Reading Web of Power (Bai et al., 2022)

The paper by Bai et al. (2022) has been discussed a lot (particularly by Chinese researchers) since its publication on The Quarterly Journal of Economics, perhaps because of its novel idea or special data. Here, I'm going to summarize this paper, replicate some of its results (by Stata 18), and write some comments, just for fun.

To run my codes, please install the following Stata packages in advance:

ssc install listtex, replace
ssc install outreg2, replace
ssc install estout, replace
ssc install reghdfe, replace
ssc install ftools, replace
ssc install parmest, replace
net install grc1leg.pkg, replace
ssc install ivreghdfe, replace
ssc install ranktest, replace

For people interested in history of Qing Dynasty and modern China (in the 20th century), I strongly recommend a book: The Rise of Modern China by Immanuel Chung-Yueh Hsü (written in English and first published in 1970).

Research Idea and Difficulty

Bai et al. (2022)'s main argument is that individuals can affect macro-level outcomes via their personal networks, especially the connections among elites. It is hard to empirically prove this idea due to the difficulty of measuring personal networks and estimating their specific effects. Bai et al. (2022) overcome this difficulty by exploring a specific context in Chinese history: Taiping Rebellion from 1850 to 1864, during which the famous stateman Zeng Guofan (曾国藩) used his personal networks to organize an army in his hometown and finally helped the Qing Dynasty win the war. As Bai et al. (2022) explain, this context is useful because

It features a well-defined elite network based on the imperial examination system (科举). It's well known (at least in China) that examiners and examinees in a triennial provincial-level (乡试) and national-level exams (会试) tended to build up a master-disciple relationship, and those successful examinees attending the same exam built up a quasi-classmate relationship. These relationships (called "baseline networks" by the authors) could assist (or sometimes kill) each other in the future careers.
In this context the authors are able to measure the mobilization outcome of the elites. They have the digitalized data on soldier deaths in 1850-1864 for all counties in Hunan province (Zeng Guofan's hometown). The data are collected from the Hunan Gazetteers.
In this context the authors are able to measure elite power; they have a database (from The Chronicle of Officials in the Qing Dynasty) of information on the Chinese bureaucrats in provincial- and central-government-level offices in 1820-1910. They focus on officials at these two levels because only these officials played key roles in national decision making.

Data

The baseline measure of a county's connections in the elite networks are constructed as $$EliteConnections_c=\sum_{n=1}^{N_c} \frac{1}{d_{c,n}}$$ where $N_c$ is the number of elites from county $c$ and $d$ is the degree of separation from Zeng Guofan. The alternative measures include counting the number of connected elites from a country (i.e., an unweighted measure) and per capita measures (i.e., dividing weighted/unweighted measures by county's population). The authors also constructed 12 country-level variables; see Section III.A.3 of the paper for details.

The summary statistics of country-level connectedness measures and 12 country-level variables are replicated and presented in the table below. Click here to see Stata codes. I tried to use dtable (a command introduced in Stata 18) or outreg2 (an add-in command) but neither result was satisfying. Finally, I used listtex package, but the coding of using outreg2 are also shared in my do file in case that you are interested.

Effect on Soldier Death

The number of soldier deaths in connected-to-Zeng counties increased highly after Zeng Guofan came to power, as presented in the following figure (see here for coding). This is motivational evidence for this research.

Empirical Strategy and Main Results

Bai et al. (2022) employs a static difference-in-differences (DID) strategy to estimate the impact of elite connections on the number of soldier deaths. The main specification has a form $$\ln(SoldierDeath_{c,t}+1) = \beta EliteConnections_c \times Post1853_t + \alpha_c + \lambda_t + \theta X_c \times Post1853_t + \epsilon_{c,t}$$ where $\alpha_c$ denotes county fixed effects, $\lambda_t$ denotes year fixed effects, and $X_c$ is a vector of 12 country-level control variables. All standard errors are clustered at country level. Different from a textbook DID, this specification focuses on a continuous treatment ($EliteConnections_c \times Post1853_t$) instead of a binary treatment. A theoretical econometric paper related to DID with continuous treatment is Callaway et al. (2021).

This specification uses a balanced panel data with 75 Hunan counties in 1850-1864, and it exploits two differences:

Group difference: whether or not county $c$ has elite connections to Zeng.
Time difference: whether or not the year $t$ is in post-1853 period.

