**Table A13: Treatment - Alternative Controls**

|Before|delegated ra|ndomizatio|n of inspector a|ssignment||
|---|---|---|---|---|---|
|**Dependent variable:**|**Time**|**Fraud**|∆**log value**|∆**log tax**|**Hyp. tax**<br>**revenue**<br>**losses**|
|**A. I**|**ncluding O**|**nly Month**|**-Year Fixed **|**Efects**||
||(1)|(2)|(3)|(4)|(5)|
|Excess interaction share|-1.481**|-0.160|-0.053*|-0.060*|0.531**|
||(0.586)|(0.101)|(0.028)|(0.030)|(0.253)|
|Observations|41,121|44,522|44,434|40,471|44,497|
|R-squared|0.263|0.174|0.116|0.099|0.028|
|**B. Inclu**|**ding Month**|**-Year and**|**Inspector Fi**|**xed Efects**||
||(6)|(7)|(8)|(9)|(10)|
|Excess interaction share|-1.519***<br>(0.519)|-0.123<br>(0.085)|-0.041*<br>(0.022)|-0.047*<br>(0.025)|0.504*<br>(0.246)|
|Observations|41,121|44,522|44,434|40,471|44,497|
|R-squared|0.287|0.178|0.121|0.103|0.030|
|**C. Including **|**Month-Yea**|**r, Inspect**|**or, and Brok**|**er Fixed Ef**|**ects**|
||(11)|(12)|(13)|(14)|(15)|
|Excess interaction share|-1.810***|-0.221**|-0.072***|-0.079**|0.282|
||(0.342)|(0.101)|(0.022)|(0.029)|(0.176)|
|Observations|41,121|44,522|44,434|40,471|44,497|
|R-squared|0.303|0.195|0.139|0.119|0.073|
|**D. Including Month-**|**Year, Inspe**|**ctor, Brok**|**er, and Sourc**|**e Country F**|**ixed Efects**|
||(16)|(17)|(18)|(19)|(20)|
|Excess interaction share|-1.937***|-0.236**|-0.072***|-0.079**|0.400**|
||(0.358)|(0.103)|(0.022)|(0.030)|(0.176)|
|Observations|41,121|44,522|44,434|40,471|44,497|
|R-squared|0.309|0.198|0.141|0.121|0.146|
|**E. Ad**<br>**(With Month-Year, I**|**ding All C**<br>**nspector, B**<br>(21)|**ovariates i**<br>**roker, So**<br>(22)|**n Table 2 as **<br>**urce Country,**<br>(23)|**Controls**<br> **and HS2 Fi**<br>(24)|**xed Efects)**<br>(25)|
|Excess interaction share|-1.806***|-0.174*|-0.057**|-0.062|0.087***|
||(0.330)|(0.102)|(0.024)|(0.038)|(0.025)|
|Observations|28,772|31,102|31,049|27,825|31,102|
|R-squared|0.323|0.213|0.167|0.143|0.964|

_Notes:_ Standard errors clustered two-way by inspector and by broker presented in parentheses. ***, **, and * indicate significance at 1%, 5%, and 10% levels, respectively. _Excess interaction share_ is the difference between the share of given broker’s declarations handled by an inspector in a given semester and the hypothetical share she would be expected to handle if the allocation of declarations to inspectors were random conditional on their productivity, as prescribed by official rules, calculated using calibration methods (as explained in Section 4). All specifications include the tax rate, the risk score, a dummy for the red channel, the share of value accounted for by differentiated products, a dummy indicating whether the declaration was mixed, and a dummy indicating the declaration was subject to valuation advice. The specifications also include in Panel A month-year fixed effects, in Panel B inspector and month-year fixed effects, in Panel C inspector, broker, and month-year fixed effects, in panel D inspector, broker, month-year, and source-country fixed effects, and in Panel E all covariates used in Table 2 and inspector, broker, source-country, HS2 product, and month-year fixed effects. "Observations" refers to the number of non-singleton observations. OLS estimation is used. The sample covers the period January 1, 2015 to November 17, 2017 (i.e., before the delegated randomization intervention).

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