Why Productivity Measures Disagree
The subject here is not whether one productivity statistic is “right” and another is “wrong.” It is what a credit-supply shock changes in the statistic we use to describe a firm. That distinction supports a practical judgment: before interpreting a productivity decline, the reader needs to know whether the study observes physical output, firm-level prices, revenue, or value added—and whether the estimate is meant to describe technical efficiency, commercial performance, or both.
The difference becomes decisive after financial distress. A firm can lower its prices to raise cash, change the mix or quality of what it sells, or produce the same physical output with the same inputs while collecting less revenue. A revenue-based measure will register those events as a productivity movement. A quantity-based measure can separate some of them, but it brings its own data and modeling requirements. The two studies therefore appear to tell different stories only until the object being measured is made explicit.
Two ways to define productivity
Productivity is a ratio in spirit, even when researchers estimate it as a production-function residual. The question is how much output a firm obtains from capital, labor, and intermediate inputs. Suppose two factories use the same number of workers, the same machinery, and the same material inputs. If one produces more physical units, it appears more technically productive. If both produce the same units but one sells at a higher price, the second may generate more revenue without having a more efficient production process.
That simple example contains the central distinction. Physical productivity, called TFPQ in the New York Fed report, is intended to capture the firm’s ability to turn inputs into physical output. The report estimates a production function using firm-level quantities and inputs, then treats the remaining variation in physical output as technical productivity. The measure is not a direct reading of a machine’s efficiency; it depends on the production-function specification and on how quantities and inputs are constructed. But its interpretation is closer to productive technology than a revenue residual is.
Revenue productivity, called TFPR in the New York Fed report, starts from revenue rather than physical output. In the Italian study, the analogous measures are productivity residuals based on net revenues or value added. Revenue is useful because it is recorded for many firms and because it captures economically meaningful changes in product quality, market access, or demand. But revenue equals a price times a quantity. If the price changes, the firm’s revenue per unit of input changes even when its physical production process does not.
The distinction is especially important for firms producing differentiated goods. A firm that improves a product’s quality may charge more, enter a more valuable market, or gain customer appeal. Those are real improvements in commercial performance, but they are not identical to producing the same product with fewer resources. Conversely, a firm can cut its price to liquidate inventory and generate cash. Its revenue productivity may fall even if its physical productivity is unchanged in the short run. A measure that bundles these margins is not useless; it answers a broader question. It simply cannot be interpreted as pure technical efficiency without additional assumptions.
The New York Fed paper has the unusual advantage of observing prices and quantities for individual products. Its Belgian PRODCOM data report product-specific revenue and quantity for manufacturing firms, allowing the researchers to construct firm-level price indices and quantity indices. For multi-product firms, the report aggregates product-price changes using a Törnqvist index, which weights continuing products by their sales shares. It then adjusts revenue for changes in finished-goods inventories and divides by the price index to recover a quantity measure. This is the empirical foundation for comparing TFPQ with TFPR.
The Italian paper has a different advantage: scale and coverage. Its CADS and Credit Register data cover a much larger panel of Italian corporations from 1997–2013, including firms across manufacturing and private services. Because comparable firm-level output prices are not available for that population, the study estimates productivity from revenue or value added and explicitly discusses the limitations. Its outcome can reflect technical efficiency, but it can also include product appeal, quality, market access, and pricing. That broader meaning is valuable when physical units are hard to define—for example, a service firm’s “quantity” may not be a comparable count across customers—but it changes what the estimate can establish.
The two lanes are related, not interchangeable. TFPQ asks about the quantity of output after accounting for inputs; TFPR asks about revenue or value added after accounting for inputs. Prices enter the second lane directly and can enter it indirectly through product mix, quality, demand, and markups. The same credit shock can therefore generate different signs or timing in the two residuals without the underlying evidence being incoherent.
The BIS paper makes this point analytically. Under a simple differentiated-good demand structure, revenue productivity can be decomposed into a component related to technical efficiency and a component related to market appeal. A process innovation is more likely to raise the former; a product innovation may mainly raise the latter. The decomposition is model-dependent, but the intuition is general: a residual built from revenue includes more than the physical transformation of inputs into output. The New York Fed study demonstrates why this matters in the specific setting of a credit shock: financing conditions can change prices themselves.
Reading the different response paths
The New York Fed results show how a single disturbance can produce a sequence that looks contradictory if the measure is not named. The study examines Belgian manufacturing firms around the 2010 European sovereign debt shock and measures cumulative changes relative to 2009. A one-standard-deviation increase in exposure to lenders holding distressed sovereign securities leads to an immediate output-price reduction of about 2 percent. Yet the estimated short-run effect on TFPQ is not statistically significant. In other words, exposed firms look less productive in revenue terms at first largely because they charge less, not because the evidence shows an immediate decline in their physical production efficiency.
