accurate than raw payments. For example, the OLS subnational investment multiplier for the whole of Europe is 0.63 for modeled payments in Table 2, but only about half as large (0.38) when calculated using raw payments (Online Appendix Table A3.2). The corresponding IV multipliers are 0.92 using modeled payments, but 0.72 using raw payments. Multipliers are also smaller at the country level using the raw payment data in the all-Europe sample; they are almost half as large using OLS (0.97 from Table 2, 0.6 from Online Appendix Table A3.2), and IV estimates lose significance using the raw payments.<sup>49</sup> Second, Online Appendix Table A3.3 reports investment multipliers winsorizing investment data at the 90% level for NUTS2-level data and at the 98% for country-level data (analogous to approach for GDP). Results are broadly similar to those in Table 2; investment usually responds robustly to EU spending. For subnational regions (Columns 1-3), investment multipliers with winsorized data are about 0.1-0.2 _smaller_ than those in Table 2 (about one standard error) though are still significant and at least 0.5 for most specifications. Countrylevel investment multipliers with winsorized data are typically 0.05-0.2 larger than those in Table 2.

Finally, Online Appendix Table A3.4 (only at the country level) shows that a 1€ increase in modeled EU fund spending increases public investment by about 0.6€ for all countries, driven by effects in CEE countries. In contrast, effects on private investment are always insignificant. For non-CEE countries both public and private investment multipliers are insignificant and usually close to zero. These estimates reinforce the findings that EU funds are actually spent, usually on public investment, but there is not much evidence of crowding-in of private investment (neither there is of crowding-out private investment, as shown earlier).

# **3.3 Cumulative Multipliers over Longer Horizons**

So far, we have found that while EU funds tend to stimulate investment, they have only modest immediate effects on GDP in the first year of the construction/implementation period. One possible explanation is that the one-year horizon considered above might be too short to observe an effect, which might appear over longer time horizons. There are two main arguments for exploring a delayed effect of EU funds on GDP. First, it could be that examining short windows misses some of the benefits of EU spending – newly-employed construction workers on an EU-funded road project might take some time to spend their wages and further boost demand. Indeed, Coelho (2019) and Durand and Espinoza (2021) find some evidence of larger multipliers over longer horizons.<sup>50</sup> Second, there might be residual concerns about some mismeasurement of the timing of spending, and so smoothing multipliers over several years would reduce mismeasurement.

> 49 Likewise, country-level CEE and non-CEE investment multipliers are always smaller (and more often negative) using raw payments than modeled payments, though for the non-CEE sample both are insignificant.

> 50 Coelho (2019) reports a medium-run multiplier of 4 after 3 years, but this is not a cumulative multiplier because it measures the cumulative response of output to a one-time spending shock. As spending is also very persistent, Coelho says she finds a cumulative multiplier of 0.9. Durand and Espinoza (2021) estimate cumulative multipliers of 1.8 over a two-year horizon, up from 1.2 contemporaneously. Canova and Pappa (2022) find cumulative multipliers above 1 after 3 years for the ESF program.

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