Calibration

I calibrate the model to match aggregate trade data from 26 OECD countries to assess the effect of the interaction of new goods gains with specialization on the magnitude of the gains from trade.

I use the dataset provided by Ramondo, Rodr´ıguez-Clare, and Sabor´ıo-Rodr´ıguez (2016). Structural parameters to be calibrated are θ and σ, in addition to country sizes L_i, research intensities µ_i, and the matrix d_ni of bilateral trade costs.

13Note that 1/N is chosen only for convenience. I discuss the effect of choosing different constants in Section III.3.4.3.

III.3.3.1 Parameters and Data

The model outlined in Section III.2 implies a log-linear gravity equation. It is therefore model-consistent to turn to the trade literature for estimates ofθ. Head and Mayer (2014) find a mean estimate of 3.78 for structural gravity estimates and Simonovska and Waugh (2014) find a value of θ between 4 and 5. I setθ = 4.

In contrast to the EK model, the value of the elasticity of substitutionσmatters for the gains from trade in this model. The larger σ, the larger is the elasticity of substitution between goods. This reduces the utility gains from new goods. I follow established estimates in the literature, e.g. Broda and Weinstein (2006), and choose σ = 4, which is also consistent with the parameter restriction needed for a finite price index, θ > σ−1.

Following Ramondo, Rodr´ıguez-Clare, and Sabor´ıo-Rodr´ıguez (2016), country sizes L_i are set to the measures of equipped labor from Klenow and Rodr´ıguez-Clare (2005).

This measure corrects for differences in physical and human capital per worker. They are also used to construct the producible goods measures in the size-proportional case, with S_i = L_i and J = P

iL_i. It is important to stress that although the producible goods shares add up to unity, producible goods shares of different countries overlap because of the random draw. As a consequence there is also a fraction of the unit measure of goods that is not produced at all as indicated in Figure III.1.

I follow Ramondo, Rodr´ıguez-Clare, and Sabor´ıo-Rodr´ıguez (2016) in setting the re-search intensity µ_i proportional to the share of country-level R&D-employment. These shares are taken from the World Development Indicators and are averaged over the 1990s.

With the assumption that Ti = µiLi, this produces a calibration of technology levels as in Ramondo and Rodr´ıguez-Clare (2013) and Ramondo, Rodr´ıguez-Clare, and Sabor´ıo-Rodr´ıguez (2016).

In principle any cross-section of trade data can be matched perfectly when trade costs are treated as free parameters. It is therefore important to discipline them as a function of known core determinants. To keep things simple, bilateral trade costs are defined as

d_ni = exp{β₁}dist^β_ni² for i6=n,

where dist_ni is the distance between the most populated cities of countries n and i from CEPII. I target a distance elasticity of −1.05, which is well in line with estimates from the literature. See Head and Mayer (2014) for a survey. With θ = 4, this implies a value of β₂ = 0.2625. β₁ is then calibrated to produce trade flows whose average matches the average bilateral trade in manufacturing in the data. Bilateral trade flows X_ni are averaged over 1996-2001 from OECD STAN. The average bilateral trade share in the data

is 0.0155.¹⁴

III.3.3.2 Calibration Procedure

The wage updating function at the heart of the code follows Alvarez and Lucas, Jr. (2007).

Given exogenous parametersθ,σ, country sizesLi and technology levelsTi =µiLi, as well as the matrix of trade costs dni and an initial wage guess, model outcomes are calculated using the equilibrium expressions for trade shares and price indeces. Aggregate exports and imports of each country are evaluated using an excess demand function. The nominal wages of countries that export more than they import are raised, the others lowered. With the updated wage, new excess demand functions are calculated. This algorithm is repeated until the percentage change in wages falls below some threshold level.

In extending the basic code to allow for different measures of produced goods across countries, the main challenge is the introduction of producer sets. With N = 26 coun-tries, there are 2^N = 67108864 producer sets to be considered. I keep track of them by converting the numbers from 0 to 2²⁶−1 into binary numbers, each with 26 places. The permutations of ones and zeros then reflect all possible permutations of producer combi-nations, where the ones indicate membership of a country in a producer set. For example, the producer set corresponding to the number 67108863 consists of N = 26 ones in the binary system and represents the producer set in which all countries are members. The producer set matrix is then an N ×2^N matrix.

Next, I use the matrix of producible goods measures S_i and J−S_i together with the producer set matrix to calculate theλ(c)s for each producer set. The producer set matrix is then applied to calculate the N×2^N matrix of Φ_n(c)-terms - each country iconsumes goods from all producer sets, which differ in their composition. Given the matrix of Φ_n(c)s, application of equation (III.7) first gives the matrix of producer set level price indeces P_n(c) and subsequent summation gives the vector of price indeces P_n consistent with the initial wage guess.

With Φ_n(c),P_n(c), andP_nin hand, theN×N×2^N matrix of trade sharesπ_ni(c) at the producer set level can be constructed. Using equation (III.8) they are then summed over the third dimension to give the N×N aggregate expenditure trade shares π_ni from which aggregate trade flows X_ni can be constructed to evaluate the balanced trade condition (III.13).

Due to the large number of producer sets the matrices take up a lot of memory, I divide the producer set matrix into several parts and let the computer calculate each part in turn before summing up to the aggregate total.

14Country-level absorption is calculated from the same data as production minus exports plus imports from the sample countries in manufacturing.

Table III.1: Model Overview

model goods measures R-squared β1 avg GT median GT Eaton-Kortum S_i/J = 1 0.9361 0.8206 16.45% 10.95%

New Goods, size-prop. S_i/J =L_i/P

iL_i 0.9303 1.1034 23.42% 13.42%

New Goods, symmetric S_i/J = 1/N 0.9379 1.0773 21.88% 14.41%

Note: The column R-squared contains the goodness of fit between the actual bilateral trade flows between 26 OECD countries and those predicted by the model. β1is a global trade cost shifter chosen so that the model produces trade flows whose average matches the average trade share in the data.

For the calibration of the parameter β₁ I add an upper level loop over the algorithm calculating the equilibrium that evaluates the average trade share produced by the model after each round. If the average trade share is larger than the targeted value of 0.0155 from the data, β₁ is increased in proportion to the difference between the target and the actual value in the next round until the model outcome equals the target exactly and vice versa.