Historical trade integration: globalization and the distance puzzle in the long twentieth century

Abstract

In times of ongoing globalization, the notion of geographic neutrality expects the impact of distance on trade to become ever more irrelevant. However, over the last three decades a wide range of studies has found an increase in the importance of distance during the second half of the twentieth century. This paper tries to reframe this discussion by characterizing the effect of distance over a broader historical point of view. To make maximal use of the available data, we use a state-space model to construct a bilateral index of historical trade integration. Our index doubles to quadruples yearly data availability before 1950, allowing us to expand the period of analysis to 1880–2011. This implies that the importance of distance as a determinant of the changing trade pattern can be analyzed for both globalization waves. In line with O’Rourke (Politics and trade: lessons from past globalisations. Technical Report, Bruegel, 2009) and Jacks et al. (J Int Econ 83(2):185–201, 2011), we find that the first wave was marked by a strong, continuing decrease in the effect of distance. Initially, the second globalization wave started out similarly, but from the 1960s onward the importance of distance starts increasing. Nevertheless, this change is dwarfed by the strong decrease preceding it.

Appendices

Appendix 1: Data sources and transformations

See Table 2.

Table 2 Data sources and transformations

Appendix 2: Estimating the state-space model

To estimate the state-space model, we need to solve for the structural parameters of the state-space model ($C$, $Z$, $T_t$, $H$ and $Q$) as well as the level of trade integration ($hti$). While it is possible to maximize the combined distribution numerically for small datasets, using a Gibbs sampler simplifies the estimation procedure considerably by splitting up the process into conditional probabilities.

For example, say we have to draw from the joint probability of two variables $p(A,B)$, when only the conditional probability of $p(A|B)$ and $p(B|A)$ are known. Starting from a (random) value $b_0$, the Gibbs sampler will draw a first value of A conditional on $B^{(0)}$: $A^{(1)} \sim p(A|B^{(0)})$. Conditional on this last draw, a value of B is drawn ($B^{(1)} \sim p(B|A^{(1)})$) which is in turn used to draw a new value for A ($A^{(2)} \sim p(A|B^{(1)})$. This process is repeated thousands of times, until the draws from the conditional distributions have converged to those of the combined distribution $p(A,B)$. After discarding the unconverged draws (the burn-in), the remaining draws of A and B can be used to reconstitute their respective (unconditional) distributions.

Because we are using a Bayesian analysis framework, we have to be explicit about the prior distribution of the parameters. In other words, we have to state what we know about their distribution before looking at the data. Because there is no prior information, we imposed flat priors on $Z$, $C$ and $log(H)$, meaning that all values in the real space (or real positive space for the variance H) are equally probable.

In the case of the state-space model, the Gibbs sampler consists of two main blocks (Kim and Nelson 1999):

• 1. If the level of trade integration ($hti$) was known, the parameters of the measurement and state equations (Eqs. 1 and 2) could be obtained using simple linear regressions. To ensure the model is identified, the variance of the error term of the state equation ($Q$) is typically set to 1. Taking, for example, the situation, where there is only one dyad to simplify notation: $hti = (hti_{1},\ldots , hti_{n})'$

  $$ p(T|hti)\propto .5 * 1\!\!1_{|T|\le 1} * N(b_T, v_T) $$

  (8)
  $$ p(Z^k,C^k|hti,y,H)\propto N(b^k_{Z,C}, v^k_{Z,C}) $$

  (9)
  $$ p(H_{(k,k)}|hti,y)\propto iWish[e^{k\prime } e^k ; \; n ] $$

  (10)

  with $v_T = (T_{t-1}'T_{t-1})^{-1}$; $b_T = v_T * T_{t-1}'T_t$; $v^k_{Z,C} = (hti'hti)^{-1}*H_{(k,k)}$; $b^k_{Z,C} = (hti'hti)^{-1} * hti'y^k$; $e^k = y^k - C^k - Z^k * hti$; and $iWish$ the inverse Wishart distribution.

• 2. Conditional on the parameters of the state and measurement equations, the distribution of $hti$ can be computed and drawn using the Carter and Kohn (1994) simulation smoother.

