Paradise Lost? Growth, Convergence and Migration in the South Pacific
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

This paper examines the determinants of growth for nine South Pacific countries during the period 1971-93, using the analytical framework of the Solow-Swan neoclassical growth model. Chamberlain’s II-matrix estimator is used to account for unobserved country-specific heterogeneity in the growth process, and to control for errors-in-variables bias in calculations of real per-capita GDP. The speed of convergence of South Pacific countries to their respective steady-state levels of per-capita GDP, after controlling for the important regional effects of net international migration, is estimated at a relatively fast 4 percent per year. In addition, private and official transfers emanating from regional donor countries have kept the dispersion of real per-capita national disposable income constant over the period, despite a significant widening in the regional dispersion of real per-capita GDP.

Abstract

This paper examines the determinants of growth for nine South Pacific countries during the period 1971-93, using the analytical framework of the Solow-Swan neoclassical growth model. Chamberlain’s II-matrix estimator is used to account for unobserved country-specific heterogeneity in the growth process, and to control for errors-in-variables bias in calculations of real per-capita GDP. The speed of convergence of South Pacific countries to their respective steady-state levels of per-capita GDP, after controlling for the important regional effects of net international migration, is estimated at a relatively fast 4 percent per year. In addition, private and official transfers emanating from regional donor countries have kept the dispersion of real per-capita national disposable income constant over the period, despite a significant widening in the regional dispersion of real per-capita GDP.

I. Introduction

In recent decades the economies of the independent island nations of the South Pacific have exhibited anemic growth performances. This has occurred against a macroeconomic background characterized by rapidly accelerating external assistance, a relatively high level of investment, a large and pervasive public sector, and an open trading regime. This pattern of slow (and even negative) rates of growth of per-capita incomes contrasts with the advances made, particularly in the 1980s, in the developing island economies of the Indian Ocean and the Caribbean. Using the analytical framework of the Solow-Swan (1956) neoclassical growth model, this paper examines the determinants of the growth performance of nine South Pacific nations over the period 1971-93.

These nine countries include seven developing Island economies--Fiji, Kiribati, Papua New Guinea, Solomon Islands, Tonga, Vanuatu, Western Samoa--and their developed neighbors, Australia and New Zealand. 1/ The latter two economies are included due to their close economic links to the island economies in the areas of trade, exchange rate management, private and public transfer payments, international migration and private capital flows.

To the best of the authors’ knowledge, this paper represents the first formal empirical analysis of growth in the above island economies. 2/ Moreover, apart from work by De Gregorio (1992) for Latin America, Easterly and Levine (1994) for Africa, and Cohen and Hammour (1994) for several Middle Eastern and North African countries, there has been little work specifically focussing on the process of economic growth in regions containing developing economies.

Two questions are explored in this paper--has there been convergence in real per-capita incomes for these island economies over the period 1971-93, and at what speed have these economies converged to their long-run levels of real per-capita income? Using an estimation technique which is robust to both the presence of unobserved country-specific effects and to errors-in-variables in the measurement of real per-capita income, the conclusion reached is that, after controlling for investment and migration, the nine island economies have been converging (in terms of real per-capita gross domestic product (GDP)) at a relatively rapid speed. Indeed, the island economies have been converging toward their respective steady-state levels of per-capita GDP at a speed of about 4 percent per year. Moreover, net private and official transfers have ensured that the dispersion of real per-capita national disposable income in the region has remained relatively constant over the period, despite a widening in the dispersion of real per-capita GDP.

The structure of the paper is as follows. Section II looks at the key economic features of the island economies, while Section III examines the concepts of convergence which follow from the Solow-Swan (1956) neoclassical growth model. Section IV discusses the data used in the study, and Section V describes the estimation techniques used here, emphasizing Chamberlain’s (1984) II-matrix estimator, and sets out the convergence results. Section VI then follows with some concluding comments.

II. Overview of South Pacific Economies

Although the region does not suffer from levels of extreme poverty, and while all members of the PAC9 are both islands and ex-colonies of European colonial powers, the geographic and demographic differences among them are more readily apparent than the similarities (Table 1). The PAC9 range from the relatively rich, populous yet sparsely-populated Australian continent to the relatively poor, small populations of densely-populated atolls such as Kiribati. While having relatively small land areas, the PAC7 countries possess large sea areas and quite high population densities; they are also characterized by high fertility rates and declining mortality rates. Moreover, the key contribution of international migration in lowering national population growth rates is evident, particularly for the high net emigration countries of Tonga, Western Samoa and (after 1987) Fiji.

Table 1.

Comparative Demographic and Geographic Indicators

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Sources: World Bank (1994), Social Indicators of Development; United Nations (1993), Statistical Yearbook for Asia and the Pacific; IMF staff estimates; South Pacific Commission (1993), South Pacific Economies: Statistical Summary 13; Authors’ calculations.

