Dispersion Over the Business Cycle: Passthrough, Productivity, and Demand

Layer 1: Overview

Carlsson, Clymo, and Joslin use Swedish manufacturing firm-level microdata for 1998–2013 to separately identify and characterize the cyclical behavior of physical productivity (TFPQ) shocks and demand shocks at the firm level, two forces that are observationally equivalent under the standard CES-demand benchmark. The paper’s central contribution is threefold: it documents new empirical facts about dispersion cyclicality, estimates a non-constant-elasticity (non-CES) demand curve directly from firm-level price and quantity data, and embeds those estimates into a quantitative heterogeneous-firm model to study the aggregate consequences of each type of dispersion shock.

The data combine four Swedish register sources: the Företagens Ekonomi (FEK) survey for bookkeeping variables; the Industrins Varuproduktion (IVP) survey for 8-digit product-level price and quantity data used to construct firm-level price indices; the Konjunkturstatistik för Industrin (KFI) survey for quarterly capacity-utilization data; and additional investment deflators. The unbalanced panel contains 3,181 unique manufacturing firms and 15,044 firm-year observations. TFPQ is measured using a Cobb-Douglas value-added production function with factor utilization adjustment; factor elasticities are estimated via cost shares at the 2-digit sector level, yielding an average labor share of 0.735.

Demand is estimated using the Gopinath-Itskhoki-Rigobon (GIR) flexible demand curve, which nests CES as the limiting case. TFPQ innovations instrument for price in a second-order approximation, following Foster, Haltiwanger, and Syverson (2008). The main-sample estimates yield theta = 2.94 (average elasticity) and eta = 4.27 (super-elasticity), both significant at the 1% level. The second-order price term is statistically significant at the 5% level in all three samples, decisively rejecting CES. These estimates imply that a 5% price increase raises the demand elasticity from 2.94 to 3.74, while a 5% price reduction reduces it to 2.42, creating a “real rigidity” in the sense of Ball and Romer (1990): raising price loses many customers while lowering it gains few.

Incomplete passthrough of TFPQ shocks is a central empirical finding. OLS estimates yield beta_z = -0.124; first-difference estimates yield -0.097. Even in the subsample of firms that adjusted all product-level prices in a given year, TFPQ passthrough remains near -0.10, ruling out Calvo or menu-cost price stickiness as the sole driver. Longer-horizon (two- and three-year) first-difference regressions produce similar estimates, ruling out Rotemberg gradual adjustment as well. The non-CES demand curve alone implies a static-optimal passthrough of theta/(theta + eta) = 3/(3 + 4.3) = 41%, so real rigidity explains most of the incompleteness even before accounting for adjustment costs. Demand shocks pass through to prices at a rate of 0.209-0.235, a non-zero result rationalized in the quantitative model by input adjustment costs.

On cyclicality of dispersion, both TFPQ and demand shock dispersion are countercyclical, but demand dispersion rises by more and is more robust across recession episodes. In 2009 (the Great Recession), the IQR of demand shock growth was 56% above its non-recession average, while the IQR of TFPQ shock growth rose 36%. Sales dispersion rose 58% (IQR) in 2009. A semi-structural variance decomposition shows that demand shocks account for 63% of average sales growth dispersion and approximately 80% of its increase in 2009; TFPQ dispersion contributes only marginally to sales dispersion because the TFPQ variance is shrunk by a factor of roughly 25 on its way to sales growth through the chain of low passthrough and demand elasticity. Demand accounts for about 50% of average price growth dispersion and 40% of its cyclical increase in 2009; TFPQ accounts for about 10% of price dispersion on average.

