Absorption Capacity, Structural Similarity and Embodied Technology Spillovers in a 'Macro' Model: An Implementation within the Gtap Framework

In this paper, all technology transfers are embodied in trade flows within a three-region, one-traded-commodity version of the GTAP model. Exogenous Hicks-Neutral technical progress in one region can have uneven impacts on productivity elsewhere. Why? Destination regions' ability to harness new technology depends on their absorptive capacity and the structural congruence of the source and destination. Together with trade volume, these two factors determine the recipient's spillover coefficient (which measures its success in capturing foreign technology). Armington competition between the outputs of the three economies and shifts in their terms of trade loom large in the general equilibrium adjustment.

.2.7 Decomposition of percentage changes in regional TOT 29 Table 5.2.8 Simulated effects on bilateral export sales 32 Table 5.3.1 Simulated regional effects of technology shock on Stuff 33 Table 5.3.2 Simulated regional effects on capital goods industry 34 Figure 1 Production structure for region 'r' in the one-commodity, three-region version of GTAP 5 Figure 2 Flow chart for the transmission mechanism in the model 7

Introduction
We implement embodied knowledge spillovers in a highly aggregated version of the GTAP model -that is, a one-traded-commodity, three-region version of GTAP. 1 At first sight it may seem surprising that a macro (onetraded commodity) model is used for this purpose. GTAP, like many CGE models, adopts Armington's (1969) treatment of commodity substitution, so that even if all regions produce the same generic commodity, the substitution elasticity between that commodity produced in region A and the "same" commodity produced in region B, is not infinite. Thus, even in a onecommodity version of GTAP the 'Law of One Price' does not hold. Working at the one-commodity level has the advantage of concentrating on interregional competition in the goods market without having to deal with the large amount of detail entailed in keeping track also of inter-generic commodity substitution.
We aggregate the GTAP database to a one-commodity and threeregion (USA, EU, and ROW) database. The generic commodity that is traded internationally will be called Stuff. Each region produces one tradable good (its own type of Stuff) and one non-tradable (its own Capital Goods). It is necessary to include a non-tradable in each region because GTAP specifies that capital formation is supplied completely by a domestic industry which does not export. Note, however, that the domestic capital goods industry in any country merely assembles a bundle of traded goods (which include foreign tradables). Consumers absorb Stuff produced at home, as well as the two imported varieties.
We consider a Hicks-Neutral general total factor productivity (TFP) shock in the Stuff sector originating in one of the three regions, viz. the USA.
Such a TFP shock is general output-augmenting by nature. Its impact on productivity in the destinations is studied via an embodiment index, an absorption capacity index, and a structural similarity index. Sections 2 and 3 describe the theoretical premise and the database corresponding to our aggregation respectively. Section 4 documents the GTAP implementation, the closure and the perturbation introduced into the system. Section 5 reports and explains the simulation results. Section 6 concludes.

Embodied Spillover Hypothesis 2
As has been argued elsewhere, growth and development of the LDCs depend not only on the extent and nature of the foreign technology which is available to them via participation in international trade in goods and services, but also on their capabilities for effectively absorbing the diffused state of the art. Current state-of-the-art technologies created by concerted research efforts are embodied in the commodities produced using the newly created ideas. The knowledge capital generated at the sources of inventions spills over to the destinations through bilateral trade linkages. This is the embodiment hypothesis: technical knowledge flows through traded goods. Note that the creation (as distinct from the transmission) of knowledge capital is beyond the scope of this paper.
The adaptability and local useability of the diffused technologies depends on the Absorptive Capacity (AC) [Cohen andLevinthal 3 (1989, 1990)] of the destinations and the Structural Similarity (SS) [Hayami and Ruttan (1985)] between the trading nations. In the literature, the importance of SS has been discussed especially in the context of agriculture. Here in a single-sector model with one trading sector per region, this focus is not valid. However, the maximum potential for productivity enhancement attainable with a given stock of ideas can be achieved only if both AC and SS are high. 4 Van Meijl and Van Tongeren (MT) (1997) related productivity growth rates of countries through international trade linkages and associated embodied knowledge-spillovers. In their model, AC is constructed as a binary (source-and destination-specific) index of human-capital-induced absorption capacity of Country A vis-à-vis Country B. They also use a binary index for SS. It is based on the similarity of factor proportions in the two regions (but unlike AC, SS is symmetric). These two indexes conjointly determine the 'productive efficiency' parameter for effective assimilation of the technology by the recipient countries. 5 Our model differs in several details. First, we restrict ourselves to a one-sector (tradable Stuff) technology for production. 6 Stuff is produced in a world divided into three regions. Like "ectoplasm" in the one-sector neoclassical growth model, Stuff is easily transmutable from consumable to investment goods. Second, unlike MT where AC is a binary index involving both source and destination, we make the AC factor destination specific only. The SS factor retains its binary affix, though. Third, as will become evident below, we have modified MT's 'embodied spillover function'. We now justify the rationale behind the latter two modifications (the reason behind aggregation of goods into a macro model has been given in the Introduction).
It is argued that domestic useability of the transmitted foreign technology depends mainly on the recipient's capability to identify, procure and utilise the diffused technology. This simplification reflects our desire to keep the model simple by concentrating on first-order effects. It seems likely that if region C is good at absorbing technology from region A, it will be equally good at absorbing technology from another region B which (from C's point of view) is structurally similar to A. Thus, the AC factor is made destination-specific only (unlike in MT where they carry both source and destination affixes).
The necessary modifications made in the basic spillover equation of MT are rationalised in the next section. 5 It is worthwhile to mention here that AC depends not only on Human Capital alone, but also on a constellation of factors such as Infrastructural Facilities, Learning Effects, and Own R&D in the recipients. However, we have not considered these factors while defining AC in our model. These are on our research agenda. 6 The second commodity produced in each region (Capital Goods, CGDS) is produced according to a 'technology' which merely assembles a bundle of Stuff from the three regions. However, it is a 'fictitious' industry.