The main economic characteristics of the PAC7 at the time of independence were: a strong reliance on agricultural activity, both in subsistence (fishing, coconuts) and export-oriented (coffee, sugar and copra) agriculture; high population growth rates, abated somewhat by emigration to New Zealand and Australia; and a lack of diversification in production, which exacerbated the effects of terms of trade shocks in raising the variability of national incomes (Browne and Scott 1989). In the decades since independence, policymakers in the island economies have maintained a high level of public investment, largely financed from bilateral official grants.1/ Centralized wage-determination remains a feature of island labor markets, as is the dominance of public sector employment and public sector activity. Moreover, net current account receipts from services and transfers have grown dramatically since the early 1970s, more than offsetting the islands’ ongoing trade deficits, and exchange rates have generally been pegged to those of major trading partners (chiefly Australia and New Zealand). Three additional key influences on the rate of economic growth achieved since independence have been: the frequency and severity of natural disasters (cyclones and floods); bouts of political uncertainty; and the emigration of nationals with high stocks of human capital. 1/

The PAC7 countries do face special problems in being among the smallest nations in the world; they also have very rapid rates of population growth and are dispersed across wide expanses of the Pacific, relatively distant from major world markets. However, these features should not and do not imply that there is little scope for economic growth. In response to several development issues outlined by de Vries (1973), both Srinivasan (1986) and Cole (1993) have argued that many of the problems allegedly faced by small, isolated island economies (such as a lack of domestic economies of scale, vulnerability to external economic and climatic shocks, remoteness, and lack of access to capital markets) are either not peculiar to them, or can be addressed through appropriate policy measures; they are neither a necessary nor a sufficient barrier to sustained economic growth. 2/ Moreover, the growth-enhancing aspects of island economies are non-trivial. Relative to other developing countries, the PAC7 have: a high level of basic subsistence income; well educated, housed and healthy populations; access to large flows of international transfer payments; and a tradition of conservative macroeconomic management.

Notwithstanding these observations, at first glance economic growth among the PAC7 has been disappointing over the period 1971-93 (Table 2). Annualized real (1990 Australian dollars, A$) per-capita GDP growth rates for the full sample period ranged from a low of -2.80 percent for Kiribati to a high of 1.54 percent for Tonga. Figures for 1990 per-capita GDP range from a low of A$617 for Kiribati to a high of A$2,483 for Fiji. 3/

Table 2.

Comparative Economic Indicators

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Sources: World Bank (1994), Social Indicators of Development; United Nations (1993), Statistical Yearbook for Asia and the Pacific; IMF staff estimates; South Pacific Commission (1993), South Pacific Economies: Statistical Summary 13; OECD (1994), Geographical Distribution of Financial Flows to Developing Countries 1989-92; IMF (1993), Direction of Trade Statistics; Authors’ calculations.

ANZ denotes Australia and New Zealand.

Converted at period-average 1990 exchange rates to the A$.

In 1990 A$ terms.

Percentage with respect to New Zealand alone.

Percentage with respect to Australia alone.

Foreign aid is total net official development assistance (ODA), comprising net ODA loans (plus grants) less loan repayments.

The path of the logarithm of per-capita GDP (in 1990 A$) is also reflected in Figure 1. While per-capita income growth has been relatively steady for Australia and New Zealand, the same cannot be said for the PAC7: the collapse in Kiribati’s per-capita GDP after 1979 (due to exhaustion of its phosphate reserves) is particularly evident, as is the influence of cyclonic destruction In the per-capita GDP falls of Western Samoa in 1990 and Vanuatu in 1987, and the effects of the Bougainville political and economic crisis in the per-capita GDP fall of Papua New Guinea in 1990. 1/ The 1970s was a decade of strong growth performance for the Solomon Islands, which in 1971 was clearly the poorest economy in the PAC7. Moreover, per-capita GDP jumped sharply in 1978-79 for all countries (apart from Kiribati), reflecting a favorable terms of trade shock arising from high commodity prices for PAC7 exportables. While growth has been relatively slow for all countries in the 1980s, the performance of the Solomon Islands and Papua New Guinea has improved sharply in the 1990s, principally due to higher world prices and greater volumes for their exports of natural resources (particularly timber and minerals).

Figure 1
Figure 1

South Pacific Countries: Real (1990 Australian Dollars) Per-Capita GDP, 1971-93

Citation: IMF Working Papers 1995, 028; 10.5089/9781451844603.001.A001

Private and official transfers as a share of GDP are extremely high when compared with other countries at a similar level of development (Table 2). In the period 1987-93 Kiribati received average annual net transfers equivalent to about 63 percent of its GDP, while the figure for Western Samoa was about 45 percent. Conversely, such transfers were of negligible importance (0.5 percent) for Fiji. It is important to recognize that underlying these totals is the differing contribution of private and official sources: private transfers are the major source of current transfers for the high-emigration countries of Tonga and Western Samoa; public transfers are of considerably greater relative importance for Kiribati, Solomon Islands and Vanuatu. 2/

The PAC7 islands enjoy relatively free access to developed country labor markets in New Zealand and Australia, and migrants’ transfers serve to sustain domestic consumption at much higher levels than could be achieved in the absence of migration. Moreover, external assistance to the PAC7 is generous: South Pacific nations are among the highest per-capita aid recipients in the world (World Bank 1993). 3/ 4/ The percentage share of total net bilateral official development assistance (ODA) provided by Australia and New Zealand (ANZ) is sizeable, ranging from a period-average low of 33 percent for Kiribati to a high of 79 percent for Papua New Guinea between 1989-92 (Table 2). ANZ also dominate as sources of PAC7 imports, and are an important destination for exports from some PAC7 countries, (particularly Western Samoa and Tonga), yet relatively unimportant for others (Vanuatu, Kiribati and Solomon Islands).

