Capital Unemployment

The paper adopts a three-way classification borrowed from labour statistics, in which a capital unit counts as unemployed only if it is both idle in production and actively being searched over for trade. Formally, a unit of physical capital in a period is employed if it has been used for the production of goods and services within the period; unemployed if it has not been used for production and there has been active search to trade (sell or rent) the unit; and inactive if it has not been used and there has been no active search to trade it. The distinction matters because it separates idleness that reflects a frictional trading process from idleness that reflects retirement or abandonment. The capital-unemployment rate is defined as unemployed capital divided by “active capital” (employed plus unemployed), so inactive units are excluded from the base, mirroring the labour-force construction. The paper works with homogeneous capital in the main text and extends the definitions to multiple capital types in an appendix.

The main measure comes from commercial-property vacancy rates, and it puts average U.S. capital unemployment for structures at 10.9% over 1980–2015. The aggregate series is built from CBRE and REIS data on the share of office, retail and industrial space that is vacant and marketed as available for occupancy, weighted by BEA current-cost shares of each property type. The paper notes two advantages of nonresidential structures for this purpose: they provide systematic historical information that maps to the paper’s definition, and they represent a large share of the capital stock. For comparison, labour unemployment averaged 6.4% over the same period. Similar magnitudes appear in Greece, Ireland, Portugal, Spain and the U.K., where the paper reports an average of 11% using Jones Lang LaSalle data.

It is volatile, persistent, and countercyclical, with second moments broadly comparable to those of labour unemployment. The reported standard deviation is 2.4% in raw data and 1.2% at business-cycle frequencies (HP-filtered), against 1.6% and 1.1% for labour unemployment; autocorrelation is 0.91 raw and 0.72 filtered. The correlation with the cyclical component of real GDP per working-age person is −0.52. Decomposing the rate, the growth rate of the unemployed capital stock is five times more volatile than that of employed capital in raw data (eight times at business-cycle frequencies), and unemployed-capital growth is countercyclical while employed- and total-capital growth are procyclical — so the rate moves mainly through the numerator. The paper notes one visible exception to the countercyclical pattern: the second half of the 1980s, a period the urban-economics literature identifies as a construction boom in nonresidential structures.

They establish that individual capital units sit unsold for months and that their trading probability moves with the cycle, which is the pattern a search-and-matching model predicts. The Idealista data cover all Spanish listings on the platform for 2005–2018 — an unbalanced panel of more than 10 million monthly observations on 1.2 million listings — and record how many months each unit remains listed. Average listing duration is 8 months; for the 4% subsample where the owner confirmed the listing ended because the property was rented or sold, the average is 11 months. The listing-withdrawal rate, used as a proxy for the trading probability, fell from 36% to 17% per quarter between 2007 and 2012 as capital unemployment rose, and recovered after 2013. The paper is explicit that this fall in trading occurred despite a substantial fall in posted prices, which declined by more than 50% on average over that period. A second dataset (EIXOS) tracks over 71,000 commercial locations in Barcelona and more than 10,000 business transitions.

The paper documents three patterns that align with general predictions of search-and-matching models: costly buyer inspection, a Beveridge-curve relation, and a market-tightness/trading-probability link. Listings receive roughly 60 clicks per month on average, which the paper reads as buyers dedicating effort to inspecting units. Within a neighbourhood, period and property type, listings receiving one standard deviation more clicks than the mean have a 1 to 2 percentage point higher probability of exiting the platform in a given month — 13% to 17% higher than for the mean listing. At the aggregate level, the cyclical component of search volume and capital unemployment have a correlation of around −0.5, which the paper likens to a Beveridge curve. Appendix evidence exploiting geographic and temporal variation shows higher market tightness in the neighbourhood and month of listing is associated with a higher trading probability, and that this link appears only for units of comparable size — consistent with capital specificity.

Specificity — the property that some capital units suit some businesses better than others — is offered as a reason search frictions exist, but mismatch across markets is found to account for only a modest part of the fluctuations. The paper cites Kermani and Ma (2023), who using liquidation recovery rates report an average liquidation value of a firm’s plant, property and equipment around 33% of book value, and notes their split of 33% for equipment and 43% for structures. Using the EIXOS data, stores that change operating business repeat their 6-digit NAICS activity at a substantive frequency, which the paper reads as consistent with specificity. Applying the Şahin–Song–Topa–Violante mismatch method to the Spanish listings, the paper finds mismatch rose during the Euro-crisis contraction but that this had only a modest effect on the level of mismatch unemployment. The stated conclusion is that fluctuations in capital unemployment are likely driven more by changes in economic conditions affecting buyers’ aggregate purchasing activity than by mismatch between where buyers search and where idle capital sits.