2.2a Production Technology
The production technology tree in the GTAP model uses a nested production function. Here we specialize the notation for use with the one-tradedcommodity version.
At the top level, a composite output Y r is produced in region r with a Leontief fixed proportion technology using intermediate inputs Q r. and a primary input composite Q V r. . Q r. is intermediate input demand for Armington composite Stuff by any region r. Each Q r. is produced in a CES production nest using domestic Stuff and a composite of foreign Stuff distinguished by country of origin (using the Armington assumption). Thus, we can write the CES production function for the intermediate input nest as where r is the region using the domestically sourced tradable Stuff Q rr and the foreign inputs composite of Stuff Q F r . δ D r is the distribution parameter (a positive fraction). β r . ≠ −1 is the substitution parameter. The superscripts D and F are used to identify domestic and foreign components respectively. The substitution elasticity between domestic and foreign Stuff is [1/(1+β r. )].
For notational convenience, in Q rs the first subscript refers to the using region and the second one refers to the foreign source of Stuff. For example, let the three regions in our implementation be A, B and C so that r,s∈{A, B, C}. Then, if r = C is the using region, and s = B or A, Q rr = Q CC is the domestically sourced Stuff in C while Q CA and Q CB are Stuff imported by C from B and A respectively. Q F r is produced in region r using the Stuff imported from other regions, say, s and t. Let Q rs and Q rt be respectively the intermediate input demand for Stuff from s and t by using region r. This leads us to write the CES production nest for Q F r as below: where s,t≠r; s≠t. δ F r is the distribution parameter associated with this production nest. The elasticity of substitution in r between imported Stuffs is [1/(1+β rF )]. If β r . =β rF , (2.1b) is equivalent to writing Q r. as a CES function in Stuff from all three sources.
Primary factor composite Q V r is produced combining the primary factors land (T), labor (L), and capital (K). Q f r is the demand for primary factor f in region r where f∈{L, K, T}. The production technology is CES as given below: where the δ V rf are distribution parameters (positive fractions) (with Σ f δ V rf ≡ 1, ∀r) and ρ r is the substitution parameter. The substitution elasticity between primary factors in region r is [1/(1+ρ r )]. In the above equations, A r , A F r and A V r are technical progress parameters. Q r. and Q V r are combined using a fixed proportion technology with no scope for substitution between intermediate inputs and the primary factors. However, as seen above, there is scope for substitution between domestic and imported varieties of Stuff, as there is between L, K and T. At the top level the (Leontief) production function is: where Y r is the flow of final output and A

2.2b Spillover Equation and Productivity Shock
The spillover hypothesis (as documented in Section 2.1 above) is captured by a technology-transmission equation incorporating destination-specific AC and source-and destination-specific SS. Exports from source r to destination s determine an embodiment index E rs . The latter, together with AC s and SS rs determine the value of a spillover coefficient γ s (E rs , AC s , SS rs ) via the spillover function γ s .
The details of this chain are now explained, starting at the top. Note that there is only one source of exogenous technological improvement in the current treatment, so that r is unique. 7 Stuff produced using the improved technology embodies this technological improvement. Exports of Stuff from r to the trade partners s transmit these embodied technological advances but do not necessarily lead to enhancement of productivity in the recipient sectors of the client countries unless they are utilized as an input to production. We define an embodiment index E rs (where 0 1 ≤ ≤ E rs ) that is proportional to the amount of embodied knowledge received via bilateral trade linkages between r and s so that where X rs is the bilateral exports of Stuff from source r to the clients s and Y s is the domestic production of Stuff in s. Thus E rs measures the amount of embodied knowledge obtained via bilateral exports from r to s per unit of output of Stuff produced in client s. 8 The recipient-specific AC-index AC s (where 0 ≤ AC s ≤ 1) and the binary structural similarity index SS rs (where 0 ≤ SS rs ≤ 1) interactively determine a capture parameter θ s measuring the efficiency with which the knowledge embodied in bilateral trade flows from source r is captured by the recipients s: 9 θ s =AC s .SS rs (2.5) The productivity level realised from the potential streams of latest technology is dependent on θ s ∈[0,1] with θ s =1 implying full realisation of the foreign technology-induced productivity improvement. θ s and E rs jointly determine the value of the spillover coefficient γ s (E rs , θ s ) for the destination s. γ s (.) is a strictly concave function of E rs with the properties that γ s (0) = 0; γ s (1) = 1; ′ = γ s (1−θ s )E rs −θ s > 0; ′′ γ s = −θ s (1−θ s )/E rs 1+θs < 0 ; where primes indicate the first (′) and the second (′′) derivatives with respect to E rs .
7 An implication of the uniqueness of r is that equations carrying an r-subscripted variable on the right do not necessarily require an r subscript to appear on the left. 8 However, it is to be noted that in MT, Ers is defined as the ratio of bilateral trade flows (Xrs) from r to s in any final product sector and total bilateral trade flows (∑sXrs) to all destinations s from the source r. This ratio shows the spillover to the recipients as a proportion of aggregate 'global' spillovers from source to the client countries. This seems to neglect the public good character of knowledge capital. We have modified this definition as described in the text. 9 It has already been mentioned in footnote 5 that AC depends on several factors which we set aside in our present discussion. Depending on those factors, AC could be 'endogenously' determined via a function where these determinants combine to produce a scalar AC-index. In the current treatment, for sake of simplicity, AC is exogenously specified and related to an arbitrarily specified Human Capital index. SS is also exogenous.
We shall consider an exogenous TFP improvement in the technology for producing Stuff in region r. Specifically, the shock is a Hicks-neutral improvement in the productivity of each primary factor there. Figure 2 shows the way in which technological knowledge embodied in trade flows affects the spillover of productivity from a source to a destination region.  2)] is the appropriate technological change parameter for considering HNTP. In GTAP notation, this is AVA(r). The transmission equation showing how the productivity improvement in r affects productivity in s is as follows: where ava(s) and ava(r) are respectively the percentage improvements in the productivity 'levels' (HNTP parameters, AVA) in the value-added nest of the production function of regions r and s (the convention in the GTAP system of notation being that the lower case variables represent the percentage changes in the corresponding 'level' variables). This transmitted improvement is higher, the higher are the values of AC s and SS rs . More specifically, Being 'neutral' in nature, the exogenous HNTP shock uniformly reduces the input requirements associated with producing a given level of output of Stuff. 11

The GTAP Database and Aggregation
The aggregation procedure involves working in several steps with the computer files necessary for this task. All these files are documented in detail in the Appendix.

