Occupational Exposure to Capital-Embodied Technical Change: Caunedo, Jaume & Keller (2023)

What this is. The paper’s core results, the structural model of occupational capital and worker sorting, and the method for measuring CETC at the occupational level, with the defining equations: enough to know what was found and how, without reading the full 44 pages. To replicate or extend, read the original at doi:10.1257/aer.20211478.

TL;DR

Caunedo, Jaume, and Keller construct the first direct measures of capital-embodied technical change (CETC) at the occupational level, covering 24 BEA equipment categories and 327 US occupations from 1984 to 2015, by combining NLP-extracted tool use from the 1977 Dictionary of Occupational Titles and O*NET with BEA quality-adjusted capital stocks. They also estimate the elasticity of substitution between capital and labor in each one-digit occupation via an instrumental-variables strategy. Embedding these measures in a general equilibrium model of occupational choice (Roy 1951 tradition with Frechet efficiency draws), they find that CETC accounts for 95% of gross US labor reallocation between 1984 and 2015 and 51% of the rise in the college premium. The key driver is not the extent of CETC but heterogeneity in the elasticity of substitution across occupations: without it, CETC would generate less than 10% of the observed high-skill employment shift.

Core results

Magnitudes are as reported; locators point into the source PDF.

#	Result	Locator	Magnitude
R1	CETC accounts for 72% of the labor reallocation toward high-skill occupations (professionals, managers, technicians) between 1984 and 2015	Table 1, p. 1667	7.23 pp of 10.06 pp observed high-skill employment share increase
R2	CETC accounts for 58% of the employment loss in middle-skill occupations (machine operators, precision production, admin. services, sales, mechanics)	Table 1, p. 1667	-7.82 pp of -13.58 pp observed middle-skill employment share decline
R3	CETC drives 95% of gross labor reallocation across all occupations	Table 1, p. 1667	2.89 pp of 3.04 pp average absolute employment share change; data gross reallocation = 3.0 pp
R4	CETC accounts for 51% of the rise in the college premium between 1984 and 2015	Table 2, p. 1671	15.56 pp of 30.58 pp observed college premium increase
R5	CETC widens the gender wage gap by 17.49 pp, primarily by raising wages per efficiency unit in mechanics/transportation (male-intensive) and managerial occupations	Table 2, p. 1671	Without CETC, gender wage gap would have closed by 45.50 pp instead of 28.01 pp
R6	Occupational IV elasticities of substitution range from 0.65 to 2.18; aggregate IV elasticity = 0.88, consistent with prior aggregate estimates	Figure 3, p. 1657; App. Table B.III, p. 1681	Technicians: 0.65 (SE 0.21); mechanics/transp.: 0.73; managers: 0.93; admin. services: 2.18 (SE 0.50); aggregate: 0.88 (SE 0.24)
R7	Heterogeneity in elasticity of substitution is the primary channel: imposing a common elasticity (sigma = 0.82) reduces CETC’s high-skill employment shift from 7.23 pp to 0.40 pp, less than 10% of the baseline	Table 1, “identical elasticity” column, p. 1667	0.40 pp vs 7.23 pp baseline; equalizing CETC paths across occupations changes reallocation by only 0.19 pp

Overall (paper’s conclusion). The heterogeneity in the types of capital used across occupations, and consequently in the elasticity of substitution between capital and labor, is the primary channel through which CETC shapes employment reallocation and wage inequality. CETC reallocates employment out of middle-skill occupations (higher capital-labor substitutability) and into high-skill occupations (higher complementarity). Computer-specific CETC alone explains only 10% of the college premium rise; communication equipment and software each explain 12-15%, reinforcing the importance of broad capital measurement relative to prior estimates by Burstein, Morales, and Vogel (2019) who attributed 60% to computers. The routinization mechanism in Autor, Levy, and Murnane (2003) is broadly consistent with the findings, but the substitution channel driven by heterogeneous elasticities, not task content per se, is quantitatively primary. The capital-skill complementarity framework of Krusell, Ohanian, Rios-Rull, and Violante (2000) is extended here to allow heterogeneous substitutability across nine occupation groups.

Theory / model

The model extends Greenwood, Hercowitz, and Krusell (1997) to include multiple occupations with heterogeneous exposure to CETC, and adopts the Roy (1951) occupational choice framework with Frechet efficiency draws.

Occupational production. A representative producer in occupation $o$ uses a constant-returns CES technology combining capital $k_{ot}$ and labor $n_{ot}$ to produce occupational output $y_{ot}$ (equation (8), p. 1661):

$$y_{ot} = \left[ \alpha k_{ot}^{\frac{\sigma_o - 1}{\sigma_o}} + (1-\alpha) n_{ot}^{\frac{\sigma_o - 1}{\sigma_o}} \right]^{\frac{\sigma_o}{\sigma_o - 1}}, \tag{8}$$

where $\sigma_o \geq 0$ is the elasticity of substitution between capital and labor, which differs across occupations. Occupations differ in two dimensions: the technology embodied in capital (CETC) and this elasticity.

