Population Aging and Directed Technical Change
Yuting Huang∗
Bingjing Li†
May 12, 2020
Abstract
In this paper, we investigate the effect of population aging on technical change through a reduction in the supply of age-deteriorating skills. As a society becomes older, it faces a shrinking and aging working population, which may induce development in technologies that tend to replace younger workers (aged 25 to 44). Moreover, such pattern should be more pronounced in industries where production process intensively requires skills that deteriorate as a worker ages. We further our understanding of the demographic transition in the workforce by constructing the effective aggregate supplies of young and old workers in China during the period from 2000 to 2015. Using patent application data, we test these hypotheses and find robust empirical evidence that spatial differences in robot-related innovations are in part explained by different demographic trends across Chinese provinces. Furthermore, we find that heterogeneous skill intensities across industries are significant predictors of the variance in robotic innovations. Our significant and economically meaningful results are not driven by a specific province or industry.
∗
Department of Economics, National University of Singapore; E-mail: [email protected].
†
1
Introduction
Population aging is the most pervasive and inevitable global demographic transition of the twenty-first century, which is expected to reshape the age structure of the workforce in a large number of countries. Along with population aging, the mix of skills that an average worker of a country possesses changes, as some of these skills vary across a worker’s life cycle. Some skills are known to deteriorate with age, causing a decline in the quality and stock of those skills in an aging society. Changes in the supply of a certain skill may affect the relative costs of such skill, which could in turn raise the demand for its alternatives—in our case, robotic technologies—that tend to substitute that skill.
In this paper, we analyze the effect of population aging on technical change through a reduction in the supply of young workers and hence age-deteriorating skills. We categorize all production tasks into two types: age-deteriorating tasks and others, of which younger workers specialize in the former, and older workers have comparative advantage in the latter. The relative importance between the two tasks varies across industries. In each industry, a technology monopolist decides the innovation level and creates machines that embody such technology. A representative firm chooses whether or not to adopt such machines and automate its age-deteriorating tasks. The model delivers three implications. First, aging increases the relative wage of younger workers. Secondly, population aging spurs innovations that replace younger workers. Finally, the effects vary across industries, depending on their reliance on age-deteriorating tasks.
Existing literature on the impact of demographic transition in the work force mostly focuses on one of several dimensions—the roles of supply variations by education, by experience, or by cohort. For example, Katz and Murphy (1992) examines the changes in between-group relative wage, where different groups of workers (e.g., education or experience) are treated as distinct labor inputs. The approach assumes that similarly educated workers are perfect substitutes in production, regardless of other demographic characteristics. Under this assumption, aggregate supply of workers in each education group can be obtained by summing up the total number of workers in each category. Card and Lemieux (2001) deals with the issue of how multidimensional changes in the demographic structure of the work force could affect the returns to education. They relax the assumption on perfect substitutability between young and old workers using a two-level nested constant elasticity of substitution (CES) model. The production function is assumed to be CES in skilled and unskilled labor. Beneath the upper level CES, the aggregation functions of
skilled and unskilled labor are assumed to be a CES function that depend on the number of college and high-school graduates in each age groups.
To further understand the implications of demographic transition—population aging—in the work force, we extend the model in Card and Lemieux (2001) and explore a different version of two-level nested CES model. Specifically, we assume that aggregate output is a CES aggregate of young and old labor, while young (old) labor itself is assumed to be a CES subaggregate of young (old) workers with different educational attainments. Using Urban Household Survey data over the period from 1997 to 2009, we estimate the elasticity of substitution between skilled and unskilled workers, as well as the skill-group specific productivity parameters. Based on these estimates, we construct the effective (education-adjusted) aggregate supplies of young and old workers for each provinces in each year.
With the measures on effective aggregate supplies in hand, we construct the rates at which Chinese provinces are aging. To account for other factors that drive both the rate of aging and innovation activities, such as migration, we use the predetermined component of the provincial age and skill structure—the historical birth rates and college enrollment rates—as an instrument for the changing age structure. We leverage this variation in predicted aging to evaluate two hypotheses. Using patent application data during the period from 2000 and 2015, we identify robot-related technologies based on a keyword-classification method. The findings are consistent with the theoretical predictions that spatial differences in robotic innovation are in part explained
by differential demographic trends across Chinese provinces. We confirm that conditional on
initial conditions and year fixed effects, provinces with faster aging population tend to innovate more robotic technologies. This finding is robust to controlling for province fixed effects and to dropping one province at a time.
Another theoretical prediction that we investigate is the heterogeneous effects of population aging on robot-related activities across industries. The distinction between various types of skills and the industry-level skill intensities are supported and constructed by Cai and Stoyanov (2016). We focus on two important sets of skills: age-depreciating skills, and physical strengths. The former stresses on memorization, multitasking, and information processing, while the latter includes dynamic flexibility, strength, and body coordination. These are the skills that younger workers have comparative advantages in. Consistent with the model implications, we find that aging has disproportionately stronger effect on industries that intensively require age-deteriorating skills. The estimate indicates that a ten-percent increase in aging leads to an increase of 1.05 annual
robotic patents in an industry at the 75th percentile of reliance on physical abilities, relative to an industry at the 25th percentile. Such effect is not driven by a single province, nor by a single industry. The results are virtually unchanged when we replace the intensity measures with the first principal component of age-depreciating skills and physical abilities.
Our study connects three strands of literature. First, it is related to the induced innovation and directed technical change literatures. Theoretically, a shift in the relative supply of inputs can affect the direction of technological progress (Acemoglu, 2002, 2010). The direction is governed by two factors, the market size effect, which leads to technical progress favoring the abundant input, and the price effect, which encourages innovation towards the scarce input. Empirically, researchers have documented causal evidences on input-complementary innovations as well as input-substituted innovations. One the one hand, for example, Hanlon (2015) uses historical data in the cotton textile industry to study the effect on technology development. He finds a substantial increase in patents related to lower-quality Indian cotton during the Civil War period, as the supply of Indian cotton became relatively more abundant. In Acemoglu and Linn (2004), the authors find evidence for pharmaceutical innovation induced by an increase in the potential market size. On the other hand, it has been suggested that an increase in input prices induce firms to switch their innovation portfolio towards technologies that reduce the need for the relative expensive factor (Aghion et al., 2016; Popp, 2002). Under China’s context, Zhang et al. (2015) studies the effect of population aging on labor costs and finds that variations in age structure across Chinese provinces explain the persistent inter-provincial income disparity. Tan and Zhang (2016) reports that regional female shortage has induced innovation in Chinese industries that are relatively female-intensive. In our study, we provide evidence for aging-induced technical change, through the declines in the supply of younger workers and age-deteriorating skills.
Our research also relates to the studies on the implication of population aging. Three papers that are most closely related to ours are by Cai and Stoyanov (2016), Acemoglu (2010), and Acemoglu and Restrepo (2018). Cai and Stoyanov (2016) finds that population aging affects the pattern of comparative advantage across industries that vary in their intensity in age-dependent skills. Acemoglu (2010) develops a general framework that link labor scarcity to innovation and technology adoption. Acemoglu and Restrepo (2018) uses a task-based model and empirically investigates the effect of aging on the adoption of industrial robots across countries and across US commuting zones. In this paper, we identify age-deteriorating skills as a channel through which demographic transition affects innovation activities and determines the direction of technology
change as the working population gets older.
The remainder of the paper is structured as follows. The next section reviews the background of population aging in China. Section 3 describes and summarizes the data. Section 5 presents the econometric models and main results. We document a series of robustness checks in Section 6 and conclude in Section 7.
