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 census occupations; the matched tool series covers 324 observed three-digit occupations from 1984 to 2015. They combine 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 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; the paper reports different aggregate estimates in the text and appendix table	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 in text (p. 1657) and 0.82 in App. Table B.III (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 changes the high-skill CETC contribution from 7.23 to 7.42 pp (+0.19 pp)
R8	CETC accounts for part of the employment increase in low-skill services	Table 1, p. 1667	0.59 pp of 3.52 pp observed increase (17%)
R9	Removing occupational elasticity differences reduces total and skill-group employment effects	Table 1, p. 1667	With common sigma = 0.82, gross movement is 0.50 pp vs 2.89 pp baseline; high-skill 0.40 pp, middle-skill 0.17 pp, low-skill -0.57 pp
R10	CETC-induced employment reallocation differs across worker groups	Table 1, p. 1667	Absolute average movement: non-college 3.46 vs college 1.97; ages 16-29 3.04, 30-49 2.71, 50-65 3.08; females 4.10 vs males 2.47 (table entries are percent)
R11	Pairwise Wald tests support occupational heterogeneity in capital-labor substitution	Table B.II, p. 1681; discussed p. 1657	Reject equality for managers vs administrative services (p=0.02), professionals vs sales (p=0.03) and administrative services (p=0.01), technicians vs sales (p=0.01), administrative services (p=0.00, rounded), and precision production (p=0.03)
R12	Instrument-strength and time-series diagnostics vary across occupations	Table B.III, p. 1681; discussed p. 1658	Kleibergen-Paap F-statistics range from 6.66 to 43.24 across occupations (8.29 aggregate); Dickey-Fuller tests reject an error-term unit root for every occupation and the aggregate, at 10% for managers and 5% for the others
R13	Hicks exposure predicts the direction of reallocation but understates the general-equilibrium magnitude	Figure 5, p. 1668	General-equilibrium response is more than five times the Hicks-exposure response
R14	CETC contributes to age-premium increases, more for workers aged 30-49	Table 2, p. 1671	5.90 pp of 7.95 pp for ages 30-49; 3.80 pp of 13.83 pp for ages 50-65
R15	CETC raises both high- and middle-skill occupation premia relative to low-skill occupations	Table 2, p. 1671	7.80 pp of 16.25 pp for high-skill; 7.90 pp versus the 4.50 pp observed middle-skill premium increase
R16	Occupational demand shifts are a major force outside CETC, particularly for low-skill employment and wage premia	Table B.V, p. 1681; discussed pp. 1668-1672	Demand contributes 2.92 pp to low-skill share growth, 24.27 pp to the 30.58 pp college-premium increase, and -22.21 pp to the -28.01 pp gender-gap change
R17	CETC trends predict much of 2005-2015 high- and middle-skill employment changes	Figure 7, pp. 1672-1673	3.8 pp of 5.0 pp high-skill growth and 64% of middle-skill outflow; predicted low-skill outflow 0.35 pp vs observed inflow 0.34 pp
R18	Software and communication equipment CETC matter more than computer CETC for the college premium	Table 3, p. 1676	Contributions are 3.06 pp for computers, 3.56 pp for communication equipment, and 4.64 pp for software, or 10%, 12%, and 15% of the 30.58 pp rise
R19	Capital deepening and CETC vary substantially across occupational groups	Figure 1, p. 1651; text p. 1651	Capital per worker grows 1.1% annually in administrative services and professionals and 1.4% in sales; annual CETC exceeds 8% in managers, sales, and administrative services vs 2.9% in mechanics and 3.4% in precision production
R20	Estimated demand elasticity across occupational output exceeds one	Equation (14), p. 1664; text p. 1665	IV rho = 1.34 (SE 0.061); OLS rho = 1.11 (SE 0.008)
R21	Estimated elasticity across capital goods is above one and robust to trend controls	Equation (17), p. 1675; footnote 32, p. 1675	phi = 1.13 (SE 0.017); with a time trend 1.42 (SE 0.030); with occupation-by-capital-good trends 1.00 (SE 0.014)
R22	The 2005 CETC trends forecast the subsequent college-premium slowdown but miss the gender-gap direction	Figure 7, pp. 1672-1674; text pp. 1673-1674	Predicted college premium falls 10 pp in 2005-2015 versus a 4.17 pp data decline; predicted gender gap rises while the data gap continues to decline
R23	Occupational capital tool shares closely match CPS computer-use hours	Appendix Figure B.II, p. 1679; text p. 1654	Correlations are 0.90 in 1984, 0.96 in 2003, and 0.96 for the 1984-2003 change
R24	Allocated occupational capital aggregates align with BEA industry allocations for most equipment categories	Text p. 1654	Communication correlation 0.60 in 1984 and 0.55 in 2016; medical equipment 0.99 both years; aircraft 0.98 and 0.81; computers 0.72 and 0.30
R25	Similar CETC or capital-intensity patterns can accompany opposite employment changes across occupations	Figure 2, p. 1652; text pp. 1651-1652	Low-skill services and precision production have similar CETC but opposite employment-share changes; machine operators and administrative services have employment declines of similar size despite capital-expense-ratio growth of 2.5 vs 0.25 percentage points per year

