1년차 때 논문 열심히 읽으면 망한다(..)는 얘기를 많이 들었다. 그래서 요즘은 감 잃지 않게 NBER 메일링 받으면서 출퇴근길에 초록만 훑어본다. 그런데 이번 주에 나온 페이퍼가 눈길을 끌었다.
The Productivity Slowdown and the Declining Labor Share: A Neoclassical Exploration
We explore the possibility that a global productivity slowdown is responsible for the widespread decline in the labor share of national income. In a neoclassical growth model with endogenous human capital accumulation a la Ben Porath (1967) and capital-skill complementarity a la Grossman et al.
주제도 주제고, 저자진도 휘황찬란하다. Gene Grossman (Princeton), Elhanan Helpman (Harvard), Ezra Oberfield (Princeton), Thomas Sampton (LSE). 차마 초록만 읽고 넘어갈 수 없어서 서론과 결론 정도 더 읽어 보았다(???). 논문의 핵심은 생산성 증가율이 하락하면 요소소득이 노동에서 자본으로 옮겨가는 경향이 있다는 것이다. 저자들의 칼리브레이션에 따르면 대략 생산성증가율 1%p 하락할 때마다 자본소득분배율이 2~6%p 올라간다(당연히 노동소득분배율 하락). 이 결과는 현재 관찰되는 미국 노동소득분배율 하락을 절반에서 전부 설명한다.
논리는 대충 이렇다. 경제성장률이 하락하면 실질이자율이 하락하고, 사람들이 교육을 더 받기로 선택한다. 이는 노동-자본 대체탄력성이 비탄력적일 때 (자본-인적자본 보완관계에 의하여) 기업의 자본상대수요를 증가시킨다. 다시 말해 주어진 labor expense 하에서 자본소득분배율이 상승한다는 것. 다만 아직 인과를 말할 단계는 아니라고 거듭 강조한다.
솔직히 무엇이 새로운 것인지는 잘 모르겠다. 대가들이 흔히 하듯 간단한 모형으로 디테일한 논의를 전부 엮어낸 느낌인데(전형적인 “참 쉽죠?”) 관련 참고문헌을 다 읽을 수도 없고. 저자들이 제시하는 셀링 포인트 중 하나는 대체탄력성 실증분석 결과가 분분한 이유를 설명한다는 것이다. 피케티 21세기 자본 논쟁에서도 문제시되었던 바로 그 대체탄력성 맞다. 저자들에 따르면 몇몇 실증연구에서 대체탄력성이 1보다 큰 이유는 인적자본 선택을 감안하지 않아서 그렇다는 것. 국가간 데이터를 이용한 연구가 특히 이 문제에 취약하다. 이 모형은 (쉽게 짐작할 수 있듯이) 인적자본선택을 내생화해서 이 문제를 해결하는 한편 대체탄력성이 1보다 작아야 한다는 이론적 결론을 재확인한다.
아무튼 대충 그렇다. 정리를 다 하진 못하겠다.
초록을 옮기면 다음과 같다.
본 연구진은 세계적 생산성 둔화 현상이 노동소득분배율 하락을 야기할 가능성을 탐색한다. Ben Porath (1967) 식 내생적 인적자본축적, Grossman et al. (2017) 식 자본-숙련 보완관계를 추가한 신고전파 성장모형에서, 균제상태(steady-state) 노동소득분배율은 자본생산성 증대(capital-augmenting)·노동생산성 증대(labor-augmenting) 기술진보율과 정의 상관관계를 갖는다. 戰後 미국 데이터를 이용해 칼리브레이션한 결과 1인당 소득증가율 1% 하락은 최근 미국 노동소득분배율 하락을 절반에서 전부 설명한다.
We explore the possibility that a global productivity slowdown is responsible for the widespread decline in the labor share of national income. In a neoclassical growth model with endogenous human capital accumulation a la Ben Porath (1967) and capital-skill complementarity a la Grossman et al. (2017), the steady-state labor share is positively correlated with the rates of capital-augmenting and labor-augmenting technological progress. We calibrate the key parameters describing the balanced growth path to U.S. data for the early postwar period and find that a one percentage point slowdown in the growth rate of per capita income can account for between one half and all of the observed decline in the U.S. labor share.
핵심 문단은 대충 이 정도.
When we solve for the balanced growth path, we find simple analytical formulas for the long-run factor shares. If we further assume—in keeping with the empirical evidence—that the elasticity of intertemporal substitution is less than one, then the labor share in national income is an increasing function of the rates of capital-augmenting and labor-augmenting technological progress. Therefore, a productivity slowdown of any sort results in a decline in the steady-state labor share. The mechanism operates through optimal schooling choices. When growth slows, the real interest rate falls, which leads individuals to target a higher level of education for a given level of the capital stock. Inasmuch as skills are capital using, this reduces the effective capital to labor ratio in the typical firm, which in turn redistributes income from labor to capital, given an elasticity of substitution less than one.
How important is this redistributive channel quantitatively? To answer this question, we take parameters to match the average birth rate, the average death rate, the rate of labor productivity growth, the internal rate of return on schooling, and the factor shares of the pre-slowdown era in the United States, as well as a conservative estimate of the elasticity of intertemporal substitution. One key parameter remains, which can be expressed either in terms of the composition of technical progress in the pre-slowdown steady state or as a measure of the capital-skill complementarity in the aggregate production function. We are cautious about this parameter, because Diamond et al. (1978) tell us that it cannot be identified from time series data on inputs and outputs, while our formula tells us that it plays a central role in our quantitative analysis. We consider a range of alternatives, including some derived from estimation of the cross-industry and cross-regional relationships implied by our model. In all of the alternatives we consider, a one percentage point slowdown in secular growth implies a substantial redistribution of income shares from labor to capital, representing between one half and all of the observed shift in factor shares in the recent U.S. experience.
In this setting, if human capital is more complementary with physical capital than with raw labor and if the elasticity of substitution between physical capital and labor is less than one (holding constant the level of schooling), then the rate of labor productivity growth and the share of labor in national income will be positively correlated across steady states. Accordingly, a slowdown in productivity growth—such as has apparently occurred in the recent period—can lead to a shift in the functional distribution of income away from labor and toward capital. The mechanism requires a fall in the real interest rate, which has also been part of the recent experience. When the interest rate falls relative to the growth rate of wages, individuals target a higher level of human capital for any given size of the capital stock and state of technology. When human capital is more complementary to physical capital than to raw labor, the elevated human capital target implies a greater relative demand for capital. With an elasticity of substitution between capital and labor less than one, the shift in relative factor demands generates a rise in the capital share at the expense of labor. Moreover, if the productivity slowdown is associated with a deceleration of declining investment-good prices or with a fall in the rate of disembodied capital-augmenting technical progress, then the model predicts a slowdown in the annual expansion of educational attainment, which also matches the data in recent economic history.
Finally, we have focused in this paper on exploring a potential explanation for recent trends in the labor share. But it is possible that our story holds broader sway in economic history. Figure 7 shows the evolution of the labor share in the United States and the United Kingdom since the beginning of the twentieth century and the evolution of labor productivity in each country over the same period. Evidently, these two variables have been temporally correlated throughout modern history. For example, the period from 1900 until approximately 1930 was a period of slow productivity growth in the United States and United Kingdom. It was also a period of an historically low labor share. When productivity growth subsequently accelerated, the labor share rose in tandem. While we are cautious about drawing firm conclusions from such casual observations, it is possible that productivity growth and the functional distribution of income have been linked for quite some time.