2
Population Aging in China
At present, China is the most populous country in the world. In mid-2017, China’s population reached 1.41 billion, accounting for 18.4% of the world total population (United Nations, 2017). The country has been experiencing a reduction in fertility and substantial improvements in longevity, which lead to slower population growth and an aging population. According to current UN pro-jections, China’s population will continue to rise and reach 1.44 billion in 2030, after which there will be a slow decline. The medium age of the population increased from 21.98 in 1980 to 36.95 in
2015, and is projected to reach 47.99 by 2050.1
Yet, the story of population aging in China is unique, shaped by its distinct historical and political contexts. The implementation of a family planning policy has greatly changed the age structure and accelerated the aging of China’s population. In the early 1950s, China had a very young population: individuals under age 25 constituted 51.81% of the total population, and the elderly above age 60 constituted only 7.41%. In 1979, China introduced the One Child Policy at the national level, which limited most families to have just one child. Initially, the child dependency ratio fell with an increase in the ratio of working-age population, which showed the way for a period of demographic dividend. As the working-age population starts to enter old age, however,
the old-age dependency ratio is expected to accelerate at a faster pace.2 In 2015, only 30.72% of
the total population were under 25, and the proportion of the older persons has risen to 15.37%. According to UN projections, in 2050, the proportion of the elderly above age 60 will reach 35.10%. A greying population also means that the economy is likely to face a shrinking and aging working population (aged 25-59). This is indeed the case for China (see Figure 1). The proportion of young adults (aged 25-44) in the working-age population was 71.66% in 1990, 59.30% in 2015, and is projected to decline to 55.83% in 2050. A shrinking and aging working population puts
1. Population data in this section are drawn from the United Nation’s World Population Prospects (2017), unless otherwise mentioned.
2. Child dependency ratio is the ratio between population aged 0-14 and those between 15-64; old-age dependent ratio is calculated as the ratio between population aged 65 and above and those between 15-64.
pressures on aggregate labor supply and productivity, which may exert a significant influence on economic growth.
Spatially, the demographic transition in China progresses at different paces and presents het-erogeneous patterns across municipalities and provinces. One reason is that the One Child Policy
was not enforced uniformly across ethnicities, nor between urban and rural areas.3 As a result,
provinces where the policy was applied most strictly have the lowest fertility rates and hence the severest aging population. Secondly, young workers migrate from rural to urban area, as well as from less prosperous regions to those on the coast. As a result, the coastal provinces have richer labor resources, while the central and western provinces experience more pronounced scarcity in available young workers (Banister et al., 2012). Moreover, birth and marriage rates continue to fall in the recent years, and the problem is particularly severe in the traditional industrial areas in the northeast—Heilongjiang, Liaoning, and Jilin provinces (South China Morning Post, 2018).
Throughout our analysis, we define older workers as those aged 45-59 over the period from 2000 to 2015; and younger workers as those aged 25-44 during the same period. The severity of aging is defined by the ratio of old to young workers in each province. Figure 2 (a) presents an illustration of the demographic transition across 15 Chinese provinces, based on the Population Census data. During this period, all provinces experience increasing old-to-young ratios in the work force. In particular, aging is severest in Heilongjiang, Liaoning, and Hubei provinces, while Guangdong and Shandong face less pressure.
3
Data
We use three strands of data from the period of 1997 to 2015, including Chinese patent data, province-level demographic data, and industry-level intensity measures. In this section, we first describe the data sources and definitions, and then present the summary statistics.
3.1 Chinese Patent Data
We assess innovation activities by focusing on the number of patent applications. The data are drawn from a matched dataset that linked all patents from China’s State Intellectual Property Office (SIPO) to all firms that are covered in China’s Annual Survey of Industrial Enterprises
3. Some papers discuss the evolution of the One Child Policy and its heterogeneous enforcement across ethnicities and between rural and urban areas, for example, see Chen and Liu (2009); Zhang (2017).
(ASIE) between 1985 to 2015.4 The scope of the SIPO patent dataset includes the universe of published patent applications. It offers detailed information on patents, including the International Patent Classification (IPC) codes, patent titles, year of application, as well as the name and address of the asignees. The categorization of patents are based on information on IPC codes and patent titles. Using name and address of the assignees, we are able to pinpoint firms and their location. The ASIE is a nationwide mandatory firm-level census administered annually by the National Bureau of Statistics of China. Firms contained in the ASIE include the all state-owned firms, as well as non-state-owned firms with annual sales above 5 millions CNY. it contains unique and comprehensive information on firm-level demographics, including firm name, address, and type of ownerships. The SIPO-ASIE matching dataset provides the characteristics of each patent assignee, such as operation scale and operating industry.
For our purpose, we extract a sample of matched patents from 1998 to 2015 and group the data within mutually exclusive five-year periods. We exclude all applications solely filed by individuals, research institutions, or foreign entities. The main sample contains 7,045,264 patents. The key variables relevant to our study are the IPC code, assignee’s address and application date. We assign each patent to a three-digit Chinese industry using multiple concordance tables. Each patent is
then assigned to a province based on the reported address of the inventor.5
Importantly, we identify robotic technologies using a keyword-classification method. First, we conduct an extensive search for four keywords in the patent titles—“robot”, “robotic”, “automa-tion”, and “artificial intelligence”—from PatSnap, a patent analytics platform that allows us to
examine the patents with at least one of those keywords in the title.6 Second, we analyze the
four-digit IPC codes of these patents from the PatSnap inquiry results and rank these IPCs by their occurrence. The most frequent four-digit IPCs are used as identifiers for robotic technologies. In other words, we categorize patent applications into two groups based on the IPC codes: the
ones with identifiers are denoted as robotic patents, and the residual as non-robotic patents.7 To
prevent overly inclusive results and maximize the comparability of the chosen identifiers, we prefer
4. The SIPO and ASIE datasets are matched by the patent assignees’ names and the company names. See He et al. (2016, 2018) for details on the matching algorithm and the reliability of the data.
5. We equally divide the patents should the IPCs be associated with multiple industries. Consequently, we do not necessarily have an integer number for patent counts in each industry or province.
6. PatSnap is a patent analytics platform that is recognized by the World Intellectual Property Organization (WIPO). The Chinese patents provided in PatSnap come in two formats: (i) scanned documentations of the actual patent application in Chinese; (ii) machine translated patent applications that are structured text files in English.
7. In the Appendix, Section C documents the work flow of identifying robot and non-robot patent applications. A complete list and ranking of the twenty identifiers, along with an abstract description of the IPC codes, are presented in the Appendix, Table C4.
the most strict definition—the top ten IPC sub-classes. In our main analysis, we aggregate data to category-province-year and category-industry-province-year level.
The summary statistics of our patent data are shown in Panel A of Table 1. From 2000 to 2015, we have a total number of 7,045,264 public patent applications that are matched to individual firms across 167 three-digit industries in 11 Chinese provinces. Three percent of the matched patents are identified as robotic innovations under the top-ten definition. Across provinces, Beijing and Guangdong have the highest number of robot-related patent applications. Among all industries, Computers & Other Electronic Equipments observes the most robot-related activities (Table C5 in the Appendix).
3.2 Demographic Data
The primary sources of demographic data are the Urban Household Survey (UHS), administered by the National Bureau of Statistics of China from 1997 to 2009, and China’s Census Data from 2000 to 2015. The UHS a repeated cross-sectional data set that aims to document the basic socioe-conomic conditions of Chinese urban households, including detailed individual-level information on education, employment, earnings, and demographic characteristics of each household member. Moreover, the UHS implements a three-stage stratified and systematic sampling method, which
ensures its national representativeness.8 We use data for 16 provinces including Beijing, Shanxi,
Liaoning, Heilongjiang, Shanghai, Jiangsu, Anhui, Jiangxi, Shandong, Henan, Hubei, Guangdong, Chongqing, Sichuan, Yunnan, and Gansu.