Set Aggregation
The MODHAR programme available in the Windows version [WINGEM] of GEMPACK (General Equilibrium Modelling Package) was run interactively to create an HAR (Header ARray) file named SET1BY3.HAR from a text file (SET1BY3.TXT) defining the elements of the sets. 10 With the determinants AC and SS of θs both bounded in [0,1] and strictly exogenous, this should not present any computational problem in our GE model. 11 In our current treatment, we do not consider biased technical change of any variety. This rules out closures of the model that correspond to a balanced-growth path (as investigated by Walmsley (1998)). Apart from the exceptional case of a Cobb-Douglas production function, under such closures the only valid sustained technological shock is one which is laboraugmenting (Harrod-Neutral)-see Barro and Sala-I-Martin (1995, Ch 1.) or Powell and Murphy (1997, pp. 97-103);.

Database Aggregation
We refer to our one-traded-commodity, three-region model as 1×3GTAP.
The aggregated database comprising trade, production and input-output data was produced by running Mark Horridge's programme DAGG on the 3×3GTAP bilateral and input-output data in Version 3 of the data-base as used in GTAP short courses held in August, 1996. It involved a three step procedure as described in details in the Appendix. This database is checked for macro-balance by ensuring that (i) the zero pure profit condition is satisfied; (ii) GDP from the income and expenditure sides match each other.

Modification of Parameter Setting
The additional parameters introduced in the parameter file are HK(s) and SS(r,s). HK(s) represents AC s as described in Section 2. Their values are set arbitrarily. Assuming that the EU is more similar to the US in both SS and AC than to the ROW, higher values are assigned for these exogenous variables in case of EU as compared to ROW; that is, AC EU > AC ROW and SS EU,US > SS ROW,US . The Appendix documents them as appended in the TABLO file. The values for the elasticity of substitution parameters (see Table 3.3.1) are assumed to be common across all the regions. • Refer to figure 1 for notation.

Additional Equation
The economic model is the one described in Hertel (ed.)  where i ∈ TRAD_COMM. TRAD_COMM contains traded commodity Stuff only, VXWD(i,r,s) is the value of exports of tradable commodity i from r to s evaluated at world fob prices [i.e., X rs in equation (2.8a)]; VOW (i,s) is the value of output of tradable commodity i in s evaluated at world fob prices [i.e., Y s in (2.8a)]. The model is encoded in TABLO language for GEMPACK software as reported in the Appendix. In our implementation, we define one region at a time as the source of invention -set named SRC. The countries other than the source belong to the set named REG_NOT_SRC. These two sets are subsets of the set of all regions-REG. TABLO is an algebraic language for writing economic models and for defining the associated sets, equations, coefficients, and variables for subsequent solution specifically compatible with the GEMPACK software suite (see Harrison and Pearson, 1996). ava(i,s)=[(VXWD(i,r,s)/VOW(i,s))^(1-HK(s)*SS(r,s))]*ava(i,r); The Appendix documents the changes made in the GTAP96.TAB by defining some additional coefficients, variables and necessary equations.

Closure and Shock
In the version of GTAP we have used, there is no financial sector. A global 'bank' collects regional saving into a hypothetical global saving pool. Saving in each region is conceptually a real 'saving commodity' (qsave). After each region receives an allocation of the saving commodity from the global saving pool, it uses the purchasing power so obtained to create new capital. The commodity composition of this new investment (qcgds) is region-specific.
All savers face a common price, PSAVE (which is the numeraire in the standard closure of the model), for the savings commodity. The allocation of savings commodity depends on the specification of the closure.
Here it is assumed that the aggregate capital stock is exogenous in all regions and that regional and global nett investment move together. While no reallocation of regional shares in global investment is permitted, interindustry capital mobility within a region is allowed. This is known as the medium-run, or partial long-run equilibrium standard closure in the GTAP literature.
The parameter RORFLEX(r) determines the sensitivity of regional rates of return to these changes in regional gross investment. Here it is assumed that all regions have RORFLEX(r) =10.
In all standard closures of GTAP, the regional labor endowments are exogenous, while in the current closure new investment does not add to the capital stock available in the solution period 13 . Hence the productive capacities of all regions are unaffected in the period to which the simulation results apply. However, as investment is a component of final demand, it affects economic activity in the solution period via its impact on demand. In 13 We use 'solution period' and 'snapshot' period interchangeably to mean the period (occurring some time after the shock) for which the simulation is run and solution is obtained. Specifically, we introduce one or more sustained shocks at an initial period and maintain them through until the 'snapshot' period is reached. The solution is presented as the percentage deviation in the snapshot period in a variable of interest relative to its value in that period in a base-case or control scenario in which no shocks occur. the case of our 1×3 macro aggregation of GTAP, these compositional influences are limited to the sourcing of Stuff from different regions in the assembly of locally-specific capital goods.
The notion of TFP improvement in the CGDS sector is not valid as CGDS assembles the Armington substitutable Stuffs for capital formation without using any primary factors of production. Moreover, CGDS is produced and sold solely in the domestic market, and so is non-traded. Whilst the sector's costs are affected by TFP changes in the three sources of Stuff, CGDS itself plays no role in the technology transfer process.
Below we consider an arbitrary 2 per cent TFP shock in the USA in the Stuff sector. In the closure used here, prices, quantities of all nonendowment commodities, and regional incomes are endogenous, while policy variables, other technical change variables, and population [POP(r)] are exogenous to the model.  Figure 3 displays a schematic presentation of the simulation results for the macro-variables in the model.

