Trade policy substitution: theory and evidence

Abstract

With the help of a political economy model, we show that the extent of ‘trade policy substitution’—namely, substitution of tariffs with non-tariff measures (NTMs)—depends on the cost differential between domestic and foreign firms in complying with product standards. The model suggests the prevalence of trade policy substitution in developed economies, where the costs of compliance are relatively low. We test and validate this prediction using a database on NTMs that identifies actual trade restrictions. We further examine the possible protectionist use of trade policy substitution exploiting information on the end of the Multifibre Arrangement (MFA) and on WTO notifications.

Appendices

Derivations of the results in Sect. 2

1.1 Domestic producers’ iso-profit condition

The iso-profit curve, describing the combinations of tariffs and standards that make producers indifferent between the two policy instruments, is obtained by totally differentiating (3) with respect to $\tau$ and $\sigma$, yielding:

$$\begin{aligned} d\pi \left( \tau ,\sigma \right) =\frac{\partial \pi \left( \tau ,\sigma \right) }{\partial \sigma }d\sigma +\frac{\partial \pi \left( \tau ,\sigma \right) }{\partial \tau }d\tau =\left[ \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }-\frac{\partial \phi \left( \sigma \right) }{\partial \sigma }\right] y\left( \tau ,\sigma \right) d\sigma +y\left( \tau ,\sigma \right) d\tau . \end{aligned}$$

(9)

Along iso-profit curves, $d\pi \left( \tau ,\sigma \right) =0$, giving the following condition:

$$\begin{aligned} \frac{d\sigma }{d\tau }=-\left[ \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }-\frac{\partial \phi \left( \sigma \right) }{\partial \sigma }\right] ^{-1}. \end{aligned}$$

(10)

From the perspective of domestic producers, the two instruments are substitutes if $d\sigma /d\tau <0$, which is the case if domestic producers have a cost advantage in meeting the standard, $\frac{\partial \phi \left( \sigma \right) }{\partial \sigma }<\frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }$. Domestic producers will not lobby for the imposition of a standard if this condition is not fulfilled.

1.2 Welfare function

The standard utilitarian welfare function (second term in Eq. (4)) is defined as follows:

$$\begin{aligned} W\left( \tau ,\sigma \right) \equiv \pi \left( \tau ,\sigma \right) +s\left( \tau ,\sigma \right) +\tau IM\left( \tau ,\sigma \right) +\phi ^{*}\left( \sigma \right) IM\left( \tau ,\sigma \right) . \end{aligned}$$

(11)

In expression (11), $\pi \left( \tau ,\sigma \right)$ is the producer surplus, defined in Eq. (3); $s\left( \tau ,\sigma \right)$ is the consumer surplus, which is equal to the following expression:

$$\begin{aligned} \int \limits _{1+\phi ^{*}\left( \sigma \right) +\tau }^{\overline{p}}D\left( p\right) dp, \end{aligned}$$

(12)

where $\overline{p}$ is the consumers’ reservation price; and $IM\left( \tau ,\sigma \right)$ is the level of imports, defined as the difference between demand and supply:

$$\begin{aligned} IM\left( \tau ,\sigma \right) =D\left( \tau ,\sigma \right) -y\left( \tau ,\sigma \right) . \end{aligned}$$

(13)

Note that the last term in Eq. (11) represents the rent (if any) associated with imposing the standard. The following first derivatives will be useful in the derivations in section 'Sign of the trade policy substitution condition' of Appendix:

$$\begin{aligned}&\frac{\partial \pi \left( \tau ,\sigma \right) }{\partial \sigma }=\left[ \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }-\frac{\partial \phi \left( \sigma \right) }{\partial \sigma }\right] y\left( \tau ,\sigma \right) , \end{aligned}$$

(14)

$$\begin{aligned}&\frac{\partial s\left( \tau ,\sigma \right) }{\partial \sigma }=-\frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }D\left( \tau ,\sigma \right) , \end{aligned}$$

(15)

and

$$\begin{aligned} \frac{\partial IM\left( \tau ,\sigma \right) }{\partial \sigma }=\frac{\partial D\left( \tau ,\sigma \right) }{\partial \sigma }-\frac{\partial y\left( \tau ,\sigma \right) }{\partial \sigma }=\frac{\partial D\left( \tau ,\sigma \right) }{\partial \tau }\frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }-\frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }+\frac{\partial \phi \left( \sigma \right) }{\partial \sigma }. \end{aligned}$$

(16)

In the last expression (16), we have used the assumption that consumers do not care about the standard, if not for its effect on prices. (In other words, the standard is not a demand shifter).