The UHS offers unique and comprehensive information on individual demographics and labor market characteristics, including age, gender, educational level, employment status, and annual wage. For our purpose we extract a sample that includes all individuals who (i) were between 25 and 59 years old; (ii) were not self-employed; and (ii) worked full-time and earned positive annual wage in the sampled years. We use the provincial CPI to deflate all wages to 1997 yuan. Individuals whose earnings are above or below the top and bottom 1% in 1997 yuan are excluded from our sample. By placing restrictions on age, wages, and employment status, we maximize the comparability across individuals. Moreover, we categorize individuals by age and educational attainment. Specifically, there are two age groups—workers aged 25 to 44 are classified as young and those aged 45 to 59 as old—and two skill groups—workers with at most high school education
8. Past work with the UHS data set on other topics have shown evidence of its national representativeness. For example, see Zhang et al. (2005) and Meng (2012).
are classified as low-skilled; those with at least some college education are classified as high-skilled.9 Overall, the sample contains 323,792 individuals from 1997 to 2009 (see Table A1).
Using the UHS data on age, earning, and education level, we estimate the elasticities of sub-stitution between age and skill groups, based on a model that is motivated by Card and Lemieux (2001). We use these estimated elasticities to construct the effective aggregate labor supply for each province using Census Data for 2000, 2005, 2010, and 2015.
Panel B in Table 1 presents the summary statistics of the constructed effective labor supplies are provided in . The variable on aging is constructed as the ratio of effective supplies of old-to-young workers in each province at each year. This ratio has increased sharply from 0.29 to 0.46 from 2000 to 2015.
3.3 Trade Data
We use China Customs Transactions Database to measure trade flows between China’s provinces and foreign countries from 2000 to 2015. This database has highly disaggregated information on firms’ monthly import and export transactions. We restrict attention to the imports of intermediate goods and categorize them into groups by their end-use using the Broad Economic Categories (BEC) classification. Using the firms’ address, we aggregate firms’ transaction-level imports to provincial level by sectors in each year. Finally, for each province and year, we calculate the import share in the following five sectors: Robots, Numerically Controlled Machines and Computers, Weaving and Knitting Machines, Vending Machines, and Agricultural Machinery. On average, robots and computers accounts for 0.32% and 3.64$ of imports of intermediate goods, respectively.
3.4 Province and Industry Characteristics
The remaining data are drawn mainly from Cai and Stoyanov (2016) and the NBER-CES Manu-facturing Industry Database (2000) of the corresponding US industries. The main industry char-acteristics include the intensities in age-depreciating skills and physical abilities, as well as labor
intensity (computed as the ratio of total wage bill to total capital).10 Other provincial controls
9. The UHS categories education attainments into eight groups: (1) No schooling or literacy class; (2) primary school; (3) junior high school; (4) vocational school; (5) senior high school; (6) technical colleges; (7) university; (8) graduate school. The individuals in categories 1 to 5 are grouped as “low-skilled workers”, and 6 to 8 are grouped as “high-skilled workers”.
10. Cai and Stoyanov (2016) constructs intensity measures by first looking at the occupational decomposition of every industry from the US Bureau of Labor Statistics, as well as the importance of different skills across occupations from the Occupational Information Network (O*NET) dataset. Lastly, they use the occupational employment share as weights and construct industry-level measures of skill intensities.
include the log of total population, drawn from the provincial statistical yearbooks, and effective wages in 2000 (based on authors’ computation; see Section 4.2).
We focus on two skills: (i) age-depreciating cognitive skills, such as memorization, multitasking, and information processing; and (ii) physical abilities, including dynamic flexibility, strength, and
body coordination.11 As noted in Cai and Stoyanov (2016), however, the two variables are highly
correlated (correlation equals to 0.91 as reported in Table 2). We also use the first principal component of the two in our empirical analysis. A complete list of input intensities for two-digit Chinese manufacturing industries can be found in Table C3.
4
Constructing Effective Labor Supply
Previous studies on the impact of demographic changing have focused on the role of supply varia-tions of young and old workers, by simply assuming that workers within each age group are perfect substitutes in production, regardless of their educational levels. This assumption means that the aggregate supply of young (old) workers can be obtained by simply adding up the total number of workers in a specific age range. Card and Lemieux (2001) relaxes this assumption by incorporat-ing imperfect substitution between similarly educated workers in different age groups. To further understand the demographic transition in the work place and its effect on innovation activities, we propose an alternative model with imperfect substitution between workers with different education attainments within the same age group. Then we use these estimates to construct the effective young and old labor supplies in each province at each year. The effective supply of labor depends not only on the number of available workers, but also on distribution of education attainments among workers.
11. Occupations and industries with extreme intensities in either skill are listed in the Tables C1 and C2, respec-tively.
4.1 Model
Our model features a CES-nesting structure. We consider an aggregate production function with inputs young (Y ) and old (O) workers. The first level of the nested CES function is given by:
Ypt= X j αpj· Ypjtρ 1/ρ (1a) Opt= X j βpj· Oρpjt 1/ρ (1b)
where Ypjtis the number of young workers with skill j in province p and year t. αpj and βpj are the
time-invariant province-skill specific efficiency parameters. ρ = 1 − 1/σE where σE is the partial
elasticity of substitution between similarly aged workers with different skills.
Aggregate output in province p and year t is a function of young and old labor, and the technological efficiency parameters θYpt and θptO:
ypt=
θYpt· (Ypt)η+ θptO· (Opt)η 1/η
(2)
where η = 1 − 1/σA. σA is the elasticity of substitution between young and old workers. θYpt and
θOpt are the technology parameters for young and old workers in province p at year t. The marginal
products for both types of labor are:
∂ypt ∂Ypjt = ∂ypt ∂Ypt × ∂Ypt ∂Ypjt = θYpt· Yptη−ρ· Φpt× αpj· Ypjtρ−1 (3a) ∂ypt ∂Opjt = ∂ypt ∂Opt × ∂Opt ∂Opjt = θOpt· Oη−ρpt · Φpt× βpj· Opjtρ−1 (3b) where Φpt= θptY · (Ypt)η+ θptO· (Opt)η η1−1
. If different skill groups are utilized efficiently, relative wages will be equal to relative marginal products. Then equations (3a)-(3b) imply that the relative wages of young and old workers in the same educational group satifies the following equation:
log wYpjt wOpjt = log θY pt θOpt − 1 σA − 1 σE · log Ypt Opt − 1 σE · log Ypjt Opjt + log αpj βpj + epjt (4a)
to rearrange the equation in an alternative form: log wpjtY wpjtO = log θY pt θOpt − 1 σA · log Ypt Opt − 1 σE · log Ypjt Opjt − log Ypt Opj + log αpj βpj + epjt (4b)
According to this model, the young-old wage gap for a given education group depends both on the aggregate relative supply (Ypt/Opt) and the relative supply of skill-j workers (Ypjt/Opjt) in province p and period t.
The wage index for each province at each year is
Wpt = X j δpjtY · (wY pjt)ρ+ X j (1 − δpjtY ) · (wpjtO )ρ 1/ρ , (5)
where δpjtY is the wage bill share of young workers; wpjtY and wOpjtare the average annual income for young and old workers in skill group j in province p at year t.
4.2 Implementation
We begin by estimating linear returns to young age, allowing these returns to vary arbitrarily across provinces, educational groups. Specifically, we estimate the following regression:
log(wipjt) = φpjt+ rpjt× 1(Young)ipjt+ X
0
ipjtγ + ipjt (6)
where wipjt represents individual i’s annual income, and 1(Young)ipjt is a dummy that equals to
one if individual i is classified as a young worker (aged 25-44) with skill j in province p at year t.
Xipjt includes observable worker characteristics such age, age-squared, and gender. The coefficient
rpjtcaptures the difference in annual earnings between young and old workers in the given province
p, age group j, and time period t. Thus this is the province-skill-year specific young-age premium.