III. Concepts of Convergence

Barro and Sala-i-Martin (1992a) take a Cobb-Douglas production function in units of effective labor, and a representative consumer with a utility function exhibiting constant intertemporal elasticity of substitution, log-linearize the resultant equations of motion about the steady state and derive the dynamic equation for the average growth rate of per-capita output, y, over any given interval between 0 and T:

T1ln(yT/y0)=(1eβT)T1ln(y^*/y^0)+g(1)

where β is the speed of convergence, 1/ T is the length of the time interval, ŷ is output per unit of effective labor, the * superscript denotes steady-state values, and g is the exogenous rate of labor-augmenting technical progress. In (1) convergence is conditional, as what drives β is the level of ŷ0 for each economy relative to its own ŷ* and g, which need not be homogeneous across economies.

A version of equation (1) that applies for discrete periods for any given economy i gives the geometric average growth rate over the interval t-r and t as:

ln(yi,t/yi,tr)=Ci(1eβr)ln(yi,tr)+ϵi,t(2)

where i indexes the economy, r is the length of the observation interval, t is time, yi, ([a-z]+)-r is real per-capita GDP for each economy at time t-r, the beginning of the sub-period; yi, t is real per-capita GDP at time t; β is the convergence coefficient; ∊i, t is an independent error term, and the country-specific constant is Ci=gir+(1eβr)[ln(y^i*)+gi(tr)]. If we had instead assumed (as do Barro and Sala-i-Martin 1992a) that all PAC9 economies have the same steady-gtaje levels of real per-capita GDP and steady-state growth rates (that is, y^*=y^i*andg=gi), then Ci would equal C and equation (2) would imply absolute convergence, if β>0.

Two measures of convergence follow from equation (2). The first, known as convergence, asks whether initially-poor economies tend to grow faster than initially-rich ones (that is, whether there is mean reversion in the level of real per-capita GDP across economies). Another concept is a-convergence, which considers the decline of the cross-sectional dispersion of real per-capita GDP over time. That is, it asks whether the standard deviation of the logarithm of per-capita GDP (the coefficient of variation) is shrinking across economies over time. Barro and Sala-i-Martin (1992a) note that β-convergence is a necessary but not a sufficient condition for σ - convergence, as a positive β will tend to reduce σt (the dispersion of ln(yit) in (2)) for a given distribution of ∊i, t, but new exogenous shocks to ∊i, t to raise σt.

IV. Data

We consider the period 1971-93, using data on nine South Pacific countries: Australia, Fiji, Kiribati, New Zealand, Papua New Guinea, Solomon Islands, Tonga, Vanuatu and Western Samoa. Lack of consistently-derived data has previously precluded a detailed analysis of the pattern of South Pacific growth; a relatively long time series of such data has been collected and utilized here for the first time. 1/

The 1971-93 period is, in turn, broken down into five non-overlapping sub-periods with a length of four years each, and the sub-period 1991-93, with two years. 2/ The output data used is per-capita GDP in constant (1990 A$) prices, derived from: national data on GDP, 1/ movements in the national GDP deflator (or consumer price index), mid-year population and average 1990 local currency exchange rates to the A$. 2/ Other variables used in this study include (all for the initial year of each sub-period): INV, the share of aggregate investment in GDP; AG, the share of GDP emanating from the agriculture, forestry and fishing sectors; PRIM, primary school enrollments as a share of the population aged 5-14 years; and SEC, secondary school enrollments as a share of the population aged 15-19 years. An additional explanatory variable used is (1+MIG), which is the sub-period-average annual net migration as a share of the population at the beginning of each sub-period. 3/ Estimates of national disposable income for the PAC9 are also derived, by adding data on net private and official unrequited transfers to national data on GDP. Further details on the definition, derivation and sources of all the variables used in this study can be found in the Appendix. Appendix Table A1 presents summary statistics of the above data for each of the PAC9 countries.

It should be kept in mind that measurement of national income in the island developing countries of the South Pacific is likely to involve error, due to the fact that subsistence activity is often inadequately covered in the national accounts. Moreover, differences exist across the island economies in the methods of estimation used, and in the extent of monetization of local economies. 4/

Calculations of national income are converted from local currencies to A$ - it is well known that conversion at market exchange rates biases downward the true measure of income in developing countries, as the price of nontradeables increases as per-capita income increases (Balassa 1964, Bhagwati 1984). 1/ However, the difference between the official exchange rate and the purchasing-power-corrected exchange rate should be reduced the more open are the economies under consideration, as trade should then raise the relative price of nontradeables. The PAC7 economies are relatively open when compared with others at a similar stage of development. Notwithstanding these caveats, in Section V we use an estimation technique which is robust to errors in the measurement of per-capita incomes.

