Geoffrey Barrows for The 2004 Moffatt Prize in Economics

I. Introduction

This paper seeks to refine a specific contribution to the empirical investigation of the impact of trade on standards of living. To see the connection between trade and standards of living, researchers often estimate cross-country regressions of income per person on the ratio of exports or imports to GDP. Many economists have found modest positive correlations between the two variables and have usually interpreted the correlation as causation.[1] The problem with concluding causation from correlation is that the correlation may contain a simultaneity bias. If overlooked, the bias would lead OLS estimations to overstate the effect of trade on income.

Frankel and Romer (1999) attempt to correct for the simultaneity bias by instrumenting for trade of a particular country with its geographic characteristics. As these geographic characteristics are truly exogenous, the Frankel-Romer IV regression seems plausible; however, if some other variable that affects income were also determined by geographic characteristics, then omitting such a variable would cause the Frankel-Romer IV regression to overstate the effect of trade on income by omitted variable bias. After testing a cross-sectional data set of 150 countries, Frankel and Romer were unable to conclude that OLS estimates overstate the effect of trade on income, though they argue simultaneity bias would cause it to do so. Rather, Frankel and Romer found that OLS understates the effect of trade on income. If it could be shown that Frankel and Romer omit a relevant variable from their IV regression, then omitted variable bias could explain the incompatibility of the Frankel-Romer hypothesis with the Frankel-Romer findings.

It is the purpose of this paper to: first, evaluate the validity of the Frankel-Romer instrument; second, test for omitted variable bias and suggest improvements on the instrument; and third, test the efficacy of said improvements in proving the existence of a simultaneity bias in the OLS estimations of trade's effect on income.

II. The Frankel-Romer Instrument

While there are many channels through which trade may affect income- notably specialization according to comparative advantage, exploitation of increasing returns from larger markets, exchange of ideas through communication and travel, and spread of technology through investment and exposure to new goods, we may suspect the causality to flow the opposite way as well. The channels for the reverse causality have yet to be adequately identified, but as long as we are sympathetic to the idea that countries whose incomes are high for reasons other than trade may trade more, then we have grounds to investigate the simultaneity bias. This intuition led Frankel and Romer to propose the existence of simultaneity bias in the OLS estimations of trade's effect on income and test for it using an instrumental variable for trade.

Frankel and Romer (1999) maintain that countries' geographic characteristics could serve as a plausible instrument for the trade share. According to Frankel and Romer, knowing how far a country is from other countries provides considerable information about the amount that it trades. Additionally, Frankel and Romer assert that countries' geographic characteristics do not have important effects on its income except through their impact on trade. These two insights amount to the necessary assumptions for validation of the Frankel-Romer instrument:

1. E(geographic characteristics, trade share)≠0

2. E(geographic characteristics, μ)=0

In constructing the instrument for trade share, Frankel and Romer first estimate a bilateral trade equation between country i and country j, and then aggregate the equation for all countries tested. Frankel and Romer evaluate the following equation for bilateral trade of country i with country j relative to GDP of country i:

(1) Ln(τ_ij/GDP_i) = a₀ + a₁lnD_ij + a₂lnN_i + a₃lnA_i + a₄lnN_j + a₅lnA_j + a₆(L_i + L_j) + a₇B_ij

+ a₈B_ijlnDij + a₉B_ijln_i + a₁₀B_ijlnA_i + a₁₁B_ijlnN_j + a₁₂B_ijlnA_j

+ a₁₃B_ij(L_i + L_j) + e_ij

where τ_ij is the actual trade share between countries i and j, lnD_ij is the log of the distance between countres i and j, lnN_i is the log of the population of country i, lnA_i is the log of the area of country i, L is a dummy for landlocked countries, and e is the error term. Frankel and Romer use bilateral trade data covering 63 countries from the year 1985 to estimate equation (1).[2] The estimated coefficients for (1) are listed in Figure 1 and the standard error for each coefficient is reported in parenthesis bellow.

Figure 1-Contrade

And Geographic Variables

Frankel and Romer found that the overall correlation between the constructed trade share and the actual trade share was 0.62. Figure 1 shows the break down of how each individual geographic variable contributes to the contrade. Figure 1 reports a strong negative correlation between contrade and each of distance, population of country i, area of country i, area of country j, and the dummy variable indicating if country i is landlocked. We can interpret τ_ij/GDP_i, the constructed trade share (hereafter contrade) to be the amount of trade we would expect between countries i and j considering only the geographic variables above. Frankel and Romer use contrade as an instrument for trade in estimating the effect of trade on income. In other words, Frankel and Romer use contrade to pick up the effects geographic characteristics have on income through trade.

