Productivity Spillovers in the Global Market

Abstract

This paper analyzes the effect of productivity shocks originating from other countries on economic growth in the home country. Traditionally, productivity shocks have been considered as driving forces of economic growth in their home countries. However, productivity improvements occur both at home and overseas. In liberalized global markets, economic growth is, in theory, also attributable to productivity shocks from other countries. Using data from 18 countries, we show that numerous countries benefit from productivity spillovers. Nevertheless, their impacts on the economy differ according to the origin of the economic shocks. On the one hand, US shocks are rather pervasive and affect many economies and regions, regardless of their development stage. On the other hand, shocks from other country groups exert less influence over foreign economies. Thus, homogeneous effects of productivity spillovers across countries, which are often assumed in previous studies using the standard panel data and spatial models, are inappropriate. The mixed results from previous global analyses, particularly using macroeconomic data, are attributable to such heterogeneous effects of productivity shocks.

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Appendix

1.1 GIRF and SGIRF

The generalized impulse-response functions (GIRFs) was introduced by Koop et al. (1996) and further developed by Pesaran and Shin (1998). Let us consider the model obtained during the solution of the GVAR, expressed in terms of the country-specific errors given by Eq. (14). The GIRFs are based on the definition:

$$\begin{aligned} {\mathrm{GIRF}} (y_t;u_{i,l,t};h)=E(y_{t+h}|u_{i,l,t}=\sqrt{\sigma _{ii,ll}},I_{t-1}) - E(y_{t+h}|I_{t-1}) \end{aligned}$$

(17)

where $I_{t-1}$ is the information set at time $t-1$, $\sigma _{ii,ll}$ is the diagonal element of the variance covariance matrix $\Sigma _u$ corresponding to the lth equation in the ith country, and h is the horizon. GIRFs are invariant to the ordering of variables, and they allow for correlation of the error terms (the error terms are not orthogonal).

The structural generalized impulse-response functions (SGIRFs) used in this paper allows ordering of variables to one country. As the USA is the largest and the most dominant economy in this model, it is ordered first and its variables are ordered in the way mentioned in Sect. 4.1. The SGIRFs are invariant to the ordering of other countries and their variables. Let us consider the $VARX^*(p_1,q_1)$ model for the USA.

$$\begin{aligned} y_{1,t}=a_{1,0}+a_{1,1}t+\sum \limits _{j=1}^p \alpha _{1,j}y_{1,t-j}+\sum \limits _{j=1}^q \beta _{1,j} y^*_{1,t-j}+u_{1,t} \end{aligned}$$

(18)

Let $V_{1,t}$ be structural shocks given by $V_{1,t}=P_1u_{1,t}$, where $P_1$ is the $k_1\times k_1$ matrix of coefficients to be identified. The identification conditions using the triangular approach of Sims (1980) require $\Sigma _{v,1}={\mathrm{Cov}}(v_{1,t})$ to be diagonal and $P_1$ to be lower triangular. Let $Q_1$ be the upper Cholesky factor of ${\mathrm{Cov}}(u_{1,t})=\Sigma _{u,1}=Q^{'}_1 Q_1$ so that $\Sigma _{v,1}=P_1\Sigma _{u,1} P^{'}_1$ with $P_1=(Q^{'}_1)^{-1}$ Under this orthogonalization scheme, ${\mathrm{Cov}}(v_{i,t})=I_{k_0}$

Pre-multiplying the GVAR model in Eq. (14) by

$$ P^{1}_{G_{1}}= \left[ \begin{array}{cccc} P_0 &{} 0 &{} 0 &{} 0\\ 0 &{} I_{k_1} &{} 0 &{} 0 \\ 0 &{} 0 &{} \ddots &{} 0 \\ 0 &{} 0 &{} 0 &{} I_{k_n} \end{array} \right] $$

It follows that

$$\begin{aligned} P^{1}_{G_1} G_1 y_t= P^{1}_{G_1} G_1 y_{t-1}+ \cdots + P^{1}_{G_1} G_p y_{t-p}+ v_t \end{aligned}$$

(19)

where $v_t=(v'_{1t}, u'_{1t}, \ldots , u'_{Nt})$ and

$$ \Sigma _v={\mathrm{Cov}}(v_t)= \left[ {\begin{array}{cccccc} V(v_{1t}) &{} {\mathrm{Cov}}(v_{1t},u_{1t}) &{} . &{} . &{} . &{} {\mathrm{Cov}}(v_{1t}, u_{Nt})\\ {\mathrm{Cov}}(u_{1t},v_{1t}) &{} V(u_{1t}) &{} . &{} . &{} . &{} {\mathrm{Cov}}(u_{1t},u_{Nt}) \\ \vdots &{} \vdots &{} &{} &{} &{} \vdots \\ {\mathrm{Cov}}(u_{Nt},v_{1t}) &{} {\mathrm{Cov}}(u_{Nt},u_{1t}) &{} . &{} . &{} . &{} V(u_{Nt}) \end{array} } \right] $$

with

$$ V(v_{1t})=\Sigma _{v,11}=P_1 \Sigma _{u,11} P^{1}_1\text { and }{\mathrm{Cov}}(v_{1t},u_{jt})={\mathrm{Cov}}(P_1 u_{1t}, u_{jt})=P_0 \Sigma _{u_{1j}} $$

By using the definition of the generalized impulse responses with respect to structural shocks given by

$$\begin{aligned} {\mathrm{SGIRF}} (y_t;v_{l,t};h)=E(y_{t+h}|I_{t-1}\varrho '_{l} v_{t}=\sqrt{\varrho '_{l} \Sigma _v \varrho _l,}) - E(y_{t+h}|I_{t-1}) \end{aligned}$$

(20)

it follows that for a structurally identified shock, $v_{lt}$ such as a US trade shock the SGIRF is given by

$$ {\mathrm{SGIRF}} (y_t;v_{l,t};h)=\frac{\varrho _j A_n {(P_{G_1} G_1)}^{-1} \Sigma _v \varrho _l}{\sqrt{\varrho _{l} \Sigma _v \varrho _l}},\, h=0,1,2,; j=1,2,\ldots ,k $$

where $\varrho _l =(0,0,\ldots ,0,1,0,\ldots 0)'$ is a selection vector with unity as the lth element in the case of a country-specific shock, $\Sigma _v$ is the covariance matrix of structural shocks, and $P'_{G_1} G_1$ is defined by the identification scheme used to identify the shocks.