The import price index with trade barriers: theory and evidence

There is a parallel literature analysing “quality upgrading” caused by binding quotas. The quality upgrading literature is distinctly different from the analysis in this paper. For example, Harrigan and Barrows (2009) find that prices and quality of products exported from China to the USA dropped when the multifiber arrangement ended in 2005. They generate quantity, price and quality indices over time for a particular country and run a regression to identify the reduced form effect of ending a binding quota on the exact price index using within country variation over time. In contrast, the topic of this paper is the change in imports from one country to another due trade liberalisation when there exist (quality adjusted) price differences between the supplying countries. Although both fields relate to binding quotas, the index problem of aggregating prices across countries is therefore distinctly different from “quality upgrading” within countries.

This definition is similar to the one adopted by Feenstra (1994). It is also equivalent to Eq. 4 in Balk (1989), who studied time-varying preferences (or production technology). If production technology is time varying, Eq. 6 implies a cardinal interpretation of technology. In the context of this paper, however, the production technology is assumed constant across time periods and thus represents an ordinal entity.

Harrigan and Barrows (2009) apply this price index when analysing how prices and quality of products exported to the USA dropped when the multifiber arrangement ended in 2005.

That is, \(u^\rho _{t-1}=\sum ^n_i\delta _{i}x_{i,t-1}^{\rho }\)is inserted for \(u^\rho _{t}\) in Eq. 9. It is assumed that changes in \(\bar{x}_{jt}\) are such that \( x_{n,t-1}^{\rho }-\sum ^{}_{j\in \mathcal {J}} (\delta _{j}/\delta _{n})( x_{jt}^{\rho }- x_{j,t-1}^{\rho })>0. \)

The Laspeyres index is defined as \(I_t^{L}\equiv \ (\sum _i p_{it}x_{i,t-1}) /(\sum _i p_{i,t-1}x_{i,t-1})=\sum _i s_{i,t-1}(p_{it}/p_{i,t-1})\) for \(i\in \mathcal {J}\cup \{n\}\).

See the appendix, “The bias in import prices due to trade barriers when goods are perfect substitutes” section.

Equation 13 cannot be used directly to calculate the bias when comparing aggregates and not price levels of specific goods. For a given spatial index, \((p_{jt}/p_{nt})\), and temporal indices, \((p_{jt}/p_{j,t-1}) \) and \((x_{jt}/x_{j,t-1}),\) the bias can be written in a more usable form:where \(s_{j,t-1}\) is the cost share of good j in period \(t-1\).

One can conjecture that the condition when the index \(I_t^\mathrm{PS}\) serves as an upper bound can be generalised to more flexible functional forms than CES technology. It is the relative magnitudes of the TRS between the underlying technology and TRS of perfect substitutes that determines whether the index \(I_t^\mathrm{PS}\) is an upper bound. For many technologies, the TRS is greater than the TRS for perfect substitutes when \(x_{1,t-1}/x_{2,t-1}\) is small and the TRS is decreasing with respect to \(x_1\). The cut-off point \(x_{1A}\) for another flexible functional form may, however, be different from the CES case.

\(\Delta \left( p_{jt}/p_{nt} \right) \le 0\) imply that \(p_{j,t-1}/p_{j,t-1}\ge p_{jt}/p_{nt}\).

The responsible area of the customs authorities only covers mainland Norway and its territorial waters. As a supplement, Statistics Norway uses data on important trade in goods to and from the remaining areas of the economic territory collected directly from respondents and registers.

\(\ln (1+z)\approx z\) around \(z\approx 0.\)