Step One. Next, we turn to estimate the substitution elasticity between skilled and unskilled
workers, σE using Equation (4a). We regress the province-edu-year specific young-age premium
(rpjt) on the skill-specific relative supplies of young labor, province-education effects (which absorb
the relative productivity effect log(αpj/βpj)), and province-year effects (which absorb the combined
relative technology shock (log(θptY/θOpt)) and any effect of aggregate relative supply (log(Ypjt/Opjt)−
by the inverse variances to account for heteroskedasticity. The first-step regression is: rpjt= bpj+ bpt− 1 σE · log Ypjt Opjt + epjt. (7)
Given an estimate of 1/σE, the relative efficiency parameters αpj and βpj are easily computed
by noting that equations (3a)-(3b) imply:
log wpjtY + 1 σE
· log(Ypjt) = dpt+ log(αpj) (8a)
log wpjtO + 1 σE
· log(Opjt) = dpt+ log(βpj) (8b)
where wpjtY and wpjtO are the average income of young and old workers with education level j in
province p in year t. The left-hand sides of these equations can be computed directly using the
first-step estimation of 1/σE, while the leading terms on the right-hand sides can be absorbed by a
set of province-year fixed effects. Thus, the skill-group specific productivity factors (αpj and βpj)
can be estimated as the province-skill specific efficiency parameters in a pair of regression models based on equations (8a) and (8b).
Given estimates of αpj, βpj, and ρ (which equals to 1 − 1/σE), it is then straightforward to
construct estimates of the aggregate supplies of young and old labor for each province and each year, based on equations (1a) and (1b).
Step Two. We turn to estimate Equation (4b) with the assumption that log(θY
pt/θOpt) can be represented by a province-specific linear year trend.
log wYpjt wOpjt = dpT − 1 σA · log Ypt Opt − 1 σE · log Ypjt Opjt − log Ypt Opj + log αpj βpj + epjt
The coefficient associated with the aggregate relative supply log Ypt/Opt provides an estimate
for 1/σA. The coefficient associated with the deviation between the skill-specific relative supply
and the aggregate relative supply index log Ypjt/Opjt −log Ypt/Opj provides another estiamte
4.3 Instrumental Variable Approach
A concern with the implementation strategy is that there may be unobserved factors that shifts relative supply for workers over time, leading to higher or lower relative wages, and confound-ing the estimation of substitution elasticities. For example, economics changes could affect the contemporaneous patterns of migration, thus shaping the age and skill structure of the working population. For instance, when there is an economic decline, skilled young workers may be more likely to migrate from inner to coastal provinces. It could slow down the demographic transition in the coastal regions and ease the pressure on relative wages, thus generating a bias in the estimation of substitution elasticities.
To circumvent these confounding sources, we instrument the severity of aging using the pre-determined component of age and skill composition in each province. Specifically, we use the province-specific college enrollment rate for each age group at the time when individuals in this age group graduated from high school. College enrollment rates satisfy the required exclusion re-striction since past changes in college enrollment rates are unlikely to be driven by contemporary wages or technologies, and also the relevance assumption since they explain a large portion of the variation in the population with different skills across provinces. We then multiply this enrollment rate with the projected population of this age group for each province. For example, the predicted Skilled (S) and Unskilled (U ) population aged 25-29 in province p at year t are:
Spt25−29 = CERp,t−(27−18)× Npt25−29 Upt25−29 = (1 − CERp,t−(27−18)) × Npt25−29
where CERp,t−(27−18) is the college enrollment rate at the time when individuals aged 27 (the
midpoint of the age group) in year t graduated from high school (i.e., t − (27 − 18)); Npt25−29 is the
projected population aged 25-29 in province p and year t using data on birth rates, age-specific death rates and population size at year when individuals in this age-group were born.
Finally, we construct four types of labors using the predicted skilled and unskilled population in each age bracket. The predicted supply of young skilled workers is constructed as the summation of workers aged from 25 to 44 with some college education. The supplies of young unskilled, old skilled and old unskilled workers are constructed analogously.
4.4 Estimated Results
The estimated results of the substitution elasticities are reported in the Appendix. In Table
A2, Column (1) in Panel A regresses the skill-specific wage gap on the actual skill-group specific relative supply of young and old workers, province-year, and province-skill fixed effects, based on Equation (7). The estimated coefficient on the skill-specific relative supply is -0.12. We obtain similar results when restricting attention to the coastal and provinces separately. These estimates are fairly accurate and the magnitudes imply an elasticity of substitution between workers with different education attainments in the range of 7.44 to 8.30. Panel B presents the IV estimates, where the we instrument the actual skill-specific relative supply by the predicted value. We find that the predicted relative supplies of young and old workers have considerable explanatory power for the actual age distribution (the F-statistics is on the order of 13.40). The estimated coefficients are slightly larger and more precise than the previous ones.
Table (A3) reports the estimates of the second-step models (based on Equation (9)) that include both the aggregate relative supply index and the skill-group specific relative supplies of young and old labor. The WLS and IV estimates are reported in Panels A and B, respectively. In the first three columns, we assume that the province-year specific relative technology shock (log(θptY/θOpt)) follows a linear trend, while we assume a quadratic trend in the next three columns. The instruments also have a strong first stage. For the full sample, the elasticity of substitution between skilled
and unskilled workers (σE) is between 6.72 and 7.97, which is very close to the first-step estimates.
The elasticity of substitution between young and old workers (σA) is estimated to be 9.35 (WLS
estimates, significant at 5% level) and 7.48 (IV estimates, significant at 1% level). Comparing
the results from WLS and 2SLS, the estimates for σE are quantitatively similar, but those for σA
are very different. This is perhaps because the unobserved province-year specific characteristics influence the demographic composition in the work force.
Given estimates of αpt, βpt and ρ, we construct the effective aggregate labor supplies of young
and old workers for each province from 2000 and 2015 based on Equations (1a) and (1b). The severity of population aging in province p in year t is constructed using
Agingpt= Opt Ypt = P jβpj· Oρpjt P jαpj· Ypjtρ 1/ρ ,
where Opjt and Ypjtare number of old and young workers in each education category j in province
2015 are presented graphically in Figure 2. After adjusting for the unobserved factors that shifts relative supply of workers and their educational levels over time, we find that inland regions indeed face more pressure of population aging than otherwise suggested by the Census data.
Figure A1 plots the relationship between actual and effective changes in aging from 2000 to 2015 for each province. We find that coastal provinces, such as Guangdong and Jiangsu, are near the 45-degree line, while the gap between predicted and actual aging is larger for inland or northeastern provinces, such as Hubei and Liaoning. Lastly, the provincial wage index is calculated based on Equation (5). The average growth rates in real wage across provinces are presented in Figure A2.
5
Econometric Specifications and Main Results
5.1 Aging and Innovation Activities at the Province Level
We begin by estimating the effects of population aging on innovation activity across provinces and years. Because the dependent variable, the number of patent applications, is overdispersed count
data, we adopt a fixed effects negative binomial regression model as the following:12
Npkt= α1· (Agingpt× 1(Robot)k) + α2· Agingpt+ α3· 1(Robot)k+ Xpγ + δt+ pkt (9)
where Npkt is the number of patent applications of category k in province p and year t; 1(Robot)k
is a dummy that equals one if the patent is related to robotic technologies; Agingpt is the variable
that reflects the severity of population aging in province p and year t. We control for geographic
characteristics, Xp, that may affect innovation activities, including 2000 values of the number of
patent applications, the size of population, and the provincial wage index. In the baseline, we also include year fixed effects, δt.
The interaction term Agingpt× 1(Robot)k is the variable of interest—all else equal, provinces
that face severer population aging (higher value of Agingpt) should experience higher degrees of
young-worker scarcity, which in turn leads to faster progress in robotic technologies that substitute
younger labor. Hence, we expect α1to be positive. Table 3 presents the baseline estimation results,
based on three definitions of robotic innovation. The first two columns correspond to the most
12. In Table 3, we show that the dispersion parameter (alpha) is significantly greater than zero in all specifications, which confirms that the data are overdispersed and are better estimated using a negative binomial model than a possion model.
strict definition: only the patents with the top 10 IPCs are identified as robotic innovations. The next two columns use the top 15 definition and the last ones use the top 20 definition. Under
all three definitions, the interaction term Agingpt× 1(Robot)k is positively related to the number
of robotic patent applications in each province—an increase in the severity of aging is associated with more robot-related innovation activities.