  • The Kalman filter: computes the distribution of $hti$ conditional on the information in all previous years. Starting from a wild guess, $p(hti_0) = N(0,\infty )$, the following equations are iteratively solved for $t = 1$ to $t = n$:

    $$\begin{aligned} a_{t|t}&= E(hti_t | y_1, \ldots , y_t) \nonumber \\&= T*a_{t-1|t-1} + \kappa (y_t - C - Z T a_{t-1|t-1}) \end{aligned}$$

    (11)
    $$\begin{aligned} p_{t|t}&= V(hti_t | y_1, \ldots , y_t) \nonumber \\&= p_{t|t-1} + \kappa Z p_{t-1|t-1} \end{aligned}$$

    (12)

    with $\kappa = p_{t|t-1} Z'(Z p_{t|t-1} Z' + H)^{-1}$; and $p_{t|t-1} = Tp_{t-1|t-1}T'+Q$.

  • Simulation smoother: Draws from the distribution of $hti$ conditional on all information in the data and the previous draws. Starting from the last iteration of the Kalman filter, draw $\hat{hti}_n$ from $N(a_{n|n}; \;p_{n|n})$ and iterate backwards from $t=n-1$ to $t=1$:

    $$\begin{aligned} a_{t|n}&= E(hti_t | y_1, \ldots y_n) \nonumber \\&= a_{t|t} + \varsigma (\hat{hti}_{t+1} - Ta_{t|t}) \end{aligned}$$

    (13)
    $$\begin{aligned} p_{t|n}&=V(hti_t | y_1, \ldots y_n) \nonumber \\&=p_{t|t} + \varsigma (p_{t+1|n} - Tp_{t|t}T'-Q)\varsigma ' \end{aligned}$$

    (14)

    with $\varsigma = p_{t|t}T'p_{t+1|t}^{-1}$; and $\hat{hti}_{t+1}$ a random draw from $N(a_{t+1|n}; \; p_{t+1|n})$.

Appendix 3: The historical trade network

In order to combine the historical trade integration indices into a network, the index values corresponding to countries that are integrated need to be separated from those corresponding to countries that are not. A natural way of making this distinction is to contrast countries that trade with each other ($X_{ij,t} > 0$) to those that do not ($X_{ij,t} = 0$). The problem is that this approach is skewed by a large number of very small nonzero trade flows.

Rather than choosing an arbitrary cut-off value, the hti allows us to use significant differences to determine which countries are linked. To start, we used the estimates of the structural parameters of the state-space model to generate index values for a fictional dyad where trade was zero for the entire period. Labeling these observations as $hti_{0,t}$, we defined significant levels of trade in the following way: An edge $e$ from country $i$ to country $j$ exists if, and only if, its level of trade in year $t$ is significantly higher than that of $hti_{0,t}$: $e_{ij,t} = 1 \iff \, hti_{0,t} < hti_{ij,t}$ in at least 99 % of all iterations of the (converged) Gibbs sampler. Using the $hti_{0,t}$ definition, 115,911 edges were identified (6.3 % of observations).

Panel a of Fig. 7 shows the overall network density (the fraction of dyads that are connected) gradually decreasing throughout the first globalization wave. In contrast, the trade network becomes increasingly connected during the second globalization wave. As can be seen in panel b, the number of trade links (edges) more or less continuously grows over the entire time-period and is initially offset by the rapid rise in the number of countries. This is especially noticeable when the Soviet Block breaks up in the 1990s, causing a rapid downward shift in the network density.

Fig. 7

Network density (a) and the number of nodes and edges (b) over time. a Density. b Number of nodes and edges

Similar to the distance regressions, the density was also computed when the number of countries was kept constant using the 1880 and 1950 subsets. This reveals that the decrease in density during the first globalization wave was driven by the addition of new countries. When this is kept constant, the network density almost doubles during the first wave. In addition, it reinforces the effects of the 1930 and 2008 economic crises, both causing a substantial drop in the density. To ensure that these results were not driven by the inclusion of the colonial trade data, the density was also computed using only the official countries according to the COW state system dataset. However, this did not significantly alter the conclusion (available upon request). In other words, once the density is corrected for the increasing number of countries, it conforms to the globalization pattern found in the literature.

