在Management Science2019年9月的一篇“Political Promotion, CEO Incentives, and the Relationship Between Pay and Payformance”中，看到作者在主回归中用了一个nonlinear-fits-as-instrument 2SLS回归，但不太明白具体是怎么操作的，以及原理为何，搜了一些资料也没怎么找到，因此来向各位求教。

具体而言，文章当中的主要自变量是表示CEO是否获得政治晋升的哑变量Promotion，想要研究的因变量是CEO的薪酬Compensation，同时将Promotion与公司绩效变量ROA、ROS等构造了交互项作为自变量。

但是，由于Promotion可能有内生性，文章中便用了2SLS来处理。分为两步来做：
第一步，以Promotion为因变量，公司业绩、其他财务特征、CEO特征等作为自变量进行了一个Logistic回归，同时加入了两个工具变量，分别是表示是否央企的哑变量和是否有中央ZF更替的哑变量。由此得到了一个拟合的Promotion值。
（原文表述如下：In the first step, we estimate a logit model of the likelihood of political promotion. The dependent variable is Promotion,……Because promotion and compensation are likely determined jointly, we include two instruments for identification. The first is Central government ownership, an indicator variable equal to one if the central government is the ultimate controlling shareholder of the firm. ……The second instrument is Central government turnover, an indicator variable equal to one if the year is 2005 or 2008.）

第二步，进行2SLS回归。第一阶段中将前一步Logistic回归拟合出的Promotion值作为工具变量，并将Logistic回归中的其他外生变量作为控制变量。第二阶段以CEO薪酬Compensation为因变量，第一阶段预测出的Promotion和公司绩效为自变量。
（原文表述如下：In the second step, we apply a 2SLS procedure, where the fitted values of Promotion from the logistic analysis above are used as the instruments in the first stage and all exogenous explanatory variables in the logistic regressions are included as the controls. In the second stage, we regress the natural log of CEO compensation on firm performance and the prediction of Promotion (Promõtion) from the first stage. We use this augmented 2SLS because Promotion is a dummy variable and its determinants likely follows a nonlinear function (Angrist and Pischke 2009).
此处还有一条尾注解释最后这个nonlinear function：As the instruments in the 2SLS are the fitted values from the logistic analysis, the identification essentially relies on the nonlinear logistic analysis where central government ownership and central government turnover are the exogenous instruments. If the nonlinear model provides better deterministic prediction than a linear model, this nonlinear-fits-as-instruments 2SLS has the advantage of resulting more efficient estimation than those using a linear model in the first stage (Newey 1990). We compare the results from this augmented 2SLS with those from using linear fitting or nonlinear directly in the first stage. The comparison is consistent with Newey’s (1990) prediction and thus confirms that our logistic deterministic model for political promotion and the nonlinear-fits-as-instruments 2SLS are the correct procedure to use in this setting.）


这一段我就没怎么看懂了，第二步2SLS的第一阶段中自变量已经是Promotion拟合值，那么它的因变量是什么呢？
第二阶段中Promotion的预测值和Logisitic回归中的Promotion拟合值有什么区别？
以及，文章中说是由于Promotion是哑变量的缘故，才要使用非线性2SLS，那么第二阶段中的自变量——Promotion的预测值也是哑变量，还是类似于概率的（0,1）之间的连续变量呢？
我直接搜文章中所用的nonlinear-fits-as-instrument 2SLS也没搜到什么结果，这个处理方法是否还有什么其他专门的名称？

附上全文供参考。
真心求教各位高手~~十分感谢！！！