# Why has world trade grown faster than world output?

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9 Bank of England Quarterly Bulletin: Autumn 24 Annex We start the empirical estimation with the reduced-form combination of supply and demand determinants as in Rose (1991): Dm/tfe t = a t + b 1 Dm t b 2 Dm t b 3 Dtfe t b 4 Dtfe t b 5 Drt t + b 6 Drt t g(ecm) t - 1 ECM = m/tfe d 1 evol d 2 gdpph d 3 rt d 4 tc d 6 ta d 6 sh where m/tfe denotes the import to total final expenditure ratio; m is total imports; tfe denotes real total final expenditure; (1) rt denotes the relative price of tradables to non-tradables; evol denotes exchange rate volatility; gdpph denotes GDP per head; tc denotes transport costs; ta denotes tariff rates; and sh the share of world output. All variables are in logs. Dynamic terms are included for all variables for which we have quarterly data. Statistical analysis Unit root tests For the above equation to be valid, if the data are I(1), the ECM must form a cointegrating vector. To test for this we use the panel unit root tests suggested by Im, Pesaran and Shin (1997). The tests suggest that most of the variables are not I() in levels. (2) Given that we can more clearly accept stationarity when we difference our data, we assume that the data for the overall panel are I(1). Cointegration analysis Pedroni (1999) constructs seven tests for cointegration in heterogeneous panels with multiple regressors four are based on pooling within dimensions ( panel tests ) and three based on pooling between dimensions ( group statistics ). In our full panel the test statistics allow us to reject the null of no cointegration in four out of seven tests. Estimation results We estimate a system by using restrictions across the cross-sectional dimension in the long run as in Pesaran and Smith (1995) and Pesaran, Shin and Smith (1999). They propose estimation by either averaging the individual country estimates, or by pooling the long-run parameters and estimating the model as a system (pooled mean group estimator PMG consistent with the characteristics and size of our panel). Long-run coefficients are shown in the table below. Using the SUR method, the error correction approach seems appropriate with negative and significant coefficients (at the 5% level) for all the countries in our sample except the United States. All the equation residuals are well behaved according to the LM-test for autocorrelation. Loading coefficients Belgium Canada France Germany Italy Japan Netherlands Sweden United Kingdom United States ECM p-value Pooled coefficients Coefficient p-value Exchange rate volatility.3.4 GDP per head Relative prices.48. Tariffs.14. Share of world output.59. Transport costs P-values above.5 indicate insignificant coefficients at the 5% level. (1) Import volumes and total final expenditure data are from the OECD. (2) Variables that are stationary in levels over the sample period are exchange rate volatility for Belgium, Canada, Germany, Japan, Sweden and the United States and the share of world output for Belgium. 318

11 Bank of England Quarterly Bulletin: Autumn 24 OECD (22), Intra-industry and intra-firm trade and the internationalisation of production, OECD Economic Outlook, No. 71, pages Pedroni, P (1999), Critical values for cointegration tests in heterogeneous panels with multiple regressors, Oxford Bulletin of Economics and Statistics: Special Issue, pages Pesaran, M H, Shin, Y and Smith, R (1999), Estimating long-run relationships from dynamic heterogeneous panels, Journal of Econometrics, Vol. 68, pages Pesaran, M H and Smith, R (1995), Pooled mean group estimation of dynamic heterogeneous panels, Journal of the American Statistical Association, Vol. 94, pages Rose, A K (1991), Why has trade grown faster than income?, Canadian Journal of Economics, Vol. XXIV, No 2, pages

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