But are there any other channels by which geographic characteristics affect income? If we could offer a variable that was likely correlated with income and geographic characteristics that was not trade, then we would have reason to believe that Romer's instrument contains omitted variable bias. It is easy to see econometrically that if the Frankel-Romer instrument contains an omitted variable, then their estimation of the effect of trade on income would be biased upwards. Frankel and Romer attempt to estimate

(2) Y = αT + μ

Because of the endogenous bias in the trade share, Frankel and Romer are concerned that

(3) T = βY + ε

To correct for the endogenous bias, Frankel and Romer introduce the contrade instrument, call it I

(4) T = βY + ψI + ε

Frankel and Romer conclude the quality of the instrument from the necessary assumptions

(5) E(T,I)≠0, E(I, μ)=0

If (2) included an omitted variable V, such that E(V,Y) ≠0, E(V,I)≠0, then the necessary assumption for I to constitute a good instrument would be violated, i.e.,

(6) E(I, μ)= E(I, V+ μ′)≠0

The assumption E(V,I)≠0 yields the following refinement on (2)

(7) Y = αT + δV + μ′, where

(8) μ= δV + μ′

Therefore, since E(V,I)≠0,

(9) μ = δ(φI) + μ′, where φ is the correlation between V and I.

Hence, μ does indeed depend on I thereby falsifying (5). The sign of the omitted variable bias can be derived from an estimation of (2). If we omit variable V from (2), then

E(αˆ) = (T΄T)^-1T΄Y΄

= α + δ(T΄T)^-1T΄V + (T΄T)^-1T΄μ

Where αˆ is the estimated parameter on trade and α is the true parameter on trade. Since we can infer E(T, μ) = 0 from (7), we are left with

(10) E(αˆ) = α + δ(var²V/var²T)

Thus, if there existed a variable V that correlated both with the instrument and income, then the Frankel-Romer necessary assumption would be false and their estimation of trade's effect on income would carry a bias equal to δ(var²V/var²T).

In an attempt to prove simultaneity bias in the OLS estimates of trade's effect on income, Frankel and Romer run two regressions. The first regression uses OLS to estimate:

(11) lnY = a + λT + c₁lnN + c₂lnA + γ

where Y is income per person, T is the trade share, N is the population, A is the area, and γ is the error term. The second regression Frankel and Romer run uses contrade to instrument for the trade share. Frankel and Romer's hypothesize that since there exists reverse causality flowing from growth to trade, and since OLS does not account for the reverse causality while IV does, the IV estimation of trade's effect on income would be lower than the OLS estimation. The results of the Frankel-Romer OLS and IV regression are listed bellow in Figure 2. The OLS point estimate implies that an increase in the trade share of 1% is associated with an increase 0.85% in income per person and the IV point estimate implies a 1.97% increase in income per person for the same 1% increase in trade share. The finding λ_IV > λ_OLS directly contradicts the Frankel-Romer hypothesis. This suggests that there might be something biasing upwards Frankel and Romer's IV estimation of trade's effect on income.

Figure 2- Frankel-Romer findings[3]

III. Improving on the Instrument (Correcting for Omitted Variable Bias)

Proving the omitted variable bias requires identifying a variable which satisfies the conditions of the omitted variable V in the previous section, namely a variable correlated with the geographic variables used as an instrument and correlated with income. Capital flows, more specifically FDI inflows, might be such a variable. In this paper, FDI refers to foreign direct investment as define by the IMF:

"According to the IMF Balance of Payments Manual, direct investment is a special functional category of capital flows in the balance of payments distinguishable from other categories such as portfolio investment, other investment, and reserve assets. In order to classify capital flows as direct investment, it is necessary to establish (or show a pre-existing) specific relationship between the parties involved in the transaction. In particular, the direct investor should possess or acquire a "lasting interest", or have an "effective voice" in the management of the foreign party - also called the direct investment enterprise. The treatment of direct investment as a sui generis financial flow ultimately hinges on the idea that - as a consequence of the "effective voice" on the management of the enterprise - the expected returns would be different from those derived from other types of investment (such as portfolio investment in debt and equity securities, or other investment represented by trade credits and syndicated loans)."[4]

The reasons to suspect a positive correlation between FDI inflows and income are obvious. Firstly, direct investment increases the demand for labor and thereby wages. Secondly, FDI is likely to affect income through all the same channels by which trade affects income. The reasons to suspect a correlation between FDI and geographic characteristics are less obvious. To see the correlation, consider the relationship between FDI inflows and three of the variables determining contrade- distance, area, and population.