The results in Column (1) show that, conditional on initial conditions and year fixed effects,
the coefficient α1 is positive and statistically significant at 10% level. This result confirms the
first prediction that provinces with faster aging population tend to innovate more robot-related technologies. The estimate implies that the variation in aging explains 2.20% variations in the
number of robotic patents, relative to non-robotic patents.13 After controlling for the interactions
between the robot dummy and province-specific lagged variables, the coefficient becomes slightly smaller and more precise. Moreover, we obtain positive and statistically significant results for alternative definitions of robotic patents. The effects become smaller as we turn to broader defi-nitions (Columns (3)-(6)). This is reassuring as the robot-related innovation activities under the most limited definition are the most responsive to population aging.
The results above provide evidence that population aging induces robot innovations. Does the increase in robot-related patent applications imply greater use and development of robotic technologies? We explore this possibility by exploring the implications of aging on the imports of intermediate inputs. In Table 4, we regress the share of imported intermediate goods in various industries on log of the degree of aging in each province and each year. We find that provinces with severer aging indeed import more robot-related intermediates. Specifically, the OLS estimates in Panel A suggest that a 1% increase in aging leads to 3% increase in robot-related imports.
To further understand the implication of aging on the import of robot-related intermediates, we conduct an age-threshold analysis. Specifically, we divide the working population to nine five-year age groups: 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59. The severity of aging in each province
and year Agingpt is measured as the share of workers from a given age group among the
working-age population. We trace out changes in the coefficients of α as the definition on the severity of aging changes. The results are presented in Table 5. All specifications include year fixed effects
and provincial lagged controls. In Column (1), Agingptis defined by the share of 25-29 year-olds in
the work force. From the estimation results, we find that α is negative and statistically significant
13. Given that the sample mean of the log number of patents is 6.14, the variation in aging explains e2.3253/e6.1428= 2.20% variations in robotic patents.
at the 5% level, with the point estimate of 7.55. This indicates that provinces with a larger share of workers aged 25-29 are less prone to importing of robot-related inputs. In the next two columns, we replace the definition of aging as the share of workers aged 30-34 and 35-39, respectively. The coefficients are slightly larger in magnitude but the estimates become less precise. From Column (5) onwards, the estimated coefficient of α becomes positive and significant, implying that an increase in the share of older workers leads to greater imports of robot-related intermediate inputs.
Finally, in Column (10), Agingptis defined by the ratio between the number of workers aged 44-59
and those aged 25-44. The results confirm that provinces with larger share of older workers indeed tend to import more robotic inputs.
5.2 Aging and Innovation Activities at the Province and Industry Level
In this section, we turn to examine the differential effects of aging on robotic innovation activities across industries. The hypothesis is that an industry will be more responsive to population aging if it relies more on certain skills. We apply a zero-inflated negative binomial model as the following:
Npjkt= β1· (Agingpt× 1(Robot)k× Ij) (10)
+ β2· (Agingpt× 1(Robot)k+ β3· (Agingpt× Ij) + β4· (1(Robot)k× Ij) + β5· Agingpt+ β6· 1(Robot)k+ β7· Ij+ Xpγ + θj + δt+ pjkt
where Npjkt denotes the number of patent application of category k in industry j, province p, and
year t; Ij is industry j’s intensity in certain skills, including labor input, age-depreciating skills,
and physical abilities; Xp includes the same time-invariant province-level controls. In the baseline
regression, we include industry and year fixed effects.
In Equation (10), we are interested in the coefficient on the triple interaction term Agingpt×
1(Robot)k×Ij. Since aging reduces the supply of younger workers, it should have disproportionately
stronger effect on industries that intensively require age-depreciating and physical skills. We expect
β1 to be positive. We present industry-level evidence in Table 6. The first three columns use the
top-10 definition for robot-related patents. We regress the number of patent application on the
interaction term, Agingpt× Ij× 1(Robot)k, controlling for all first-order and main terms, the 2000
values of provincial covariates, as well as year and industry fixed effects. In Column (1), Ij is
defined by the age-depreciating skill intensity in industry j. The coefficient β1 is positive and
when their production process relies more on skills that tend to depreciate in worker’s age. We obtain similar results when using the use of physical strengths to measure skill intensity (Column (2)). The results are also robust to using the first principal component of age-depreciating skills and physical abilities (Column (3)).
In Table 7, Columns (1)-(3) replicates the results in when each of the skill measures is included alone. The next three columns report results for a specification when we include interactions of aging and the robot dummy with other industry-level characteristics, including labor intensity, age-appreciating skills intensity, and the number of patents in the past period. This model does not substantially change the coefficient estimates for physical abilities, however, the estimates for age-depreciating skills becomes much smaller. This is perhaps because the industry-level intensities in physical skills and age-depreciating skills are highly correlated. Columns (7)-(9) further controls includes interactions of aging and the robot dummy with lagged provincial characteristics. The results are virtually unchanged.
Summing up, we find provincial evidence that population aging leads to more robotic innovation activities. Moreover, within each province, the response in robotic innovation to aging is stronger for industries that rely more on age-depreciating and physical skills.
5.3 Heterogeneous Results
Lastly, we explore the heterogeneity effects related to the number of colleges and universities across provinces. To do so, we divide the full sample based on the median of colleges in each province in
2000. Columns (2)-(4) of Table 8 presents the estimates for β1 for provinces with above-median
number of colleges, while the columns (5)-(7) reports those for provinces with below-median number of colleges. The impacts of aging vary in the two subsamples. We find that the main results found in Section 5.2 are driven by provinces with larger number of higher-education institutes. As we have excluded patent applications filed by individuals, universities, and research institutes, this result implies positive technology spillover effects within each province.
6
Robustness Tests
In Table 9, we explore the robustness of our first result to the exclusion of provinces one at a time. The first entry in Column (1) replicates the baseline results reported in Column (2) of Table 3. The remaining entries show that the coefficients on the main variables of interest are virtually
unchanged compared to the baseline sample and they remain statistically significant at the 1% level. The coefficient becomes larger when we remove Guangdong. This is perhaps because the robotic innovation activities in Guangdong are less resulted from population aging in the region. Though once known for low-end sweatshops and copycat products, Guangdong has been attracting many technology entrepreneurs. For example, Shenzhen, one of the major cities in Guangdong, is home to Huawei, ZTE, and Tencent—three of China’s most innovative and valuable high-tech multinationals. It is also reported that companies in Shenzhen file more international patents of high quality than those in the European countries (The Economist, 2017). These innovation activities are not solely induced by aging, but also a series of government policies that encourages automation and innovation. As a result, when Guangdong is removed in our analysis, robot-related innovation activities are more responsive to population aging on average. We also check the robustness of our second result to the removal of two-digit industries. The results of removing the top eight industries are presented in Table 10. The coefficients are stable compared to the baseline results. All of them are positive and statistically significant.
7
Conclusion
This paper finds evidence of different rates of population aging across Chinese provinces, as well as different skill intensities across industries, direct technological progress. We argue that aging in the working population induces the decline in the quality and stock of age-deteriorating skills, such as memorization and physical strengths. It follows that provinces with faster population aging tend to develop more technologies that replace younger workers, so as to reduce the demand for these skills. Moreover, such pattern is more pronounced in industries that require age-deteriorating skills intensively. We test and confirm these predictions in Chinese provinces and industries. In particular, we find that there is a statistically significant effect of population aging on robotic innovations. Furthermore, heterogeneous skill intensities across industries is a significant predictor of the variations in the patented robotic technologies.
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Figures and Tables
Figure 1 Demographic Transition in the Workforce
Note: Data are from the United Nations, Population Division (2017). Numbers are given in millions. Figures after 2015 are projections using the medium fertility variant.