Note that in this context, there is only one treatment time: 1853, the year Zeng took power to organize an army in Hunan. Therefore, the static DID strategy is valid under parallel trend, no anticipation, homogeneous and time-invariant treatment effect assumptions (see Sun & Abraham, 2021 for theorems).

The main results are reported in the following table. The estimated impacts of elite connections are significantly positive in all specifications.

Click here to see Stata coding, where I run the DID specifications by the reghdfe command (xtreg, areg, and xtdidregress can also work and return the same coefficient estimates; standard error estimates and R-squared are slightly different because of different degree-of-freedom adjustments). To successfully print out my table in LaTeX, you need to load the adjustbox package (documentation) in your preamble. You may find the table exported by estout doesn't look exactly like the printed one above, because I manually adjusted it for better presentation.

To check whether identification assumptions (especially parallel trends) hold, the authors run an event-study (also called dynamic) DID regression: $$\ln(SoldierDeath_{c,t}+1) = \sum_{k\in \{1850, …, 1864\}/\{1853\}} \beta^k EliteConnections_c \times 1\{t=k\} + \alpha_c + \lambda_t + \delta_{pt} + \theta X_c \times Post1853_t + \epsilon_{c,t}$$ where $\delta_{pt}$ denotes prefecture-year fixed effects. Year 1853 is used as a base year. The results are shown in the following figure. We can see that pre-treatment coefficient estimates are not different from zero at 95% confidence level, regardless of the ways to measure county's elite connections. This gives us assurance that the Hunan counties didn't underwent different trends before Zeng came to power.

Robustness Check

Of course, elite connections were not only constructed on the exam relationships. In the robustness check, Bai et al. (2022) expand their definition for elite networks by including marriage, friends, and clan relationships. Note that the authors define the clan relationship by county and surname: If people were from the same county and they share the same surname, then they belong to the same clan. This is a coarse definition, but maybe the "optimal" definition due to the limitation of data. In addition, the authors examine the results when focusing on specific types of exam connections.

The results (reported in the two following tables) show that the impacts of elite connections are always significantly positive regardless of the measure of elite networks. See here for coding. Notice:

In Columns (1)-(4), the reghdfe command drops 15 singleton observations so that the number of observations becomes 1,110 (instead of 1,125 reported in the paper).
In Columns (5)-(7), the standard errors are multi-way clustered at county and surname levels (instead of at only country level as mis-described in the paper).

Table 3: The Effect of Elite Connections on Soldier Deaths (Types of Links)

Placebo Tests

Two placebo tests are done:

Assume that Zeng would pass the national-level exam in 1836 or 1840 (rather than 1838 in fact). Then the authors use these two placebo timings of exams (and thus placebo elite connections) to check the relevance of true elite connections. The authors even use an instrumental variable (IV) method:
1. Stage 1: Run a regression of true national-level exam network on the baseline connections; then, predict the baseline connections.
2. Stage 2: Run a regression of predicted baseline connections on the soldier deaths.
Use Huai region (i.e., Anhui and Jiangsu provinces) as a placebo for Hunan province. This placebo test is valid because Zeng Guofan only mobilized soldiers in Hunan by his personal networks.

The results are presented in the following tables. Here is my coding. I use the ivreghdfe command (extended from ivreg2 and reghdfe) to run the IV regressions. To use this command, four packages must be installed: ftools, reghdfe, ivreg2, and ranktest.

Table 4: The Effect of Elite Connections on Soldier Deaths (Placebo Networks)

Effect on Postwar Power

Bai et al. (2022) also want to check whether elite connections with war contributions further shaped the distribution of postwar elite power. However, a challenge is that we hardly know how the elite connections without war contribution would affect elite power distribution. One proposed solution is using non-Hunan counties as a comparison group, given that those non-Hunan counties had elite connections in Zeng Guofan's personal networks but did not have soldier deaths in Hunan army.

The motivational evidence is presented in the figure below (coding), where the power distribution is proxied by the average number of national-level offices held by different groups (Hunan versus non-Hunan, connected versus unconnected). The two dashed blue lines denote the starting and ending years of Taiping Rebellion. Obviously, the average number of national-level offices held by officers from Hunan-connected counties increased largely during and after the war.