Macroeconomic Effects in Each Region
With fixed supplies of land, labor and capital and no factor-bias, a 2 per cent TFP-shock in Stuff in the USA leads to an increase in output in that sector and real GDP at factor cost of exactly 2 per cent. After the HNTP shock, we effectively have 2 per cent more of each factor after allowing for the improvement in its quality. Thus, in the snapshot period, one-hundred input-hours of composite real value-added are equivalent to one hundred and two quantity units of composite value-added measured in terms of constant efficiency units applicable in the base-period. Hence, there has been no change in the usage of primary factors of production (as measured in conventional units) between the base case and the shocked solution. This leads to a zero percentage change in value-added (not quality adjusted) by factors of production [row 6, The increase in productive efficiency of the raw primary composite input (measured in conventional units) leads to an increase in its marginal productivity (MP) -i.e., 2.00, 1.07, and 0.05 per cent for USA, EU and ROW respectively 14 . Since factors are paid according to their marginal 14 The percentage changes in marginal (physical) productivities can be verified from computed GTAP variables as follows. In the levels, the value of the MPs of factors should equal their prices: P stuff * MP f = P f ( where f∈{L, K, T})  Accounts module à la Adams (1996) and incorporating into it the 'Tec_Chg' variable as documented in the Appendix. These are the same as figures in row 9 after this adjustment has been made.
We have computed GTAP results for the percentage changes in P stuff and in each P f -p stuff , p L , p K , and p T (say)-in each region. Then, for example, we can use the above relationship to compute the percentage change in the marginal physical product of labour by: per cent change in MP L = ({[P f (initial) * (1+p f /100)] / [P stuff (initial) * (1+p stuff /100)]}-1)*100 = 100* [{(p f /100)-(p stuff /100)}/(1+p stuff /100)] Note that this accurate calculation is not replicated by simply subtracting 'p stuff ' from 'p l '.  products, these increases in MP lead to increases in the price of value-added and their constituents in all three regions. Being neutral in nature, this TFP improvement causes equal percentage increases in the real rewards of all primary factors within any given region.

A. TECHNOLOGY TRANSMISSION BLOCK
We observe that there has not been full transmission of technical change from the source to the destinations -EU and ROW. Table 5.1.2 suggests that the value of the spillover coefficient depends more strongly on θ s than on E rs alone. Thus, whilst trade is the prime vehicle for transmission of knowledge flows, AC s and SS rs (and hence, θ s ) are critical for effective transmission of technology from r to s. This is supported by the fact that even when E rs has lower values, the magnification of them by θ s can lead to a high rate of capture of the technological improvement. Thus, EU with higher values of both AC s and SS rs , does better than ROW at capturing the TFP improvement occurring in the USA despite ROW having a higher value of E rs . Consequently, in Table 5.1.1 we see a greater improvement in technology in EU (1.07) as compared to that in ROW (0.05). Stuff being the only sector whose production involves value-added, its share in total value-added is unity in all three regions. As the TFP improvements cause real value-added by factors of production (quality adjusted) to increase by the same percentages, the percentage change in real GDP at factor cost in each region is equal to the respective TFP shock (see rows 1 and 8, Table 5.1.1). Also, the price indexes for value-added in Stuff (row 9 of Table 5.1.1) and for GDP at factor cost (row 18) are identical. Changes in real nett indirect taxes (which are of fairly small magnitude) account for the wedges between real GDP at market prices and real GDP at factor cost. Now, the recorded nominal GDP at factor cost [NA_gdpfc] (row 12, Table 5.1.1) is calculated on the basis of price and quantity indexes of valueadded measured in conventional units [pva]. These are taken as given from the GTAP results. As the real value-added measured in constant efficiency units (i.e., 'quality-adjusted') increases in all regions by the same percentage as the TFP improvement, the effective price of value-added has to adjust accordingly so that the nominal value-added measured in constant efficiency units matches the GTAP results. The increases in real value-added (measured in constant efficiency units) of about 2 and 1 per cent respectively in USA and EU lead to falls in the corresponding price indices of about 0.3 and 0.2 per cent (rows 8 and 9, Table 5.1.1). In case of ROW, the small rise in real value-added (with least TFP improvement) is not enough to depress the corresponding price given the attendant general equilibrium effects (to be discussed below) -in fact, it rises there by 0.14 per cent. Table 5.2.1 shows that, region by region, there have been increases in nominal regional household income [y(r)] and its uses ( rows 1, 7, 5 and 4). We first explain post-shock differential impacts on nominal income [y(r)] which is the sum of primary factor payments and receipts from various transactions taxes nett of depreciation. Table 5.2.2 breaks up the componentwise effects on y(r). Earlier discussion shows that the HNTP shock increases 'pva' and its components (row 7, Table 5.1.1). The increase in y(r) has primarily been caused by the uniform increases in primary factor payments in all regions (row 2, Table 5.2.2). With fixed regional supplies of capital stocks at the beginning of the solution period, ex post there have been no percentage changes in it and hence none in physical depreciation (row 3). Changes in the price of capital goods (pcgds) cause a revaluation of existing capital stock; however, capital gains/losses do not enter into our definition of regional income. But changes in pcgds affect the cost of capital consumption, which enters our income definition as a debit. As pcgds falls in the USA and EU (row 5, Table 5.1.1), the replacement cost of existing capital goods falls in these regions (row 4, Table 5.2.2), contributing small rises to nett incomes. In case of ROW, the increase in pcgds causes the nominal cost of replacing depreciated capital to go up and this, in turn, dampens the effect of the small increase in endowment income. With exogenously fixed tax rates, the changes in prices reflect only the effects of the TFP shock per se. Given output tax rates, an increase in output causes a rise in tax revenues on commodities (row 5,   We now turn to the discussion of impacts on sources of various income uses.