Anhui Beijing Gansu Guangdong Heilongjiang Henan Hubei Jiangsu Jiangxi Liaoning Shandong Shanghai Shanxi Sichuan Yunnan (.246,.334] (.115,.246] (.097,.115] [.0578,.097] No data (a) Actual Anhui Beijing Gansu Guangdong Heilongjiang Henan Hubei Jiangsu Jiangxi Liaoning Shandong Shanghai Shanxi Sichuan Yunnan (.141,.211] (.118,.141] (.0896,.118] [.0827,.0896] No data (b) Effective
Figure 2 Actual v.s. Effective Changes in Aging, 2000-2015.
Note: This figure shows the aging work force across fifteen Provinces in China during the period from 2000 to 2015. Aging is defined as the ratio between old (45-59) and young (25-44) workers. The actual changes are drawn from Census data, while the changes in effective relative supplies are based on authors’ calculation.
0 20 40 60 80 100 Age Groups male female Heilongjiang, 1990 0 20 40 60 80 100 Age Groups male female Heilongjiang, 2015 0 20 40 60 80 100 Age Groups male female Guangdong, 1990 0 20 40 60 80 100 Age Groups male female Guangdong, 2015
Figure 3 Demographic Transition, Provincial Evidences Source: Population Census (1990, 2015).
Table 1 Summary Statistics
Variable N Mean SD Min Max
A. Patent data Top 10 7,045,264 0.0288 0.1673 0 1 Top 15 7,045,264 0.0420 0.2006 0 1 Top 20 7,045,264 0.0681 0.2519 0 1 B. Province-level, aging 2000 11 0.2904 0.0437 0.1852 0.3401 2005 11 0.3669 0.0715 0.2740 0.5162 2010 11 0.3963 0.0754 0.2614 0.4924 2015 11 0.4550 0.0735 0.3152 0.5297 2000-2015 44 0.3817 0.0892 0.1852 0.5797
C. Trade data, share in provincial intermediate goods imports (%)
Robots 44 0.3225 0.5058 0.0250 3.3805
Computers 44 3.6351 2.4492 0.2348 10.5768
Weaving machines 44 0.3789 0.3817 0.0008 1.8667
Vending machines 44 0.0022 0.0040 0 0.0217
Agricultural machinearies 44 0.2423 0.2843 0.0273 1.7475 D. Industry-level factor intensities
Age-depreciating skill 167 -0.0188 0.5194 -1.6100 0.7455 Physical Ability 167 -0.0476 0.5255 -1.5680 0.7345 First PC 167 0.3947 1.3852 -4.3877 2.6325 Age-appreciating skill 167 0.1608 0.5119 -1.0200 1.3200 Labor Intensity 167 1.2823 0.8705 0.0816 5.9693 Skill Intensity 167 0.2966 0.0621 0.2224 0.4438
Share of workers below age 44 167 0.6553 0.0593 0.5289 0.8692 Note: Patent data in Panel A are from the from the State Intellectual Patent Office (SIPO) matched with the Annual Industrial Survey (ASIE) data sets; demographic data in Panel B are constructed by the authors using the Urban Household Survey (UHS) and Census data; trade data in Panel C are from the China Customs Transac-tions dataset from 2000, 2005, 2010, and 2015; industrial characteristics in Panel D are from Cai and Stoyanov (2016) and the NBER-CES Manufacturing Industry Database (2000). See text for variable definitions and constructions.
Table 2 Correlation between Skill and Factor Intensity Measures
Age dep- Age app- % of
reciating Physical First reciating Labor Skill Capital workers skill ability PC skill intensity intensity intensity below 44 Age-depreciating skill 1.0000 Physical skill 0.9128 1.0000 First PC 0.9798 0.9798 1.0000 Age-appreciating skill -0.3557 -0.3897 -0.3804 1.0000 Labor intensity 0.1318 0.0049 0.0698 -0.3360 1.0000 Skill intensity -0.5766 -0.5073 -0.5532 0.4251 -0.2893 1.0000 Capital intensity 0.0060 0.0889 0.0484 -0.0396 -0.2864 -0.0091 1.0000 % workers below 44 0.0991 -0.0105 0.0452 -0.2806 0.2016 -0.1977 -0.0563 1.0000 Note: Data are from Cai and Stoyanov (2016) and the NBER-CES Manufacturing Industry Database (2000). First PC is derived from principal component analysis of age-depreciating skill and physical ability.
Table 3 Innovation Activities, Evidence at the Province Level
Top 10 Top 15 Top 20
(1) (2) (3) (4) (5) (6)
Mean of dependent variable 6.1428 6.1428 6.2948 6.2948 6.3636 6.3636
Aging × Robot 2.3253* 1.8227** 1.6049* 0.2715 0.4765 0.2577 (1.3278) (0.7200) (0.8212) (1.4136) (1.2533) (1.3397) Aging -3.6483 -9.2252** -4.1520* -8.9169* -4.2511* -9.2365* (2.4770) (4.6226) (2.4239) (4.6982) (2.4788) (4.8421) Robot -0.9537 -1.4469* -1.2707 -1.7573** -0.4765 -1.8469** (0.8323) (0.8849) (0.8171) (0.8738) (1.2533) (0.8294) Year effects (base = 2000)
2005 2.0042*** 2.0171** 2.0459*** 2.0563** 2.0205*** 2.0580** (0.2565) (0.9879) (0.2516) (1.0015) (0.2567) (1.0412) 2010 3.7219*** 3.8979* 3.7851*** 3.9428* 3.7649*** 3.9847* (0.3927) (1.5654) (0.3882) (2.1785) (0.3986) (2.2725) 2015 2.9892*** 3.5080 3.0383*** 3.5434 3.0278*** 3.6356 (0.5793) (3.5268) (0.5658) (3.5963) (0.5799) (3.7577) Other controls
Lagged wage × Robot 0.00014** 0.00010* 0.00011+
(0.00007) 0.00006 (0.00007)
Lagged per capita GDP × Robot -1.0918 -0.6525 -0.7862
(1.5654) (1.5325) (1.5578)
Lagged population × Robot -0.0004 -0.0004 -0.0004
(0.0004) (0.0004) (0.0004)
NB parameters
Overdispersion (alpha) 0.2586 0.1818 0.2156 0.1839 0.2417 0.1735
(0.0537) (0.0359) (0.0386) (0.0341) (0.0520) (0.0343) Year fixed effects
# Observations 88 88 88 88 88 88
Note: All regressions are negative binomial (NB) regressions. The dependent variable is Npkt, which is the
num-ber of patent applications of category k in province p and year t. In Columns (1) and (2), robot-related patents are defined as those with the top ten IPCs (listed in Table (C4)); in Columns (3) and (4), the top fifteen; and Columns (5) and (6), the top twenty. The dispersion parameter (alpha) is significantly greater than zero in all specifications, which confirms that the data are overdispersed and are better estimated using a negative binomial model than a zero-inflated Poisson model. Standard Errors in parenthesis are clustered at the province level. * significant at 10%, ** significant at 5%, and *** significant at 1%.
Table 4 Imports of Intermediates, Evidence at the Province Level
Numerically Weaving
Intermediates Robots controlled machines and knitting Vending Agricultural and computers machines machines machinery
(1) (2) (3) (4) (5)
A. OLS estimators, dependent variable: ln(share)
ln Aging 3.0456** 0.2864 2.7131+ -4.6189 1.4631**
(1.2127) (0.6759) (1.5913) (3.6918) (0.5530)
Provincial lagged controls Year fixed effects
# Observations 33 33 33 33 33
R-squared 0.3404 0.4695 0.4177 0.4302 0.2541
B. IV estimators, dependent variable: ln(share)
ln Aging 7.2470*** 1.8084+ 2.1919 -6.1487** 2.4789
(2.1784) (1.3746) (2.9593) (2.8490) (1.7999)
F-Stat 13.818 11.453 10.381 8.032 13.864
Provincial lagged controls Year fixed effects
# Observations 33 33 33 33 33
R-squared 0.4086 0.3966 0.2306 0.4234 0.2329
C. Long-difference estimator, dependent variable: ∆(share)
∆Aging 0.1749* 0.0485* 0.0353** -0.0005** 0.0131
(0.0762) (0.0229) (0.0214) (0.0002) (0.0100)
Provincial controls Year fixed effects
# Observations 33 33 33 33 33
R-squared 0.6189 0.1108 0.5618 0.1902 0.359
Note: Dependent variable is the share of total imports of the intermediate goods indicated in each column header, normalized by total imports of intermediate goods. Standard Errors in parenthesis are clustered at the province level. * significant at 10%, ** significant at 5%, and *** significant at 1%.
