The treatment effect of borders on trade. The great war and the disintegration of Central Europe

Abstract

This paper investigates the impact of changes in national border demarcation on economic integration. It treats the national breakups in Central Europe due to WWI as a natural experiment. The set-up allows to control for selection bias when estimating the impact of national borders on trade. A gravity model of trade is used to analyze goods-specific trade among Central European regions. The main results are, first, that systematic deviations of the observations under “border treatment” are found. Regions pairs that became separated by a new national border after WWI, tended to have below average levels of economic integration already before the war. A comparison of actual and biased result for goods-specific trade yields a difference of between 21 and 86% ad-valorem tariff equivalent, and might well be higher for certain goods. Second, the analysis indicates that cross-border integration was indeed lower after WWI but that this change was economically significant only for certain sectors. Third, in the interwar period, international trade was less diverted by borders first established after the war than by borders existing already before WWI. The results stress the importance of relative barriers to trade in attenuating the adverse effects of WWI on economic integration.

Appendices

Appendix A: Derivation of the gravity equation

Anderson and van Wincoop (2004) formulate the consumer maximization function as follows

$${\mathop {\max}\limits_{c^{k}_{{ij}}}}\;\;U_{j} = {\sum\limits_k {{\left({{\sum\limits_i {{\left({\beta ^{k}_{i}} \right)}^{{(1 - \sigma_{k})/\sigma_{k}}} {\left({c^{k}_{{ij}}} \right)}^{{(\sigma_{k} - 1)/\sigma_{k}}}}}} \right)}^{{\sigma_{k} /(\sigma_{k} - 1)}}}} \hbox{s.t. the budget constraint}$$

(13)

$$Y_{j} = {\sum\limits_k {E^{k}_{j}}} = {\sum\limits_k {{\sum\limits_i {p^{k}_{{ij}} c^{k}_{{ij}}}}}}$$

(14)

where

c ^k _ij :

denotes region j’s consumption of region i’s goods in product class k.

σ _k :

is the elasticity of substitution between all goods in product class k.

β ^k _i :

is some positive distribution parameter.

Y _j :

is the nominal income of region j’s inhabitants.

E ^k _j :

is the nominal expenditure of region j’s inhabitants on product k.

p ^k _ij :

denotes the price charged by region i for exports of product k to region j.

Demand for region i’s goods by region j’s consumers has to satisfy maximization of (13) subject to the budget constraint (14). From the Lagrangian we obtain the first order conditions:

$${\left({{\sum\limits_i {{\left({\beta ^{k}_{i}} \right)}^{{(1 - \sigma_{k})/\sigma_{k}}} {\left({c^{k}_{{ij}}} \right)}^{{(\sigma_{k} - 1)/\sigma_{k}}}}}} \right)}^{{1/(\sigma_{k} - 1)}} {\left({\beta ^{k}_{i}} \right)}^{{(1 - \sigma_{k})/\sigma_{k}}} {\left({c^{k}_{{ij}}} \right)}^{{- 1/\sigma_{k}}} \frac{{\sigma_{k} - 1}}{{\sigma_{k}}} = \lambda {\kern 1pt} p^{k}_{{ij}} \quad \forall i \ne j$$

(15)

$${\left({{\sum\limits_i {{\left({\beta ^{k}_{i}} \right)}^{{(1 - \sigma_{k})/\sigma_{k}}} {\left({c^{k}_{{ij}}} \right)}^{{(\sigma_{k} - 1)/\sigma_{k}}}}}} \right)}^{{1/(\sigma_{k} - 1)}} {\left({\beta ^{k}_{j}} \right)}^{{(1 - \sigma_{k})/\sigma_{k}}} {\left({c^{k}_{{jj}}} \right)}^{{- 1/\sigma_{k}}} \frac{{\sigma_{k} - 1}}{{\sigma_{k}}} = \lambda {\kern 1pt} p^{k}_{{jj}} $$

(16)

$${\sum\limits_k {{\sum\limits_i {p^{k}_{{ij}} c^{k}_{{ij}} = Y_{j}}}}}$$

(17)

where (15a) and (15b) hold for all sectors k. Set equal (15a) and (15b). Rearranging them yields

$$p^{k}_{{ij}} c^{k}_{{ij}} = {\left({\frac{{\beta ^{k}_{i}}}{{\beta ^{k}_{j}}}} \right)}^{{(1 - \sigma_{k})}} c^{k}_{{jj}} {\left({p^{k}_{{ij}}} \right)}^{{1 - \sigma_{k}}} {\left({p^{k}_{{jj}}} \right)}^{{\sigma_{k}}} \quad \forall i,k$$

(18)