5.2.a Region-wide impact on sources of final demands
In GTAP, each region's demands for private expenditure [PRIVEXP(r)], public expenditure [GOVEXP(r)] and saving [SAVE(r)] are determined by maximisation of a per capita Cobb-Douglas utility function subject to the constraint that these three items totally exhaust the regional income [INCOME(r)]. Under this specification, their fixed shares of income result in the equality of percentage increases in nominal demand for the income uses with the percentage increases in total nominal income.
In the present closure with PSAVE as the numeraire, the percentage increase qsave is the same as that in nominal income and changes in real and nominal saving, qsave, are the same.
Given the equality of percentage changes in the nominal variables 15 PRIVEXP and GOVEXP in each region, we observe that the corresponding real variables in each region move together but not strictly in proportion to each other (see rows 5 and 7, Table 5.2.1). The changes in real consumption expenditures are attributed to the differential impacts of movements in pgov (the aggregate government purchase price index) and ppriv (the consumer price index or, CPI) -the divergence being caused by the diverse purchase patterns of the private and public 'households' 16 . Back-of-the-envelope calculation shows that changes up(r) and ug(r) are almost exactly the differences between percentage changes in nominal PRIVEXP and 15 In terms of the TABLO file, strictly speaking, PRIVEXP and GOVEXP are coefficients which are equal to the levels values of the variables 'yp' and 'yg'. The latter one is added in the original TABLO file for computational conveniences. 16 According to base-period data, the share of domestic Stuff in government consumption is 96 per cent for USA, 99 per cent for EU and 97 per cent for ROW. This is higher than that in the private sector's consumption -95 per cent for USA, 96 per cent for EU, and 93 per cent for ROW. As well, the regional composition of imported Stuff differs between the two categories of consumption. GOVEXP (rows 6 and 7, Table 5.2.1) and ppriv and pgov respectively (rows 17 and 18, Table 5.2.1).
The private household price index (pp) and government household price index (pg) are both share weighted averages of percentage changes in a composite import price index and in a domestic price index for domestic Stuff at purchaser's prices. For each category of consumption, domestically-sourced Stuff represents a larger share (on an average 96 per cent for GOVEXP and 93 per cent for PRIVEXP) than composite imports in all three regions.
With domestically sourced Stuff dominating the CPI in every region, the falls in the price of Stuff in USA and EU by 0.30 and 0.19 per cent respectively translate into declines in the CPI in these two regions of 0.28 and 0.18 per cent respectively. Similar considerations explain the slightly larger falls of the pgov in these two countries -compare rows 17 and 18 in Table 5.2.1. For ROW, on the other hand, the increase in the price of domestic Stuff by 0.12 per cent leads to a 0.10 per cent increase in the CPI whereas pgov registers a slightly larger percentage rise (0.11) there. Now, the percentage increases in real private and public consumption demand for composite Stuff are larger than the corresponding increases in domestic supply in every region (rows 5 and 8, Table 5.2.1 and row 2, Table  5.1.1). In spite of the small percentage increments in the market price of composite imports in USA (0.05) and EU (0.02), this leads to increases in private household import demands of 1.35 and 0.7 per cent in USA and EU respectively 17 . The much larger fall in the price of domestically sourced Stuff -0.3 per cent in USA and 0.19 per cent in EU -causes the relative price of domestic-vis-a-vis foreign-sourced Stuff to fall by 0.35 and 0.21 per cent in USA and EU respectively. Given the expansionary effect on demand (qp) for composite Stuff due to the general increase in consumption demand, this leads to substitution in favour of domestic Stuff in USA and EU and reinforces the expansion effect. This is reflected in increases of 2.2 and 1.2 per cent in private consumption demand for domestic Stuff in USA and EU respectively.
As opposed to this, in the case of ROW, a decline in the price of composite imports by 0.05 per cent and a rise of 0.12 per cent in the price of domestic Stuff causes the relative price of domestic Stuff to increase by 0.17 per cent. This leads to substitution in favour of imported Stuff with a relatively larger percentage increase (0.5) in demand for foreign composite Stuff as compared to that in domestic Stuff (0.07). Since Armington elasticities are the same across uses and regions, similar considerations apply in the case of public consumption. The aggregate utility index [u(r)] proxies regional real income 18 . In the model, percentage changes in the sub-utility indexes for the public [ug(r)] and private [up(r)] household consumption are equal to the percentage changes in real quantities purchased by the representative government and private households respectively. The Cobb-Douglas utility function is self-dual 19 as it generates an unit cost function of the same functional form as the primal. Following this property, the income deflator [incdeflator(r)] for y(r) is defined as the sum over the products obtained by multiplying the Cobb-Douglas price indexes for each income use viz., ppriv(r), pgov(r) and psave with their corresponding region-wise shares in total income 20 .  