The Slowdown in Global Trade: A Symptom of a Weak Recovery?

Abstract

Global trade growth has slowed since 2012 relative both to its strong historical performance and to overall economic growth. This paper aims to quantify the role of weak economic growth and changes in its decomposition in accounting for the slowdown in trade using a reduced form and a structural approach. Both analytical investigations suggest that the overall weakness in economic activity, particularly investment, has been the primary restraint on trade growth, accounting for about 80% of the decline in the growth of the volume of goods trade between 2012–2016 and 2003–2007. However, other factors are also weighing on trade in recent years, especially in emerging market and developing economies, as evidenced by the non-negligible role attributed to trade costs by the structural approach.

Appendix: General Equilibrium Model

This Appendix lays out the details of the structural model discussed in Section IV. The framework is the same as that developed by Eaton et al. (2010) except for the modeling of the commodities as a separate sector.

1.1 Sectors

There are four sectors: two manufacturing sectors broken down into durables and nondurables, commodities and a residual sector labeled as services. The commodities sector includes “mining and quarrying” and “coke, refined petroleum products and nuclear fuel.” The residual sector comprises primarily services but also includes “agriculture, hunting, forestry and fishing.” The sets of all sectors and tradable sectors are defined as $\Omega = \{ Dr, N, C, S\}$ and $\Omega _{T} = \left\{ {Dr, N, C} \right\}$, respectively, where Dr, N, C, and S denote the durable, nondurable manufacturing, commodities, and services sectors.

1.2 Gross Production, Absorption, and the Trade Balance

There are I countries indexed by i and sectors are indexed by j. Goods markets are perfectly competitive, and production is constant returns to scale. $Y_{i}^{j}$ and $X_{i}^{j}$ denote gross production and absorption, respectively, of country i in sector j. The difference between production and absorption yields the sectoral trade deficit, $X_{i}^{j} - Y_{i}^{j} = D_{i}^{j}$, whose sum across all sectors yields the overall trade deficit of country i: $\sum\nolimits_{{l \in\Omega }} {D_{i}^{j} = D_{i} }$. The world market clearing requires the sum of all countries’ deficits in each sector to sum to zero: $\sum\nolimits_{i = 1}^{I} {D_{i}^{j} = 0}$. Output can be used as intermediate good in production or as final good. A Cobb–Douglas aggregator is used to aggregate sectoral inputs that enter production.

1.3 Input–Output Structure

Value-added in each sector is a share $\beta_{i}^{j}$ of the sector’s gross output. The share of a sector l as an intermediate good in the production of sector j is denoted by $\gamma_{i}^{jl}$ where $\sum\nolimits_{{l \in\Omega }} {\gamma_{i}^{jl} = 1}$. Following Eaton et al. (2010), we assume both the value-added and intermediate input goods’ shares to be constant over time but variable across sectors and countries. Given the assumed input–output structure, the relationship between gross output and GDP is: $\sum\nolimits_{{j \in\Omega }} {\beta_{i}^{j} Y_{i}^{j} = Y_{i} }$. GDP is also given by $Y_{i} = X_{i} - D_{i}$ where $X_{i}$ is absorption. Labor is mobile across sectors within a country. Denoting wages and labor as $w_{i}$ and $L_{i}$, respectively, GDP is also simply $Y_{i} = \sum\nolimits_{{j \in\Omega }} {w_{i} L_{i}^{j} = w_{i} L_{i} }$ since investment and capital are not explicitly modeled.

1.4 Sectoral Demand

Total demand for a sector’s output is the sum of demand for final consumption and for use as an intermediate good. Denote $\alpha_{i}^{j}$ the share of sector j consumption in country i’s final demand. Using the input–output structure introduced, the following condition characterizes sectoral demand:

$$X_{i}^{j} = \underbrace {{\alpha_{i}^{j} X_{i} }}_{\begin{subarray}{l} {\text{Final}} \\ {\text{demand}} \end{subarray} } + \underbrace {{\mathop \sum \limits_{{l \in\Omega }} \gamma_{i}^{lj} \left( {1 - \beta_{i}^{l} } \right)Y_{i}^{l} }}_{\begin{subarray}{l} {\text{Intermediate}} \\ {\text{input}}\;{\text{demand}} \end{subarray} },$$

where the second term on the right-hand-side sums the use of sector j output as intermediate inputs across all sectors. Since trade in sector S is not explicitly modeled, the services sector can be “folded in” after some algebra, and the sectoral demand equations can be reduced to three, one for each traded sector:

$$X_{i}^{j} = \tilde{\alpha }_{i}^{j} \left( {w_{i} L_{i} + D_{i} } \right) - \delta_{i}^{j} D_{i}^{s} + \mathop \sum \limits_{{l \in\Omega _{T} }} \tilde{\gamma }_{i}^{lj} \left( {1 - \tilde{\beta }_{i}^{l} } \right)Y_{i}^{l}$$

