Controlling for Import Price Effects in Civil War Regressions

1 Introduction

In order to understand how economic factors affect civil conflict, several papers estimate the effects of commodity export prices (Aguirre, 2016; Andersen, Nordvik & Tesei, 2017; Bazzi & Blattman, 2014; Bellemare, 2015; Brückner & Ciccone, 2010; Berman et al., 2017; Dube & Vargas, 2013; Maystadt et al., 2014; Sanchez de la Sierra, 2015).^[1] The fact that commodity prices are economically important for developing economies and the prices are highly volatile and mainly determined by global factors facilities economistic identification. Most of these papers, however, study the effects of commodity export prices, and the general equilibrium theory of international trade (Agénor & Montiel, 2008; Dixit & Norman, 1980; Feenstra, 2015; Obstfeld & Rogoff, 1996) usually predicts that – at least under textbook conditions with secure property rights – export and import prices have symmetric effects. Under balanced trade, for example, export price increases matched by proportional import price increases should not affect the trade balance or output. Intuitively, paying more for imports decreases the residual budget that the population can spend on domestic goods as much as a corresponding decline in export earnings.^[2] In order to identify the empirical effects of export prices on conflict, therefore, it is, potentially, important to either control for import prices or replace the export price measure with the terms of trade, that is, the ratio between export prices and import prices. Due to the high correlation that is often observed between commodity export and import prices (the bivariate correlation between the growth rates of the commodity export and import price indices we study below is 0.57), the failure to control for import prices in the regressions can, potentially, bias the export-price estimate.

In Section 2, we calculate the theoretical omitted variables bias that results from regressing conflict on export prices without controlling for import prices. In Section 3, we estimate the empirical sign and magnitude of the bias in a country panel by following a three-step procedure:

1. Estimate the conflict regression with just the export price measure.

2. Add the import price measure and re-estimate the equation.

3. Observe whether the import price measure is statistically significant and/or significantly changes the export price estimate. In both cases, the import price measure arguably belongs in the regression.

In order to select a specific baseline-regression model in the theoretical section and to get a dataset with consistently defined export and import price measures in the empirical section, we draw on Janus and Riera-Crichton (2015), henceforth JRC. JRC estimate the effects of terms of trade shocks on the risk of onset of civil wars. Specifically, the authors regress an onset indicator on the annual growth rate of a 3-year-moving-average commodity terms of trade index – that is, on the growth rate of the 3-year-moving-average ratio of commodity export-to-import prices.

Section 2 shows that the theoretical proportional bias equals the ratio of the import to the export price effect on conflict times the coefficient from regressing import prices on export prices and the other controls in the conflict regression. In Section 3, we start by showing that the proportional bias in the JRC sample would have been relatively small. The reason is that, while import-price shocks have large conflict effects – the effects are larger than the export-price estimates – the conditional correlation between export and import price changes is relatively small: after we control for country and year effects as well as country-specific time trends, the regression of import-price innovations on export-price innovations only produces a coefficient of 0.10.

In order to examine whether alternative samples can increase the bias, we also relate commodity export and import prices in a larger dataset. The dataset is a balanced country panel that tracks 161 countries from 1970 to 2009. The results show that, after controlling for country and year effects as well as country-specific time trends, regressing the change in export prices on the change in import prices generates an import-price coefficient equal to 0.37 (t = 1.41). In order to search for countries whose omission from conflict regressions should be relatively likely to increase the omitted-variables bias, we also design an algorithm. In each iteration, the algorithm systematically drops the country that decreased the t-statistic the most in the previous iteration. The results show that fossil fuel exporters play a critical role. By the tenth iteration, when we have removed the nine countries that contribute the most to decreasing the t-statistic on import prices, the import-price coefficient becomes 0.62 with a t-statistic of 2.3. All of the eliminated countries are major oil producers.

Finally, we show that when we estimate the JRC regressions without the import-price controls and we further omit a collection of fossil fuel producers, the omitted variables bias greatly increases. The addition of the import-price control close to doubles the export-price coefficient. Thus, the export-prices-alone regression appears to have a large, but upward omitted-variable bias, that is, it underestimates the effects of export price declines on civil war onsets.

In the remainder of the paper, Section 3 derives the theoretical omitted-variables bias. Section 4 assesses the empirical bias in country panels. Section 4 concludes the paper.

2 The theoretical bias

Consider equation (1) in JRC:

where d_jt is a dummy for civil war onset in country j in year t and ΔCTOT_j(t–1) is the lagged growth rate of the 3-year moving average commodity terms of trade (CTOT) index defined below. ΔPj(t−1)X and ΔPj(t−1)M are the lagged growth rates of the 3-year moving average export and import price indices in the CTOT index while μ_j, z_t and ρ_jt are country and year fixed effects and a country-specific time-trend. Finally, ɛ_jt is the error term.