V. Estimation Techniques and Results

Studies in the literature on empirical growth analyses have predominantly been cross-sectional in nature, often using the International Comparison Project (ICP) data of Summers and Heston (1991). 2/ Analyses of time series-cross sectional (TSCS) data in the context of the neoclassical growth model have been previously conducted by De Gregorio (1992), Khan and Kumar (1993), Knight, Villanueva and Loayza (1993), Keller (1994), and Barro and Lee (1994), among others. Beyond the advantages of TSCS data in increasing the number of degrees of freedom and controlling for the time dimension of the data, its main advantage is that it introduces cross-country heterogeneity in the growth process and allows researchers to control for any potential bias due to measurement error in the lagged dependent variable (ln(yi, t-r)). This section begins with an examination of the relationship between initial income and subsequent growth, and the relationship between initial income and net migration. It then analyzes the results from TSCS estimation of β-convergence in the Solow-Swan (1956) model, and concludes by reviewing the extent of σ-convergence across the PAC9 over the period 1971-93.

1. Initial real per-capita GDP, subsequent growth and migration

Figure 2 presents the relationship between ln(y1971) and the geometric average rate of growth of per-capita incomes between 1971-93: the positive relationship between them indicates divergence for the PAC9 countries (the simple correlation between initial income and growth is 0.323). Figure 3 plots the same variables, yet excludes Australia and New Zealand, which are highly unlikely to display preferences and technology similar to those of the relatively homogeneous PAC7, and hence are converging to different steady-state levels of per-capita income. While Kiribati appears to be an outlier with a period-average per-capita growth rate of over -2.5 percent per annum, the resulting inverse relationship between ln(y1971) and per-capita income growth between 1971-93 indicates β-convergence: the simple correlation between them is -0.057. Similarly, Figure 4 displays the long-term relation between the annual rate of net migration between 1971-93 and ln(y1971). positive association is evident, with the simple correlation between the two of 0.479. As expected, both Western Samoa and Tonga are outliers, with below-average initial incomes and very high net emigration rates of over 1.5 percent per year. Little net migration has occurred in the Solomon Islands, Kiribati, Vanuatu, and New Zealand between 1971-93.

Figure 2
Figure 2

Convergence of Real Per-Capita GDP Across Nine South Pacific Countries: 1971 GDP and 1971-93 GDP Growth

Citation: IMF Working Papers 1995, 028; 10.5089/9781451844603.001.A001

Figure 3
Figure 3

Convergence of Real Per-Capita GDP Across Seven South Pacific Countries: 1971 GDP and 1971-93 GDP Growth

Citation: IMF Working Papers 1995, 028; 10.5089/9781451844603.001.A001

Figure 4
Figure 4

Net Migration and Initial Real Per-Capita GDP: 1971-93

Citation: IMF Working Papers 1995, 028; 10.5089/9781451844603.001.A001

2. β-Convergence in the South Pacific

In this sub-section we will examine the speed with which the members of the PAC9 approached their respective steady-state levels of per-capita GDP, over the period 1971-93. We utilize two methodologies--the first uses standard time series-cross sectional estimators (pooled least squares, fixed and random effects), while the second uses Chamberlain’s II-matrlx estimator, which, as we will explain below, corrects the deficiencies inherent in the standard estimators. Three key assumptions are made in using either methodology: (i) the speed of convergence is similar across the PAC9 economies, conditional on ŷ* (the steady-state level of per-capita output); (ii) the explanatory variables INV and (1+MIG) condition appropriately for ŷ*; and (iii) the explanatory variables are exogenous to the dependent variable (the rate of economic growth).

a. Pooled least squares, fixed (FE) and random effects (RE) estimators

For the countries of the PAC9 and for the five sub-periods, ordinary least squares (OLS) regression estimates of equation (2) based on the pooled TSCS data yields the results given in column (1) of Table 3. The dependent variable is the change in the natural log of real per-capita GDP over the sub-period (ln(yi, t/yi, t-r)) and the independent variables are an overall constant term and the natural log of real per-capita GDP in the initial year of each sub-period (ln(yi, t-r)) where r is the length of each sub-period. 1/ The value of the coefficient on ln(yi, t-r) 0.014 and is not significant, though it implies a value for the speed of convergence of -0.32 percent per year, that is β-divergence. 2/

Table 3.

Regression Results for the South Pacific, 1971-93 1/

(Dependent Variable is ln(yt/yt-r))

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The regressions use time series-cross sectional (TSCS) techniques to estimate equations of the form: ln (yi, t/yi, t-r) = Ci - (1-e-βr) ln(yi, t-r) + other variables where yi, t-r is real (1990 A$) per capita GDP in country i at the beginning of each sub-period; yi, t is real per-capita GDP at time t; r is the length of each sub-period; Ci is a country-specific constant term; “other variables” are ln(INVi, t-r), the share of investment in GDP for country i at the beginning of each sub-period, and ln(1+MIGi, t-r), each sub-period’s average annual net migration into country i as a share of country i’s population at the beginning of each sub-period. See Section IV and the Appendix for further details. Beneath the estimated coefficients are (in parentheses) the associated t-statistics; β is the implied speed of convergence. Lagrange Multiplier (LM) and Hausman statistics test the null hypotheses of: the variance of the random disturbance for the ith country observation is zero; and the individual effects are uncorrelated with the other repressers, respectively. The p-value (given in square brackets) for each test statistic corresponds to a X2 with 1 (LM, columns (3) to (5)), 1 (Hausman, column (3)), 2 (Hausman, column (4)) and 3 (Hausman, column (5)) degrees of freedom, respectively. All regressions are run with a constant term (except FE), a one-factor (country effects) estimation technique, and an autocorrelatad (AR1) error structure (reported as ρ). The TSCS techniques used are pooled least squares (OLS), fixed effects (FE) and random effects (RE).

