Rural Pensions, Labor Reallocation, and Aggregate Income: An Empirical and Quantitative Analysis of China

The paper asks what accounts for the large sectoral labor productivity gaps observed in developing countries — unobserved worker characteristics and sorting, or barriers to worker mobility — and whether any concrete policy can improve labor allocation and thereby raise aggregate productivity and income; it answers in the context of China. The authors state the research challenge plainly: both sorting and mobility barriers are likely to matter, and the difficulty is empirically separating the two channels. Their instrument for doing so is the New Rural Pension Scheme, introduced in 2009 and extended to every rural county in mainland China by the end of 2012. Because migrant workers commonly leave elderly parents behind in the countryside, a cash pension paid to those parents lets the elderly shift time from farm work into home production, which frees younger household members to supply more market labor and migrate. In the paper’s language, the NRPS “effectively reduces the migration costs of young workers in households with pension-eligible family members” — so its staggered rollout supplies exogenous variation in migration costs that is plausibly unrelated to workers’ own potential earnings.

The primary source is the annual National Fixed Point Survey of Agriculture (NFP), a longitudinal survey run by the Research Center of Rural Economy of China’s Ministry of Agriculture and Rural Affairs, covering roughly 20,000 households and 80,000 individuals in 350 villages across mainland China in each year of the 2003 to 2013 window the authors use. The waves from 2003 onward carry an individual-level questionnaire recording age, gender, schooling, industry, working days and — critically — whether the individual worked outside the township of his hukou residence during the year, plus migrant earnings for those who did. The analysis sample is restricted to individuals aged 20 to 55 with no more than 12 years of schooling who are observed for at least two years, trimmed at the top and bottom 1% of the annual income distribution in each sector, leaving 48,801 individuals and 229,849 person-year observations. A worker is classified as non-agricultural in a year if he worked more than 180 days out of town, so “migration” and “working in the non-agricultural sector” are used interchangeably in the reduced-form analysis; in-town non-agricultural workers are treated as agricultural because the survey does not record their non-agricultural earnings. The authors note the panel’s main drawback: it carries limited information on migration destinations, so the analysis is about rural-to-urban sectoral movement rather than spatial movement across provinces and cities.

About 30% of sample workers migrated out of town for non-agricultural work at some point during the period, and their mean log daily earnings exceed those of agricultural workers by 27 log points — but because migrants also work far more days (302 against 208 a year on average), the sectoral gap in annual earnings, at 78 log points, is much larger than the gap in daily earnings. Migrants are also younger, healthier, more educated, more likely to be male, and more likely to have a household member aged 60 or above. The authors read these differences as direct evidence of sorting on observables, and as a reason to expect sorting on unobservables too — which is what motivates the identification strategy rather than a simple earnings comparison.

The sector-of-employment indicator is instrumented with the interaction of the share of the year the NRPS has been in effect in the county and an indicator for the presence of a household member aged 60 or above, which makes the design a triple difference. A plain difference-in-differences would exploit only the differential timing of the rollout across counties; adding the eligibility dimension compares households with and without a pension-eligible elderly member within the same village and year, which differences out village-specific shocks to migration costs or incomes that happen to coincide with the rollout, and so addresses the concern that the NRPS was rolled out endogenously across counties. All specifications include village and province-by-year fixed effects with standard errors clustered at the village-by-year level. The exclusion restriction is that, conditional on observables, the NRPS does not affect income differently for members of eligible and ineligible households other than through its effect on sector choice, and is uncorrelated with other village-specific shocks whose income effect varies with elderly eligibility. The authors defend it on the reasoning that cash transfers to the elderly would not change younger members’ innate sectoral abilities, and support it with a mediation check: once the sector dummy is included, the instrument has no independent effect on earnings, economically or statistically.