In percentage change form, the first-order condition for this optimisation exercise yields: u (r) = [PRIVEXP (r)/INCOME (r)] * up (r) + [GOVEXP (r)/INCOME (r)] * ug (r) + [SAVE (r)/INCOME (r)] * qsave (r) Thus, percentage changes in real income are calculated by summing over the percentage changes in the sub-utility indexes multiplied by their corresponding shares in aggregate income. 19 The duality between production and cost function is formally analogous to the duality between utility and expenditure function-this implies that minimization of total outlay on public and private consumption and saving subject to the specified level of utility will give the same demand equations for these income uses. For a discussion on 'self-duality' between Cobb-Douglas production and cost function, see Varian (1984) Microeconomic Analysis, 2nd edition, pp. 62-64, 69-73. 20 The mathematical expression for incdeflator (r) is: incdeflator (r) = [PRIVEXP (r)/INCOME (r)] * ppriv (r) + [ GOVEXP (r)/INCOME (r)] * pgov (r) + [SAVE (r)/INCOME (r)] * psave. With PSAVE being the numeraire in the model, psave = 0 so that the last term in the equation vanishes to yield the price index for income in general. Now, the GDP deflator (pgdp) is weighted sum of percentage changes in the index of the price of the domestic absorption (NA_prigne), in the export price index (pxw), in the price index for exports to the international transportation sector (pm) and in the aggregate import price index (pim)the weights being the shares in GDP of gross national expenditure (GNE), of exports (VXWD), of sales to the global transport sector (VST), and of imports (VIWS) 21 .
pgdp includes the change in the price of exportable Stuff (pxw) with a positive weight that includes exports rather than just domestic consumption -as in the case of NA_prigne. Also, pgdp includes pim with a negative weight. Hence, the percentage increase pim and the percentage fall pxw lead to a more negative change in pgdp than NA_prigne. Now, the consumption deflators include the price of imports with positive weight. These consumption deflators are included in NA_prigne and thus, it includes the import price index with a positive weight.
From Table 5.2.4, it is evident that the difference between pgdp and NA_prigne clearly relates to the percentage deviation of the terms-of-trade (TOT ) from the control scenario 22 . The fall in TOT in USA and EU does not cause CPI, pgov and hence, NA_prigne to fall as much as pgdp -see rows 1 and 5 in Table 5.2.4. This implies that a decline in TOT implies a rise in the consumption deflators (which include price of imports) relative to pgdp (which includes price of exports) in these regions. Similar considerations explain relatively larger percentage changes in pgdp relative to NA_prigne and the consumption deflators in case of ROW.
In our simulation, an increase in nominal income [y(r)] leads to equiproportionate increases yp(r) and yg(r) for any given region (as discussed in subsection 5.2.a). For USA and EU, CPI and 'pgov' do not fall as much as the GDP deflators and this results in comparatively higher 21 The GDP deflator, pgdp, can be broken down into the following components as below: pgdp=NA_prigne*(GNE/GDP)+pxw*(VXWD/GDP)+pm*(VST/GDP)-pim*(VIWS/GDP) It is to be noted that 'pm' and 'pxw' are the same. Nominal domestic absorption, GNE(r) is expressed as: GNE(r)= PRIVEXP(r)+GOVEXP(r)+REGINV(r). Thus, the GNE deflator is: NA_prigne(r)=ppriv ( The variable (pxw − pim), the percentage change in the ratio of export prices to import prices, is a conventional measure of the change in the terms-of-trade. Although the GTAP standard TOT definition also includes the price of the non-traded regional investment goods, QO(CGDS, r), here we use the more conventional definition introduced above. percentage increases in real consumption than in real GDP. In the case of ROW, relatively smaller percentage increases in the consumption deflators than in pgdp cause the percentage change in real consumption to be higher than in real GDP (row 5, 8 and 19 in Table 5.2.1).
In the base-case, for both USA and EU, nominal GNE exceeds GDP (and hence, each has an initial trade deficit) whereas in ROW, GDP outweighs GNE (and hence, ROW has initial trade surplus). However, despite moving in the same direction in every region, real GNE [NA_realgne(r) ] diverges from real GDP [qgdp(r) ] -compare rows 9 and 19 in 5.2.1 23 . GNE includes gross investment expenditure -the value of output of the capital goods sector [REGINV(r)]. We now turn to the explanation of why the investment results look the way they do. 23 We can write in nominal terms, GDP (r) = GNE (r) + TBAL (r) where TBAL (r) is the regional trade balance. Thus, in percentage change form we get gdp (r) = gne (r) * [GNE (r)/ GDP (r)] + DTBAL (r)/GDP (r) where DTBAL is the ordinary change in TBAL. Using the expression for [pgdp − NA_ prigne] when TBAL ≠ 0 [as in Footnote 23] and the expression for gdp (r) as derived above, algebraic manipulation yields, for any region, the difference between qgdp and NA_realgne as: qgdp − NA_realgne = DTBAL/GDP − [TBAL/GDP ] * NA_realgne − [ pxw * (VXW/GDP ) − pim * (VIWS/GDP )] When TBAL = 0, i.e., there is balanced trade so that VXW = VIWS, DTBAL = 0, the above difference can be written as: qgdp − NA_realgne = − [VIWS/GDP] * (pxw − pim). Thus, the differential between qgdp and realgne is ascribed to changes in TOT and relevant trade share/s.

