The Model and Calibration

For this purpose I need to maintain the main features of the baseline model as much as possible. The simplest way to do this is to eliminate the fixed cost component,F, from the manufacturing production function. The composite index of manufacturing consumption now looks similar to that of primary consumption Cmi = [γmbm ρm i,b +γmusm ρm i,us+γmrwm ρm i,rw] 1/ρm

As a result the manufacturing price index becomes

Gmi= γσm mb(pmbT m bi) 1−σm_+γσm mus(pmusT m usi) 1−σm_+γσm mrw(pmrwT m rwi) 1−σm1/(1−σm)

Basically droppingF eliminates the increasing returns component and the number of manufacturing firms is no longer endogenously determined so that the consumers consume a fixed proportion of manufacturing goods from each region. Therefore the number of variety (or firms) is fixed or one can think of a representative firm in each region producing everything. In this sense the number of firms is indeterminate under CRTS but it does not matter because it is fixed over time. Essentially the model is very similar to the standard CGE model with an Armington assumption.

The procedure of restricting the parameters is almost identical to the case of IRTS except thatγm,iis pinned down in the same way asγa,i. More

detailed calibration procedure is described in the appendix at the end of the chapter. The resulting benchmark equilibrium and parameter values are exactly identical to the IRTS case. This is convenient as I can ignore the possibility that the difference (between IRTS and CRTS) comes from the differences in parameter and initial equilibrium values.

However the CRTS specification has different implications for the changes in manufacturing TFP and trade costs. To see this more closely, I derive the

change in manufacturing TFP under the CRTS specification, the counter- part of equation (34). Am,1913 Am,1870 = X1870 X1913 1₁−₋αm_σm Lm,1870 Lm,1913 αm Ym,1913 Ym,1870 αm (36)

Using (34) and (36), I can derive a relation between a change in TFP under IRTS and that implied by CRTS as follows:

Am,1913 Am,1870 CRTS = Am,1913 Am,1870 IRTS Ym,1913 Ym,1870 1_σm−αm₋₁ | {z } A (37)

First thing to note from (37) is that givenαm <1,σm >1 and Y_Ym,_m,1913₁₈₇₀ >1,

_A m,1913 Am,1870 CRTS is bigger thanAm,1913 Am,1870 IRTS

. It says that what is perceived as a purely exogenous technological change in the CRTS model actually contains an endogenous component (underbraceAon the right hand side of equation) if there are IRTS. But ifαm = 1 then the underbraceAbecomes one and the

change in TFP under CRTS is identical to that of IRTS. This means that the manufacturing sector using itself as intermediate goods is the crucial feature that makes the difference between CRTS and IRTS.

_A m,1913

Am,1870

CRTS

for Britain and the U.S is 1.20 and 1.63, respectively. As expected the CRTS model yields larger TFP changes than the baseline model. If I compare these values with the external sources, they are not so different from each other. For comparison, I reiterate the TFP shocks measured under the different approaches again in Table 22.

Under the ‘IRTS’ and ‘CRTS’ are the measured TFP shocks under the assumption that there exist IRTS and CRTS in manufacturing sectors, re- spectively. The values under ‘External’ are the ones taken or recovered from the external sources, including capital. Overall the measured values and the values culled from the external sources are quite similar. One noted differ-

Table 22: TFP shocks IRTS CRTS External Aa,b 1.09 1.09 1.07 Am,b 1.14 1.20 1.27 Aa,us 1.22 1.22 1.26 Am,us 1.40 1.63 1.62

ence is U.S. manufacturing TFP shock between ‘IRTS’ and ‘External’. As discussed earlier, Kendrick (1961) implicitly assumes CRTS technology and the TFP is inevitably over-estimated if there exists IRTS. Instead the shock measured under the assumption of CRTS is almost identical to the value taken from Kendrick (1961). In this sense, my measures of TFP shocks also represent the realtotal factor productivity well.

I discuss more about the implications of using the external TFP shocks. TFP is conventionally measured as a residual from the production function after accounting for factor inputs. This means one usually needs to make an assumption about the form of production function to measure TFP. The ex- ternal TFP shocks in Table 22 are derived by assuming that the production function exhibits CRTS, as far as I understand. I also demonstrated that those values for Britain and the U.S. are very similar to the TFP shocks inferred from my CRTS model earlier. If there really exists IRTS in an economy, the TFP shocks inferred from a CRTS assumption actually in- clude the components contributed by the IRTS effects. Therefore if I use the external TFP shocks inferred from CRTS models to simulate an IRTS model, the effects of the scale economy are ‘double-counted’ and there is an inevitable over-prediction of simulated results. In this sense it can be problematic to use TFP shocks inferred from CRTS on IRTS model. What I do in section 2.4.1 is to identify this effects coming from the assumption of IRTS. To reiterate, the TFP change under CRTS,Am,1913

Am,1870

and the change under IRTS,

_A m,1913

Am,1870

IRTS = 1.40 for the U.S. and the dif-

ference between these numbers can be identified as the effects of IRTS. For the CRTS case, applying the external TFP shocks generates very similar results as the baseline case (using the measured shocks), so I do not report the results here.

Next I calibrate the changes in trade costs under CRTS specification. The way that the changes in trade costs are calibrated, implies that those under CRTS would take on different values from IRTS specification. Ta- ble 23 reports the values below. One pronounced difference is in the change in manufacturing trade costs between Britain and the U.S. Under the IRTS specification, Tm

b,us decreases while T m

us,b increases but under the CRTS we

get the opposite result. This is probably because the IRTS gives relatively more comparative advantage to U.S. manufacturing than the CRTS case (even though Am,us is higher under CRTS). And because of this, a lower

trade cost from Britain to the U.S. is needed under IRTS to match the given amount of Britain’s manufacturing exports to the U.S. Also for the same reason, the trade cost from the U.S. to Britain should be higher under the IRTS to account for U.S. manufacturing exports to Britain.

Table 23: Changes in trade costs under CRTS (growth factor)

∆Ta

b,us ∆Tus,ba ∆Tb,rwa ∆Trw,ba ∆Tus,rwa ∆Trw,usa 0.850 1.084 0.669∗ 1.906 0.595∗ 1.696

∆T_b,usm ∆T_us,bm ∆T_b,rwm ∆T_rw,bm ∆Tus,rwm ∆Trw,usm 1.044 0.968 1.508 0.717∗ 1.532 0.489