2 Methodology

In line with other empirical studies of cross-country growth spillovers, this paper employs a VAR methodology, which explicitly allows for dynamic interactions between variables. The main tool employed is the so-called structural vector autoregressive (SVAR) model, which in our context is used to specify that a small country (specifically New Zealand) can be affected by, but does not influence, growth in a large country (China or the US, say).

Representing output growth for the foreign country and New Zealand in a particular period t (typically a quarter) by y_F,t and y_NZ,t, respectively, the form of the SVAR[3] often used in this context can be written as

      (1)

in which y_NZ,t depends on contemporaneous y_F,t (through the term in the second equation),but not vice versa, while the lagged variables capture cross-country and internal growth dynamics. Additional lags, beyond one period, can easily be accommodated in this system and are also discussed below. Each equation is a dynamic regression model and, provided that the SVAR captures all the dynamics of growth, the disturbances u_F,t and u_NZ,t are uncorrelated over time. Further, through the imposition of the assumption that contemporaneous causality runs from y_F,t to y_NZ,t, these disturbances are also mutually uncorrelated. Since they cannot be predicted by the system, u_F,t and u_NZ,t are often referred to as 'shocks'. The VAR then permits estimation of the effects over time of a shock (such as a 1% increase) in output growth in the large foreign country on growth in the small country.

The form of the SVAR given in (1) embeds economic information through the causality assumption that the small open economy will not have contemporaneous feedback to the large economy[4]. An assumption of this type is made by virtually all papers concerned with international growth spillovers to small countries, including Sun (2011). However, we prefer to impose a stronger assumption.

Although the contemporaneous causality is assumed to apply only from the large to the small economy, the SVAR model of (1) treats the two countries in a symmetric way in terms of potential feedbacks or spillovers over time. However, it is a priori implausible that a small country like New Zealand will affect growth in China or the US in any way. This implies that the restriction b₁₂ = 0 (with corresponding zero restrictions also on any further lags) should be imposed in (1), so that the system becomes

      (2)

and output growth in the large economy is influenced by its own past, but not y_NZ,t-1. Restrictions of this form, often referred to as exogeneity restrictions, were popularised by Cushman and Zha (1997) in the context of modelling Canada and the US. Such exogeneity restrictions are imposed in the New Zealand studies of Buckle et al. (2007) and Dungey and Fry (2009), while Sato et al. (2011) use the form of (2) when analysing the role of shocks in China or the US on individual East Asian economies. Although Sun (2011) leaves the lags unrestricted as in (1), she notes that the estimated spillover effects from Australia and New Zealand to large economies are small[5]. Nevertheless, using the Cushman and Zha (1997) model for Canada and the US, Zha (1999) illustrates the undesirable implications that the SVAR can yield when these restrictions are not imposed on the role of the small economy.

Additional countries can easily be incorporated in the analysis. Indeed, Sun (2011) employs five GDP growth series, namely for the US, 'emerging Asia' (including China), the rest of the world, Australia and New Zealand. In the framework of (1), and hence imposing no restrictions on the coefficients of lagged values, she assumes that the first three series represent large economies that contemporaneously cause growth in Australia and New Zealand, with Australia in turn contemporaneously causing New Zealand output growth. As noted above, however, this analysis imposes only the direction of contemporaneous causality, allowing feedbacks across all series. Following the arguments of Bayoumi and Swiston (2009), no specific stance is taken on the causal ordering between the first three growth rate series. Rather, the main analysis is based on averaging across the SVARs that result from considering each of the six possible causality orderings between the US, emerging Asia and the rest of the world.

Recognising the small size of the New Zealand economy, the analysis of the present paper is based on the more restricted form of (2). Therefore, exogeneity restrictions are employed to avoid the anomalous implications of the estimated SVAR model for the effect of the small economy on the dominant large one over time, as documented by Zha (1999). However, in the light of the role of Australia as New Zealand's largest trading partner, a generalisation of (2) is employed, which for three countries is given by

      (3)

where the countries are ordered as China (or the US), Australia and New Zealand. In other words, and in line with the relative sizes of these economies, output growth in China/US (country F₁) is exogenous to both Australia (country F₂) and New Zealand, while Australia is similarly exogenous to New Zealand.

The models outlined so far in (1) to (3) consider only output growth. However, it is also important for macroeconomic policy that the impacts of output growth in China (or, indeed, the US or Australia) influence other key variables for New Zealand, namely inflation, interest rates and the exchange rate. This block of domestic variables then replaces y_NZ,t in (3). In an analogous way to that for the variables in (1), a contemporaneous causal ordering is imposed within the domestic variable block in the extended model. This follows the conventional contemporaneous causal order widely used in empirical SVAR modelling, namely output growth, inflation, interest rate and the nominal exchange rate. Therefore, domestic output growth responds to foreign output growth in the current quarter but not to current values of any domestic variables, inflation can respond to contemporaneous values of both foreign and domestic output growth, interest rates respond to current foreign and domestic output growth and (domestic) inflation, while the exchange rate is affected by all variables. The lagged coefficients are unrestricted within the domestic block, so that the lags of all (foreign and domestic) variables are included in the equation for each variable in this block.

The above discussion assumes the presence of only one large economy, China or the US. When both are included, in (3) becomes a two variable vector. Although our models then permits dynamic feedback in both directions, US economic growth is assumed to contemporaneously cause that in China. The extension to include world commodity prices takes a similar form, with this being added as a third variable in the block, with the order of contemporaneous causality being US growth, China growth, world commodity price inflation.

In summary, the SVAR model we employ in matrix form is

      (4)

in which y_tis a vector containing all the variables of the model, while A and B₁ are matrices. The specific form used imposes A to be lower triangular (with diagonal elements of unity), while zero restrictions are placed on appropriate lagged coefficients in B₁ in order to impose the restrictions of (2) or (3) that growth spillovers do not occur from a small country to a large one. Although intercepts are not included in (4) for notational ease, in practice all estimated equations include an intercept. With the contemporaneous relationships captured through A, the disturbances u­_t are assumed to be mutually uncorrelated and (following the usual convention in the literature) are referred to as shocks.