The cross-sectional OLS estimate is 31 log points, the instrumental-variable estimate is 86 log points, and the control-function estimate is 33 log points — and it is the near-equality of the first and third, rather than the size of the second, that carries the paper’s conclusion about sorting. Conditional on individual characteristics, daily earnings in the non-agricultural sector are 31 log points higher (38 log points when individual fixed effects are added). The first stage shows younger members of pension-eligible households are 4.2 percentage points more likely to work in the non-agricultural sector, with a Kleibergen-Paap F-statistic of 31.02, well above the Stock-Yogo 10 percent weak-instrument threshold. The second stage implies working in the non-agricultural sector raises daily wages by 86 log points; the authors are careful that this is a local average treatment effect capturing the marginal workers whose sector choice the NRPS changed, and that it corresponds to the weighted average of the effective migration costs among those compliers — so it says migration costs for switchers were around 86 log points, not that migration pays 86 log points on average. Compliers, they show, are disproportionately workers facing higher baseline barriers, such as women with young children, which partly explains why the local estimate is so large. The control-function approach of Card (2001) and Cornelissen et al. (2016), which adds normal selection terms so that the sector coefficient recovers the average treatment effect, yields 33 log points. Because the difference between the average treatment effect and OLS is exactly the selection bias from sorting, their similarity implies that selection bias in the observed gap “is almost negligible in the case of China.”

The NRPS works through the household’s internal allocation of time: elderly recipients reduce market labor and shift toward home production, which lets young members increase market labor and migrate. Regressing elderly working days on the rollout gives a significantly negative effect, robust to a Poisson quasi-maximum-likelihood specification for the zero-heavy count data; the triple-difference specification gives a positive effect on young workers’ labor supply, again robust to Poisson. In magnitudes, the estimates imply the NRPS cuts the labor supply of the elderly by 9.5 days and raises that of young workers by 3.4 days, against sample averages of 105 and 236 days respectively. The authors also check the obvious alternative channels through which a cash transfer could change migration — savings, fixed-capital investment, and liquidity or credit constraints — and report no evidence that these play a major role.

The model is a general-equilibrium household model with joint agricultural production, shared home production, endogenous labor supply and migration, in which old and young members of a rural household are identical within groups but play a non-cooperative Nash game against each other. That non-cooperative structure is load-bearing: the authors note in the paper that a collective household model would predict the pension reduces young members’ labor supply, contradicting the reduced-form evidence, whereas the non-cooperative version predicts the observed increase. Human capital depends on observables plus sector-specific unobserved ability and an i.i.d. sector-specific shock; all household members share the same agricultural ability, which also absorbs the household’s land endowment and quality. Technology, ability-distribution, migration-cost and home-production parameters are estimated by indirect inference on micro moments — earnings levels, trends, variances, Mincer coefficients, serial correlations for sector stayers and switchers, working days of old and young members in migrant and non-migrant households, and the reduced-form triple-difference effect of the NRPS on migration — while preference parameters are calibrated, with the inverse intertemporal elasticity of substitution set to 1.2 and the Frisch elasticity of labor supply to 0.5 from the macro-labor literature. The estimated average migration cost is 76% of non-agricultural earnings; migration costs are lower for workers who are male, more educated and younger, and fall strongly with the Hukou Index, whose average rise from 2.06 in 2003 to 3.61 in 2013 implies average migration costs fell by 2.68 percentage points a year over that decade. The model reproduces several untargeted moments, including the labor-supply responses of young and old workers to the NRPS and a rising observed APG (0.047 a year in the model against 0.051 in the data) driven by faster TFP growth in the urban non-agricultural sector (0.110 against 0.057).

Removing the NRPS from the estimated 2013 economy lowers GDP by 2.241 log points, mainly through a 2.029-log-point fall in aggregate labor supply; stated the other way round, the paper reports that the NRPS raises migrants’ labor supply by 6% and GDP by 2.4%, cuts the labor supply of elderly rural workers by 34%, and raises aggregate welfare, measured in consumption-expenditure equivalents, by 15%. The between-sector effects are real but modest by comparison: the NRPS raises the migration rate by about half a percentage point and migrants’ share of employment by about 1.5 percentage points, and it lowers the observed APG by 4.3 log points (1.4 from the underlying gap and 2.9 from the human capital gap). In the 2013 baseline the observed APG is 35.6 log points against an underlying APG of 31.5, so the human capital gap between migrants and agricultural workers is 4.1 log points — the model’s own restatement of the reduced-form finding that selection plays a minor role, and one that holds in every counterfactual the authors run. Welfare gains accrue to both rural groups, not just the recipients: because young members were spending too much time on home production and the elderly too much on farm work, the transfer relieves a within-family misallocation and benefits old and young rural workers alike. Urban workers lose, since in the baseline the transfers are financed by a lump-sum tax on urban households.