It is a stochastic neoclassical growth model with two additions: directed search in the capital market, and financial frictions on firms’ capital purchases. Households produce capital goods and firms employ capital in production. Sellers of idle units post a price, buyers devote hours of work to searching and can direct their search to a submarket with a specific price — the competitive-search structure used in labour models by Shimer, Moen and Menzio–Shi, which the paper argues matches how capital is actually posted and searched over in the data. Each unit of a firm’s employed capital receives, with probability ψ, a match-specific shock that renders it unusable for that firm, generating separation flows that map to establishment exit. The financial block follows Gertler and Kiyotaki (2010): frictional intermediaries mediate financing between firms and households, and financial shocks primarily hit intermediaries’ net worth and hence the severity of financial frictions. Labour markets and all other markets are Walrasian in the baseline; the paper reports an extension with frictional labour markets.

It is calibrated quarterly to the U.S. economy for 1980–2015, using standard values for the neoclassical block and targeting capital-market and financial moments for the new parameters. The neoclassical parameters are conventional: β = 0.994 (a 4% annual real rate), capital share α = 0.35, quarterly depreciation δ = 0.021 (8% annually), a Frisch elasticity of one, and ρ_A = 0.95, σ_A = 0.006 for TFP. The separation rate is set to ψ = 0.008, corresponding to a 3.2% average establishment exit rate from Census data. Matching efficiencies for new and used capital (m_new = 5.62, m_used = 0.58) are pinned down by targeting a 64% ratio of matching flows from used capital to exit flows, taken from Becker et al. (2006) — the estimated gap is consistent with used capital facing greater trading frictions. The matching elasticity is set symmetrically at η = 0.5. The financial parameters target a 100-basis-point average annual excess return of nonfinancial firms over the risk-free rate, plus the volatility of investment and of intermediaries’ net worth. On business-cycle moments the model produces output volatility of 1.4% against 1.3% in data and investment volatility of 3.4% against 4.7% (both targeted), and untargeted consumption and hours volatilities close to their data counterparts. The paper flags one shortfall it accepts: constraining ρ_A to 0.95 yields an output autocorrelation of 0.58, below the 0.87 observed.

Yes, within a range that depends on the matching-technology assumption, and the average unemployment rate it generates is untargeted and close to the data. The calibration implies an untargeted average capital-unemployment rate of 12.8%, which the paper describes as a plausible value given the 10.9% measured for structures. In the data, capital unemployment for U.S. structures has a volatility of 7% and a −0.55 correlation with output; the baseline model delivers a volatility between 6% and 11% and a correlation with output between −0.18 and −0.55, depending on whether new and used capital are given different matching efficiencies. The model also matches capital-price volatility (9% in data, 6% in the baseline specification with heterogeneous matching technology). For trading probabilities no systematic U.S. data exist, but the model’s predictions are described as consistent with the Spanish evidence, where listing-withdrawal rates have a volatility of 23% and a 48% correlation with output.

Because financial shocks move intermediaries’ stochastic discount factor and hence firms’ cost of capital sharply, while TFP shocks barely do. A contractionary financial shock raises intermediaries’ marginal cost of external finance and lowers their discount factor, contracting the supply of funds and raising firms’ cost of capital; that reduces the shadow price of employed capital, firms’ capital purchases and their search effort, which lowers the trading probability faced by sellers and raises unemployed capital. TFP shocks have only a minor impact on that discount factor, so market tightness and trading probabilities move little; moreover, a contractionary TFP shock reduces production of new capital, so its net effect is a fall in unemployed capital and in the unemployment rate — the opposite of what the data show in bad times. Setting either the financial friction (φ = 0) or the financial shock (σ_ζ = 0) to zero leaves the model predicting capital-unemployment and capital-price volatility one order of magnitude smaller than in the data, which the paper links to the well-known result that canonical RBC models generate too little asset-price volatility.

The paper tests two natural alternatives and reports that neither reproduces the joint behaviour of capital unemployment and capital prices. Shocks to the technology for producing new capital goods, calibrated to match the observed volatility of capital unemployment, generate procyclical capital unemployment, because an expansionary shock raises new-capital production and hence the stock of idle units along with output. Shocks to matching efficiency generate counterfactually countercyclical capital prices, since higher matching efficiency lowers the shadow price of employed capital in an expansion. The paper’s stated conclusion is that in a real-business-cycle model, the joint pattern generated by financial shocks cannot be easily replicated by these other shock types. It also notes that the procyclical pattern predicted by investment-specific technology shocks matches the 1980s construction-boom episode, suggesting such shocks may have mattered in that period, while the rest of the U.S. sample is countercyclical.

Two: some specialisation of search labour, and financial frictions concentrated on final-goods producers rather than capital producers. If labour is perfectly substitutable between final-goods production and search activities, the model predicts counterfactually acyclical capital unemployment — the fall in search effort after a negative financial shock pushes wages down, which raises hours and activity in final-goods production. The paper concludes that some degree of specialisation in search activities is important to account for a volatile and procyclical trading probability. Separately, a version in which capital producers face the same financial frictions as final-goods producers also generates acyclical capital unemployment and too little capital-price volatility, because the shock then contracts the supply of capital goods and reduces the stock of idle units. By contrast, extending the model to frictional labour markets preserves the main predictions, and appendix results report that volatile countercyclical capital unemployment obtains across a wide range of plausible trading-friction parameters.