The CTOT index comes from Ricci, Milesi-Ferretti, and Lee (2008) and Spatafora and Tytell (2009). It is defined as

where PjtX=Πi⁡(Pit/MUVt)Xji is the commodity export price index for country i in year t and PjtM=Πi⁡(Pit/MUVt)Mji is the commodity import price index for country j in year t. P_jt is a common price index for each of six commodity categories (food, fuels, agricultural raw materials, metals, gold, and beverages). Xji represents the average share of exports of commodity i deflated by GDP from 1970 to 2006. Mji is the average share of imports. Due to the fact that the trade weights in the CTOT index are GDP shares, as long as the weights are approximately accurate for a particular year, a CTOT increase of X% should in principle increase GDP by X% on impact.

Taking the log-difference shows that the growth rate of the CTOT index approximately equals the growth rate of the export price index minus the growth rate of the import price index,

The growth rate of the 3-year moving average CTOT index, similarly, is^[3]

which gives us the second equality in equation (1).

Had we, alternatively, followed the existing empirical conflict literature, we would have omitted the growth rate of import prices in equation (1) and estimated the following equation:

which replaces the terms of trade growth rate with the export price growth rate. The fact that (5) does not control for the growth in import prices implies that the growth in import prices becomes a part of the error term, that is,

where η_jt is the residual error term. Assume now that the import and export price growth rates are potentially conditionally correlated, such that

where ν_jt is another error term and, potentially, θ≠0. Substituting (6)–(7) into (5) shows that

As long as the growth in import prices is the only endogeneity source, E(ν_j(t–1)η_jt) = 0 and

unless β^Mθ = 0. In other words, the coefficient on the export price shock is biased unless either (a) changes in import prices do not affect civil war onsets (β^M = 0) or (b) the export and import price shocks are conditionally uncorrelated (θ = 0). The proportional bias is

The proportional bias thus depends on

1. Whether export and import prices have symmetric conflict effects, i.e. β^M/|β^X| = 1.

2. The conditional correlation between export and import prices indicated by θ.

3 Results

Table 1 reports selected summary statistics from JRC. We refer to their paper for the detailed variable definitions and data sources. Given that the authors only identify a negative effect of terms of trade declines on civil war onsets in intermediately ethnically diverse countries (defined as countries with a Herfindahl-Hirschman ethnic diversity or fractionalization index in the second to third quartiles), we, too, restrict attention to that sample.

In Table 2, Column (1) displays the estimates for equation (5) above. In Column (2), we control for the growth in import prices. The results show that both export price declines and import prices increases are associated with a higher civil war risk. In fact, the import price estimate is twice as large as the export price estimate. Nonetheless, we cannot reject the null that the shocks effects are symmetric (H₀: β^M = −β^X).

Despite the significant import price effect, the coefficient on the growth in export prices did not change drastically. Column (3) shows why this is the case: when we estimate equation (7), the conditional correlation between the export and import price shocks, θ in equation (7), is relatively small. The proportional bias is therefore just

which is about a 20% upward bias.

Although the bias is relatively small in this case, its sign and magnitude generally depends on the estimating sample. In order to explore this idea, we start by noting that (i) we cannot reject that (β^M/|β^X|) = 1, which is consistent with standard international trade theory; and (ii) as long as this coefficient ratio is not zero, it only determines the magnitude and not the existence of the omitted-variables bias. In the following, therefore, we consider how sample changes affect the conditional correlation between export and import prices θ.

Table 3 present the relationship between import and export price changes in a global commodity price dataset. The commodity export and import price data is the same as in JRC, but the sample is about twice as large. It covers 161 countries from 1970 to 2009. The sample is only limited by the availability of data. In order to study the relationship between import and export price changes, we use an algorithm that regresses the change in the import price index on the change in the export price index. The regressions control for country and year effects as well as country-specific time trends. Each iteration excludes the country that reduced the t-statistic the most in the previous regression. The idea is that a smaller t-statistic in the import-export price regression indicates a lower probability of omitted-variables bias in the corresponding regression linking the dependent variable (in this paper, conflict) to export prices. The algorithm identifies the countries that generate the largest marginal bias-reduction and which should therefore, ideally, be included in regression sample in order to limit the bias. As regressions omit more of these countries, they become increasingly exposed to omitted-variables bias.

The results show that, as we gradually remove the most bias-reducing economies from the sample, the conditional correlation between import and export price changes increases from 0.37 to 0.62 after 10 iterations. Inspecting the list of bias-reducing countries shows that, overwhelmingly, they tend to be fossil fuel, and particularly oil exporters. The reason is, potentially, that the oil-exporting economies mainly export oil and import other commodities. Erten and Ocampo (2013) find that non-oil commodity prices are demand-determined by global output, while the causality for oil price has historically run in the opposite direction. The bivariate price correlations across commodity groups are also relatively smaller (less positive) when one of the two commodities is oil. Thus, oil exporters should experience relatively less correlated export and import price shocks compared to countries where oil represents a smaller trade share.