5.2.b Regional Effect of investment allocation mechanism §
The increase in pva and each of its components by the same percentage leads to an increase in the rental or supply price of capital as an input into production in every region by the same magnitude as 'pva' -compare row 3 in Table 5.2.5 with row 7 in Table 5.1.1. With PSAVE being the numeraire in the model (as in the base-case), the price of the global saving good is unaltered in any simulation. As explained in subsection 5.2.a, the increases in y(r) lead to equal percentage increases in the corresponding regional demands for nett savings, qsave (nominal and real) which are aggregated into a global nett saving pool so that the global supply of saving -used to finance global expenditure on nett investment -increases following the shock. The percentage increase in the global supply of capital goods composite [globalcgds] is a weighted average of qsave (row 4, Table 5.2.1) 24 .
As all other markets are in equilibrium (which is checked by inspecting the updated post-simulation data-base), the market for the 'saving' commodity must clear à la Walràs' Law. We checked that the § Space limitations prevent us from reporting all the calculations in this section. As has been mentioned elsewhere, since CGDS is non-traded and investment is not available online for production in the solution period, the investment allocation mechanism does not enrich the story associated with the technology transmission via trade. This consideration made us parsimonious while drafting this section. However, interested readers can contact the author for an unabridged version of this particular section named "Elaboration of investment allocation mechanism". 24 The formula used for this calculation is: globalcgds = ∑ r [SAVE(r)/GLOBINV] * qsave (r). The values for these shares in the base case are 0.048, 0.242 and 0.71 for USA, EU and ROW respectively. endogenous walraslack variable is zero to ensure market-clearing in the omitted market and post-shock equilibrium in the global economy.
Since the portfolio of regional nett saving commodities provides a composite investible fund, the increase globalcgds [≡ walras_sup] in the omitted market translates into a matching change in global nett saving demand [walras_dem] as well in that market. In this closure, as the world pool of the real CGDS composite is distributed across regions in the same fixed proportion 25 of NETINV(r) to GLOBINV as in the base-case, because of its higher base-period proportion, ROW gets a larger allocation (67 per cent) from the global nett saving pool than USA (7 per cent), while EU receives the remainder (26 per cent).
Given the fixity of the regional composition of global nett investment, the region-specific ratios of NETINV(r) to the GLOBINV pool are (in the solution period) unchanged from the base case, so the percentage changes in regional real nett investment demand are equal to globalcgds i.e., 0.48 per cent. Regional demand for real gross domestic capital formation [qcgds(r)] is determined by multiplying a region-specific ratio of conversion from nett to gross investment 26 . Thus, the allocation mechanism causes real gross investment demand in ROW to increase by a higher percentage than in USA and EU, leading to a surge in GNE relative to GDP in ROW.
In the control scenario, USA and EU had trade account deficits and ROW had a trade surplus. According to the TFP shock-induced mechanism, USA and EU are able to reduce their trade and saving deficits, whereas ROW sees a fall in its surpluses (compare Tables 5.2.6a with 5.2.6b). Whilst ROW receives a higher allocation of globalcgds than USA and EU, the percentage increase in saving in ROW, (qsave) is less than that in USA and EU (see row 4, Table 5.2.1). This follows from the fixed budget-share of regional saving in regional income under the Cobb-Douglas specification. However, a fall in the level of gross investment in USA as opposed to a relatively large rise in the level of gross saving has caused a reduction in the saving gap there. In the case of EU, a modest rise in gross saving coupled with a very weak rise in gross investment has managed to reduce the saving gap in this region also (compare rows 3, Tables 5.2.6a and 5.2.6b). As there has 25 Here the proportion refers to the base-case values of a region-specific ratio-NETINV(r)/GLOBINV, where GLOBINV = ∑ r NETINV (r) and NETINV (r) is regional nett investment. These ratios differ from the corresponding regional shares of the global capital stock in the data-base. There is nothing to ensure that the region-wise beginning of period capital stock to global capital stock ratio is kept constant during a simulation. Consequently, the ratio applied here must be interpreted strictly in terms of region-wise fixed nett investment flows. 26 The values for the 'proportion' of NETINV(r) to REGINV(r) calculated as per the base-case data are respectively 0.176, 0.389 and 0.514 for USA, EU and ROW. The increase qcgds(r) is this ratio times the percentage deviation (0.48) of regional nett investment demand from the base-case.  been a higher percentage increase in the value of exports than in the value of imports in both USA and EU, the trade deficits in these two regions are reduced. These improvements in trade balances are equal to the differences between row 4 of Table 5.2.6b and the same row in Table 5.2.6a; they account for the 'reduced' saving deficits in USA and EU so that the declines in the trade deficits almost exactly match the reductions in the saving gaps.
As is evident from Tables 5.2.6a and 5.2.6b, ROW initially had a 'saving surplus' to lend investible funds to USA and EU. After the shock, ROW is still a nett external creditor to USA and EU, although not as strongly so as previously. We see that ROW's surplus has declined by US $ 4744.7 million. However, the TFP shock causes the value of imports of Stuff in ROW to rise by a larger proportion (0.403 per cent) than that of its exports (0.16 per cent). This is associated with a fall of US $ 4750 million in the trade surplus in ROW (compare rows 4, Tables 5.2.6a and 5.2.6b).
Not having generated adequate domestic saving for meeting its relatively large gross investment demand, ROW must finance the gap by capital inflow, which shows up here as a fall in its trade surplus. This is matched by the sum of the improvements in the trade balances of USA and EU (the sources of the capital inflows) 27 . In the solution period, the sum over regions of the differences between gross regional saving and investment [regional savings gap] equals zero (excepting the discrepancy due to the rounding errors) as does the sum of the regional trade balances 28 .
In this closure, regional capital stocks in use are kept at their control equilibrium values [fixed capital stocks (KB(r))].With full capacity utilization, the percentage changes in the flow of capital services, ksvces(r), from these stocks, also remain unchanged. 29 As the percentage change in KE(r) 30 depends on the change in real gross investment flows in a region and on the base-period value of INVKERATIO(r) -the ratio of gross regional investment [REGINV(r)] to [ KE(r) ] -higher values of INVKERATIO(r) and qcgds(r) in ROW are reflected in relatively larger percentage changes in its end-of-period capital stock as compared to that in EU and USA (row 7, Table 5.2.5).
Assumption of identical sensitivity of the prospective rate of return (for the period following the solution period) to the prospective proportional expansion in the regional capital stock across all regions implies that a relatively larger percentage increase in KE(r) and a smaller value of current rates of return rorc(r) 31 in ROW cause rore(r) to fall there. 32 On the other hand, a relatively larger rorc(r) and very small percentage increases in KE (r) in USA and EU causes rore(r) to increase in the period following the solution period in these two regions (row 6, In GTAP, there is no option for meeting the current account deficit by 'equity investment flow' mechanism. The only way to meet the 'gap' is by incurring new debts from overseas. 28 Since for each region, Gross Save (r)-REGINV (r)= VXW (r)-VIW (r), for the global economy as a whole to be in equilibrium, ∑ r [Gross Save (r)-REGINV (r)]= ∑ r [VXW (r)-VIW (r)]= 0. 29 Here, fixing aggregate capital stock exogenously means flow of services from that stock in the solution period, ksvces(r)=0. 30 In levels form, the stock-flow relation for KE(r) and KB(r) is: KE(r)= KB(r)*[1-DEP(r)] + REGINV(r). Corresponding percentage change form is given by: ke(r)= INVKERATIO(r)* qcgds (r) + kb(r) * [1-INVKERATIO (r)]. When kb(r)=0, ke(r) is endogenously determined by changes in gross real regional investment-qcgds(r). With kb(r)=0 and given INVKERATIO(r), rore(r) depends on rorc(r) and qcgds(r). 33 Note that these changes are percentage, not percentage-point, changes in expected rates of return.