In this formulation, the input–output parameters have been redefined and renormalized as $\delta_{i}^{j} = \frac{{\gamma_{i}^{Sj} \left( {1 - \beta_{i}^{S} } \right)}}{{1 - \gamma_{i}^{SS} (1 - \beta_{i}^{S} )}}$, $\tilde{\alpha }_{i}^{j} = \alpha_{i}^{j} + \delta_{i}^{j} \alpha_{i}^{S}$, $\tilde{\beta }_{i}^{j} = \beta_{i}^{j} + \frac{{\gamma_{i}^{jS} \left( {1 - \beta_{i}^{j} } \right)\beta_{i}^{S} }}{{1 - \gamma_{i}^{SS} (1 - \beta_{i}^{S} )}}$, $\tilde{\gamma }_{i}^{jl} = \gamma_{i}^{jl} + \gamma_{i}^{jS} \frac{{\gamma_{i}^{jS} \left( {1 - \beta_{i}^{j} } \right)\beta_{i}^{S} + \gamma_{i}^{jl} \beta_{i}^{S} }}{{1 - \gamma_{i}^{SS} (1 - \beta_{i}^{S} ) - \gamma_{i}^{jS} \beta_{i}^{S} }}$ and $\mathop \sum \limits_{{l \in\Omega _{\text{T}} }} \tilde{\gamma }_{i}^{jl} = 1 .$.

1.5 Technology

The production structure follows Eaton and Kortum (2002) in that each sector comprises a continuum of goods indexed z, which are produced with an efficiency of $a_{i}^{j} (z)$. As standard in this type of models, $a_{i}^{j} (z)$ is a random variable with a country- and sector-specific Fréchet distribution specified as $F_{i}^{j} (a) = \Pr \left[ {a_{i}^{j} \left( z \right) \le a} \right] = e^{{ - T_{i}^{j} a^{ - \theta } }}$. $T_{i}^{j}$ governs the location of the distribution, i.e., country i’s overall efficiency in sector j. $\theta$ controls the dispersion of efficiencies within the distribution and thus the strength of comparative advantage.

1.6 Prices and Trade Costs

Denoting the input cost, which includes the cost of labor and intermediate goods, with $c_{i}^{j}$, and the constant returns to scale assumption, the cost of producing a unit of good z is $c_{i}^{j} /a_{i}^{j} (z)$. Trade is subject to standard iceberg costs, $d_{ni}^{j}$. Therefore, the price offered by country i of good z in county n is: $p_{ni}^{j} \left( z \right) = c_{i}^{j} d_{ni}^{j} /a_{i}^{j} (z)$. Countries shop around for the lowest price supplier, and thus, the price actually paid for good z is the minimum of the prices offered by potential trading partners, i.e., $p_{n}^{j} \left( z \right) = \mathop {\hbox{min} }\limits_{i} \left\{ {p_{ni}^{j} (z)} \right\}$.

Taking prices as given, buyers maximize a CES objective function with an elasticity parameter of $\sigma^{j}$ subject to their budget constraints. Utilizing the properties of the efficiency distribution and the CES objective function, sectoral prices can be written as, where $\varphi^{j}$ a function of $\sigma^{j}$ and $\theta$:

$$p_{n}^{j} = \varphi^{j} \left[ {\mathop \sum \limits_{i = 1}^{I} T_{i}^{j} \left( {c_{i}^{j} d_{ni}^{j} } \right)^{ - \theta } } \right]^{ - 1/\theta } .$$

Noting that the cost can be written as $c_{i}^{j} = \frac{1}{{A_{i}^{jS} }}w_{i}^{{\tilde{\beta }_{i}^{j} }} \mathop \prod \limits_{{l \in\Omega _{T} }} \left( {p_{i}^{l} } \right)^{{\gamma_{i}^{jl} \left( {1 - \beta_{i}^{j} } \right)}}$ to take into account the cost of labor and intermediate inputs, and substituting it in the sectoral price equation above yields:

$$p_{n}^{j} = \varphi^{j} \left[ {\mathop \sum \limits_{i = 1}^{I} \left( {w_{i}^{{\tilde{\beta }_{i}^{j} }} \left( {\mathop \prod \limits_{{l \in\Omega _{T} }} \left( {p_{i}^{l} } \right)^{{\tilde{\gamma }_{i}^{jl} \left( {1 - \tilde{\beta }_{i}^{j} } \right)}} } \right)\frac{{d_{ni}^{j} }}{{A_{i}^{j} }}} \right)^{ - \theta } } \right]^{{ - \frac{1}{\theta }}} .$$

