The model year is 1996. I take the expenditure sharesδk(si), k ∈ {N o, So},andi∈ {N, T} directly from the data. The remaining parameters are jointed calibrated by solving the model and matching relevant targets in the data as described below.
Elasticity of substitution between varieties η This parameter determines the degree of substitutability across varieties, hence market power, and therefore has implica-tions for the fraction of the population that are workers as opposed to managers. Using 1997 census data, Guner, Ventura and Yi (2008) argue that a literal interpretation of managers, that would be consistent with the model in my paper as well, suggests that around 95% of the US population are workers. Similarly, using PSID data, Chang (2000) claims that a lower bound for the fraction of labor force that are workers is 85%. So my target for the fraction of employees that are workers in the North is 90% (the quantitative results are robust over this entire range).
TFP termsAk, k∈ {N o, So} I normalize AN o= 1 which is without loss of gener-ality. I target the ratio of real income per-worker (South to North) in the data which has a value of 0.116 to discipline ASo. Real income per-worker in the data is computed from the Penn World Tables version 6.1; see Heston, Summers and Aten (2002). To compute the real income per-worker in the North for instance, I need two numbers; total real GDP in the North, and the total workforce in the North. Total real GDP in the North is the
1I introduced curvature by settingg(z) = 200(1−z)α−1. This implies that zη−1g(z) is proportional to a beta density which MATLAB can integrate pretty efficiently. Curvature does strongly affect how many workers there are in each country, but only weakly affects the sorting of managers across tradables and nontradables, the dimension of first-order importance of this paper.
sum of each of its members’ real GDP. Workforce for a given member is total real GDP divided by real GDP per-worker. The total workforce in the North is then the sum of each of its members’ workforce. This aggregation is taken as opposed to averages to allow for a more realistic interpretation of treating the North as indeed one country. The same procedure is applied to the South.
Iceberg costs to tradeτkl I target bilateral trade shares, or import shares, which are constructed as in Bernard, Eaton, Jenson and Kortum (2003). To construct these I need the following statistics: North’s exports to the rest of the world, South’s exports to the rest of the world and total flows between North and South. To map trade flows into the unit interval I need to compute absorbtion figures which requires South’s total manufacturing production, as well as North’s. Data on bilateral trade flows is compiled from Feenstra, Lipsey, Deng, Ma and Mo (2005) using the year 1996, which is available on the web page of Robert Feenstra: http://cid.econ.ucdavis.edu/. Manufacturing output data is from INDSTAT3, a database maintained by UNIDO, see UNIDO (1996-). Total manufacturing in the North is just the sum of each of its members’ manufacturing output.
North’s exports to the rest of the world are the sum of each of its members’ exports to the rest of the world, minus each members’ exports to other countries in the North.
Finally, total trade flows from South to North are the sum of what each country in the North gets from each country in the South. The absorbtion figure in say the North is AbsN o = MfgN o+ ImpN o,So−ExpW d,N o, where MfgN o is total manufacturing output in the North, ImpN o,So are total trade flows from South to North, and ExpW d,N o are total exports to the world from the North. The fraction of the manufacturing goods available in the North that was imported from the South is then ImpN o,So/AbsN o. In my model, this corresponds toψN o,So(sT)η−1. A similar procedure is applied to find the import share in the South coming from the North.
The fixed costs (in units of labor)fk I target the average establishment size in manufacturing for both the North and South. To construct these statistics, I take data on the number of manufacturing establishments as well as the number of paid employees in manufacturing, both from INDSTAT3. The total number of establishments in the North is the sum of establishments of its members; the same summation is applied to the number of employees. Average establishment size is then the number of employees divided by the number of establishments. In the model, I count both managers and workers as employees; where the amount of workers includes workers used to cover fixed costs as well
Table 1: Calibrated Parameters ASo = 0.135 TFP term Real relative income
(South/North)
Notes: (1) Fixed costs are in units of labor. (2) All parameters except for the expenditure shares are jointly calibrated by solving for the entire equilibrium.
as workers used in actual production.
The results of the calibration are given in Table 1. The implications for relative prices are as follows: the price of nontradables relative to tradables in the North is 0.92 (in the data it is 0.62), and the price of nontradables relative to tradables in the South is 0.69 (in the data it is 0.39). The model over-predicts both of these, but the question the paper addresses is the relative magnitude of these ratios; that is, the interest lies in explaining the ratio 0.62/0.39 = 1.59. To this end, the model generates a ratio of relative prices equal to .92/.69 = 1.34. On a log scale, this means that the model explains about 63% of the observed difference in the price of nontradables relative to tradables. Moreover, across countries, the model predicts that the price of tradables differs by a factor of about 1.3, while the price of nontradables differs by a factor of 1.72. This is consistent with the fact that both tradables and nontradables are more expensive in rich countries, and the fact that the cross-country difference is larger in nontradables; Simonovska (2008)
discusses the case for cross-country differences in prices of tradables.
Some interesting statistics for the calibrated (baseline model) are described in Table 2. First, the fraction of managers that are in the nontradable sector, relative to the tradable sector, is of greater magnitude in the South than in the North. This is partly what is generating the relative price differences. As the fixed cost increases, domestic competition in tradables falls relative to nontradables which deflates the relative price.
Second, the presence of nontrivial import costs in the South blocks competition from abroad which in turn decreases competition in the South’s tradable sector and also shows up in relative prices. Finally, when productivity is measured as output per-worker, the model predicts that there are larger cross-country productivity differences in nontradables than in tradables, going against the Balassa-Samuelson hypothesis.
Another interesting result of the baseline calibration is that trade costs are asym-metric, and the South faces a larger import cost than does the North. This is counter to existing studies in the gravity literature; see, for example, Waugh (2009). His study reveals that in order to reconcile ICP prices, poor countries must face larger export costs, which are also modeled as iceberg costs. Since my model includes an extensive margin, the variation in export costs are getting picked up by fixed costs, and therefore predicting an opposite conclusion with respect to trade (iceberg) costs on the intensive margin, while still being consistent with ICP measures of prices. On the other hand, my calibration only has two countries. With more countries, it is possible for a given country to have both larger average export costs, and larger average import costs. In a two-country setting this is simply not possible.