and to one another. Steam must arrive in a condition the engine can use. The output must reach the machinery at a usable rate. A means of delivering more power is an improvement only for a use that can benefit from it, and it may require changes elsewhere before that benefit can be obtained. This is the point at which an account of production becomes a guide to changing production, rather than a description of what has already been acquired.

Consider a proposed improvement in a boiler, now as an engineering example rather than a further episode in the exhibition's history. If it supplies the same usable steam with less fuel under comparable conditions, a defined conversion has become more efficient. A competent operator could still decline to install it. The saving might be worth less than the equipment and the changes needed to use it, especially where fuel is cheap or demand gives little reason to enlarge production. Elsewhere, the same saving could release an undertaking from an expensive limit on supply. The engineering result survives both decisions; its economic significance develops through the conditions of use. Counting the new equipment, the fuel saved and the output obtained gives the inquiry substance. It does not entitle us to infer one from another.⁹

The growth accountant faces a related choice. A better measured capital input may assign some of an improvement to the services of new equipment. Another specification may leave more in productivity. The economic event has not been manufactured by the choice, but its allocation among the measured contributions changes. A small residual does not mean that little knowledge went into the transformation. Much of that knowledge may have become available through assets and skills now counted among the inputs. A large residual does not tell us which unmeasured changes deserve the credit. The size of the remainder is not a scale on which to rank the ingenuity of a civilization.

A better account of conversion can expose a real mechanism, and it can also expose how much else had to change for that mechanism to become useful. The gain is not necessarily waiting inside one machine. It may arise through a different relation among machines, buildings, supplies and work. Replacing a boiler can be the beginning of such a change; replacing a name in an equation cannot stand in for investigating it.

Where the work reaches

Howells's engineer can now return to his newspaper without being required to represent the disappearance of human work. The image remains attractive. Arranging a process so that it demands less immediate exertion is an achievement, and the intervals it releases need not be distrusted merely because the machinery still requires support. But the observer has seen a moment in an operating arrangement. What preceded that moment, what must continue elsewhere, and what would have to change to extend the service are different inquiries.

The exhibition makes one of them unusually accessible. The boiler houses offered the visitor another view; the report gives the later reader a route from the central engine to the coal vault, the railway and the low roof. There is no need to extinguish the admiration in order to follow it. What changes is the object of admiration. It becomes possible to see an accomplishment distributed through a place, with the central machine drawing together work that it did not perform alone.

A measured gain can become a recommendation to invest, reorganize or imitate. At that point the difference between registering a result and explaining its production becomes practical. If new buildings, supplies or operating knowledge were part of the achievement, someone must obtain them or find another way to perform their work. The machine's success elsewhere gives a reason to investigate that prospect. It does not deliver the missing conditions along with the purchase. Nor does a productivity comparison, however well constructed, relieve the new undertaking of discovering what its own circumstances will permit.

Energy conversion is consequential because it lets us ask a more definite question. How much usable work could the production system obtain from its fuel, and what changed in that relation? A watt assigned to an engine is not yet work delivered to its users. A quantity of fuel entering a site does not specify the motion, heat or other service obtained from it. Following those transformations can reveal gains that the purchase of fuel alone does not describe. It can also show why an enlarged capacity remained unused, or why another part of the arrangement had to be rebuilt before the gain became available.

That is the claim the useful-work account must now make good: that tracing conversion explains something consequential in the growth record, beyond what the existing measures already capture. Its authority will depend on the comparison it improves. But the historical question has already become harder, and more useful. A society does not acquire another society's productive powers merely by purchasing its celebrated machines. It must discover how to make the work possible in its own circumstances. At Philadelphia that work reached into the shape of the roof and under the railway. Any account that promises to explain the advance must be able to follow it there.