1.7 Trade Shares

Define $\pi_{ni}^{j}$ as the share of country n’s expenditures on sector j goods imported from country i. Total demand for country i’s sector j goods summed across all importers add up to its output:

$$Y_{i}^{j} = \mathop \sum \limits_{n = 1}^{I} \pi_{ni}^{j} X_{n}^{j} .$$

As in Eaton and Kortum (2002), trade shares can be written as

$$\pi_{ni}^{j} = \frac{{T_{i}^{j} \left[ {c_{i}^{j} d_{ni}^{j} } \right]^{ - \theta } }}{{\mathop \sum \nolimits_{k = 1}^{I} T_{k}^{j} \left[ {c_{k}^{j} d_{nk}^{j} } \right]^{ - \theta } }}.$$

Substituting in the expressions for input costs and sectoral prices above yields:

$$\pi_{ni}^{j} = \left[ {w_{i}^{{\tilde{\beta }_{i}^{j} }} \left( {\mathop \prod \limits_{{l \in\Omega _{T} }} \left( {p_{i}^{l} } \right)^{{\tilde{\gamma }_{i}^{jl} \left( {1 - \tilde{\beta }_{i}^{j} } \right)}} } \right)\frac{{\varphi^{j} d_{ni}^{j} }}{{A_{i}^{j} p_{n}^{j} }}} \right]^{ - \theta } .$$

1.8 Market Clearing

The market clearing conditions equalize country $i$’s gross output (on the left) to global spending on this county’s tradable output (on the right).

$$Y_{i}^{Dr} + Y_{i}^{N} + Y_{i}^{C} = \mathop \sum \limits_{{l \in \varOmega_{T} }} \mathop \sum \limits_{n = 1}^{I} \pi_{ni}^{l} X_{n}^{l}$$

Substituting the expression for the trade shares in the sectoral demand function yields:

$$X_{i}^{j} = \tilde{\alpha }_{i}^{j} \left( {w_{i} L_{i} + D_{i} } \right) - \delta_{i}^{j} D_{i}^{S} + \mathop \sum \limits_{{l \in \varOmega_{T} }} \tilde{\gamma }_{i}^{lj} \left( {1 - \tilde{\beta }_{i}^{l} } \right)\left( {\mathop \sum \limits_{n = 1}^{I} \pi_{ni}^{l} X_{n}^{l} } \right)$$

Labor supply is fixed, so labor market clearing requires $L_{i} = \bar{L}$.

1.9 Solving for the Counterfactual Scenarios

As described in the main text, the solution procedure utilizes the “exact hat algebra” a la Dekle et al. (2007). Denoting changes using “hat”s and next period or counterfactual values using “prime”s, where $\hat{x} = x^{{\prime }} /x,$ key equations that pin down the model’s equilibrium for a given set of wedges can be rewritten as follows.

Market clearing:

$$\left( {X_{i}^{Dr} } \right)^{\prime } + \left( {X_{i}^{N} } \right)^{\prime } + \left( {X_{i}^{C} } \right)^{\prime } - \left[ {D_{i}^{\prime } - \left( {D_{i}^{S} } \right)^{\prime } } \right] = \mathop \sum \limits_{n = 1}^{I} \left( {\pi_{ni}^{Dr} } \right)^{\prime } \left( {X_{n}^{Dr} } \right)^{\prime } + \mathop \sum \limits_{n = 1}^{I} \left( {\pi_{ni}^{N} } \right)^{\prime } \left( {X_{n}^{N} } \right)^{\prime } + \mathop \sum \limits_{n = 1}^{I} \left( {\pi_{ni}^{C} } \right)^{\prime } \left( {X_{n}^{C} } \right)^{\prime }$$

Sectoral demand (noting that $Y_{i}^{{\prime }} = \hat{w}_{i} Y_{i}$ given fixed labor supply):

$$\left( {X_{i}^{j} } \right)^{\prime } = \left( {\tilde{\alpha }_{i}^{j} } \right)^{\prime } \left( {\hat{w}_{i} Y_{i} + D_{i}^{\prime } } \right) - \delta_{i}^{j} \left( { D_{i}^{S} } \right)^{\prime } + \mathop \sum \limits_{{l \in \varOmega_{T} }} \tilde{\gamma }_{i}^{lj} \left( {1 - \tilde{\beta }_{i}^{l} } \right)\left[ {\mathop \sum \limits_{n = 1}^{I} \left( {\pi_{ni}^{l} } \right)^{\prime } \left( {X_{n}^{l} } \right)^{\prime } } \right]$$