Summing up (16) over all i and using the definition from the budget constraint (14) gives

$${\sum\limits_i {p^{k}_{{ij}} c^{k}_{{ij}}}} = E^{k}_{j} = {\left({\beta ^{k}_{j}} \right)}^{{- (1 - \sigma_{k})}} c^{k}_{{jj}} {\left({p^{k}_{{jj}}} \right)}^{{\sigma_{k}}} {\sum\limits_i {{\left({\beta ^{k}_{i} p^{k}_{{ij}}} \right)}^{{^{{(1 - \sigma_{k})}}}}}}\quad \forall k$$

(19)

Now, one replaces the terms in (17) that do not depend on i (except for E ^k _j ) by the terms in (16) that do not depend on i. After some rearrangement that yields

$$\frac{{{\left({p^{k}_{{ij}} \beta ^{k}_{i}} \right)}^{{(1 - \sigma_{k})}}}}{{{\sum_i {{\left({\beta ^{k}_{i} p^{k}_{{ij}}} \right)}^{{^{{(1 - \sigma_{k})}}}}}}}}E^{k}_{j} = p^{k}_{{ij}} c^{k}_{{ij}} = X^{k}_{{ij}} \quad \forall k$$

(20)

where the latter equation stems from the definition that demand X in region i for products k from region j is given by price times quantity, i.e. ${X_{ij}^k = p_{ij}^k\, c_{ij}^k}.$ One may simplify (18) assuming equal weights β ^k _i for each region of origin. This assumption yields

$$X^{k}_{{ij}} = {\left({\frac{{{\mathop p\nolimits_{ij}^k}}}{{{\mathop P\nolimits_j^k}}}} \right)}^{{1 - \sigma_{k}}} E^{k}_{j} $$

(21)

where P ^k _j is the CES price index in j defined as

$$P^{k}_{j} \equiv {\left[ {{\sum\limits_i {{\left({{\mathop p\nolimits_{ij}^k}} \right)}}}^{{1 - \sigma_{k}}}} \right]}^{{1/(1 - \sigma_{k})}} $$

(22)

Prices p ^k _ij differ between locations due to a mark-up on p ^k _i , which is the supply price received by producers of k in region i. To achieve a formulation like (19) and (20), several assumptions were needed. (i) I assumed that the mark-up on prices contains only the ad-valorem tariff equivalent of trade costs t ^k _ij . (ii) A further assumption is that trade costs are proportional to trade volumes. Taken together, (i) and (ii) imply ${p_{ij}^k = p_i^k\, t_{ij}^k}.$ (iii) Trade costs are assumed to be borne by the exporter, i.e. formally the exporter incurs export costs equal to (t _ij − 1) for each good shipped from i to j. The nominal value of exports from i to j is, thus, the sum of the value of production at the origin p _i   c _ij plus the trade cost that the exporter passes on to the importer, i.e. ${X_{ij}^k = p_{ij}^k\, c_{ij}^k = p_i^k c_{ij}^k + (t_{ij}^k - 1) p_i^k c_{ij}^k}.$ Imposing market clearing conditions for all regions and sectors

$$Y^{k}_{i} = {\sum\limits_j {{\mathop X\nolimits_{ij}^k}}} \quad \forall \,i,k$$

(23)

and inserting equations (19) into (21) as well as the assumption on the equivalence of trade costs and trade volumes (ii) into (19) gives that

$$Y^{k}_{i} = \;\;\;{\sum\limits_j {{\left({\frac{{{\mathop p\nolimits_{ij}^k}}}{{{\mathop P\nolimits_j^k}}}} \right)}^{{1 - \sigma_{k}}} E^{k}_{j}}}\;\; = \;\;{\sum\limits_j {{\left({\frac{{{\mathop p\nolimits_i^k}{\mathop t\nolimits_{ij}^k}}}{{{\mathop P\nolimits_j^k}}}} \right)}^{{1 - \sigma_{k}}} E^{k}_{j}}}$$

(24)

which has to be rearranged in order to solve for p ^k _i :

$${\left({p^{k}_{i}} \right)}^{{1 - \sigma_{k}}} = \frac{{Y^{k}_{i}}} {{{\sum\nolimits_j {{\left({{\mathop t\nolimits_{ij}^k}/{\mathop P\nolimits_j^k}} \right)}^{{1 - \sigma_{k}}} E^{k}_{j}}}}}\,\;,\quad \forall {\kern 1pt} i$$

(25)

Now, Eq. 23 can be substituted in Eqs. 19 and 20. The result is the theory-based gravity model, which is described by Eqs. 1–3.

Appendix B

Table 8 Compilation of regions; definition of center cities