This result is not surprising, given that we have not controlled for the differing steady states of the developed and developing South Pacific countries. 1/ The speed of convergence is relatively faster using FE (column (2)) and RE (column (3)) estimation: β-convergence is observed, at implied speeds of 1.04 and 0.21 percent per year, respectively. While a Likelihood Ratio (LR) test of the null hypothesis of a constant intercept for all countries is rejected (LR-35.581, p-value-0.00001), both the Lagrange Multiplier (LM) and Hausman tests argue in favor of the RE model over OLS and FE (Table 3). 2/

When ln(INVi, t-r) is included to control for likely differences in steady states across the PAC9 (column (4)), RE is again the preferred specification, yielding β-divergence, with an implied speed of -0.27 percent per year. The coefficient on ln(INVi, t-r) is found to be positive and statistically significant. 3/ Similarly, when ln(1+MIGi, t-r) to capture the influence of migration on the process of growth (column (5)), the preferred RE specification yields a coefficient on ln(yi, t-r) which is lower, although it still results in slight β-divergence (at -0.12 percent per year). An additional question concerns the assumed exogeneity of ln(1+MIGi, t-r) It is possible that a country’s per-capita growth rate and its net migration rate are jointly determined, which could be underpinning the unexpected results of column (5), and this question will be examined further below.

b. Chamberlain’s II-matrix estimator 4/

Assuming that there is a set of variables xi, t, unobserved country-specific effects μi, and time-specific effects, ξi, that appropriately control for the economy’s steady-state level and growth rate, we can transform equation (2) into the following regression equation:

Zi,tZi,tr=θ/Xi,t+γZi,tr+ξt+μi+εi,t(3)

where zi, t=ln(yi, t), and γ=-(1-e-βr). To emphasize the lagged-dependent-variable nature of growth regression (3), we can rewrite it as follows:

Zi,t=θ/Xi,t+(1+γ)Zi,tr+ξt+μi+εi,t(4)

We assume that the set x consists of the following two variables: ln(INVi, t-r), where INV is the percentage of investment in GDP at the start of the period; and ln(1+MIGi, t-r), where MIG is the sub-period-average annual net migration into an economy as a percentage of Its initial sub-period population. We use the variable (1+MIGi, t-r), a monotonic transformation of MIGi, t-r, because in many cases MIG is negative, and thus Its logarithm is undefined.

While we assume that the independent regressors, x, are well measured in the data, we do allow for the possibility of errors in variables regarding the lagged dependent variable, zi, t-r. Observed output may not correspond to the model’s output variable for two reasons. First, output may be poorly measured. Second, and most Importantly, observed output has a business cycle and a growth (or trend) component. Since our working model explains only the latter, there is a potential estimation bias. Errors in the dependent variable are a potential source of bias, because lagged output is one of the regressors.

Let us consider the following estimation strategy. To account for the time effects we process the data by removing the time means from each variable. Then, we can ignore the ξt’ and the regression can be fitted without a constant (MaCurdy 1982).

Least-squares estimation ignoring the country-specific effects and the errors-in-variables problem produces biased estimators. In particular, the estimate of (1+γ) in equation (4) is biased in an unknown direction: measurement error biases the estimate downwards, while the country-specific effect tends to bias it upwards.

Using the FE estimator (or any other panel-data estimator based on time-differencing) to correct for the country-specific-effects bias is inappropriate. The specific-effects bias disappears, but the downward measurement-error bias tends to worsen; this is due to the reduction in “signal” variance brought about by time-differencing. Furthermore, given the presence of a lagged dependent variable, time-differenced estimators by construction create an additional downward bias. Therefore, in general FE and other time-difference methods underestimate (1+γ). In contrast, the direction of bias in the RE estimator is similar to OLS in that it is ambiguous, despite RE’s use of a more efficient variance-covariance matrix than OLS. In RE the downward bias of errors-in-variables remains, as does the upward bias attributable to the neglect of country-specific effects.

Given the above deficiencies of the standard TSCS estimators in the context of growth regressions, we will use the II-matrix estimation procedure outlined in Chamberlain (1984). This procedure allows us to correct for both measurement-error and specific-effects biases. Chamberlain’s II-matrix estimation procedure consists of writing both the lagged dependent variable and the country-specific effect in terms of the independent regressors, thus obtaining reduced-form regressions from which to calculate the coefficient estimates of interest.