Because the stock of idle capital is a state variable that lowers the probability of selling capital, and so lowers the incentive to produce new capital goods. Starting from a total capital stock at its steady-state level but capital unemployment above steady state, the model’s transition is non-monotonic: the capital stock first falls and then converges back. Two forces oppose each other — below-steady-state employed capital raises the marginal product of capital and encourages accumulation, while above-steady-state unemployment lowers the selling probability and discourages production of new units. Initially the second dominates, and absorption of unemployed capital crowds out investment; as idle units are absorbed, the selling probability recovers and so does capital production. Strikingly, the paper shows that even when the total capital stock starts below steady state — a configuration that in the neoclassical model implies high investment and monotonic convergence — a large enough initial capital-unemployment rate produces an initial period of below-steady-state investment.

Through the lens of the model, almost half of the gap between the data and a neoclassical benchmark, in the capital stock’s deviation from trend during the recovery. The paper first documents the puzzle: three years after the recession trough the U.S. capital stock was still falling relative to trend, reaching about 4% below trend by 2013, and capital unemployment had risen to levels 35% above its mean by 2010. It then simulates the recovery from the observed capital stock and capital unemployment in 2010.II under an estimated sequence of shocks, and compares it to a counterfactual starting from the steady-state unemployment rate and to a neoclassical benchmark. The neoclassical model, driven by the TFP slowdown, predicts a deviation from trend about a third of that observed. The capital-unemployment model with only productivity shocks tracks the data more closely, while the same model started from steady-state capital unemployment predicts a path close to the neoclassical one. The paper reports that the model also accounts for almost half of the persistence in the capital-unemployment rate itself, and notes in a footnote that additionally extracting financial shocks from the observed path of capital unemployment brings the predicted slump closer still to the data.

Yes, described by the paper as descriptive evidence: U.S. metropolitan areas with more idle capital at the Great Recession trough had lower investment through the recovery. Using MSA-level data on structures, the paper measures each area’s capital unemployment in 2010.II relative to its historical mean and its average investment rate over 2010–2014 relative to its historical mean. The correlation between the two is −0.52. The negative relationship is statistically significant and survives controls for the deviation of the capital stock from trend and for labour unemployment at the trough. Extending the model to multiple regions and simulating each region’s predicted investment path from its observed capital-unemployment rate, the slope obtained from model-simulated data lies within the confidence intervals estimated in the data. The paper frames this exercise as supportive of the model’s transitional-dynamics prediction rather than as an identified causal estimate.

The peak output response to a one-standard-deviation contractionary financial shock is 0.8% with trading frictions, roughly an order of magnitude larger than the 0.06% in a comparable Walrasian-capital-market model. In the Walrasian version, financial shocks move aggregate investment a lot — a peak effect of 4% — but the capital stock, which is the production input there, moves only modestly, so output barely responds. With trading frictions the production input is employed capital, and employed capital responds substantially more than the total capital stock, because the shock lowers firms’ capital demand and search effort and so the selling probability of idle units. The paper is careful to bound the claim: trading frictions do not produce substantially larger output responses to TFP shocks, precisely because TFP shocks move capital unemployment so little.

They are complementary rather than substitutes: aggregate utilisation is the product of the employment rate of capital and the utilisation rate of employed capital, and the two components respond to different shocks. Extending the model with an intensive utilisation margin (with the Christiano–Eichenbaum–Evans cost curvature set to 5.4 from Justiniano, Primiceri and Tambalotti), output can be written with total aggregate utilisation equal to (1 − uᵏ)·ε. All else equal, variations in the two components have identical effects on gross output — but the paper identifies two dimensions where the distinction matters. First, unemployed capital is a state variable that shapes the transitional dynamics of the capital stock, whereas variable utilisation of employed capital is a control variable whose introduction alone does not disturb monotonic convergence in the neoclassical model. Second, the response of total utilisation to TFP shocks is dominated by variable utilisation, while its response to financial shocks is dominated by capital unemployment; contractionary financial shocks in fact raise utilisation, because the decline in employed capital raises the marginal benefit of using it harder. The paper adds that in the last four pre-pandemic recessions, capital unemployment displays patterns that differ significantly from traditional utilisation measures.

It argues that the interaction between trading frictions and financial shocks — not trading frictions alone — is what makes these frictions macroeconomically relevant. Kurmann and Petrosky-Nadeau (2007), the first paper to study search frictions in the physical-capital market, did so without financial frictions and found capital-market search frictions were not quantitatively important for the business cycle. The paper reports that absent financial shocks its own model reproduces that result: the small capital-unemployment fluctuations it then implies have modest macroeconomic consequences. Introducing financial frictions and shocks that primarily affect their severity generates data-sized fluctuations in capital unemployment and quantitatively significant effects on output and investment — a result the paper links to Hall (2017) on discount-factor shocks in labour-market search models.

The paper’s focus is explicitly positive, and it flags normative questions as future work rather than delivering policy conclusions. The conclusion notes that combining the search frictions studied here with asymmetric information could open scope for policies related to asset purchases and subsidy programmes, citing Guerrieri and Shimer (2014), and that given the interaction between capital unemployment and investment it would be interesting to study the relationship between capital unemployment and monetary policy. Both are described as extensions planned for future research.