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:

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

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):

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

Producer and worker conditions. Occupational producers choose capital and labor to maximize profit, the final-good producer chooses occupational outputs, and the capital producer chooses investment goods. These are equations (9)-(11), p. 1662:

$$\max_{\{k_{ot},n_{ot}\}} \lambda^y_{ot} y_{ot} - \lambda^k_{ot} k_{ot} - \lambda^n_{ot} n_{ot}. \tag{9}$$ $$\max_{\{y_{ot}\}} \lambda^y_t y_t - \sum_o \lambda^y_{ot} y_{ot}. \tag{10}$$ $$\max_{\{x_{ot}\}} \lambda^k_{ot} q_{ot} x_{ot} - \lambda^y_t x_{ot}. \tag{11}$$

The comparative advantage of labor type h over type h’ in occupation o relative to occupation o’ is equation (12), p. 1663:

$$\left(\frac{T_{oht}/T_{o'ht}}{T_{oh't}/T_{o'h't}}\right)^{1/\theta}. \tag{12}$$

The model-implied average wage for labor group h, used to match wage outcomes in the calibration, is equation (15), p. 1670:

$$w_{ht} = \left(\sum_o T_{oht}(\lambda^n_{ot})^\theta\right)^{1/\theta}\Gamma\left(1-\frac{1}{\theta}\right). \tag{15}$$

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.

Multiple capital goods. In the extension with equipment categories as distinct capital goods, the CES capital aggregator’s optimal input mix and occupational capital price are equation (16), p. 1674:

$$\frac{\xi_{ojt}}{\xi_{oj't}} = \frac{k_{ojt}}{k_{oj't}}\left(\frac{\lambda^k_{jt}}{\lambda^k_{j't}}\right)^\phi, \qquad \lambda^k_{ot} = \left(\sum_{j\in\Omega^k_{ot}} \xi_{ojt}(\lambda^k_{jt})^{1-\phi}\right)^{\frac{1}{1-\phi}}. \tag{16}$$

The elasticity across capital goods is estimated by OLS from equation (17), p. 1675, using 24 goods, nine occupations, and 32 annual observations from 1984-2015:

$$\ln\left(\frac{\lambda^k_{jt}k_{ojt}}{\lambda^k_{j't}k_{oj't}}\right) = \beta_1 \ln\left(\frac{\lambda^k_{jt}}{\lambda^k_{j't}}\right) + \epsilon_{jt}. \tag{17}$$

The paper reports the coefficient and standard error (phi = 1.13, SE = 0.017); this specification has no fixed effects, and the text does not state a standard-error correction.

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):

The target elasticity is defined in equation (4), p. 1655, as the response of the capital-labor ratio in efficiency units to the relative input price:

$$\sigma_o = \frac{d\ln(k_{ot}/n_{ot})}{d\ln(\lambda^n_{ot}/\lambda^k_{ot})} = \frac{d\ln(k_{ot}/\tilde n_{ot})}{d\ln(\tilde\lambda^n_{ot}\exp(\gamma_{ot})/\lambda^k_{ot})}. \tag{4}$$ $$\ln\!\left(\frac{k_{ot}}{\tilde n_{ot}}\right) = \beta_{1o} + \beta_{2o} t + \beta_{3o} \ln\!\left(\frac{\tilde\lambda^n_{ot}}{\lambda^k_{ot}}\right) + \varepsilon_{ot}, \tag{5}$$

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 inverse regression representation, equation (6), p. 1658, is:

$$\ln\left(\frac{\lambda^k_{ot}}{\tilde\lambda^n_{ot}}\right) = \bar\beta_{1o} + \bar\beta_{2o}t + \bar\beta_{3o}\ln\left(\frac{k_{ot}}{\tilde n_{ot}}\right) + \bar\varepsilon_{ot}. \tag{6}$$

Each occupation is estimated on its 1984-2015 annual time series (32 observations), with an occupation-specific intercept and linear time trend, no pooled fixed effects, and the occupation-specific labor-supply instrument described above; trade-shift instruments are used for low-skill services and mechanics and transportation. Figure 3 reports 95% confidence intervals and Appendix Table B.III reports standard errors; the article does not state a standard-error correction in the main text. The specification allows a 2000 trend break as an online-appendix robustness check.

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).

Equation (14) uses nine occupations over 1984-2015 (288 occupation-years), an intercept and occupation-specific linear time trends, and the average-capital-cost Bartik instrument. The reported estimates are OLS rho = 1.11 (SE 0.008) and IV rho = 1.34 (SE 0.061); the paper does not specify a standard-error correction.

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.