to show that: Hence, the bias of the IV is given by _γ/π_ 1 and the bias increases as _π_ 1 becomes smaller. Alternatively, the consequences of any small violation of the exclusion restriction are amplified by the presence of a weak instrument.

We can use Equation (9) for a back-of-the-envelope calculation of the possible bias linked to the joint presence of a weak instrument and the violation of the exclusion restriction. To do so, we need to find values for _π_ 1 and _γ_ . For _π_ 1, we can use the first stage estimates of Table C.1 and set _π_ 1 = 1 _._ 2. Choosing a value for _γ_ is more difficult.

We proceed as follows. We use Jaimovich and Panizza’s (2007) estimate of the effect of a real external shock on GDP growth which is 1.7.<sup>14</sup> We then set _γ_ = 1 _._ 7 _×_<sup>_<u>σSHOCK</u>_</sup> _σIV_ . We are thus making the extreme assumption that _all_ the variation of our instrument is driven by the real shock.<sup>15</sup> This yields _πγ_ 1<sup>=</sup> 1<sup><u>1</u></sup> _._<sup>_<u>.</u>_</sup> 2<sup><u>1</u>= 0</sup><sup>_._9.Ifweweretosubtractthisback-of-the-envelopeestimateof</sup> the bias from the IV point estimates of columns (2) and (4) of Table 4, we would find that FDI has a _negative_ effect on growth (the point estimates would be between -0.25 and -0.3).

However, we obtained this correction by assuming that the exclusion restriction is completely violated. If we relax this extreme assumption and assume that half of the real external shock affects GDP growth through our instrument, we get that _πγ_ 1<sup>=</sup><sup><u>1</u></sup> 1<sup>_<u>.</u>_</sup> _._<sup><u>1</u></sup> 2<sup>=0</sup><sup>_._45whichisexactlythe</sup> difference between the OLS estimates of columns (1) and (3) of Table 4 and the IV estimates of columns (2) and (4). We thus think that the OLS coefficients provide a reasonable estimate of the causal effect of FDI on growth.

# **4.3 Panel IV Regressions**

In our last exercise, we use our instrument to estimate a panel data model that uses overlapping 10-year growth spells. We estimate two types of models: one that only includes year fixed effects (Columns 1 and 2 of Table 5) and one that includes both year and country fixed effects (columns 3 and 4). As before, we estimate the model for the same sample using both OLS (columns 1 and 3) and TSLS (columns 2 and 4).

When we only include time fixed effects, we find that FDI inflows are associated with higher growth and, as in the cross-sectional estimates, the effect is about three times larger in the IV estimations. We also find high values for both the Cragg-Donald Wald F-Statistics and the Kleibergen-Paap rk LM statistics. We are thus confident that, for the model of column (3), weak instruments or underidentification are not an issue. The first stage regression (column 1, Table C.5) shows that there is a significant correlation between the IV and FDI inflows, and the IV is

> 14Jaimovich and Panizza (2007) build the real external shock by using the weighted average of GDP growth in country _i_ ’s export partners. Formally: _SHOCKit_ = _EXPGDPii_ � _j_<sup>_φij,t−_1</sup><sup>_GRj,t_.Wherewhere</sup><sup>_GRj,t_measuresreal</sup> GDP growth in country _j_ in period _t_ , _φij,t−_ 1 is the fraction of exports from country _i_ going to country _j_ , and

> _EXPi_<sup>country</sup><sup>_i_’saverageexportsexpressedasashareofGDP.JaimovichandPanizza(2007)findthat</sup> _GDPi_<sup>measures</sup> in emerging and developing countries _GRi,t_ = 1 _._ 7 _× SHOCKi,t_ .

> 15We adjust by the relative standard deviations so that a one standard deviation shock to the instrument

> ( _σIV_ = 1 _._ 1) is equivalent to one standard deviation shock of the real shock ( _σSHOCK_ = 0 _._ 7).

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