Source notes

Footnotes

1. William Dean Howells, “A Sennight of the Centennial,” The Atlantic Monthly 38, no. 225 (July 1876), pp. 92–107, especially p. 96. The original printed page was inspected in a digitized scan, alongside the extract supplied by Yale's Energy History project. The engineer, newspaper, oiling, threatened mastery, displaced industry and sewing-machine observations are Howells's account. His language of intelligence is figurative; it supplies no staffing census, safety assessment, employment estimate or technical performance comparison. The interpretation of his changing attention is this chapter's. ↩

2. United States Centennial Commission, International Exhibition, 1876: Reports and Awards, vol. II, Grounds and Buildings of the Centennial Exhibition, Philadelphia, 1876, edited by Dorsey Gardner (Philadelphia: J. B. Lippincott, 1878), pp. 82–83. The description connects the boiler houses to fuel delivery by rail, coal vaults and visitors' platforms; p. 83 describes the twenty Corliss boilers and the underground steam pipe. These are the commission's retrospective descriptions, not independent measurements of seasonal performance. The report establishes neither thermal efficiency from the installation’s appearance nor an uninterrupted six-month run. ↩

3. Commission, Grounds and Buildings, pp. 77–81, especially p. 78 on steam-conveyance distance and roof framing. United States Centennial Commission, International Exhibition, 1876: Official Catalogue, part III, Machinery Hall, Annexes, and Special Buildings (Philadelphia, 1876), p. 10, on the stated 1,400 horsepower, eight shaft lines and countershafts. Capacity, actual delivered work and fuel efficiency remain distinct. The chapter does not estimate the installation's efficiency or its contribution to national productivity. Hunter and Bryant's 1991 volume was identified, but its formerly cited pp. 207–208 were unavailable for inspection; no retained factual assertion is certified through them. ↩ ↩²

4. Commission, Grounds and Buildings, p. 25. The water-supply discussion links the fountain, lake and condensing apparatus. The later building description on pp. 81–82 describes a lake pipe as supplying boilers; the chapter follows the specific condenser account on p. 25 and does not conflate condensing water with boiler feedwater or reconstruct the entire circuit. No water-use quantity is needed for the inference here. ↩

5. Moses Abramovitz, “Resource and Output Trends in the United States Since 1870,” American Economic Review 46, no. 2 (May 1956), pp. 5–23, inspected in NBER's Occasional Paper 52 reprint, which retains the printed journal pagination. The comparison and definitions are on pp. 6–11; the qualification of the input/productivity division is on pp. 12–13. The national-product comparison uses decadal averages, not single-year observations for 1869 and 1953. The phrase quoted is part of his statement about ignorance concerning causes, not a definition of productivity as an error. ↩

6. Robert M. Solow, “Technical Change and the Aggregate Production Function,” Review of Economics and Statistics 39, no. 3 (August 1957), pp. 312–320: assumptions and broad usage on pp. 312–313; sample and measurement on pp. 314–315; interpretation on pp. 316 and 320. In the familiar neutral, constant-returns formulation, the residual growth rate is $g_A=g_Y-s_Kg_K-s_Lg_L$, with the causal interpretation requiring the stated production and pricing assumptions and adequate measurement. This is not an ordinary regression error term. The seven-eighths figure concerns Solow's decomposition of the increase in output per hour in his historical private nonfarm sample; it is not a universal technological share or a share assigned to energy. ↩

7. Solow, p. 314, on the desired flow of capital services, the available stock series, durability and idle capacity. His example holds annual capacity constant while durability increases. It does not deny the value of durability or imply that the asset's lifetime services remain unchanged. His utilization adjustment is reported as an acknowledged approximation, not endorsed as an adequate contemporary method. ↩

8. Charles R. Hulten, “Total Factor Productivity: A Short Biography,” in New Developments in Productivity Analysis, ed. Hulten, Edwin R. Dean and Michael J. Harper (University of Chicago Press, 2001), pp. 1–54, especially pp. 5–10, 13–15 and 36–38. This is the published chapter, not the 2000 working paper. The account grants its defense of measurement, disaggregation and industry connections. Neither netting intermediate transactions in aggregation nor using value added demonstrates that energy has been ignored. The chapter offers no new theorem about capital aggregation or causal identification. ↩ ↩²

9. The boiler and purchasing discussions are hypothetical reasoning, not additional documented transactions at the Centennial. Conversion efficiency requires specified input and output forms and comparable operating conditions; it is not identical to economic productivity, profitability or welfare. The argument concerns the grounds for moving from a demonstrated service or an accounting result to a claim about obtaining another improvement. The useful-work studies and their empirical limitations remain the work of Chapter 3. ↩