First, if distance between two countries increases, holding all else constant, what would happen to the FDI flows between the two countries? We might expect the FDI flows to decrease because a greater distance means larger costs for transporting equipment, supplies, and people which would all be necessary to compliment the capital investment. But, we might also expect distance to have no effect on FDI because moving funds requires no transportation cost at all. For example, an investment banker can press a button in New York and move billions of dollars to China at negligible cost. We might even expect increasing the distance to increase the FDI inflow. To see this effect, consider an example in which country i would like to break into the market of country j. Country i can either: produce goods domestically and ship them to country j, or it can invest directly in country j, manufacturer the goods there, and then bring them to the market in country j. Since transportation costs increase as the distance between country i and country j increases, the direct investment option becomes more appealing as the distance increases. The overall effect of distance on FDI remains ambiguous.

Next, consider what happens to FDI when the area of a country increases, holding all else constant. Greater area means more space for the construction of factories. Greater area also probably translates into more natural resources for extraction. Since the primary means for foreigners to capitalize on the natural resources of a country is by investing directly, we might expect FDI to increase as the area of a country increases.

Finally, consider the effect of population on FDI inflows. There are two ways in which FDI might correlate with population. First, foreigners will want to invest in populations which offer cheap labor forces. Cheap labor arises in countries with comparative advantages in labor, which we can expect to find in countries with large labor forces. Secondly, foreigners will want to invest in countries with large consumer bases, i.e. large populations, so that investors are ensured large end markets. Both of these points suggest that FDI will be positively correlated with population.

Since the relationship between distance and FDI is likely ambiguous, I will only test for correlations between FDI and population and area. To test the hypothesis that FDI is correlated with population and area, I regress lnFDI inflow from the year 1985 as reported by the World Bank Financial Database on lnpopulation and lnarea. The population and area figures come straight from Frankel and Romer (1999). I find a coefficient of 0.725 on lnPop and a t-statistic of 5.69. A scatter plot of lnFDI against lnpopulation is listed bellow in Figure 3. The t-statatistic for lnArea is -0.25, which supports the null hypothesis that the effect of area on FDI is 0. These findings constitute strong evidence to suspect that FDI is correlated with population, and hence the Frankel-Romer instrument used for trade.

Figure 3- FDI vs Population

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-3.61192 lnPop 6.41733

Since the correlation of population with FDI falsifies the necessary assumption of the Frankel-Romer model, E(I, μ)= 0, all that needs to be done to prove omitted variable bias is to check that FDI belongs in the equation estimating income. When I regress lnInc on lnFDI, lnPop, lnArea, and Trade Share, I find a coefficient of 0.36 for lnFDI with a t-statistic of 8.35 (see Figure 4 bellow). This yields overwhelming evidence to keep FDI in the regression as an independent variable. Therefore, since E(FDI,I)≠0, thereby rendering E(I, μ)= 0 false, and E(Income, FDI)≠0, we may conclude that FDI is an omitted variable in the Frankel-Romer IV regression and should be controlled for when using contrade to estimate trade's effect on income.

IV. Inserting the Omitted Variable into the Model and Re-estimating

It is the position of this paper that Frankel and Romer fail to verify their hypothesis because they do not account for a relevant variable. In so doing, Frankel and Romer use an instrument that picks up the effect of FDI on income and lumps it together with the effect of trade on income. In order to isolate the effect of trade on income, I insert FDI inflows into the equation estimated by Frankel and Romer. I estimate:

(12) lnY = d + gT + p₁lnN + p₂lnA + qlnFDI + ε

where Y, T, N, A are the same variables as in the Frankel-Romer model, FDI is FDI inflow, and ε is the error term. I first estimate (12) by OLS, and then estimate by IV using the same contrade variable as Frankel-Romer to instrument for trade. Since it has been seen that FDI does in fact constitute a relevant omitted variable in Frankel-Romer's regression, once FDI is accounted for, the estimates of trade's effect on income should decrease. While Frankel and Romer used a sample size of 150, I only tested the 94 of those 150 countries for which I could find FDI data for the year 1985. The results of the regressions are listed in Figure 4 bellow. Reg 3 estimates (12) by OLS and Reg 4 estimates (12) by IV. As Figure 4 shows, the coefficient of the trade share drops from 1.59 in the Frankel-Romer IV regression to 1.2 in the IV regression which accounts for FDI. This significant decrease in the estimation of trade's effect on income strongly supports the hypothesis that the Frankel-Romer IV regression overstates the effect by picking up the additional effect of an omitted variable.

