3 Taxation under Learning by Doing
3.2 Wedge: Deadweight Loss
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3.3 Abstract
我们研究了工人生产力随机（stochastic）且因为干中学（learning by doing）具有内生性的情况下的最优税收方案。
干中学导致了更高的税收效率扭曲，改变了税率和效率扭曲之间的关系。
在校准模型中，我们发现改革美国税法能带来显著社会受益。一个不考虑过往收入的简单税法是近似最优的。
通过比较干中学和生产力外生两种情况下的税法，我们单独考察了干中学的影响。
We isolate the role of learning by doing by comparing the aforementioned tax code to its counterpart in an economy that is identical to the calibrated one except for the exo- geneity of the productivity process.
忽视干中学后的结果完全不同。
3.4 Intro
“Learning by doing” refers to the positive effect of the time spent at work on the agents’ productivity.
- a side product of the labor supply process.
Agents’ productivity
- stochastic
- private
- evolves endogeny
The mechanism described above is specific to economies in which the agents’ productivity is their private information, is endogenous, and evolves stochastically over the life cycle, which are natural features of economies with LBD.
Findings
- 无效损失更大in the presence of LBD, labor wedges are higher than those in the absence of LBD
- 边际税率和无效损失的关系改变the presence of LBD alters the relation between wedges and marginal tax rates under optimal tax codes and 对全周期的税收规模、累进性和机制影响很大has a significant impact on the level, progressivity, and dynamics of taxes over the life cycle.
- We also find that most of the welfare gains from the optimal reform can be generated with a simple tax code where taxes are invariant to past incomes but age dependent.
New tax code
- higher tax rates for young workers, whereas for old workers it features higher tax rates at low income percentiles but lower tax rates at high income percentiles
- less progressive for young workers and is regressive, instead of progressive, for old workers
- a smaller differential between the average tax rate for old workers and the average tax rate for young workers
Comparison to a counterfactual economy where productivity is exogenous
- features lower tax rates for young workers, whereas for old workers it features lower tax rates at low income percentiles but higher tax rates at high income percentiles
- is progressive, instead of regres- sive, for young workers but is less regressive for old workers
- a larger differential between the average tax rate for old workers and that for young workers
In the presence of LBD, agents have incentives to work harder to boost their future productivity.
Under complete information, this effect contrib- utes positively to welfare.
Private: agents must receive rents to reveal their private information.
Such rents represent welfare losses and call for downward distortions in labor supply. These rents are higher for highly productive agents. LBD, by shifting the productivity distribution in future periods to- ward higher productivity levels, contributes to higher expected future rents and thus to higher expected future welfare losses.
3.5 Model
two period \(t1,\ t2\)
Linear labor production
Period 1: productivity: \(\theta_1\)
- Private
- \(cdf:F_1\)
Period 2: productivity: \(\theta_2\)
- private
- \(cdf:F_2(·|\theta_1,y_1)\)
- dependence on \(y_1\)
Period-t flow utility \[ v\left(c_{t}(\theta_t)\right)-\psi\left(y_{t}(\theta_t), \theta_{t}\right) \] Discount factor: \(\delta\)
Expected life-time utility \[ V_{1}\left(\theta_{1}\right)=\mathbb{E}\left[\sum_{t} \delta^{t-1}\left(v\left(c_{t}\left(\tilde{\theta}^{t}\right)\right)-\psi\left(y_{t}\left(\tilde{\theta}^{t}\right), \tilde{\theta}_{t}\right)\right) \mid \theta_{1}, y_{1}\left(\theta_{1}\right)\right] \] Expected life-time tax bill \[ R_{1}\left(\theta_{1}\right)=\mathbb{E}\left[\sum_{t} \delta^{t-1}\left(y_{t}\left(\tilde{\theta}^{t}\right)-c_{t}\left(\tilde{\theta}^{t}\right)\right) \mid \theta_{1}, y_{1}\left(\theta_{1}\right)\right] \] Dual problem
- \(\int R_{1}\left(\theta_{1}\right) d F_{1}\left(\theta_{1}\right)\)
- \(\int V_{1}\left(\theta_{1}\right) d F_{1}\left(\theta_{1}\right) \geq \kappa\)
3.6 First best
3.7 Second best
Need to give high types ”rents”: higher consumption (lower taxes) than under FB
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3.9 Comments
当存在干中学时：
一阶段工作影响二阶段收入——一阶段税率应低于二阶段税率
应鼓励高禀赋工人工作
要求：1）干中学；2）能力不可被观测
可能应用到对企业征税？央地税收改革中的地方能力似乎不是private info。