# **4.  Benchmark Estimates of the Government Spending Multiplier**

Table 4 reports benchmark estimates of the government spending multiplier based on Equation (1). The three panels of the table report the ordinary least squares (OLS), two-stage least squares (2SLS), and first-stage regressions, while the three columns refer to the three country samples discussed in the previous section. In addition, Figure 3 displays the scatterplots corresponding to the first-stage and second-stage regressions, partialling out the country and year fixed effects. The OLS estimates of the multiplier are quite similar across samples, ranging from 0.26 to 0.31, and are very precisely estimated, with standard errors ranging from 0.04 to 0.05. As discussed above, however, these OLS estimates are likely to be biased to the extent that fluctuations in government spending are correlated with other shocks to GDP growth that are reflected in the error term. The 2SLS estimates in Panel B, which are designed to correct for such biases, are somewhat larger than the OLS estimates, ranging from 0.38 to 0.42. They are also fairly precisely estimated, with standard errors between 0.20 and 0.25.<sup>16,17,18</sup> While the estimated multipliers are significantly greater than zero in the IDA and highdisbursement samples, in all three specifications I can reject the null hypothesis that the multiplier is equal to one at the 5 percent level. A further noteworthy feature of these benchmark results is that in all cases the 2SLS estimates of the multiplier are larger than the OLS estimates, suggesting that the latter are biased downwards. This may reflect a combination of (a) attenuation bias in the OLS estimates due 16 These estimated standard errors for spending multipliers are respectable when compared with other papers in the literature. For example, Barro and Redlick (2011) use US data over the past century to estimate defense spending multipliers, and obtain standard errors ranging from 0.06 to 0.27 (their Table 2, first row). Similarly, the confidence bands around VAR-based impulse responses reported in Figure 5 of Blanchard and Perotti (2002) imply a standard error for the impact multiplier of 0.35.

17 The predicted disbursements measure is a generated instrument (consisting of actual loan commitments multiplied by estimated average disbursement rates). However, this does not matter for the asymptotic distribution of the 2SLS estimator as long as actual loan approvals in year t are not correlated with macroeconomic shocks in year t+1 and higher, as per my core identifying assumption. See Wooldridge (2002) Chapter 6.1.2. 18 One notable assumption underlying these estimates and standard errors is that cross-sectional dependence in the error term is adequately captured by year fixed effects. This embodies the simple but unappealing assumption that common shocks have the same effect on all countries, and can be swept out using year dummies, as I do in the default specification. As a robustness check, I relax this assumption in two ways: 1) I implement the estimator based on the cross-sectional averages of moment conditions which is asymptotically valid as under very general cross-sectional dependence, as proposed by Driscoll and Kraay (1998), and 2) I implement the correlated common effects estimator of Pesaran (2006) and extended to the 2SLS setting by Harding and Lamarche (2011), which is asymptotically valid as under the assumption that the cross-sectional dependence can be captured by a very general unobserved factor structure. The first option delivers slightly smaller estimates of the multiplier ranging from 0.22 to 0.29, with standard errors ranging from 0.17 to 0.29, while the second option delivers slightly larger multipliers around 0.63 with estimated standard errors ranging from 0.18 to 0.23.

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