Though the evidence clearly supports omitted variable bias, the Frankel-Romer question of simultaneity bias remains ambiguous. The fact that the coefficient on trade is still higher than the 0.53 estimate of trade's effect on income obtained by OLS estimation of (11) would not support the simultaneity hypothesis. However, the t-statistic on the trade share coefficient decreases from 0.60 in Reg 2 to 0.51 in Reg 4. Coupled with a p-value of 0.613, the low t-statistic in Reg 4 gives reason to accept the null hypothesis that the coefficient is actually 0. Reducing the coefficient on trade share to 0 would certainly lend support to Frankel and Romer's thesis that OLS overstates trade's effect on income.

Or would it? Reducing the coefficient on trade to 0 would support a much stronger thesis than the one advanced by Frankel-Romer- that is the thesis that OLS manufactures a positive effect of trade on income that actually does not exist. Such a thesis would contradict an enormous body of economic literature including the well accepted Ricardian model of comparative advantage. Surely, claiming that OLS manufactures a nonexistent connection is too strong a conclusion. Frankel and Romer set out to prove that OLS merely overstates the effect, not manufactures the effect. That my regression has led me to the overly-strong conclusion that OLS manufactures the effect of trade on growth, I suspect that something is still amiss in the model; therefore I suspend any verification of the Frankel-Romer simultaneity bias hypothesis at this time.

Figure 4-Trade and Income

V. Conclusion

In this paper I have taken up the old question of trade's effect on standards of living. I have addressed the question by seeking a refinement on the Frankel-Romer instrumental variable estimations of trade's effect on income. While Frankel and Romer fail to prove the thesis that OLS overstates the effect of trade on income because of simultaneity bias, I believe it is not because the thesis is false, but rather because their instrument is flawed. It is true that geographic characteristics can tell us a lot about how much a country trades, but they can also tell us a lot about how much foreign direct investment the country receives. FDI is likely to be positively correlated with area and population, and possibly even distance, as investors seek to minimize transportation cost, minimize labor costs, and maximize end market size. I observe that FDI is strongly positively correlated with population, and therefore the Frankel-Romer instrument for trade. This correlation violates a necessary assumption of the Frankel-Romer model. When I repair the Frankel-Romer model by accounting for FDI, I find that Frankel and Romer overstate the effect of trade on income due to omitted variable bias. The evidence also supports the conclusion that OLS manufactures an effect of trade on income that does not show up in the IV regression, but I find this conclusion too contradictory with accepted economic literature to verify at this time. Rather, I restrict the positive affirmation of this paper to the existence of omitted variable bias in the Frankel-Romer IV regressions. Additionally, I merely suggest that there may exist simultaneity bias in the OLS estimates of trade's effect on income, but verification of this thesis would require further investigation.

Appendix 1

References

Broda, C. and J. Romalis, "Identifying the effect of Exchange Rate Volatility on Trade" mimeo University of Chicago, GSB, 2003.

Feenstra, R. "Integration of Trade and Disintegration in Production in the Global Economy," Journal of Economic Perspectives, April 1998.

Fischer, Stanley, "Growth, Macroeconomics, and Development," in Olivier Jean Blanchard and Stanley Fischer, NBER macroeconomics annual 1991. Cambridge, MA: MIT Press, 1991, p. 329-64.

Frankel, J. and D. Romer, "Does Trade Cause Growth?," American Economic Review, Vol. 89, no. 3 (June 1999): 379-399.

Frankel, J and D. Romer, "Trade and Growth: an empirical Investigation." NBER working paper No. 5476. Cambridge, MA: March 1996.

Levine, Ross and Renelt, David, "A Sensitivity Analysis of Corss-Country Growth Regressions," American Economic Review, Vol 82, no. 4 (September 1992): 942-63.

Rand McNally. Quick reference world atlas. Chicago: Rand McNally, 1993.

World Bank web cite, A Database on Foreign Direct Investment. http://www1.worldbank.org/economicpolicy/globalization/data.html

[1] See for example, Stanley Fischer (1991), Ross Levine and David Renelt (1992)

[2] This data was taken from the IFS Direction of Trade statistics

[3] This table was taken straight from Frankel and Romer (1999). I am not reporting the results of a regression that I ran, rather, I am merely presenting the results that Frankel and Romer found.

[4] World Bank Web Site, A Database on Foreign Direct Investment. http://www1.worldbank.org/economicpolicy/globalization/data.html