In order to use this method, we need to make explicit the restrictions that our model imposes on the II matrix. After removing the time means, our basic model in equation (4) can be written as

Zi,t=θ/Xi,t+(1+γ)Zi,tr+μi+εi,tE[εi,t|Xi,1,,X1,T=0]fort=1,,T(5)

Recursive substitution of the zt-1 term in each equation gives

Zi,0=Zi,0Zi,1=θXi,1+(1+γ)Zi,0+μi+ωi,1Zi,2=(1+γ)θXi,1+θXi,2+(1+γ)2Zi,0+[1+(1+γ)]μi+ωi,2Zi,3=(1+γ)2θXi,1+(1+γ)θXi,2θXi,3+(1+γ)3Zi,0+[1+(1+γ)+(1+γ)2]μi+ωi,3Zi,T=(1+γ)T1θXi,1++θXi,T+(1+γ)TZi,0+[1+(1+γ)++(1+γ)T1]μi+ωi,TE*[ωi,T[Xi,1,,Xi,T]=0fort=1,,Tandi=1,,N

Chamberlain (1984) proposed to deal with the correlated country-specific effect (μi) and the initial condition (zi,0) by replacing them by their respective linear predictors (given in terms of the exogenous variables) and error terms, which by construction are uncorrelated with the exogenous variables. The linear predictors are given by

E*(zi,0|Xi,1Xi,2,Xi,T)=λiXi,2++λτXi.TE*(μi|Xi,1,Xi,2,Xi,T)=τ1Xi,1+τ2Xi,2+τTXi.T

As we will see below, our panel data consists of 4 cross sections for the exogenous variables x and 5 cross sections for the variable z; the additional cross section for z is given by the initial condition z0.

Thus, the multivariate regression implied by our model is

[Zi,0Zi,1Zi,2Zi,3Zi,4]=II·[Xi,1Xi,2Xi,3Xi,4](6)II=[B+ζλ+Φτ]

where

B=[0000θ000(1+γ)θθ00(1+γ)2θ(1+γ)θθ0(1+γ)3θ(1+γ)2θ(1+γ)θθ]
ζλ=[1(1+γ)(1+γ)2(1+γ)3(1+γ)][λ1λ2λ3λ4]
φτ=[011+(1+γ)1+(1+γ)+(1+γ)21+(1+γ)+(1+γ)2+(1+γ)3][τ1τ2τ3τ4]

Since we allow for group-wise heteroskedasticity and correlation between the errors of all regressions, we use the seemingly unrelated regression (SUR) estimator.1/

Table 4 presents the estimated parameters of equation (5) using Chamberlain’s II-matrix procedure. Of particular relevance is the fact that through the II-matrix procedure, the endogenous variable (ln(yi, t)) is not used in its lagged form as a regressor, and so any related errors-in-variables no longer induce biased parameter estimates. However, when the estimation is done assuming no unobserved country-specific heterogeneity, the upward bias arising from country-specific effects remains. Moreover, the bias is clearly greater when ln(1+MIGi, t-r) as a measure of the contribution of net migration to national population growth, is excluded as a regressor.

Table 4.

Regression Results for the South Pacific Using Chamberlain’s II-Matrix Procedure, 1971-90 1/

(Dependent Variable is ln(yt/yt-r))

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The regressions use Chamberlain’s (1984) II-matrix procedure to estimate equations of the form: ln(yi, t/yi, t-r)=Ci-(1-e-βr)ln(yi, t-r) + other variables where yi, t-r is real (1990 A$) per capita GDP in country i at the beginning of each sub-period; yi, t is real per-capita GDP at time t; r is the length of each sub-period; Ci is a country-specific constant term; “other variables” are ln(INVi, t-r), the share of investment in GDP for country i at the beginning of each sub-period, and ln(1+MIGi, t-r), each sub-period's average annual net migration into country i as a share of country i's population at the beginning of each sub-period. See Section IV and the Appendix for further details. Beneath the estimated coefficients are (in parentheses) the associated t-statistics; β is the implied speed of convergence. As explained in Section V: γ refers to -(1-e-βr), the coefficient on ln(yi, t-r); θ' = [θI, θM] is the vector of coefficients on the explanatory variables, where θI is the coefficient on ln(INVi, t-r) and θM is the coefficient on ln(1+MIGi, t-r). “Specific effects” refers to allowance for unobserved, country-specific heterogeneity. The Wald test (and associated X2 with 4 (column (7)) and 8 (column (9)) degrees of freedom) pertains to a test of the null hypothesis of no country-specific effects; the p-value for this test is given in square brackets.

The estimates of γ obtained conform to our a priori expectations in two key respects. First, estimates which control for country-specific effects produce lower values for γ (higher values for β) than those which do not (-0.159 (column (9), compared with 0.026 (column (8)). When country-specific effects are controlled for, we move from finding β-divergence (columns (6) and (8)) to finding either insignificant β-divergence (column (7)) or β-convergence (column (9)). Moreover, Wald tests of regressions (7) and (9) strongly reject the null hypothesis that there are no country-specific effects (that the coefficients in the linear predictor of μi are all equal to zero, H0: r'1=…=r'4=0). In analyzing the heterogeneous countries of the PAC9 it is clearly important to control for unobserved, country-specific effects. Indeed, the large difference between the cross-sectional estimates of β found in the literature (which center on β=0.02 per year) and our preferred estimate of β=-0.0432 per year is most likely due to the inability of cross - sectional studies to control for country-specific effects.