Finally, note that the conditional correlation between export and import prices is 0.37 even before we exclude the first country. This observation suggests that even regressions containing a significant fraction of oil-exporting economies could lead to omitted-variables bias unless they somehow control for import-price effects. The correlation in the JRC sample in Table 2, Column (3) is only relatively small (0.10) because the intermediately ethnically diverse country sample in these regressions contain quite a lot a lot of fuel exporters.

In Table 2, Column (4), we highlight the special properties of oil exporters in the conflict dataset. In order to do so, we retain the Column (3) sample and interact the import-price term with an indicator for fossil fuel exporters from Janus and Riera-Crichton (2018). The indicator equals one when the economy’s average export share of fossil fuels in GDP from 1970 to 2006 exceeded both its average import share and 2% of GDP. The fossil fuel category includes coke, coal and briquettes, petroleum and petroleum products, and natural and manufactured gas, but it mainly singles out a number of oil-dependent countries: Bahrain, Canada, Colombia, Ecuador, Iran, Iraq, Kazakhstan, Malaysia, Mexico, Oman, Russia, Saudi Arabia, Trinidad and Tobago, Turkmenistan, and Venezuela. The results in Column (4) indicate that there is a sharp divergence in the export-import price correlation across the fuel and non-fuel exporters. The sample split quadruples the conditional correlation parameter θ for the non-fuel exporter compared to Column (3). For the fuel-exporters, the parameter estimate is roughly zero.

In Table 4, Columns (1)–(3) show that, when we reproduce Table 1, columns (1)–(3) without the fuel exporters,

1. The growth rate of commodity export prices alone is statistically insignificant.

2. Adding the import price shock restores the significance of the export price shock.

3. The export-prices-alone estimate is β^Mθ/−β^X ≈ (−0.508−(−0.928))/0.928 ≈ 45% upward biased.

In Columns (4)–(6), we again reproduce Table 1, Columns (1)–(3). This time, however, instead of omitting all of the 15 fuel exporters, we only drop the eight that appear most likely to generate reverse causality in the conflict regression linking commodity prices to conflict. Many researchers might omit these countries in their robustness checks. The omitted countries are either large oil producers or located in the Middle East and, potentially, affected by the region’s geopolitical dynamic. Thus, we omit Bahrain, Iran, Iraq, Mexico, Oman, Russia, Saudi Arabia, and Venezuela. The upward bias in the export-price coefficient (about 50%) remains similar to before. Additionally, the import-price effect remains significant; adding the import price control makes the export price effect significant; and we cannot reject that import and export prices have symmetric conflict effects.

In Columns (7)–(9) we only omit the Middle Eastern producers (Bahrain, Iran, Iraq, Oman, and Saudi Arabia). The qualitative results are similar and we get a 35% upward bias. In Columns (9)–(12), we only omit Bahrain, Oman, and Saudi Arabia. The bias decreases to 22%. Going from Columns (3) to (6), (9), and (12) shows that the conditional correlation coefficient θ smoothly decreases as we gradually add the fuel exporters back into the sample.

The fact that excluding the fuel exporters increases the export-import price correlation the most – although the correlation also exists in the initial sample – suggests that studies that relate export prices to conflict, but which exclude influential fuel exporters, should be more likely to suffer omitted-variables bias. In practice, there could be several reasons to omit, particularly, oil producers from conflict regressions: data limitations, the desire to limit the risk of reverse causality from conflict to oil prices, wishing to focus on other parts of the world, and wishing to study non-oil commodity prices. Additionally, based on the resource-curse literature (Auty, 2002; Basedau & Lay, 2009; Cotet & Tsui, 2010; Elbadawi & Soto, 2015; Lei & Michaels, 2014; Lujala, 2010; Ross 2004; Ross 2006; Ross 2012), one might expect oil producers to be special and respond differently to commodity-price shocks.

Although excluding the oil producers without controlling for import-price effects increases the omitted-variables bias, at least in our dataset, it appears to be an upward bias. Thus, the export-prices-alone regressions underestimate the onset effect of export price declines. The bias should make it harder to reject the zero-effect null hypothesis.

4 Conclusions

In this note, we have argued that in regressions linking civil war outcomes to export prices, it is potentially important to control for import prices. Economic theory suggests that, at least in textbook economies with well-defined property rights, it is the change in export prices relative to import prices rather than the change in export prices alone that affects national income. In that case, the change in the export/import price ratio (that is, terms of trade changes) should be a better empirical proxy for income shocks than export prices alone. Moreover, even if researchers wish to estimate the effects of export prices alone, the fact that there can be a high correlation between export and import prices suggests that the omitted import-price control could bias the estimates.