Part 1 - AL-Tax

International Taxation Handbookcountry 1 also affects country 2. The resultant bias in OLS estimates of ρ can beshown (with a little further simplification) to equal:ρˆρ12 12ρ21Var( ε1)( 1 ρρ21 12)βρ Var ( ε ) Varε ( ) .22 2 212 1(3.11)which, assuming ρ 12 ρ 21 1, implies that OLS estimates of diffusion from countryj to i will have bias of the same sign as the diffusion from i to j (N.B. all terms exceptρ 21 in equation (3.11) are necessarily positive). This means that, if ‘feedback’ fromj to i and i to j reinforce (both positive as in Figure 3.1, or both negative), then OLSestimates of interdependence will be inflated. If feedback is dampening (e.g.opposite slopes in Figure 3.1), which is probably less likely in most substantivecontexts (but possible in Persson and Tabellini’s model, as noted), OLS estimateswill be attenuated. We can also show, moreover, that this bias in the estimatedstrength of interdependence, ρ, induces an attenuation bias in the estimate of β,the effect of X (i.e. domestic and/or exogenous-external factors):ˆ β1Var( ε1)ρ21ββ 1 1 2βρ Var( ε ) Var ( ε ) .2 2 212 1 2(3.12)Thus, typically, OLS estimates of C&IPE models will tend to overestimate theimportance of interdependence – e.g. tax competition – and underestimate that ofdomestic, exogenous-external, and/or domestic-context-conditional exogenousexternalmechanisms (i.e. OE-CPE arguments).On the other hand, OLS estimates of OE-CPE models that ignore interdependence,i.e. that omit spatial lags, will suffer the converse omitted-variable biases,which we have (more easily, using the usual omitted-variable-bias formula) shownin the simplest case to equal:ρρβˆβ 1 β11 ρρ12 21 112 21ˆ ρρβ 12 21 2ββ 2 2 .1 ρρ12 21(3.13)(3.14)Again, if feedback is reinforcing (same-signed ρ 12 , ρ 21 ) these are inflation biasesand if feedback is dampening these are attenuation biases. Thus, in the positivefeedbackcase that we suspect is more common, OLS estimates of OE-CPE modelsthat ignore interdependence will tend to overestimate the power of domestic,exogenous-external, and/or domestic-context-conditional exogenous-external56