Final good producer. Final consumption is a CES aggregator of occupational goods (p. 1662):

$$y_t = \left( \sum_o \omega_{ot}^{1/\rho} y_{ot}^{(\rho-1)/\rho} \right)^{-\rho/(\rho-1)},$$

where $\rho$ is the (absolute) demand elasticity for occupational output and $\omega_{ot}$ is an occupational demand shifter capturing offshoring and structural change forces.

Capital producer. Each unit of occupational capital is produced from the final good at a rate of transformation $q_{ot}$, so the user cost satisfies $\lambda^k_{ot} = 1/q_{ot}$. CETC in occupation $o$ is the decline in the user cost of occupational capital relative to consumption: a rise in $q_{ot}$ is the capital-embodied improvement.

Worker occupational choice. The economy has $H$ labor groups (defined by age, gender, education). Worker $i$ of type $h$ draws efficiency units $n_{oht}(i)$ from a Frechet distribution with scale $T_{oht}$ and shape $\theta$. Worker $i$ of type $h$ chooses the occupation that maximizes wages:

$$o^*_h(i) = \arg\max_o \{ w_{oht}(i) \}, \tag{13}$$

where $w_{oht}(i) = n_{oht}(i) \lambda^n_{ot}$ is compensation and $\lambda^n_{ot}$ is the wage per efficiency unit (endogenously equated across workers in equilibrium). The Frechet property delivers a closed-form occupational allocation (equation (21), p. 1678):

$$\pi_{oht} = \frac{T_{oht} (\lambda^n_{ot})^\theta}{\sum_{o'} T_{o'ht} (\lambda^n_{o't})^\theta}, \tag{21}$$

with labor supply elasticity $\eta_{n\lambda^n_o} = \theta - 1 = 0.30$ (using $\theta = 1.30$ estimated from Mincerian wage residuals).

Equilibrium wages. From the zero-profit condition of the occupational producer, the wage per efficiency unit satisfies (equation (18), p. 1677):

$$\lambda^n_{ot} = \left[ \left(\frac{1}{1-\alpha}\right)^{\sigma_o} (\lambda^y_{ot})^{1-\sigma_o} - \left(\frac{\alpha}{1-\alpha}\right)^{\sigma_o} (\lambda^k_{ot})^{1-\sigma_o} \right]^{\frac{1}{1-\sigma_o}}. \tag{18}$$

Method

The method has two parts: measuring occupational CETC from newly constructed data, and estimating the capital-labor elasticity via instrumental variables. It builds on instrumental-variables, panel-regression, text-classification, and roy-occupational-sorting.

Occupational capital stocks and CETC. The paper covers all 24 BEA equipment and software categories. Quality-adjusted stocks for each category $j$ are initialized in 1984 using nominal stocks as the base and then iterated forward:

$$k_{ot} = k_{ot-1} e^{\gamma^k_{ot}}, \quad k_{o,1984} = \sum_j \lambda^k_{j,1984} k_{oj,1984}, \tag{1}$$

where $\gamma^k_{ot} = \sum_j \omega_{ojt} \gamma^k_{ojt}$ is the expenditure-share-weighted average growth rate of the equipment categories used in the occupation. The user cost of capital for equipment $j$ follows the Jorgenson (1963) no-arbitrage condition (p. 1647):

$$\lambda^k_{jt} = \frac{p^k_{jt-1}}{\lambda^c_{t-1}} \left[ R - (1-\bar\delta_{jt}) \frac{p^k_{jt}/\lambda^c_t}{p^k_{jt-1}/\lambda^c_{t-1}} \right],$$

where $p^k_j$ is the quality-adjusted price, $\lambda^c$ is the price of consumption, $R = 1.02$ is the gross return on a safe asset, and $\bar\delta_{jt}$ is the average physical depreciation. Occupational CETC is then the implied user cost of occupational capital (equation (2), p. 1647):

$$\lambda^k_{ot} = \frac{\sum_j \lambda^k_{jt} k_{ojt}}{k_{ot}}. \tag{2}$$

Occupational capital requirements. The capital requirement index assigns the fraction of each equipment category’s aggregate services to each occupation, using the tools reported by workers in that occupation (equation (3), p. 1649):

$$\text{req}_{ojt} = \frac{\tau_{ojt} l_{ot}}{\sum_o \tau_{ojt} l_{ot}}, \tag{3}$$

where $\tau_{ojt}$ is the count of tools from category $j$ used by occupation $o$ at time $t$, and $l_{ot}$ is full-time-equivalent workers. The tool data for 2015 come from O*NET; for 1984, NLP string matching is applied to the 1977 Dictionary of Occupational Titles (DOT) to extract the same tool taxonomy, and then linearly interpolated between the two years.