The quantitative heterogeneous-firm model extends Bloom (2009) and Bloom et al. (2018) to continuous time with both TFPQ and demand shocks, non-CES demand (theta = 3, eta = 4.3 from the estimates), and non-convex input adjustment costs on a composite scale factor covering both capital and labor. The resale loss kappa = 0.3565 is taken from Bloom et al. (2018). The model is calibrated to match IQRs of 0.2 for TFPQ and demand shock log-changes in the low-uncertainty state, consistent with pre-crisis Swedish data. For the high-uncertainty state, the calibration targets the Great Recession peaks: a 30% rise in TFPQ dispersion (sigma_z(2) = 1.38 sigma_z(1)) and a 60% rise in demand dispersion (sigma_epsilon(2) = 1.90 sigma_epsilon(1)), reflecting the empirical finding that demand dispersion increases more.

A simulated transition to the high-uncertainty state causes aggregate output to fall by 3.5%. Decomposing into the Bloom (2009) “volatility effect” (realized shocks drawn from the high-dispersion distribution, firms believe low) and “uncertainty effect” (firms believe high, shocks drawn from low distribution), the paper finds both effects are negative in the non-CES model, in sharp contrast to Bloom (2009) where the volatility effect is positive (the Oi-Hartman-Abel effect). Non-CES demand amplifies the total output decline by approximately 40% relative to the CES model (peak fall 2.5% vs. 1.75%), primarily by reversing the sign of the volatility effect. Increased demand dispersion drives almost all of the first-year output decline and the majority of the uncertainty effect; TFPQ dispersion is the main driver of the negative volatility effect via markup dispersion. The inaction rate among firms jumps from 50% to 95% on impact of the uncertainty shock, then recovers within one year. TFPQ uncertainty induces little wait-and-see behavior because firms optimally adjust inputs by only 23% of the TFPQ shock size (versus 200% under CES), so uncertainty about TFPQ translates mainly into markup uncertainty. Demand uncertainty triggers strong wait-and-see behavior because demand directly maps one-for-one into desired input use.

Layer 2: Deep Dive

What is the paper’s core identification strategy for separating TFPQ and demand shocks, and what are the main threats?

The authors identify TFPQ from a utilization-adjusted Cobb-Douglas value-added production function, then estimate demand using TFPQ innovations as instruments for price. TFPQ innovations are valid instruments because they shift marginal cost without directly shifting demand, tracing out the demand curve. The utilization adjustment (from the KFI managerial survey) is critical: without it, demand shocks that reduce utilization would appear as negative TFPQ shocks, biasing demand elasticity estimates upward and breaking instrument validity. The paper validates the adjustment by showing that firms reporting ‘insufficient demand’ exhibit 15% lower utilization on average, and 23% lower during the Great Recession. A second threat is quality change in firm-level prices; the authors address this with (a) robustness using the Eslava et al. (2023) CUPI quality-adjusted price index and (b) a single-product-firm subsample. Demand and passthrough results are similar across all three price index approaches. The within-firm focus (demeaning by firm and sector-year fixed effects throughout) mitigates cross-sectional comparability issues but limits misallocation-level analyses analogous to Hsieh and Klenow (2009).

How is the non-CES demand curve identified, and what exactly does the super-elasticity parameter eta measure?

The GIR demand curve is q = (1 - eta * log p)^(theta/eta). A second-order approximation around the firm’s average price yields log q = -theta * p_hat - (etatheta/2) * p_hat^2 + fixed effects + epsilon, where p_hat is the firm’s demeaned log relative price. Regressing real sales on p_hat and p_hat^2, instrumented by demeaned TFPQ and its square, recovers theta = -b1 and eta = 2b2/b1. Because p_hat is demeaned at the firm level, the estimates capture within-firm nonlinearity in the price-sales relationship, not cross-sectional heterogeneity in elasticity levels. The parameter eta is the ‘super-elasticity’: it measures how much the demand elasticity itself changes with the price. When eta > 0, a firm that raises its price faces an increasingly elastic demand curve (loses customers rapidly), and one that lowers its price faces a less elastic curve (gains customers slowly). The estimated eta = 4.27 in the main sample is roughly half the value of 10 studied (but not estimated) in Klenow and Willis (2016) and larger than the approximately 2 used in Berger and Vavra (2019).

