Let’s Call their Bluff: The Politics of Econometric Methodology

2.1 Do we buy immigrants?

Are OECD governments so keen to attract immigrants from poor countries that they bribe their governments to send more of them? Eyeballing Figure 1 might suggests so, as we observe a positive correlation between the number of migrants entering OECD countries and the Official Development Assistance (ODA) disbursed by the host countries in this scatter diagram. Azam and Berlinschi (2010) have tackled this empirical puzzle and shown that this impression is undoubtedly misleading. Table 1 displays their most important findings. Column 1 shows the findings of a regression analysis that does not control for the endogeneity of foreign aid disbursements in response to possible surges in immigration flows from lower- and lower middle-income countries. It shows that adding control variables helps to mitigate the misleading impression given by Figure 1’s scatter diagram. Adding the (lagged) unemployment rate and the (lagged) share of social expenditures in GDP reduces the upward bias shown by the chart to insignificance. However, it leaves unexplained why rich countries are giving so much aid money to migrants’ source countries.

Figure 1:

The positive correlation between foreign aid and immigration.

Source: Azam & Berlinschi, 2010.

2.2 Revealing donors’ hidden agenda

Controlling for endogeneity solves this problem by showing that OECD countries give aid money because it helps to reduce immigration from low and lower middle income countries, among other things. This is shown at column 2 by the fact that (i) the negative impact of foreign aid disbursements has a highly significant impact on the flow of immigrants facing the donors, and (ii) the estimated endogeneity bias is also highly significant according to the Nakamura and Nakamura (1981) version of the Hausman (1978) test (more on this below). This is performed by introducing in the equation beside the endogenous regressor, here ODA, the residuals of the first-stage equation explaining the latter presented at column 3. The latter includes all the same controls as the two previous equations and public expenditures on order and security as the instrumental variable. Hence, right-wing governments, as revealed by their levels of expenditures on law and order, disburse more foreign aid to control immigration from poor countries than the others.

It is thus clear that foreign aid is effective at something after all, but donors are not too proud to say what it is good for. It is effective for controlling immigration and it is actually used for that. I now have the strong suspicion that the (French) socialists prefer keeping fiscal resources for their own public expenditures and they raise the minimum wage and payroll and profit taxes, and hence unemployment, maybe to deter immigration. However, we did not think about performing such a test in 2009, when we researched this paper with Ruxanda Berlinschi. This is a pity as it would have been so easy to do then. Nevertheless this would explain the massive increases in payroll and corporate taxes implemented by Prime Minister Jean-Marc Ayraud from 2012 on under the aegis of President François Hollande, resulting in a predictable three percentage point increase in unemployment, at the time when the Libyan crisis was in full gear.

3.1 The setting

The econometrician wants to test whether a policy tool p is effective for reducing the quantity q of an outcome that the policy-maker deems “bad”. These two variables are linked by a linear relation:

where x, e, and ε are exogenous variables. The Greek parameters, including {α, β, γ, δ}, are positive unless specified otherwise, while ε is a random disturbance such that E(ε)=0.

We make the following key assumptions:

Assumption 1: Asymmetric information:

1. The policy maker observes x, e and p ex ante and q ex post.

2. The econometrician observes q, x and p ex post.

Assumption 2: Efficient Information Processing:

The policy maker uses her information efficiently so that E(eε) = 0.

Assumption 3: Quadratic Loss Function:

The policy maker seeks to minimize the following loss function:

The parameter θ increases the policy maker’s aversion to q and it is her private information, i.e. unobserved by the econometrician.

The policy decision is derived from this model by solving (2) to yield the first-order condition (FOC):

Figure 2 depicts the outcome of this optimization exercise performed by the policy maker. The downward-sloping line represents the causal equation taken as the constraint by the policy maker according to (2), while the upward-sloping line represents the first-order condition (3). Her choice is found at the intersection of the two lines. It is then obvious from the diagram that the chosen value of the policy variable p* is a function first of the set of parameters {α, β, γ, δ, π} but also and more importantly of the pair of unobservable variables {θ, e}.

Figure 2:

The policy maker’s optimal choice.

The presence of this pair of unobservable variables lies at the heart of the identification problem faced by the econometrician. The key point is that they impact the econometrician’s problem in two opposite directions. Changes in θ across observations are playing on the econometrician’s side, as they just shift the upward-sloping line, to the right in case of an increase in θ, tracing out the causal relations under scrutiny. However, changes in e across observations are playing against the econometrician, as an increase in e would shift the downward-sloping line upwards, tracing out the upward-sloping first-order condition line. This would thus contaminate the estimation of the causal relation. Imagine now that the two unobservable variables θ and e turned out to be positively correlated in the econometrician’s sample, although they might in fact be independent in theory and would be so in a very large sample. Then, the two lines would tend on average to move in the same direction and an upward-sloping regression line might result from the estimation process if the variance of e was larger than that of θ. In such a case, regression analysis would tell you more about the fortuitous correlation that exists in your sample between the two unobserved variables that about the true slope of the causal relation that you are looking for.