Second, estimates which use the migration measure as an explanatory variable produce lower values for γ (higher values for β) compared with those that do not, even after allowing for cross-country heterogeneity (-0.159 (column (9) compared with 0.092 (column (7)). The latter effect is due to omitted variables bias in columns (6) and (7), when compared with columns (8) and (9). The former two regressions suffer from this bias, given that net migration is an important part of the growth process in the South Pacific and is positively correlated with ln(yi, t-r). 1/ Accordingly, the omission of migration in columns (6) and (7) imparts an upward bias to estimates of γ which means that the estimated β coefficient will be biased downward--it will appear that initially-rich regions grow faster (initially-poor regions grow slower), so there is no β-convergence. 2/ This conforms with our expectations, given the importance of net migration to several of the PAC9 countries, particularly (in declining absolute value) Tonga, Western Samoa, Australia, Fiji, and Papua New Guinea (Appendix Table A1 and Figure 4).

The consistent estimate for γ (-0.159) is reported in column (9) of Table 4, and implies a value for β of 0.0432 [p-value-0.12]. This result is about twice the typical speed of convergence found in the cross-sectional literature (Barro and Sala-i-Martin 1992a, 1992b). At such a speed divergences from the steady-state level of per-capita income are not very persistent; the half-life of convergence (the time it takes for a typical PAC9 economy to move half-way from its actual per-capita income level to its own steady-state level) is a relatively fast 17 years. 3/ While such a rapid speed of convergence appears at first glance to be favorable news for the relatively poor members of the PAC9, it should be kept in mind that this is the speed of convergence to each country’s own steady-state level of per-capita income; it is highly unlikely that such a level is the same for Australia and New Zealand as for members of the PAC7. 1/ 2/

As mentioned earlier, there is the possibility that, as ln(1+MIGi, t-r) is a sub-period-average measure of net migration, it may be affected by the rate of growth of sub-period per-capita incomes. However, using a Hausman test we cannot reject the hypothesis that ln(1+MIGi, t-r) is exogenous. The Hausman test for endogeneity was carried out by adding the residuals from a regression of ln(1+MIG) on a set of independent variables (ln(yi, t-r), ln(INV) and ln(DEN), the log of national population density) to the preferred Chamberlain regression (column (9)). The t-statistic on this variable, 0.0018, was not significant (Nakamura and Nakamura 1981). 3/ Our other explanatory variable is not likely to be endogenous, as the share of investment in GDP at the beginning of each sub-period ln(INVi, t-r) cannot be caused by economic growth over the subsequent sub-period ln(yi, t/yi, t-r).

It is also of interest that the estimated coefficients on initial income obtained using pooled OLS, FE and RE regressions (reported in Table 3) agree with our predictions for their divergence from the consistent estimates of column (9) in Table 4. Both the pooled OLS and RE estimates of the coefficient on (ln(yi, t-r) are biased upward (0.014 and 0.0054, respectively), indicating that for the PAC9, the country-specific bias exceeds the errors-in-variables bias. The FE estimates (-0.045) are biased downward, as expected, due to errors-in-variables in the dependent variable.

3. σ-Convergence in the South Pacific

This sub-section examines the absolute convergence of real per-capita income across the PAC9; that is, we do not control for the disparate steady states to which the island economies are converging. We do this by estimating the extent of σ-convergence across the PAC9 for the period 1971-93, using as our measure of dispersion the unweighted cross-sectional standard deviation of ln(yit), σt. Figure 5 to 8 show the results for three versions of the dispersion of real per-capita income across the economies: (i) σGDP, the dispersion of real per-capita GDP; (ii) σGDPRIV, the dispersion of real per-capita adjusted income (GDP plus net private transfers); and (iii) σNDI, the dispersion of national disposable income (GDP plus net private and official transfers). 1/ Given the presence of both private and official transfers, which flow from relatively rich to relatively poor economies, it would be expected a priori that the dispersion of per-capita income would be greatest for σGDP, followed by σGDPRIV, followed by σNDI. For each of the three versions of the dispersal of real per-capita income, the countries selected comprise: the PAC9 (Figure 5); the PAC7 (Figure 6); the PAC5: PAC7 less the relatively developed island economies of Fiji and Papua New Guinea (Figure 7), and the PAC4: PAC5 less the atoll microeconomy of Kiribati (Figure 8).