How does the paper distinguish the ‘volatility effect’ from the ‘uncertainty effect’ in the quantitative model?

Following Bloom (2009), the paper simulates two counterfactuals. The uncertainty effect holds shocks drawn from the low-dispersion distribution (s=1) but lets firms believe that the high-uncertainty state (s=2) has arrived; this isolates the precautionary wait-and-see channel. The volatility effect draws shocks from the high-dispersion distribution (s=2) but lets firms believe they are in the low-uncertainty state; this isolates the direct effect of realizing more extreme shocks on aggregate output. In the non-CES model, both effects are negative. The uncertainty effect is dominated by demand uncertainty because demand shocks directly affect desired input use one-for-one, so uncertainty about future demand creates strong incentives to pause investment. TFPQ uncertainty induces little wait-and-see behavior because the optimal scale adjustment to a TFPQ shock is only 23% of the shock magnitude (vs. 200% under CES). The volatility effect is dominated by TFPQ dispersion because realized TFPQ shocks generate markup dispersion via incomplete passthrough, creating misallocation. Under CES, the volatility effect from TFPQ is positive (OHA effect: convex output-productivity relationship); non-CES demand makes the output-productivity relationship concave for eta large enough, flipping the sign.

What mechanism makes TFPQ passthrough so low in both the data and the model?

Two mechanisms operate. First, non-CES demand itself: when eta > 0, raising price increases the demand elasticity, and lowering price decreases it. This means the benefit to revenue from a price cut (following a productivity gain that reduces costs) is muted because the firm gains fewer customers than under CES. The static optimal passthrough is theta/(theta + eta) = 3/(7.3) = 41%. Second, non-convex input adjustment costs further reduce passthrough by making firms reluctant to change their scale in response to TFPQ shocks. In the model, the investment threshold is nearly flat across a wide range of TFPQ values (shown in Figure 6, left panel), reflecting that optimal scale barely responds to productivity. Together these mechanisms reproduce TFPQ passthrough of 20-30% in model-simulated data vs. 10-24% in the actual data, both far below the CES benchmark of 100%. The paper also verifies that low passthrough persists in the subsample of flexible-price firm-years, ruling out sticky prices as the primary driver.

Why does demand shock dispersion, rather than TFPQ dispersion, dominate the variance decompositions of sales and price growth?

The contribution of TFPQ dispersion to sales dispersion is (1-theta)^2 * beta_z^2 * Var(z). With beta_z = -0.097 and theta = 2.99, the TFPQ variance is shrunk by approximately (1-2.99)^2 * (0.097)^2 = 4 * 0.0094 ≈ 0.04, so only about 4% of TFPQ variance propagates to sales variance. This extremely small multiplier reflects two successive attenuation steps: low TFPQ passthrough to prices (beta_z^2 ≈ 0.01) and a small price-to-sales elasticity. Demand shocks, by contrast, affect sales directly through the demand curve without a price intermediary: the contribution is ((1-theta)*beta_epsilon + 1)^2 * Var(epsilon). With beta_epsilon = 0.209 and theta = 2.99, the multiplier is ((1-2.99)*0.209 + 1)^2 = (1 - 0.416)^2 = 0.34, about eight times larger than for TFPQ even though both shocks have similar variance. The cyclical increase is even more skewed toward demand because demand dispersion rises by 56% vs. 36% for TFPQ in 2009.

How does the paper relate to TFPR dispersion, and what does it say about using TFPR as a sufficient statistic?

TFPR = p * z. For arbitrary passthrough, TFPR growth = beta_epsilon * delta_epsilon + (beta_z + 1) * delta_z. Because passthrough from both shocks is incomplete, TFPR growth reflects a mixture of both underlying shocks. The paper shows via a variance decomposition of TFPR that TFPQ is the main driver of TFPR growth dispersion—accounting for roughly 60% on average—because low passthrough means prices move little, leaving TFPQ changes to dominate TFPR. However, this finding obscures the importance of demand shocks for aggregate outcomes: demand dispersion is the dominant driver of sales growth dispersion and wait-and-see behavior, yet TFPR growth dispersion mostly reflects TFPQ. A researcher relying on TFPR dispersion to infer uncertainty would correctly detect productivity uncertainty but would miss the more cyclically important demand uncertainty channel.