Empirical specifications

Elasticity of substitution (Section II.A). The structural equation for the capital-labor ratio is estimated as a time-series regression for each one-digit occupation (equation (5), p. 1655):

$$\ln\!\left(\frac{k_{ot}}{\tilde n_{ot}}\right) = \beta_{1o} + \beta_{2o} t + \beta_{3o} \ln\!\left(\frac{\tilde\lambda^n_{ot}}{\lambda^k_{ot}}\right) + \varepsilon_{ot}, \tag{5}$$

where $k_{ot}/\tilde n_{ot}$ is the observed capital-labor ratio (labor adjusted for efficiency via observable demographics), $\tilde\lambda^n_{ot}/\lambda^k_{ot}$ is the ratio of the measured labor price to the capital user cost, $\beta_{3o}$ identifies $\sigma_o$, and $\beta_{2o}$ captures the rate of factor-augmenting technical change. The OLS estimate is biased because relative factor prices are endogenous to capital-labor ratios. Instruments exploit exogenous labor supply shifts: (i) 16-year lagged live births interacted with 1984 occupation-education shares $sh^e_{oe,1984}$, and (ii) aggregate trade shocks for occupations with weak first-stage F-statistics (mechanics/transportation and low-skill services). All regression series span 1984 to 2015 (32 annual observations per occupation).

Workers’ exposure to CETC (Section II.B). Under constant returns and competitive markets, the cross-price elasticity of occupational labor demand with respect to the user cost of capital (equation (7), p. 1659) is:

$$-\frac{d\ln(n_o)}{d\ln(\lambda^k_o)} = \frac{\eta_{n\lambda^n}(\rho - \sigma_o) \frac{\lambda^k_o k_o}{\lambda^y_o y_o}}{\rho + \eta_{n\lambda^n} + (\sigma_o - \rho) \frac{\lambda^k_o k_o}{\lambda^y_o y_o}}, \tag{7}$$

where $\sigma_o$ is the elasticity of substitution (Section II.A), $\eta_{n\lambda^n} = 0.30$ is the labor supply elasticity, $\rho = 1.34$ is the demand elasticity across occupational outputs, and $\lambda^k_o k_o / (\lambda^y_o y_o)$ is the capital expenditure share. Exposure is positive (CETC raises labor demand) when $\sigma_o < \rho$ and negative when $\sigma_o > \rho$.

General equilibrium quantification (Sections III-IV). The model is parameterized to the US 1984-2015 period using two steps. First, $\sigma_o$ and the capital user costs $\lambda^k_{ot}$ come from Sections I-II. Second, the scale parameters $T_{oht}$ of the Frechet distribution are inferred from observed occupational choices and wages using the equilibrium conditions (equations (21) and (22)). The demand elasticity $\rho = 1.34$ is estimated from the regression (equation (14), p. 1664):

$$\ln\!\frac{\lambda^y_{ot} y_{ot}}{\lambda^y_{o_0 t} y_{o_0 t}} = \beta_1 + \beta_{2o} t + \beta_3 \ln\!\frac{\lambda^y_{ot}}{\lambda^y_{o_0 t}} + \varepsilon_{ot}, \tag{14}$$

instrumented by a Bartik-style shift in the average cost of capital by occupation. Counterfactuals are run by removing exogenous forces (CETC, demand, demographics, comparative advantage, group composition) one at a time in all orderings, then averaging the marginal contributions (Shapley decomposition approach).

Datasets used

Dataset	Role in paper	Wiki page
BEA Fixed-Asset Tables (24 equipment/software categories)	Quality-adjusted capital stocks by equipment category; investment series; depreciation rates	no page yet
O*NET Tools and Technology module (2010s)	Occupational tool use for 2015 assignment of capital to occupations	no page yet
Dictionary of Occupational Titles (DOT, 1977)	NLP-extracted tool use for 1984 capital assignment; interpolated with O*NET to build time series	no page yet
March Current Population Survey (CPS, Flood et al. 2019 / IPUMS)	Annual labor market statistics: employment shares, wages, full-time-equivalent workers, by occupation and demographic group, 1984-2015	no page yet
October CPS computer supplement (1984, 2003)	External validation of computer tool assignment against workers’ self-reported computer use at work	no page yet

Sample: 324 3-digit census occupations (9 one-digit groups), 1984-2015, annual frequency. Capital stocks initialized 1984; base year for normalization is 1985.

When to read the full paper

Read the original when: constructing occupational-level capital exposure measures (Section I describes the data construction and NLP assignment in full detail); estimating occupation-specific factor substitution elasticities (the IV strategy and weak-instrument diagnostics in Appendix Tables B.II-B.III are essential for replication); building a multi-occupation Roy-model GE framework (Appendix A derives all equilibrium conditions); or studying the differential role of specific equipment categories (Table 3 decomposes CETC by computers, communication, and software). The replication data and code are at zenodo.7591599 and the occupational capital dataset is available at www.capitalbyoccupation.weebly.com.

Attribution and rights

Source: peer-reviewed, American Economic Review 113(6), June 2023. Freely accessible via pubs.aeaweb.org after the AEA’s 12-month delayed open-access period. No CC licence; redistribution is extract-only. This distillation was extracted by an LLM on 2026-06-25 and is not human-verified or independently reproduced.

Caunedo, Julieta, David Jaume, and Elisa Keller. “Occupational Exposure to Capital-Embodied Technical Change.” American Economic Review 113, no. 6 (June 2023): 1642-1685. DOI: 10.1257/aer.20211478.