Table 4: OLS vs. IV with Cross-Sectional Data

||(1)<br>1990-|(2)<br>2009|(3)<br>1992-|(4)<br>2011|(5)<br>1994|(6)<br>-2013|(7)<br>1996-|(8)<br>2015|(9)<br>1998|(10)<br>-2017|
|---|---|---|---|---|---|---|---|---|---|---|
||OLS|IV|OLS|IV|OLS|IV|OLS|IV|OLS|IV|
|FDI|0.150*|0.597**|0.187**|0.652**|0.154**|0.821|0.161**|0.883|0.107|0.934|
||(0.088)|(0.296)|(0.080)|(0.322)|(0.070)|(0.501)|(0.072)|(0.574)|(0.066)|(0.681)|
|_GDPt−_1|-1.175***|-1.108***|-1.168***|-1.093***|-1.295***|-1.167***|-1.286***|-1.182**|-1.349***|-1.389***|
||(0.262)|(0.309)|(0.248)|(0.311)|(0.251)|(0.442)|(0.283)|(0.516)|(0.282)|(0.516)|
|Pr. Cr.|2.813**|2.275**|2.895**|2.511**|2.627**|1.958|2.227*|2.397*|2.317*|3.043*|
||(1.071)|(1.040)|(1.168)|(1.074)|(1.173)|(1.378)|(1.185)|(1.430)|(1.179)|(1.678)|
|School|1.436**|1.297*|1.760***|1.518**|2.272***|2.036**|2.426***|2.097**|2.690***|2.726***|
||(0.585)|(0.697)|(0.560)|(0.719)|(0.563)|(0.917)|(0.655)|(0.961)|(0.681)|(0.966)|
|Inf.|0.041|-0.149|0.148|-0.013|0.292|-0.144|0.166|0.049|0.077|0.005|
||(0.170)|(0.188)|(0.185)|(0.216)|(0.261)|(0.430)|(0.341)|(0.474)|(0.343)|(0.530)|
|Trade|-1.181**|-2.611***|-1.374**|-2.849***|-1.289**|-3.543**|-1.222**|-3.861**|-1.009*|-4.536*|
||(0.567)|(0.916)|(0.537)|(0.985)|(0.501)|(1.568)|(0.536)|(1.892)|(0.570)|(2.598)|
|Govt. Cons.|0.279|0.332|-0.218|-0.063|-0.363|0.001|-0.582|-0.318|-0.628|-0.367|
||(0.549)|(0.671)|(0.534)|(0.668)|(0.519)|(0.778)|(0.553)|(0.882)|(0.535)|(1.046)|
|Instit.|0.700***|0.587**|0.628***|0.536**|0.603***|0.400|0.489***|0.336|0.407**|0.276|
||(0.194)|(0.244)|(0.174)|(0.231)|(0.160)|(0.323)|(0.155)|(0.350)|(0.164)|(0.400)|
|SSA|-1.502***|-1.449***|-1.185***|-1.276***|-0.842**|-1.264*|-0.856*|-1.497*|-0.926*|-1.766*|
||(0.433)|(0.491)|(0.412)|(0.495)|(0.379)|(0.675)|(0.444)|(0.824)|(0.510)|(1.022)|
|B. M. P.|13.703|14.213*|13.949*|14.359*|15.231**|14.428|12.286|10.707|13.048|15.184|
||(9.531)|(8.057)|(7.397)|(7.974)|(7.152)|(11.111)|(9.057)|(13.726)|(10.120)|(15.000)|
|Constant|-1.560|3.715|0.022|4.970|-0.463|8.549|2.790|12.856|2.421|13.477|
||(7.027)|(7.055)|(5.518)|(7.233)|(5.213)|(11.153)|(5.851)|(13.005)|(6.280)|(14.875)|
|N. Obs|72|72|72|72|72|72|72|72|72|72|
|_R_<sup>2</sup>|0.505|0.317|0.526|0.295|0.531|-0.122|0.489|-0.502|0.502|-0.982|
|CD F-test||7.286||6.558||4.554||3.909||2.805|
|Underid-test||4.934||4.810||3.581||2.989||2.358|
|P. val.||0.026||0.029||0.058||0.084||0.125|

**Notes:** The dependent variable is the average annual GDP per capita growth rate. The columns alternate between OLS and IV regressions results. The instrument for FDI is constructed from bilateral flows from all countries to emerging or developing countries (see Table A.2). The 20-year time span is indicated in each column heading. All variables are as in Table A.3. The bottom rows show the Cragg-Donald F-statistic for the first stage results and the underidentification test with its associated p-value. Robust standard errors are in parentheses. Significance levels are denoted as: *** p _<_ 0.01, ** p _<_ 0.05, * p _<_ 0.1.

case, the results of overidentified TSLS estimates are comparable with those of LIML estimates (see Tables C.3 and C.4 in the Appendix).

Next, we follow Andrews et al. (2019) and build Anderson-Rubin confidence sets that are robust to weak identification and are efficient when the model is just-identified. We find that our instrument generates weak-instrument-robust confidence intervals which exclude zero for all 20-year periods (see Figure 7).<sup>13</sup> Finally, we explore how the presence of a weak instrument can amplify the consequence of a small violation of the exclusion restriction. This is important because exclusion restrictions are never airtight and we want to make sure that a small violation of the restriction does not lead us completely astray. To fix ideas, consider the following model in which we want to assess the effect of _FDI_ on growth ( _GR_ ) and we want to use _Z_ as an instrument for _FDI_ : In our setting, we need to assume that the instrument has no direct effect on growth: _γ_ = 0. The strength of the instrument is instead given by _π_ 1.

Now, let us consider a small violation of the exclusion restriction, so that _γ_ = 0. It is possible

> 13We also confirm the weak-instrument robust confidence intervals exclude zero for other 20-year periods not shown in the main results (see Appendix Figure C.2).

21