1.3 Sign of the trade policy substitution condition

To sign the trade policy substitution condition (5), we start with the first order condition for the government’s second best problem, $\left. \frac{\partial V\left( \tau ,\sigma \right) }{\partial \sigma }\right| _{\widetilde{\tau }}=0$:

$$\begin{aligned}&\left. \frac{\partial V\left( \tau ,\sigma \right) }{\partial \sigma } \right| _{\widetilde{\tau }}=\left. \frac{\partial \pi \left( \tau ,\sigma \right) }{\partial \sigma }\right| _{\widetilde{\tau }}+a\left. \frac{\partial W\left( \tau ,\sigma \right) }{\partial \sigma }\right| _{ \widetilde{\tau }}=0\Rightarrow \end{aligned}$$

(17)

$$\begin{aligned}&\left[ \left. \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}-\left. \frac{\partial \phi \left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}\right] \underbrace{y(\widetilde{\tau },\sigma ^{u})}_{>0} \underbrace{-\text { }a\left. \frac{\partial \phi \left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}y\left( \widetilde{\tau },\sigma ^{u}\right) +a\left( \left. \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}+\widetilde{\tau }\right) \left. \frac{\partial IM\left( \tau ,\sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}}_{<0}=0, \end{aligned}$$

(18)

where $\sigma ^{u}$ is the level of the standard that satisfies (17). From this FOC, it is clear that a necessary condition under which tightening the standard is optimal for the government is that domestic producers have a marginal cost advantage:

$$\begin{aligned} \left. \frac{\partial \phi \left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}<\left. \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}. \end{aligned}$$

(19)

Applying the implicit function theorem on (17), we get:

$$\begin{aligned} \left. \frac{\partial V\left( \tau ,\sigma \right) }{\partial \sigma } \right| _{\widetilde{\tau }}=0\Rightarrow \left( \frac{d\sigma ^{u}}{d\tau }\right) =-\left. \frac{\partial ^{2}V\left( \tau ,\sigma \right) }{\partial \tau \partial \sigma }\right| _{\sigma ^{u}}\underbrace{\left[ \left. \frac{\partial ^{2}V\left( \tau ,\sigma \right) }{\partial \sigma ^{2}}\right| _{\sigma ^{u}}\right] ^{-1}}_{<0}, \end{aligned}$$

(20)

where the negative sign on the last term follows from the second order condition for a maximum. Therefore,

$$\begin{aligned} {{\,{\mathrm{sign}}\,}}\left( \frac{d\sigma ^{u}}{d\tau } \right) ={{\,{\mathrm{sign}}\,}}\left( \left. \frac{\partial ^{2}V\left( \tau ,\sigma \right) }{\partial \tau \partial \sigma }\right| _{\sigma ^{u}} \right) ={{\,{\mathrm{sign}}\,}}\left( \left. \frac{\partial ^{2}\pi \left( \tau ,\sigma \right) }{\partial \tau \partial \sigma }\right| _{\sigma ^{u}}+a\left. \frac{ \partial W^{2}\left( \tau ,\sigma \right) }{\partial \tau \partial \sigma }\right| _{\sigma ^{u}}\right) . \end{aligned}$$

(21)

Consider the first element on the right-hand side of (21), $\left. \frac{\partial ^{2}\pi \left( \tau ,\sigma \right) }{\partial \tau \partial \sigma }\right| _{\sigma ^{u}}$. From (14), this derivative can be computed as:

$$\begin{aligned} \left. \frac{\partial ^{2}\pi \left( \tau ,\sigma \right) }{\partial \tau \partial \sigma }\right| _{\sigma ^{u}}=\left. \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}-\left. \frac{\partial \phi \left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}. \end{aligned}$$

(22)

From (14), (15) and (16), we get:

$$\begin{aligned} \left. \frac{\partial ^{2}W\left( \tau ,\sigma \right) }{\partial \tau \partial \sigma }\right| _{\sigma ^{u}}=\left. \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}\left( \left. \frac{\partial D\left( \tau ,\sigma \right) }{\partial \tau }\right| _{\sigma ^{u}}-1\right) +\left[ \phi ^{*}\left( \sigma ^{u}\right) +\tau \right] \left. \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}\left. \frac{\partial ^{2}D\left( \sigma ,\tau \right) }{\partial \tau ^{2}}\right| _{\sigma ^{u}}. \end{aligned}$$

(23)

Note that the last term on the right-hand side of (23) is of second-order. With little loss of generality, we assume linear demand, so that $\left. \frac{\partial ^{2}D\left( \sigma ,\tau \right) }{\partial \tau ^{2}}\right| _{\sigma ^{u}}=0$. We are therefore left only with the first term on the right-hand side of (23). From Eqs. (22) and (23), a necessary condition for trade policy substitution is the following:

$$\begin{aligned} \left. \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}-\left. \frac{\partial \phi \left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}<a\left. \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}\underbrace{\left( 1-\left. \frac{\partial D\left( \tau ,\sigma \right) }{\partial \tau }\right| _{\sigma ^{u}}\right) }_{>0}. \end{aligned}$$

(24)

The two necessary conditions for trade policy substitution, (19) and (24), together imply that trade policy substitution occurs if:

$$\begin{aligned} 1<\kappa <\underbrace{\left[ 1-a\left( 1-\left. \frac{\partial D\left( \tau ,\sigma \right) }{\partial \tau }\right| _{\sigma ^{u}}\right) \right] ^{-1}}_{>1}, \end{aligned}$$

(25)

where $\kappa \equiv \left. \frac{\partial \phi ^{*}\left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}\left( \left. \frac{\partial \phi \left( \sigma \right) }{\partial \sigma }\right| _{\sigma ^{u}}\right) ^{-1}$ is the (marginal) cost advantage of domestic producers relative to foreign producers in meeting the standard. This is expression (6) in the main text.

Appendix 2

See Table 11.

Table 11 List of countries in the sample