Sectoral price:

$$\hat{p}_{n}^{j} = \left( {\mathop \sum \limits_{i = 1}^{I} \pi_{ni}^{j} \hat{w}_{i}^{{ - \tilde{\theta } \tilde{\beta }_{i}^{j} }} \left( {\mathop \prod \limits_{{l \in \varOmega_{T} }} \left( {\hat{p}_{i}^{l} } \right)^{{ - \theta \tilde{\gamma }_{i}^{jl} \left( {1 - \tilde{\beta }_{i}^{j} } \right)}} } \right)\left( {\frac{{\hat{d}_{ni}^{j} }}{{\hat{A}_{i}^{j} }}} \right)^{ - \theta } } \right)^{ - 1/\theta }$$

Trade shares:

$$\left( {\pi_{ni}^{j} } \right)^{\prime } = \pi_{ni}^{j} \hat{w}_{i}^{{ - \tilde{\theta }\tilde{\beta }_{i}^{j} }} \left( {\mathop \prod \limits_{{l \in \varOmega_{T} }} \left( {\hat{p}_{i}^{l} } \right)^{{ - \theta \tilde{\gamma }_{i}^{jl} \left( {1 - \tilde{\beta }_{i}^{j} } \right)}} } \right)\left( {\frac{{\hat{d}_{ni}^{j} }}{{\hat{A}_{i}^{j} \hat{p}_{n}^{j} }}} \right)^{ - \theta }$$

The four equations above constitute a system of nonlinear equations with four sets of unknowns: wage changes, price changes, counterfactual or end-of-period sectoral demand, and trade shares. The solution procedure starts with a conjecture for wage changes. It then solves for prices changes by iterating on the sectoral price equation above. Conjectured wage changes and price changes consistent with the wage change conjecture are plugged in the trade share equation to obtain counterfactual trade shares, which are subsequently used to compute sectoral prices. Finally, the procedure checks whether the market clearing condition holds and updates the wage conjecture accordingly. If the market clearing is satisfied up to a low numerical error threshold, the procedure stops.

1.10 Obtaining the Wedges

The sectoral demand equation using matrix notation is:

$${\mathbf{X}}_{i} = {\mathbf{Y}}_{i} + {\mathbf{D}}_{i} = {\varvec{\upalpha}}_{i} X_{i} + {\varvec{\Gamma}}_{i}^{T} {\mathbf{Y}}_{i}$$

where ${\varvec{\Gamma}}_{i}$ is a matrix with $\gamma_{i}^{lj} \left( {1 - \beta_{i}^{l} } \right)$ in the lth row and jth column and the sectors are ordered as Dr, N, C, and S. Demand composition wedges can then be calculated by substituting in the empirical counterparts of the right-hand-side variables in the following equation:

$${\varvec{\upalpha}}_{i} = \frac{1}{{X_{i} }}\left( {{\mathbf{X}}_{i} - {\varvec{\Gamma}}_{i}^{T} {\mathbf{Y}}_{i} } \right),$$

Trade deficit wedges, $D_{i}^{j}$, are exogenous and simply fed from the data.

Changes in trade cost wedges are obtained using data on bilateral trade shares and sectoral prices, and the standard gravity equation in changes: $\left( {\hat{d}_{ni}^{j} } \right)^{ - \theta } = \frac{{\hat{\pi }_{ni}^{j} }}{{\hat{\pi }_{ii}^{j} }}\left( {\frac{{\hat{p}_{i}^{j} }}{{\hat{p}_{n}^{j} }}} \right)^{\theta }$. The condition to back out changes in the productivity wedges can be derived by rearranging the above equation that characterizes the changes in trade shares:

$$\hat{A}_{i}^{j} = \left( {\hat{\pi }_{ii}^{j} } \right)^{1/\theta } \hat{w}_{i}^{{\tilde{\beta }_{i}^{j} }} \left( {\hat{p}_{i}^{j} } \right)^{{\tilde{\gamma }_{i}^{jj} \left( {1 - \tilde{\beta }_{i}^{j} } \right) - 1 }} \mathop \prod \limits_{{l \in \varOmega_{T} , l \ne j }} \left( {\hat{p}_{i}^{l} } \right)^{{\tilde{\gamma }_{i}^{jl} \left( {1 - \tilde{\beta }_{i}^{j} } \right)}} .$$