Appendix 4: Estimating models with high-dimensional fixed effects

Following Guimarães and Portugal (2009), the number of fixed effects can be reduced by half by first demeaning both dependent and explanatory variables in the sender-year dimension, leaving only the sender-target dummies. Using conditional probabilities, the fixed effects ($c_i$) can be separated from the explanatory variables ($X_{i,t}$), which significantly reduces the size of the matrix that needs to be inverted.

$$ y_{i,t} = c_i + X_{i,t} \beta + \epsilon _{i,t} \quad \hbox {with } \epsilon _{i,t} \sim N(0,\sigma ^2) $$

(15)

Equation 15 can be estimated using a three-step Gibbs sampling procedure. For example, when using flat (uninformative) priors, the conditional probabilities are:

• 1. $\beta | c_i, \sigma ^2 \sim N(e_\beta ,v_\beta )$

  $e_\beta = (X'X)^{-1}(X'(y-c))$ with $\{X\}_{i,t} = X_{i,t}$ and $\{y-c\}_{i,t} = y_{i,t}-c_i$

  $v_\beta = \sigma ^2 (X'X)^{-1}$

• 2. $c_i | beta, \sigma ^2 \sim N(\bar{c_i},\sigma ^2/n)$

  $\bar{c_i} = \sum ^n_t(y_{i,t} - X_{i,t}\beta )/n$ with $n$ the number of observations of country $i$

• 3. $\sigma ^2 | beta, c_i \sim \hbox {iWishart}(e'e,N)$

  $e = y_{i,t} - c_i - X_{i,t}\beta$

Appendix 5: Country subsets

Group 1: included in 1880< and 1950<
Algeria	Egypt	Italy	Romania
Argentina	El Salvador	Jamaica	Russia
Ascension	Falkland Isl.	Japan	Senegal
Australia	Fiji	Liberia	Sierra Leone
Austria	Finland	Luxembourg	Singapore
Barbados	France	Macau	South Africa
Belgium	French Guiana	Madagascar	Spain
Belize	Germany	Maldives	Sri Lanka
Bermuda	Ghana	Malta	St. Pierre and Miquelon
Bolivia	Gibraltar	Mauritius	Suriname
Brazil	Greece	Mexico	Sweden
Bulgaria	Guadeloupe	Morocco	Switzerland
Canada	Guatemala	Mozambique	Thailand
Chile	Guyana	Netherlands	Trinidad and Tobago
China	Haiti	New Zealand	Tunisia
Colombia	Honduras	Nicaragua	Turkey
Costa Rica	Hong Kong	Norway	UK
Cuba	Iceland	Paraguay	USA
Denmark	India	Peru	Uruguay
Dominican Rep.	Indonesia	Philippines	Venezuela
Dutch Antilles	Iran	Portugal	Yugoslavia
Ecuador

Group 2: included in 1950<
Afghanistan	Djibouti	Lebanon	Saint Lucia
Albania	Dominica	Lesotho	Saint Vincent
American Samoa	Equatorial Guinea	Libya	Samoa
Angola	Eritrea	Lithuania	Sao Tome and Principe
Antigua and Barbuda	Estonia	Malawi	Saudi Arabia
Bahamas	Ethiopia	Malaysia	Seychelles
Bahrain	Faroe Islands	Mali	Solomon Islands
Bangladesh	French Polynesia	Mauritania	Somalia
Benin	Gabon	Mongolia	South Korea
Bosnia	Gambia	N. Mariana Isl.	St. Kitts and Nevis
Botswana	Greenland	Namibia	Sudan
Brunei	Grenada	Nauru	Swaziland
Burkina Faso	Guam	Nepal	Syria
Burma	Guinea	New Caledonia	Tanzania
Burundi	Guinea-Bissau	Niger	Togo
Cambodia	Hungary	Nigeria	Tonga
Cameroon	Iraq	North Korea	Tuvalu
Cape Verde	Ireland	Oman	UAE
Central African Rep.	Israel	Pakistan	Uganda
Chad	Jordan	Palestine	Vanuatu
Comoros	Kenya	Panama	Vietnam
Congo, Rep.	Kiribati	Papua New Guinea	Wallis and Futuna
Congo, Dem. Rep.	Kuwait	Poland	Yemen
Cote d’Ivoire	Laos	Qatar	Zambia
Cyprus	Latvia	Rwanda	Zimbabwe
Czechoslovakia