T able 5 Imp orts of Rob ot-Related In termediates, Age Th re shol d Analysis (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) ln (25-29) share -7.5545** (3.1974) ln (30-34) share -8.8961* (4.6005) ln (35-39) share -12.6478+ (9.6726) ln (40-44) share 2.4613 (2.3755) ln (45-49) share 18.7745* (12.2967) ln (50-54) share 16.5846* (9.6465) ln (55-59) share 13.0603* (8.0023) ln (40-59) share 15.5882* (9.0294) ln (45-59) share 14.1153* (7.8701) ln Aging, (45-59)/(25-44) 7.2470*** (2.1784) F-stat 13.126 13.724 9.600 47.351 12.272 13.235 12.131 11.485 9.130 13.818 Pro vincial lagged con trols Y ear fixed effects # Observ ations 33 33 33 33 33 33 33 33 33 33 R-squared 0.6497 0.6 605 0.5027 0.7609 0.3053 0.1519 0.1122 0.5621 0.5236 0.4086 Note : Dep enden t v ariable is the log of share of rob ot imp orts, normalized b y total imp orts of in termediate go o ds. IV regressions. Column (10) repro duces the resu lts in panel B column (1) in 4. Standard Errors in paren thesis are clustered b y pro vince. * significan t at 10%, ** significan t at 5%, a nd *** significan t at 1%.
T able 6 Inno v ation Activities, Pro vince and Industry Lev el T op 10 T op 15 T op 20 (1) (2) (3) (4) (5) (6) (7) (8) (9) Choice of in tensit y mea sures AgeDep Ph ys First PC AgeDep Ph ys First PC AgeDep Ph y s First PC Mean of dep enden t v ariable 1.2199 1.2199 1.2199 1.2651 1.2651 1.2651 1.3116 1.3116 1.3116 Aging * In te nsit y * Rob ot 1.2983*** 1.0220*** 0.673 5*** 0.9295*** 0.7810*** 0.4955*** 0.8941*** 0.7382*** 0.4685*** (0.1960) (0.1619) (0.1000) (0.2003) (0.2059) (0.1145) (0.2123) (0.1605) (0.1057) Aging * Rob ot -2.0529*** -2.4241*** -2.3115*** -0.3181 -0.5256 -0.4618 -0.9764 -1.2554* -1.1600* (0.5910) (0 .6201) (0.6080) (0.7303) (0.7394) (0.7328) (0.6660) (0.6824) (0.6814) Aging * In te nsit y 0.7936 *** 0.7223** 0.4537*** 0.9097*** 0.8469** 0. 5259*** 0.8719*** 0.7929** 0.4984*** (0.2264) (0 .2822) (0.1496) (0.2325) (0.2939) (0.1548) (0.2170) (0.2730) (0.1437) In tensit y * Rob ot -1.584 5*** -1.4242*** -0.8811*** -1.1924*** -1.1636*** -0.6911*** -1.4049***” -1.3210*** -0.7986*** (0.1152) (0 .0993) (0.0603) (0.1142) (0.1262) (0.0679) (0.1179) (0.0971) (0.0607) Aging -2.6051 -2.6491 -2.6845 -2.5096 -2.5662 -2.6030 -2.6050 -2.6416 -2.6871 (2.0555) (2 .0697) (2.0624) (2.1365) (2,1458) (2.1399) (2.0545) (2.0662) (2.0591) In tensit y 0.4992*** 0.549 6*** 0.2929*** 0.4266*** 0.4871** 0.2527** 0.4701*** 0.5304*** 0.2787*** (0.1246) (0 .1596) (0.0833) (0.1320) (0.1701) (0.0886) (0.1217) (0.1572) (0.0815) Rob ot -1.7142*** -1.451 8*** -1.4831*** -1.8540*** -1.7215*** -1.7145*** -1.9282*** -1.7257*** -1.7394*** (0.3284) (0 .3401) (0.3356) (0.4299) (0.4319) (0.4291) (0.3761) (0.3868) (0.3825) Pro vincial con trols Industry fixed effects Y ear fixed effects ZINB mo del p ar ameters: Ov erdisp ersion (alpha) 0.2670 0.4697 0.3958 0.4173 0.4196 0.4163 0.4164 0.4131 0.4132 (0.0500) (0.0452) (0.0365) (0.0325) (0.0333) (0.0328) (0.0308) (0.0314) (0.0310) Inflated v ariable -0.0058 0.0003 -0.0058 -0.8945 -0.1846 -0.4295 -0.4152 -0.0555 -0.6907 (0.0005) (0.0001) (0.0005) (0.0008) (0.0011) (0.0039) (0.0029) (0.0001) (0.0038) # Observ ations 17,072 17,072 17,072 17,072 17,072 17,072 17,072 17,072 17,072 # Non-ze ro observ ations 14,593 14,593 14,593 14,593 14,594 14,594 14,597 14,597 14,597 Note : Zero-inflat ed negativ e binomial (ZINB) regressions. The dep enden t v ariable Npj k t is the n um b er of paten t applications of category k in industry j , pro vince p , and y ear t. T he choice o f in tensit y measures is indicated in eac h column header. Rob otic paten ts are defined as those with the top ten/ fifteen/ tw en ty IPCs as list ed in T able C4. The disp ersion parameter (alpha ) is significan tly greater than zero in all sp ecifications, whic h confirms that the data are o v erdisp ersed and are b etter estimated using a zero-inflated negativ e binomial mo del than a P oisson mo del. Standard errors in paren thesis are clustered at pro vince-y ear lev el. * significan t at 10%, ** significan t at 5%, and *** significan t at 1%.
T able 7 Inno v ation Activities, Pro vince and Industry with Additional Con trols T op 10 (1) (2) (3) (4) (5) (6) (7) (8) (9) Choice of in tensi ty mea sures AgeDep Ph ys First PC Age D e p Ph ysical First PC AgeDep Ph ysical First PC Mean of dep enden t v ariable 1.2199 1.2199 1.2199 1.2199 1.2199 1.2199 1.2199 1.2199 1.2199 Aging * In te nsit y * Rob ot 1.2983*** 1.0220*** 0.6735*** 0.4956** 0.5034** 0.2781** 0.5996** 0. 4618** 0.2952** (0.1960) (0.1619) (0.1000) (0.1730) (0.2590) (0.1221) (0.1987) (0.2128) (0.1217) A ddition al industry-level contr ols: Aging * Lab or In tensit y * Rob ot 0.0661 0.2936* 0.1564 0.2243 0.1984 0.1654 (0.2303) (0.1783) (0.2102) (0.2288) (0.2138) (0.2326) Aging * AgeAppr * Rob ot -0.8432*** -0.8797** -0.8835*** -0.8692*** -0.8510*** -0.8533*** (0.2434) (0.3048) (0.2724) (0.2265) (0.2749) (0.2488) Aging * Skill In tensit y * Rob ot -6.5292*** -6.1103*** -6.3393*** -5.6197*** -7.1084*** -6.6279*** (1.3088) (1.3856) (1.3317) (1.2126) (1.2366) (1.2341) Aging * Input In tensit y * Rob ot 0.0639** 0.6673** 0.0 655** 0.0690*** 0.0647*** 0.0657*** (0.0213) (0.0213) (0.0213) (0.0201) (0.0195) (0.0194) Aging * % W ork er b elo w 39 * Rob ot -4.2517 -3.5666 -3.9296 -3.5502 -4.0364 -4.3000 (3.4810) (3.3418) (3.4381) (3.2821) (3.3541) (3.4071) Aging * Lagged P aten ts * Rob ot 0.0092 0.0087 0.0089 0.0107 0.0110 0.0110 (0.0082) (0.0084) (0.0082) (0.0077) (0.0077) (0.0077) A ddit ion al pr ovincial lagge d contr ols: Lagged c ollege studen t share * In tensit y * Rob ot 2.0593 4.7560 1.0699 (11.0668) (11.5531) (4.1984) Lagged m fg emplo ymen t Share * In tensit y * R ob ot 0.2795 0.2077 -0.0131 (0.1816) (0.1630) (0.1012) Lagged A ging * In tensit y * Rob ot 0.0105 0.0110 0.0686 (0.0283) (0.0223) (0.0538) First-order and main terms Pro vince fixed effects Industry fixed effects Y ear fixed effects # Observ ations 17,072 17,072 17,072 17,072 17,072 17,072 17,072 17,072 17,072 # Non-ze ro observ ations 14 ,593 14,593 14,593 14 ,593 14,593 1 4,593 14,593 14,593 14,593 Note : Zero-inflate d negativ e binomial (ZINB) regressions. Columns (1)-(3) repro duces the base line results in columns (1)-(3) T able 6. The disp ersion paramete r (alpha) is omitted in this tab le b ecause of space constrain t. The parameter is significan tly greater than zero in all sp ecifications, whic h confirms that the data are o v erdisp ersed and are b etter estimated using a negativ e binomial mo del than a zero-inflated P oisson mo del. Standard errors in paren thesis are clustered at pro vince-y ear lev el. * significan t at 10%, ** sig nifican t at 5%, and *** significan t at 1%.