How do the Oi-Hartman-Abel (OHA) and wait-and-see mechanisms work differently under non-CES vs. CES demand?

Under CES demand, sales of each firm are s = z^(theta-1) * exp(epsilon), and aggregate output is E[z^(theta-1)] which is convex in z, so a mean-preserving spread in TFPQ raises aggregate output (OHA effect). Under the estimated non-CES parameters (theta=3, eta=4.3), the approximate relationship yields output proportional to z^0.82, which is concave, so a mean-preserving spread in TFPQ reduces aggregate output. The mechanism is that under non-CES demand, TFPQ shocks pass through incompletely to prices and thus create markup dispersion: high-productivity firms have high markups, low-productivity firms have low markups, and the resulting misallocation reduces total output even relative to a social planner who would set p=mc. For wait-and-see: under CES, optimal input adjustment to a TFPQ shock equals (theta-1) times the shock, which is 200% for theta=3; under non-CES with eta=4.3, it is only (theta^2/(theta+eta) - 1) * shock = 0.233 * shock = 23%. This means firms adjust scale very little in response to TFPQ uncertainty, dampening the wait-and-see channel for TFPQ. TFPQ uncertainty then causes uncertainty about markups, which is costly but does not trigger large investment adjustments.

What role do adjustment costs play, and how robust are the results to the structure of those costs?

Non-convex adjustment costs on a composite firm-scale factor x = k^alpha * l^(1-alpha) create an inaction region: firms neither invest nor disinvest until shocks are sufficiently large. In the low-uncertainty state, the model generates a yearly inaction rate of 25.4% (consistent with pre-crisis Swedish data showing roughly 15%). When uncertainty rises, the inaction region widens, the inaction rate jumps to 95% on impact, and firms let their scale shrink via depreciation. The baseline calibration uses the resale loss kappa = 0.3565 from Bloom et al. (2018). The paper also calibrates kappa to the Swedish inaction rate (kappa = 0.1165), which delivers qualitatively identical dynamics but a smaller amplitude recession (1.7pp vs. 3.5pp output fall). The paper also solves a version with adjustment costs only on capital (as in Bachmann and Bayer, 2013): the wait-and-see effect is dampened but the qualitative results hold—demand uncertainty still dominates TFPQ uncertainty in driving wait-and-see, and non-CES demand still reverses the sign of the OHA effect.

What is the role of the price wedge and time-varying passthrough?

The passthrough equation residual (price wedge, tau) captures price changes unexplained by TFPQ and demand shocks. It could reflect un-modeled shocks (e.g., financial constraints, as Gilchrist et al. (2017) document for Sweden), markup decisions, or measurement error. The price wedge makes a meaningful contribution to both average sales/price dispersion and to the rise in 2009. Time-varying passthrough is also documented: TFPQ passthrough is countercyclical (more negative in recessions), while demand passthrough is procyclical (falls in recessions when firms receive more extreme idiosyncratic demand shocks). Redoing the variance decomposition with year-by-year passthrough estimates makes demand’s contribution to sales dispersion in 2009 even larger, because firms adjust prices less to demand shocks during the recession, leaving more of the demand shock impact in sales.

What heterogeneity is documented across industries and firm types?