3.2 Preference proxies

Imagine now that, for whatever reason, the econometrician is tempted to guess that the preference proxy z such that:

might have some empirical relevance. This is a testable piece of guesswork using a two-stage approach to overcome the problem that θ is not directly observable. The idea is to capture some of the beneficial identifying property of the changes in the policy maker’s preferences over the sample thanks to the preference proxy z using a first-stage equation that explains the policy decisions actually made. Then, most of that equation’s unobservable disturbance will reveal the changes in e rather than in θ. Hence, that remaining unobservable disturbance will encapsulate some information about the policy-maker’s information about e that can in fact be estimated via the first-stage equation. This is done by estimating a reduced-form equation for the chosen policy tool, which thus reveals the hidden information used by the policy maker as the residuals. This works as follows:

Substituting the preference proxy for θ, the FOC becomes:

We can substitute for E(q) = α + βx – γp + δe and rearrange the terms to get the reduced-form policy equation as:

where r ^ are the residuals of the regression of p on x and z. Notice that (i) r ^ is correlated with e, but (ii) it contains some noise produced by ς, whose variance is lower the better z does proxy for θ. Then, r ^ can be inserted in the second-stage equation as a control function, i.e. a noisy proxy for e.

Then, it is straightforward to show that the second stage regression equation yields under the control-function approach exactly the same estimates as 2SLS would in linear models:

where p − r ^ is the fitted value of p from the first-stage equation, what 2SLS uses as the regressor, and r ^ can be dropped from this latter regression equation, as it is orthogonal to all the included regressors, by construction. This proves the exact equivalence between the two methods of controlling for endogeneity in linear models. However, the control function approach yields the natural test for endogeneity that ϕ ^ is significantly different from zero (see Nakamura & Nakamura, 1981), and it can be used in many other contexts where 2SLS are inappropriate. In particular, it works when the assumed distribution is a negative binomial, the most popular assumption when analyzing count data. Notice that r ^ is a noisy proxy for e, as explained above. This entails that there is a measurement issue that will bias ϕ ^ towards zero, i.e. against the endogeneity assumption. Hence, this attenuation bias will play against the econometrician and it will often reject the endogeneity diagnosis while it should be validated. In contrast, when the endogeneity test concludes significantly by rejecting exogeneity, then the econometrician’s confidence in the endogeneity diagnosis is obviously strengthened by the bias.

4.1 Basic findings

We find here that the residuals of the first-stage equation are significant in the second-stage one. This reveals that there is a piece of information that is affecting simultaneously the killing performed by the two sides. This measure of the impact on the number of people killed by the local forces is just estimated as that part of the police violence that cannot be explained by the control variables and the instruments introduced in the first-stage equation, as explained above. On the one hand, this might simply capture some orders given by the hierarchy to the policemen or militiamen, when relevant, unobserved by the econometrician. On the other hand, that information should have leaked to the rebels who got organized very quickly to retaliate. This tends to strain credulity given the rebels’ known level of organization (Roy, 2011; Shah, 2010). More realistically, this might simply capture the fact that the rebels have observed the numbers of tribal people killed in the districts and have apportioned their retaliation to those numbers. It thus seems that the rebels know how much violence has been inflicted on the tribal people when they attack the policemen, what would not make sense if they really were the aggressors as claimed by the Federal and State governments. The significance of the positive impacts on the rebellion’s activity of the presence of iron or coal resources hints at the part played by mining interests in triggering the uprising.

4.2 Political diagnosis

Then, we find that the observed number of people killed by the local forces has a highly significant positive impact on the killing perpetrated by the rebels, an estimate that is “purged” of the endogenous reverse causality by the control for endogeneity. Hence, police killing of civilians is a major cause of the Naxalite uprising. This disproves the federal government’s claim that the Adivasis are animated by the Maoist ideology with a view to topple the Indian democracy. The positive impact of the killing performed by the local forces deserves a bit more emphasis, by comparison with the theoretical framework discussed in the previous section. There, a negative sign was specified for the impact of the policy variable p to capture the idea that the outcome variable q was deemed bad by the policy maker. Azam and Bhatia (2017) introduce the concept of “provocation” to capture the idea that the rebels’ violence does not seem to be regarded as a “bad” in that sense by the policy maker. Moreover, a closer look at the first-stage regression allows us to look deeper into the fundamental motivations for these attacks, via the preference proxies that are used as instrumental variables.

We observe first that the presence of a large Adivasis population and a large forest cover rate, where the former live most often, come up with a significant negative sign. Hence, the police seem to stay away from such poor areas. However, most of the killing of civilians performed by the state police occurs in areas where a large share of the people are tribal ones and there are significant deposits of iron ore and a significant forest cover. The latter mainly exists where bauxite deposits retain the mountains’ moisture in these semi-arid areas (Padel & Das, 2010). Hence, it is the interaction between the presence of mining potential riches and the largely tribal population of the area that entails significant violence against civilians by the police, although the presence of coal resources seems to attract police violence independently of the importance of the tribal population in the district.