Raising the transfer fivefold raises GDP by a further 4.173 log points and welfare by a further 28.5%, again mainly through aggregate labor supply, and this time with a quantitatively significant gain in average human capital of 0.829 log points. The migration rate actually falls slightly under the scaled-up policy, because the sharp withdrawal of elderly labor raises the marginal product of young workers on the farm and keeps some of them there — while those who do migrate supply much more labor, so migrants’ share of total labor supply still rises. The authors draw the general lesson that assessments of rural pension policy must look at the intensive margin of labor supply and not only the extensive margin of who migrates. On financing, they also consider paying for the fivefold transfer with a lump-sum tax on young rural workers instead of urban households: GDP rises further, to about 4.7% above baseline, and elderly rural workers, young rural workers and urban workers are all better off than under the current NRPS — urban workers because the relative price of non-agricultural goods rises.

A hypothetical reform setting every destination city to the most liberal hukou policy raises GDP by 2.039 log points, close to the 2.241 log points attributable to the NRPS — but the two policies operate through different margins. Under the hukou reform the migration rate rises by 2.8 percentage points, migrants’ share of labor supply by 1.6 and the non-agricultural sector’s share of effective labor by 1 percentage point; average human capital rises 1.596 log points and aggregate productivity 0.905 log points, while aggregate labor supply actually falls by 0.462 log points. The observed APG drops by 16.4 log points, from 35.6 to 19.2 — a 46% reduction — with 15 log points of that coming from the underlying gap. The authors’ decomposition is explicit: the pension raises GDP primarily by reducing within-household labor misallocation and raising aggregate labor supply, the hukou reform by reallocating labor between sectors and thereby improving aggregate productivity and average human capital. They also check that the pension still matters in a low-barrier world: eliminating NRPS transfers under the hypothetical hukou reform still reduces GDP by 2.045 log points, so “the impact of the rural pension policy remains important even if migration costs and the APG are much lower than those observed in China in 2013.”

Setting each region’s Hukou Index back to its 2003 value and removing the NRPS, the authors find that the combination of the pension and the hukou liberalization actually carried out between 2003 and 2013 raised the migration rate by 6.5 percentage points and GDP by 6.556%, with aggregate productivity, average human capital and aggregate labor supply higher by 1.498, 3.145 and 1.913 log points, and the observed APG lower by more than 40%. That is smaller than the 8.3% GDP gain Hao et al. (2020) attribute to reductions in out-of-county agriculture-to-non-agriculture migration costs over 2005 to 2015, and the authors give three reasons for the difference: Hao et al. allow for all migration-cost changes their model needs to fit observed migration rates while this paper prices only two explicit policies; Hao et al. assume migrants and urban workers are equally productive, whereas this paper’s micro-data estimation finds a significant productivity gap between them and so a smaller gain from migration; and their model is spatial, so migration there relieves spatial as well as sectoral misallocation, while this model abstracts from spatial variation.

The authors flag the gap between migrants and urban residents as their main unresolved margin. Calibrating urban human capital from goods-market clearing gives 8.16 against an average of 2.95 for migrant workers, an implied wage gap of about 2.8 to 1 that the authors note is close to the roughly 3 to 1 urban-rural household income gap reported for 2013 in the China Statistical Yearbook. So on top of the agricultural productivity gap between migrants and rural agricultural workers, there is a second, separate productivity gap between migrants and urban residents that “limits the gain from rural-urban migration in China,” and the authors describe investigating its sources as an interesting avenue for future research. The paper’s headline claim is correspondingly bounded: it is that the absence of adequate old-age security in rural areas acts as a barrier to sectoral labor reallocation, and that rural pension programs can improve labor allocation and raise aggregate income and welfare — established for China over 2003 to 2013, within an estimated model whose migration-cost function is disciplined by the hukou policy variation of that decade.