Sectoral demand elasticity estimates from the pooled 22-sector sample yield an average theta of 3.89 and median of 2.73 for the linear CES model; for the non-linear model, average theta is 3.26 and average eta is 7.42, with substantial positive skew. The median non-linear eta of 5.37 is larger than the pooled estimate of 4.27, indicating the pooled estimate is pulled down by some sectors with smaller deviations from CES. Key empirical results (greater cyclicality of demand dispersion, incomplete TFPQ passthrough) hold within each major sector and across balanced panels, the single-product subsample, and the CUPI price-index sample. Time-varying passthrough is also found to be systematically higher by about 25% in the post-2008 period compared to the pre-2008 period, suggesting a structural shift in how demand shocks transmit to prices, though the paper does not investigate the source of this change.

What robustness checks are run on the demand and passthrough estimates?

Demand estimation robustness: (1) piece-wise linear specification (elasticity of 2 below average price, 4 above average price, significant at 0.1% level); (2) balanced panel; (3) excluding the Great Recession; (4) using Statistics Sweden firm identifiers instead of authors’ own; (5) CUPI price index; (6) single-product firms; (7) sector-by-sector estimation; (8) including firm and sector-year fixed effects directly in the nonlinear regression (rather than pre-demeaning). All exercises confirm statistically significant eta and broadly similar theta. Passthrough robustness: (1) OLS vs. IV (lagged shocks) vs. first-differences; (2) balanced panel; (3) single-product subsample; (4) two-period lagged instruments (beta_z = -0.294, beta_epsilon = 0.249); (5) flexible-price subsample; (6) longer-horizon (two- and three-year) first differences for TFPQ. Corroboration: TFPQ innovations are positively associated with reported process innovations in Eurostat CIS data (7% greater TFPQ growth for process innovators); negative demand shocks are correlated with managers reporting ‘insufficient demand’ in KFI data (8% lower demand growth).

How does this paper differ from and relate to Bloom (2009) and Bloom et al. (2018)?

Bloom (2009) and Bloom et al. (2018) model a single composite firm-level shock (implicitly TFPR) in a CES-demand economy, finding that uncertainty shocks reduce output through wait-and-see behavior but generate a positive volatility effect (OHA) that partly offsets the uncertainty effect. The present paper adds two departures: (1) it separates TFPQ and demand shocks and shows they have distinct empirical and aggregate implications; (2) it replaces CES demand with an estimated non-CES demand curve. Departure (2) reverses the OHA effect, amplifying the total output decline by around 40% relative to the CES model. Departure (1) shows that the uncertainty channel operates primarily through demand, while TFPQ operates primarily through the volatility channel. The quantitative model uses the same non-convex adjustment cost structure and calibration approach as Bloom et al. (2018) to ensure comparability. The paper also relates to Bachmann and Bayer (2013) and Mongey and Williams (2017), who find smaller aggregate effects with adjustment costs only on capital; the present paper notes that adjustment costs on both capital and labor are needed for large wait-and-see effects, but qualitative conclusions are unchanged with capital-only costs.

What are the policy and theoretical implications of the findings?

First, policies aimed at reducing firm-level demand uncertainty (e.g., demand stabilization, aggregate demand management) have larger aggregate output effects than policies addressing productivity uncertainty, because demand uncertainty triggers wait-and-see investment behavior while TFPQ uncertainty is largely absorbed in markups without changing investment much. Second, TFPQ dispersion is still harmful but through misallocation: policies that reduce markup dispersion induced by productivity differentials can raise aggregate output without requiring reduced dispersion per se. Third, the finding that TFPR dispersion is a poor proxy for demand shock dispersion has implications for how researchers use TFPR as a measure of misallocation or uncertainty: it conflates two distinct forces with different aggregate implications. Fourth, the estimated super-elasticity provides a data-disciplined input for calibrating models with real rigidities, directly relevant for the Ball-Romer nominal non-neutrality question—higher real rigidities amplify the output effects of monetary policy shocks. The authors flag this as a natural extension. The scope conditions are: Swedish manufacturing, annual data 1998-2013, partial equilibrium model (aggregate price level exogenous), firms with matching price and utilization data (large-firm bias).

What additional findings are documented regarding the cyclicality of other firm-level variables?

