extreme during the same period (high leverage). Consequently, care needs to be taken to ensure the results reflect a general relationship, rather than a few high-influence periods. To improve our robustness to influential observations, we first winsorized GDP growth rates data at the 98% level for country-level data and at 90% for NUTS2-level data.<sup>26</sup> Second, we dropped countries and year observations one-by-one to identify influential observations (where the multiplier estimates change substantially with their exclusion). At the country level, this algorithm identifies Estonia in 2011 (EE11) as influential in OLS regressions, and Croatia in 2016 (HR16) for IV specifications (the first-stage changes). Consequently, we drop both for all country-level specifications. No individual observations are influential by the algorithm in NUTS2-level specifications. Descriptive statistics are presented in Online Appendix Table A2.1 and illustrate the extreme volatility of many of our variables.<sup>27</sup>

# **2.3 Measuring EU Fund Spending**

Unlike most types of government spending, EU structural funds mostly operate on a _reimbursement basis_ which can disconnect the recorded timing of spending from the time it actually occurred.<sup>28</sup> This is potentially problematic for estimating fiscal multipliers – which require spending and its effects to happen at the same time or within a fixed interval after that—and can lead to biased multiplier estimates.

EU structural and investment fund spending proceeds in a roughly three-step process. First, is the _planning stage_ at the start of the 7-year programing period, when the EU spells out the type and size of each program, governments make submissions, and those submissions are approved by the EU. This means that the plan on types and total amount of spending to each country and/or subnational NUTS2 region is usually known well in advance before any actual spending takes place.<sup>29</sup> Second, is the _implementation step_ during the 7-year program which involves (i) some prepayments from the EU to member governments in advance of anticipated work to “provide liquidity” (for example, to provide an advance on a contract), (ii) work on the actual project, and (iii) the firm or government applying for _reimbursement_ from the EU as the work is done. The EU usually does not reimburse 100 percent of the costs (depending on the Fund) as the national government often has to make a copayment. The final step is the closure of the program, which involves the EU paying any remaining balances, conditional on the project being implemented satisfactorily. The closure of the program can take place years after the end of the program period. For example, the 2007–13 program was closed on 31 March 2017 (European Court of Auditors, 2018, p13).<sup>30</sup>

> 26 That is, suppose that 1% of observations are greater than a cutoff , and 1% are below (which implicitly defines and ). Then the winsorized data replaces the top 1% extreme observations with (rather than ii,tt 1HH 1LL dropping them) and replaces the bottom 1% of observations with XX . We call this 98% winsorized. Relative to dropping XX XX 1HH 1LL 1HH observations (an alternative approach), this winsorized data keeps the extreme observations in the sample but reduces XX XX XX 1LL their influence. We winsorized at the 90% level for NUTS2 data because it is more volatile than country-level data. XX 27 Other data we use for other regressions can be found in Online Appendix Tables A2.2 and A2.3.

> 28 There are also prepayments (payments to provide liquidity for future work), which further disconnects the timing of payments from the timing of activity.

29 More specifically, the Cohesion Fund is allocated nationally, while the structural funds (regional development, social fund) are allocated by NUTS2 region.

> 30 There are also some delays relative to the planned closing in March 2017. For example, the six NUTS2 regions in Bulgaria (BG31, BG32, BG33, BG34, BG41 and BG42) received payments in 2018 that were for the 2007-2013 programming period. For the programming periods we are using, modeled payments include payments that go up to 2009 (3 years) for 2000-2006 and up to 2015 (2 years) for 2007-2013. While actual payments go up to 2015 (9 years) for 2000-2006 and up to 2018 (5 years) for 2007-2013.

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