6  Methodology

6.1  Data

We have assembled data for a large panel of countries for every year from 1981 to 2001. The minimum number of countries included in the panel in our benchmark specifications is 171; the maximum is 179. We include substantially more observations than any previous studies of trade and migration, with the exception of Wagner, Head, and Ries (2002). As discussed below, the reason for assembling a large panel dataset is to address problems of unobserved heterogeneity and selection bias.

Our data on imports and exports come from the United Nations Statistics Division’s Comtrade Database. The UN obtains estimates of New Zealand imports and exports from Statistics New Zealand. We treat the data as complete. If no trade is reported between New Zealand and a given country in a given year, we assume that the true value for that year was zero.

Estimates of the foreign-born population in New Zealand come from unpublished tabulations prepared by Statistics New Zealand using data from the 1981, 1986, 1991, 1996, and 2001 Censuses. To calculate exact values for the inter-censal years it would be necessary to have data on deaths and international movements by place of birth, which are not available. An alternative would be to interpolate. We decided, however, to use the total from the most recent Census for the whole inter-censal period, so that, for instance, migrant stock in years 1981, 1982, 1983, 1984, and 1985 is set equal to the Census estimate in 1981. The advantage of this method, besides its simplicity, is that it gives partial protection against the possibility that migration is responding (in the short term) to trade.

Data on New Zealand’s GDP and population come from the World Bank’s World Development Indicators database. Data on language come from Grimes (1996), and distance from New Zealand from the website Great Circle Distances Between Capital Cities.[7]

6.2  Unobserved heterogeneity[8]

The variables available to us cannot possibly capture all influences on New Zealand’s trade. In other words, there is likely to be unobserved heterogeneity across our sample. Applying ordinary cross-sectional techniques in the presence of unobserved heterogeneity can lead to incorrect standard errors and biased coefficient estimates.

Use of panel data, however, permits models of the form

(3)    

where is a time-varying idiosyncratic error, and is an unobserved country-specific effect that represents the permanent cross-country heterogeneity. If the are assumed to be uncorrelated with the explanatory variables, then Equation 3 can be estimated using a Random Effects approach. The assumption of zero correlation is, however, difficult to justify in our case. No such assumption is required under a Fixed Effects approach. Under Fixed Effects, however, it is not possible to obtain coefficients for variables that are constant over time, such as Language and Distance.

Previous econometric studies of migration and trade have used either ordinary cross-sectional techniques or Fixed Effects. There is, however, an alternative approach, referred to as Correlated Random Effects, that avoids the zero correlation assumption and allows the inclusion of variables that are fixed over time. Under Correlated Random Effects, the correlation between the country-specific fixed effect and the explanatory variables is explicitly modelled using the expression

(4)    

where the are vectors of “projection coefficients” and is a true random effect that is uncorrelated with the explanatory variables. We assign the same weight to all time periods, so that

(5)     ,

and

(6)     .

Substituting this expression into Equation 3 (and absorbing , a constant, into ) gives

(7)     ,

which can be estimated using Random Effects.

Some unobserved heterogeneity also potentially takes the form of shocks affecting New Zealand’s trade with all countries more or less equally at the same time. An important example is the trade liberalisation that New Zealand began in the mid-1980s (Evans, Grimes, Wilkinson and Teece 1996). We allow for such affects by adding a time dummy for the period 1995 to 2001 to all equations.

6.3  Sample selection

Equation 7 does not allow for zero trade. In practice, however, 29% of our observations for imports are zeros, as are 20% of our observations for exports. Following previous studies of migration and trade, we interpret the zeros to mean that observed trade values emerge from a two-step process. Countries in effect decide whether to trade, and then decide how much to trade (Head and Ries 1998; Dunlevy and Hutchinson 1999: fn20; Wagner, Head, and Ries 2002: 518). Our model is

(8a)     

(8b)     

(9)    

We assume that and are non-autocorrelated, and that , with a correlation, , between the two that may not equal zero. Equations 8a and 8b together make up the “selection equation,” while Equation 9 is the trade equation. If the correlation between the two error terms is not zero, then simply using Equation 7 on the sub-sample with non-zero trade will lead to biased estimates.

As explained in LIMDEP (Version 8.0), this sample selection model can be estimated as a random parameters model by treating and as random coefficients. We adopt this approach and estimate the model in two steps by maximum simulated likelihood method. We first fit a random parameters probit model and store the results for use in the next phase where we fit the trade equation.

Following previous studies, we use the log of migrant numbers in . In some cases, however, the number of migrants equals zero, so that the log is undefined. Simply omitting these cases could potentially create a selection bias. We therefore adopt an approach used by Wagner, Head, and Ries (2002). We introduce a dummy variable called Zero Migrants that takes a value of one when there are no migrants, and zero otherwise. We set our Migrant Stock variable equal to zero when there are no migrants, and the log of the number of migrants otherwise. The Zero Migrants variable shows the change in trade that occurs when New Zealand has exactly one migrant from a country rather than none. In principle, it should be close to zero.