Beyond TFPQ and demand dispersion, the paper documents that dispersion of sales growth, price growth, labor, intermediate goods, and capacity utilization are all countercyclical. The IQR of sales growth was 58% above the non-recession average in 2009 and 9% above in 2001; the IQR of price growth was 83% above in 2009 and 5% above in 2001. The one notable exception is investment, which displays procyclical dispersion (less dispersed during the Great Recession). The paper also documents that roughly 30% of firms report insufficient demand at all their plants in the survey data; average capacity utilization is 88% with median 91% and standard deviation of 14.1%; and about 25% of firm-year observations involve utilization at or above 100%.

Key Concepts

Physical total factor productivity (TFPQ): Firm-level quantity productivity: output per unit of inputs, measured from a utilization-adjusted Cobb-Douglas value-added production function. Distinct from revenue TFP (TFPR = p*z) because it abstracts from demand conditions and price-setting. In this paper, TFPQ is estimated within firm over time using the cost-share approach and a capacity-utilization correction from managerial survey data.

Demand shock (epsilon): The idiosyncratic component of a firm’s demand curve that captures its ability to sell more (or fewer) units at a given price in a given year, reflecting changes in customer base size or customers’ willingness to pay. Estimated as the residual from the GIR demand curve after controlling for firm fixed effects, sector-time fixed effects, and the firm’s own price.

Non-CES demand curve / super-elasticity (eta): A demand specification adapted from Gopinath, Itskhoki, and Rigobon (2010) in which the demand elasticity is not constant but rises with the firm’s price. The parameter eta (estimated at 4.27 in the main sample) governs how fast the elasticity rises with the price: when eta > 0, firms gain few customers by cutting price (elasticity falls as price falls) and lose many customers by raising price (elasticity rises as price rises). This is the source of ‘real rigidity’ that makes incomplete TFPQ passthrough optimal.

Incomplete TFPQ passthrough: The empirical finding that firms reduce their prices by far less than one-for-one in response to a productivity gain (estimated beta_z = -0.097 to -0.124, far from the CES benchmark of -1). The paper attributes this primarily to non-CES demand real rigidity (which implies an optimal static passthrough of only 41% given the estimated parameters) and secondarily to adjustment costs.

Oi-Hartman-Abel (OHA) effect: The positive ‘volatility effect’ in standard CES-demand uncertainty models: because output is a convex function of TFPQ under CES, a mean-preserving spread in productivity raises aggregate output (lucky firms expand more than unlucky firms contract). The paper overturns this result by showing that with non-CES demand (eta sufficiently large), the output-productivity relationship becomes concave, so TFPQ dispersion reduces aggregate output via markup misallocation.

Wait-and-see channel: The mechanism by which uncertainty about future shocks causes firms with non-convex input adjustment costs to pause investment: firms prefer to remain inactive and let inputs depreciate rather than invest or disinvest, at the risk of having to pay an irreversibility cost if the shock turns out to have been in the opposite direction. In this paper, this channel is driven primarily by demand uncertainty because demand shocks determine how many units a firm can sell and hence its desired input level; TFPQ uncertainty does not trigger strong wait-and-see behavior because the optimal scale response to TFPQ shocks is small under non-CES demand.

Markup dispersion / misallocation: Dispersion across firms in the ratio of price to marginal cost, arising in this paper from incomplete TFPQ passthrough: firms with high productivity set high markups rather than passing through productivity gains as price cuts. The resulting wedge between prices and marginal costs means that resources are misallocated (too little output at high-productivity firms relative to the social optimum), reducing aggregate output. This is the channel through which TFPQ dispersion harms the aggregate economy in the model.

Price wedge (tau): The residual from the passthrough regression: the component of firm price changes unexplained by the estimated TFPQ and demand shocks. Interpreted as capturing un-modeled shocks (financial constraints, markup adjustments) and potentially measurement error. The price wedge makes a meaningful contribution to both average sales/price dispersion and to the Great Recession increase in dispersion.