El incremento de la movilidad por razón de trabajo/estudios

In this section, we discuss the baseline calibration of the model as well as the implied importance of pricing-to-market in generating the observed cross-border price dispersion.

3.4.1 Parameter Values

Table 23 shows the calibrated parameters values required to match the four pricing facts presented above. On the retailer side of the model, we fix the elasticity of substi- tution between retail goods at η = 5, a value standard in the literature, which yields

retail markups of 20%. We set the retailers’ search cost parameter at k= 0.006, which, given η, implies an unconditional producer markup of 15%.

We calibrate an AR(1) process for the relative money supply, MHs

Ms F

, in order to match the variance and high persistence of the US-Canada nominal exchange rate. We set the persistence, ρM = 0.95 and the volatility of innovations, σεm = 0.029. These values

yields an exchange rate with the same persistence, ρe= 0.95, and a variance (in growth

rates), σ∆e = 0.03.

On the producers’ side, we assume that average relative productivity is distributed ac- cording tot∼ N(0, σ2), and that producer-specific productivity shocks are distributed

within each period according toζi ∼ N(0, σ2ζ,c), withc∈ {us, can}. We calibrate the cost

shock parameters to match the main moments of the cost data for the US and Canada considered by Burstein and Jaimovich (2009). These data correspond most closely our interpretation of the model as an interaction between retailers and wholesalers. We choose the shock variances (σ2

ζ,us, σζ,can2 , σ2) to match the variability of good-level real

exchange rates: σ∆dt,us = 0.06, σ∆dt,can = 0.05, and σ∆dt,bord = 0.13. Generating higher

variability of good-level real exchange rates across the border requires a fairly large variance of the shock to relative productivities, hence we set σ = 0.059. We generate

higher dispersion within the US versus Canada by assuming a higher variance of US idiosyncratic shocks, setting σζ,us = 0.093 and σζ,can = 0.052.

The regional bias parameters are selected in order to match the correlation of ag- gregate real exchange rates with the nominal exchange rate (fact 1). For the baseline calibration, we assume symmetry, so thatα1 =γ3. Since Burstein and Jaimovich (2009)

do not provide an numerical correlation, we target a correlation coefficient of 0.70. This requires a very high regional bias (α1 =γ3 = 0.998), so that retailers in all regions are

3.4.2 Implications for Price Dispersion

The first and second rows of table24show that the baseline calibration of the model can almost perfectly match the targeted moments. In particular, the average relative price for the search good is highly correlated with unit labor costs (fact 1), changes in real relative prices are far more volatile across countries than within (fact 2), and relative prices across countries are approximately four times more volatile than the nominal exchange rate (fact 3). The shock to relative aggregate productivities is essential for matching fact 3 because it increases the dispersion of international relative prices, beyond the levels that would be created with a relative unit labor cost shock alone.

Table 25 shows that the model has reasonable implications for other moments. In particular, price-change correlations are approximately 80%within the US and Canada, and are very close to zero across countries (fact 4). The shock to relative aggregate productivities is also important for matching this final fact, since it decreases the corre- lation of international price changes, relative to the correlation of within-country price changes. Finally, the average relative price also closely follows the unit labor costs ratio, which is natural given the assumption of fixed nominal wages.

The model can match evidence of price dispersion using a regional bias parameter that is close to one. In fact, assuming complete segmentation yields pricing statistics that are almost identical to our baseline results, as shown in row four of table 24 and in row three of table25. This result is consistent with the evidence presented in Gopinath et al (2011), who conclude that the US and Canadian markets are virtually fully segmented. However, we generate this result using regional segmentation alone. We return to the issue of identifying regional versus national segmentation in section 3.5.

3.4.3 The Importance of Pricing-to-Market

We next investigate to what extent our results are driven by pricing-to-market, as opposed to retailers simply sampling from producers with different marginal costs. Since producers in our model only set one price in each period, we define pricing-to-market as the tendency of producers with equal marginal costs to set different prices depending on the market in which they are located. We parameterize the model so that search costs are high enough that, in equilibrium, retailers always purchase from the first producer they search, and producers always charge the monopoly price (rather than one of the reservation prices). This parameterization shuts down the pricing-to-market created by the presence of different reservation prices across countries.

The third row of table24shows that, under this calibration, the degree of additional price dispersion created by the border is significantly reduced, though it is still evident. Yet, qualitatively, the pricing facts cited above remain unchanged. In our model, the basic pricing facts can be matched without any pricing-to-market. Further study is required in order to determine if a similar model, with detailed locations of production, can generate the pricing-to-market evidence of Burstein and Jaimovich (2009) for goods sold in both countries, but produced in a common location.