The first specification introduced here, and also most widely used in the context of literature on gravity as well as gravity and immigration, is based on the OLS model. In the context of panel data, the OLS model gets additional attributes due to the repetitive cross sectional observations over time and therefore it is often called pooled OLS. This name reflects the idea that there are by assumption no unique attributes of individuals within the measurement set, and no universal effects across time, although the latter effects will also be controlled in our OLS estimation. After the simple OLS model is conducted, a test for time fixed effects as well as a test for normality and heteroskedasticity of error terms will be conducted to see if clustered, heteroske-
63 dasticity robust standard errors are needed to be used in the study. The specification tests in- clude, for example, Breusch-Pagan LM test for the heteroskedasticity of error terms and Shapiro Wilks W test for autocorrelation of the errors.30
First, the specification presented here is based on standard gravity equation in the log- linear form.31 The log-linear form of gravity model is used under the assumption of trade costs taking a form that the logarithm of distance as well as logarithm of immigrants affect trade, other trade costs, such as language, majorly presented by dummies. The model also takes the home country GDP (Finnish GDP) invariant across trade partners, included in the year dummy in pooled OLS regression. The partner country’s GDP, in turn, is included in logarithmic form in regression. Santos-Silva and Tenreyro (2006: 642) emphasise that the estimation of the log- linearised equation by OLS is only valid when the error term is statistically independent of the regressors. Hence, as introduced in section 3.1 the error term should follow E(εijt | Y, Z…) =
E(lnUijk | Y, Z…) = 0.32 This, however, can be easily violated since the logarithm of a random
variable depends on its mean and its higher moments; i.e. if the variance of error term Uijk , for instance, depends on other regressor(s), then the logarithm of this error term is also dependent of the variance and the condition of E(lnUijk | Y, Z…) = 0 of OLS might be violated (Santos- Silva and Tenreyro 2006). This leads us to the consideration of another estimation model (in section 4.5.3), however, before that considerations of OLS regression are continued.
Results obtained from the OLS regression using data on Finnish immigration are shown in section 5.2. Moreover, to check the robustness a different regression without the EU countries and without the former SSSR could be included in the study. Furthermore, exclusion of the EU from the study from a theoretical perspective would be probably suitable. Since no tariffs exist in the EU and tariffs probably affect trade between countries, tariff data should be included as an independent variable, which is not the case here. Hence, to exclude the invisible effects of tariffs may show up as a favourable outcome for the EU trade, from which there are also a lot of immigrants, and therefore the EU is excluded to count for the possible upward bias that the
30 However, these tests do not solve the problem that heteroskedastic error terms might cause to the model. Santos- Silva and Tenreyro (2006) indicate that the pattern of heteroskedasticity and the higher moments of the conditional distribution of the error term actually might affect the consistency of the estimator, for which the solution would be not to use OLS estimator. The use of heteroskedasticity robust error terms in the OLS estimation and in the fixed effects estimation therefore does not solve the problems that the pattern of errors might cause to the estima- tion model since the error term is likely to affect the parameter estimates. Thus the Poisson estimation with het- eroskedasticity robust error terms is introduced in section 4.5.3.
31 For instance, White’s (2007) approaches the estimation using a similar specification. 32 Here Y, Z, … denotes regressors, i.e. GDP, distance and so on.
64 immigrant stock coefficient might have due to not counting for the tariff barriers or other formal trade barriers.
The specification (either with or without the EU and the SSSR) excludes data on nega- tive trade flows and zero trade flows and can be presented as below.
(i) ln(tradeFINjt) = βo + β1lngdpjt + β2lndistFINj + β3lnbirthjt + β4CONTROLjt + β5YEAR + εijt
Above, βo is the constant, tradeFINjt refers to the logarithm of Finnish import or export flows (which are studied separately) from country j, lngdpjt refers to partner country GDP reflecting the economic mass at time t, lndistFINj is the logarithm of distance of country j from Finland,
lnbirthjt alludes to the immigrant stock from a trade partner country j at time t, and the CON-
TROLjt variables include dummies for colony, EU membership and other variables introduced in section 4.3.2; basically these variables get a value 1 if they share a common feature with Finland. Finally, β5YEAR includes year dummies.33
Finally, the proxies for multilateral resistance can be included in the specification, which changes the functional form slightly.
(ii) ln(tradeFINjt) = βo + β1lngdpjt + β2lndistFINj + β3lnbirthjt + β4CONTROLjt + β5MRjt + β6YEAR + εijt
In the above, MRjt refers to multilateral resistance of each country j at time t, and is captured either by the logarithm of real effective exchange rate, lnreer, or the logarithm in the change of price index, lnCPIfor. It is assumed that the year dummy partially absorbs the Finnish MR.
Different empirical specifications have been used in studying the effects of immigration on bilateral trade, based on either theoretical assumptions or intuition on whether data on all the trading countries are studied instead of concentrating only on bilateral data. As the theory suggests, to draw reliable conclusions from the use of gravity equation the model would require considering all the countries although only a single country’s trade relation with its partners would be under interest – this would be the only way to take into account properly the multi- lateral resistance that exists between the trading country and all the other countries except for its trading partner. As introduced earlier, the country pair fixed effects and year dummies in
33 A modified version is the one presented below to count for zeros in trade data.
ln(1+tradeFINjt) = βo + β1lngdpjt + β2lndistFINj + β3lnbirthjt + β4CONTROLjt + β5YEAR + εijt
The only difference with the previous specification is the change in the dependent variable to lnimp1 or lnexp1 (see section 4.3.1), which indicates that omitted values are transformed to zeros.
65 this kind of a model would depict these effects as well as some other measures. However, con- structing a purely theory-based specification with this data is not possible due to the omission of country-year dummies.