Figure 5
Figure 5

Dispersion of Real Per-Capita GDP: PAC9, 1971-93

Citation: IMF Working Papers 1995, 028; 10.5089/9781451844603.001.A001

Figure 6
Figure 6

Dispersion of Real Per-Capita GDP: PAC7, 1971-93

Citation: IMF Working Papers 1995, 028; 10.5089/9781451844603.001.A001

Figure 7
Figure 7

Dispersion of Real Per-Capita GDP: PAC5. 1971-93

Citation: IMF Working Papers 1995, 028; 10.5089/9781451844603.001.A001

Figure 8
Figure 8

Dispersion of Real Per-Capita GDP: PAC4, 1971-93

Citation: IMF Working Papers 1995, 028; 10.5089/9781451844603.001.A001

In Figure 5 there is a clear indication of σ-divergence for σGDP over the period 1971-93; there is somewhat less σ-divergence for σGDPRIV, and almost no σ-divergence for σNDI. For σNDI, the widest definition of national income, there is only slight σ-divergence over the 1971-93 period for the PAC9: σNDIt rises from 1.084 in 1971 to 1.100 in 1993, after reaching a period-high of 1.141 in 1989 and a period-low of 1.015 in 1979. For all three measures of σ, the jump in commodity prices in 1979 induced rapid σ-convergence, which was followed by rapid σ-divergence in the early 1980s, slowly-rising σ-divergence in the period to 1990, then a resumption of σ-convergence in the early 1990s, as commodity prices recovered. The above results illustrate the sensitivity of incomes in South Pacific countries to fluctuations in their terms of trade.

In a similar manner, σNDIt for the PAC7 rises from 0.332 in 1971 to 0.346 in 1993, after reaching a period-high of 0.404 in 1975, and a period-low of 0.269 in 1979 (Figure 6). Indeed, there is σ-convergence for the PAC4 countries (Tonga, Solomon Islands, Vanuatu and Western Samoa) with respect to σGDP: σGDPt declined from 0.329 in 1971 to 0.289 in 1993 (Figure 8). Moreover, σGDPRIV,σNDI > σGDP after 1977, due to the relatively small receipt of current transfers by the poorest member of the PAC4 - the Solomon Islands. Finally, σNDIt for the PAC4 declines from 0.330 in 1971 to 0.325 in 1993, after reaching a period-high of 0.428 in 1972, and a period-low of 0.252 in 1978.

While the per-capita GDP component of per-capita NDI has become more unequal for the PAC9 countries over the 1971-93 period, there has been an increase in net private and public transfers from initially-rich economies (Australia and New Zealand) to initially-poor economies (the PAC7) over this same period. The result has been relatively little change in the dispersion of per-capita NDI in the South Pacific, as receipts from migrants and intergovernmental transfers have compensated for the widening dispersion of per-capita GDP brought about by relatively slow growth in initially-poor economies (Figure 5). Whether by accident or design, and particularly since the precipitous fall in the region’s terms of trade after 1979, donor countries have varied their migration policies and official transfer payments to maintain the dispersion of PAC9 per-capita NDI at about 1.10. 1/ 2/

A further useful disaggregation of the data is to examine whether the initially-rich PAC7 economies in 1971 (Fiji and Vanuatu) experienced a-convergence as a sub-group, and whether the initially-poor economies (Solomon Islands and Western Samoa) did likewise. The results reveal that while σ-convergence applies for the initially-poor economies (σNDIt falls from 0.280 in 1971 to 0.185 in 1993), there is σ-divergence for the initially-rich economies (σNDIt rises from 0.151 in 1971 to 0.189 in 1993). 3/

VI. Conclusion

Using time series-cross sectional data on nine South Pacific countries, this analysis confirms the conditional convergence predictions of the neoclassical growth model (Solow 1956, Swan 1956). That is, over the period 1971-90, the nine countries converged on their respective steady state levels of per-capita GDP at the relatively rapid speed of about 4 percent per year. Moreover, during 1971-93 both private and official net transfers, largely emanating from developed countries of the region, acted to prevent a widening of the dispersion of real per-capita national disposable income across the nine countries. However, the dispersion of real per-capita GDP, which excludes such transfers, clearly widened over this same period.

The estimation technique used was a methodological improvement over previous work, as it controlled for errors-in-variables bias and unobserved country-specific heterogeneity. We also demonstrated the direction of the biases inherent in parameter estimates emanating from cross-sectional and time series-cross sectional techniques which erroneously assume that errors-in-variables and country-specific effects are absent from the data.

The developing island economies of the South Pacific clearly have a direct and important role to play in implementing policies which will enhance their rate of per-capita GDP growth. At the same time, this analysis reveals that developed countries, through their policies toward official transfers and international labor flows, can ameliorate inequalities in per-capita national disposable income across the islands.

Paradise Lost? Growth, Convergence and Migration in the South Pacific
Author: Norman Loayza and Mr. Paul Cashin
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    South Pacific Countries: Real (1990 Australian Dollars) Per-Capita GDP, 1971-93

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    Convergence of Real Per-Capita GDP Across Nine South Pacific Countries: 1971 GDP and 1971-93 GDP Growth

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    Convergence of Real Per-Capita GDP Across Seven South Pacific Countries: 1971 GDP and 1971-93 GDP Growth

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    Net Migration and Initial Real Per-Capita GDP: 1971-93

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    Dispersion of Real Per-Capita GDP: PAC9, 1971-93

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    Dispersion of Real Per-Capita GDP: PAC7, 1971-93

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    Dispersion of Real Per-Capita GDP: PAC5. 1971-93

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    Dispersion of Real Per-Capita GDP: PAC4, 1971-93