Table 8 Heterogeneous Effects by the Number of Colleges
Top 10
(1) (2) (3) (4) (5) (6) (7)
Full sample Above-median subsample Below-median subsample
Mean of dependent variable 1.2199 1.3896 1.3896 1.3896 1.0165 1.0165 1.0165
Aging × AgeDep × Robot 1.2983*** 1.5941*** -0.5411
(0.1960) (0.2064) (0.6932)
Aging × Phys × Robot 1.0220*** 1.1910*** -0.1670
(0.1619) (0.1961) (0.6080)
Aging × First PC × Robot 0.6735*** 0.8111*** -0.2211
(0.1000) (0.1138) (0.3809)
Other controls and FEs
# Observations 17,072 9,312 9,312 9,312 7,760 7,760 7,760
Note: Zero-inflated negative binomial (ZINB) regressions. Sample is divided based on the number of colleges in each province above or below the median level in 2000. Column (1) reproduces results for three baseline regressions in columns (1)-(3) in Table 6. Standard errors in parenthesis are clustered at province-year level. * significant at 10%, ** significant at 5%, and *** significant at 1%.
Table 9 Robustness Checks: Removing Provinces
Top 10
(1) (2) (3) (4)
Omitted province Full Sample Beijing Shanxi Liaoning
Aging × Robot 1.8227** 1.780*** 1.634*** 1.921**
(0.7200) (0.7342) (0.6893) (0.8172) Other Controls and Fixed Effects
# Observations 88 80 80 80
Shanghai Jiangsu Anhui Jiangxi
Aging × Robot 1.756** 1.796** 1.843** 1.617**
(0.7294) (0.7519) (0.7365) (0.6721) Other Controls and Fixed Effects
# Observations 88 80 80 80
Shandong Henan Hubei Guangdong
Aging × Robot 2.043*** 1.837** 1.870** 3.305***
(0.7677) (0.7384) (0.7579) (0.6019) Other Controls and Fixed Effects
# Observations 88 80 80 80
Heilongjiang Sichuan Yunnan Gansu
Aging × Robot 1.729** 1.789** 1.638** 1.827**
(0.7478) (0.7306) (0.8054) (0.7669) Other Controls and Fixed Effects
# Observations 88 80 80 80
Note: Negative binomial regressions. Column (1) reproduces the results in column (2) in Ta-ble 3. Standard errors in parenthesis are clustered at province-year level. * significant at 10%, ** significant at 5%, and *** significant at 1%.
Table 10 Robustness Checks: Removing Industries
Top 10
(1) (2) (3) (3)
Omitted industry
Full Sample
Computers and Special General communication purpose purpose devices machinery machinery
Aging × Robot × First PC 0.2952** 0.356* 0.278** 0.233*
(0.1217) (0.1905) (0.1201) (0.1258)
Other Controls and Fixed Effects
# Observations 16,280 16,280 16,280 16,280
Omitted industry Transportation Medicines Rubber Metal
equipments products
Aging × Robot × First PC 0.392*** 0.314*** 0.298** 0.232**
(0.1110) (0.1129) (0.1188) (0.1156)
Other Controls and Fixed Effects
# Observations 16,280 16,280 16,280 16,280
Note: Zero-inflated negative binomial (ZINB) regressions. Column (1) reproduces the results in column (9) Table 7. Standard errors in parenthesis are clustered at province-year level. * significant at 10%, ** significant at 5%, and *** significant at 1%.
A
Appendix
A1 Estimating Substitution Elasticities using UHS Data
Table A1 Summary Statistics of the UHS Sample
N Mean SD Min Max
A. Pre-WTO, 1997-2001
Age 67,830 40.31 7.79 24 61
Female 67,830 0.45 0.50 0 1
Young (aged 25-44) 67,830 0.68 0.47 0 1
Skilled (some college or above) 67,830 0.26 0.44 0 1 Real annual income 67,830 9,277.07 6,349.57 1376.53 64,749.09 B. 2002-2005
Age 146,439 41.00 8.19 24 60
Female 146,439 0.43 0.50 0 1
Young (aged 25-44) 146,439 0.63 0.48 0 1
Skilled (some college or above) 146,439 0.36 0.48 0 1 Real annual income 146,439 13,549.96 9,016.32 1,375.44 64,964.30 C. 2006-2009
Age 109,523 42.02 8.11 24 61
Female 109,523 0.42 0.49 0 1
Young (aged 25-44) 109,523 0.63 0.48 0 1
Skilled (some college or above) 109,523 0.41 0.49 0 1 Real annual income 109,523 19,209.35 11,904.41 1,382.56 64,974.70 Note: Data are from the Urban Household Survey from 1997 to 2009. The main sample in-cludes all individuals who (i) were between 25 and 59 years old; (ii) worked full-time with positive annual wage; and (iii) were not self-employed in the survey years. Skilled workers are defined as those with some college education or above (i.e., more than 14 years of school-ing). Young workers are defined as those aged 25-44 in the surveyed year. Annual earnings are deflated to 1997-level in each province. See text for details on sample restrictions.
Table A2 Constructing Effective Labor Supplies, Step I
All Coastal Provinces Inland Provinces
(1) (2) (3)
Panel A. OLS estimates
Edu-specific relative supply -0.1242+ -0.1344** -0.1204+
(−1/σE) (0.0828) (0.0673) (0.0800)
Prov-year fixed effects prov-edu fixed effects
# Observations 66 36 30
R-squared 0.8936 0.6700 0.5130
Panel B. IV estimates
Edu-specific relative supply -0.1635** -0.1837*** -0.1333*
(−1/σE) (0.0573) (0.0521) (0.0913)
F-Stat 13.40 12.63 24.53
Prov-year fixed effects prov-edu fixed effects
# Observations 66 36 30
R-squared 0.8912 0.8912 0.8481
Note: Data are from the Urban Household Survey from 1997 to 2009. The main sample includes all individuals who (i) were between 25 and 59 years old; (ii) worked full-time with positive annual wage; and (iii) were not self-employed in the survey years. Panel A reports the WLS estimates, using the inverse sampling variances of the wage differentials as weights; Panel B reports the IV estimates, where we instrument the severity of aging using the predetermined component of age and skill composition in each province. Stan-dard errors in parentheses are clustered at province-year level. * significant at 10%, ** significant at 5%, and *** significant at 1%.