The price response later changes direction. Firms more exposed to the shock eventually raise prices relative to less-exposed firms, with the cumulative difference reaching as much as about 4 percent in the years after the shock before moving back toward zero. At the same time, the TFPQ response becomes significant around three years after the shock and reaches a 6.4 percent contraction in cumulative physical-productivity growth by the end of the sample. The long-run TFPR decline is about half as large as the TFPQ decline because the later price increase lifts revenue relative to physical output.
The result is a timing trap. Looking only at TFPR suggests a productivity slowdown immediately after the credit crunch, when the quantity-based measure shows no significant short-run effect. Looking only at its long-run change suggests a smaller loss than the TFPQ estimate indicates, because higher prices partially mask the deterioration in physical efficiency. The revenue measure is not merely imprecise around the physical measure; it is responding to a different combination of margins at different horizons.
The underlying arithmetic is straightforward. In rough terms, the change in revenue per input can come from a change in physical output per input, a change in the price received, or both. When firms cut prices to generate cash, the price component pushes revenue productivity down. When financing costs rise and lower efficiency is passed through into prices, the price component pushes revenue productivity up relative to physical productivity. A revenue residual can consequently be biased upward in the short run and downward in the long run as an estimate of the physical response. The direction of the bias depends on the price path, not just on the size of the credit shock.
This is why the Italian estimates should not be treated as a direct contradiction of the Belgian estimates. Manaresi and Pierri find that a 1 percent increase in their firm-level credit-supply shifter raises value-added productivity growth by about 0.1 percent and revenue productivity growth by about 0.02–0.03 percent. They also find effects that persist for at least four years. Those results support the proposition that lender-driven credit availability affects firms’ ability to generate output or value from inputs. They do not isolate the physical-productivity timing that the Belgian price and quantity data make visible.
The larger Italian sample also captures margins that the physical Belgian measure may intentionally exclude. Easier credit is associated with greater IT intensity of the capital stock, more patenting, a higher probability of engaging in R&D and exporting, and better management scores in the additional data. Some of these changes can raise a firm’s market appeal or the value of its output, even if a clean quantity measure would classify them differently from process efficiency. Treating every revenue response as a price error would therefore throw away economically important information. The correct interpretation is conditional: revenue productivity is a broad performance measure whose components must be identified before the effect is assigned to technology.
There is no universal winner between the two measures. TFPQ is preferable when the question is technical efficiency and reliable product-level quantity and price data exist. It is particularly informative for the Belgian manufacturing setting, where the authors can separate output prices from quantities and test the timing of the physical response. Revenue or value-added productivity is often more feasible for large administrative panels and for services, where product quality and market access are part of performance and physical units may be poorly defined. It can also be the only practical way to study small or less standardized firms. Its broader scope is an advantage when the question is commercial performance, but a liability when the question is purely technical efficiency.
The outcome definition also determines how a claim should be worded. “Credit supply lowers firm productivity” is too vague to compare the studies. A more precise statement would say that, in the Italian panel, a lender-driven increase in credit is associated with higher value-added and revenue productivity growth, while in Belgian manufacturing a sovereign-exposure shock produces a delayed and persistent reduction in quantity-based physical productivity and a price-driven divergence in the revenue measure. The second statement preserves geography, period, exposure definition, outcome, and timing. Those details are not academic decoration; they determine the causal meaning.
The measurement problem also changes how one evaluates mechanisms. An immediate TFPR decline could be explained by lower prices, weaker demand, an inefficient use of inputs, or some combination. The New York Fed evidence narrows the interpretation because TFPQ is initially stable while prices fall. The later TFPQ decline then aligns more naturally with an investment channel whose effects take time to appear. By contrast, the Italian revenue measure detects a persistent response and helps identify activities associated with credit access, but it cannot by itself say whether the productivity residual changed through process efficiency, product quality, market appeal, or pricing.
A useful reading rule follows. When a financial study reports a productivity effect, ask five questions before deciding what it means. What is the output? Physical quantity, revenue, or value added? Are firm-level prices observed? If not, which price and demand movements may be inside the residual? What is the horizon? An immediate flow, a one-year response, or a cumulative multi-year change? What is the comparison? A standardized lender exposure, a percentage change in credit, or an aggregate crisis? What identifies the shock? A lender-side design, a natural experiment, or an observational correlation?
The questions are also a safeguard against a common interpretive error: confusing a measure’s limitation with the absence of an underlying effect. A revenue measure may fail to reveal a delayed physical-productivity loss, but that does not show that no loss occurred. Conversely, a revenue decline does not prove that technical efficiency fell immediately. Better measurement does not remove uncertainty; it places uncertainty in the correct part of the causal chain.
The central conclusion is therefore precise. The two studies are most informative when read together: the broad Italian evidence establishes that credit supply is connected to persistent firm performance and to several capability-building activities, while the detailed Belgian evidence shows that prices can disguise both the timing and size of the physical-productivity response. Once that distinction is in place, the next issue is no longer how to label the residual. It is how firms decide which future-building investments to protect or cut when current liquidity becomes scarce.