5.2.c Regional composition of international trade
Due to the Armington specification of commodity substitution, even in a world with one generic traded-commodity in every region, the relative price divergences (between the three varieties of Stuff) across regions (after the TFP shock) induce changes in regional TOT and open up the scope for interregional competition via trade. Consequently, these lead to changes in the regional composition of exports and imports depending, inter alia, on the movements in TOT.
Looking at the global economy as a whole, we observe that after the shock there has been an increase in the quantity index of global merchandise exports and imports of Armington substitutable Stuffs by 0.57 per cent 34 . However, ROW experiences a small percentage rise in the price of domestically produced Stuff as compared to relatively large percentage falls in the prices of Stuff exported by USA and EU (as explained in subsections 5.1 and 5.2.a). Thus, the price index of global merchandise exports of Stuff Decomposition of region-specific differential TOT effects identifies the forces behind such changes. We follow the decomposition à la McDougall (1993) 37 where the percentage change in regional terms of trade [tot(r)] is split into two components as below: where px(•, r ) is the percentage change in the price received for exports and pm(•, r ) is the percentage change in the price paid for imports. Suppose pxw(i, r) and piw(i, r) are respectively the percentage changes of the export and import prices of traded commodity i in any region r, and EXP_SHR(i, r) and IMP_SHR(i, r) are respectively the export share of commodity i in total export expenditure and import share of commodity i in total import expenditure in any region r. 34 The calculation involves multiplying region-wise shares of exports of Stuff in aggregate worldwide exports (at fob prices) by the corresponding percentage increases in regional aggregate volume of exports of Stuff and summation over the products thus obtained. ROW has a higher share (62 per cent) in total world exports of Stuff than USA (17 per cent) and EU (21 per cent As noted above, we adopt the conventional definition of TOT à la McDougall (1993) as opposed to the definition used in standard GTAP theory-the reason being that the TOT definition in the latter includes the price of CGDS which is a purely non-traded sector produced and sold in the local market only. Then the above expression for region r's terms of trade can be written as: With further manipulation following McDougall (1993), this expression yields: where pw(i) is the world price index for total supplies of good i and pxwwld is the price index of world trade (average of world prices of merchandise exports). The first term on the right of (5.2.3), Wpe, captures the world price effect, whilst the last two terms show the export price effect (Xpe) and the import price effect (Mpe) respectively.
Wpe shows that if the world price of commodity i falls/rises relative to the average of all world commodity prices [i.e., pw(i )≠ pxwwld ], then, depending on the sign of the regional nett trade share of good i, the direction of movement of regional TOT will be determined. If r is a nett exporter of i, and the world price of i in general (i.e., averaged over the sources) inflates relative to all prices, then, ceteris paribus, this is good for region r.
Xpe shows that if in any region, the exporters' price of good i falls relative to the world price of i [ i.e., pw(i) ≠ pxw(i, r) ], then TOT will deteriorate. Besides the size of the shock, the extent of changes in such relativities [measured by (pxw(i, r) − pw(i))] reflect the degree of product diversification in the market for i (à la Armington assumption). With low Armington elasticities, ceteris paribus, the spread between the two prices will tend to be larger. By contrast, with a very large substitution elasticity, the absolute difference between pxw(i, r) and pw(i) tends to be smaller so that they are almost equal. If there is erosion of competitiveness following a shock, the large Armington elasticity coupled with the loss in competitive edge can lead to big loss of export shares of a region and consequently, can have adverse effect on TOT. That is, there may be a large fall in EXP_SHR(i,r) − IMP_SHR(i,r) between the base case and the post-shock solution.
Mpe captures the effect of divergences [ piw(i, r) − pw(i) ]between the region-specific import price of good i and the world price of i : it shows that if the latter rises more than the former, then TOT will improve if there are no offsetting changes in Wpe and Xpe.
In a one-traded-commodity world, since EXP_SHR(Stuff, r) is identical to IMP_SHR(Stuff, r) and both are equal to unity, the first term on the right of Equation (5.2.3) for tot(r) vanishes, so that this expression simplifies to the following: Thus, in Table 5.2.7, Wpe is zero across all regions. The intuition behind this result is that Wpe is meant to capture inter-generic-commodity competition, of which there is none in this one-commodity version of GTAP.
Since the share of Stuff in every region's exports is unity, Xpe shows in its entirety the effect of changes in the export supply price of Stuff in a region relative to an index of the average world price of Stuff. Analogously, Mpe totally captures the effect of changes in the region-specific import demand price relative to the world price.  Table 5.2.7 shows that in all three regions, Xpe is the most important source of the change in TOT. The changes in regional export volumes can be ascribed to two-fold movements: along the export demand schedule and shifts of the demand curve.
As the individual regions as exporters of Stuff face downward sloping foreign demand curves for their region-specific Stuffs, a fall in the price of exports in USA and EU (as opposed to a rise in the case of ROW) is consistent with percentage rises in exports from USA and EU which are larger than the percentage expansion of exports from ROW to both of these regions -see row 14 in Table 5.2.1. In part, this has been caused by the movements along the export demand curve governed by the changes in price relativities between regions. Now, the expansion in activity level (i.e., increase in regional aggregate import demand) in each region results in outward shifts of the regional export demand curves. These changed trading conditions entail allocation of demand for aggregate composite imports of Stuff by a region across different sources of imports depending on relative price changes. Given the expansionary effect on demand for all imports of Stuff [qim(stuff,r) ] by any region r due to the increase in intermediate input demand for it by firms producing Stuff and CGDS as well as that in final demand by the public and private sectors (explained before in subsection 5.2.a), changes in relativities between the price of imported Stuff from any source k (pms(stuff,k,r)) and the aggregate import price index (pim(stuff, r)) confronting r determine changes in source-specific import demand by any region.
As products are differentiated by origin, divergences between the export price for Stuff produced in any region and the average world price for Stuff have given rise to changes in TOT. Taking any region r as the destination of exports of Stuff from two sources viz., s and k, given the Armington elasticity, the expansionary effect on aggregate imports of Stuff (qim(stuff, r)) and the import share of k in aggregate imports of r, then import of Stuff from s to r [qxs(i,s,r) ] depends on the changes in relativities between the price of imports of Stuff from k vis-a-vis that from s 38 . We discuss the change in composition of bilateral export sales which is contingent on these shock-induced relative price effects.
Aggregate imports into the USA increase by 1.0108 per cent. In USA, the market shares of EU and ROW in aggregate imports of tradable Stuff are 18 and 82 per cent respectively. A relatively large decline (0.183 per cent) in the price of imported Stuff from EU to USA as compared to a rise (0.104 per cent) in case of imports from ROW to USA causes a 2.2 per cent increase in imports of Stuff in USA from EU, whereas imports from ROW to USA rise by 0.75 per cent only. Given identical Armington elasticities across all regions (all equal to 5), this translates into an increase in demand for Stuff 38 In GTAP, we assume that imports of region r from region s are exactly the same as the exports of region s to r. Hence, the percentage change in demand for exports of 'i' from s to r can be expressed as: qxs(i, s, r)=qim(i, r)− ESUBM * MSHRS (i, k, r) * [pms (i, s, r)−pms(i, k, r)] , where k ≠ s. where MSHRS (i, k, r) is the share of imports from k to r in aggregate imports from both k and s to r and ESUBM (=5 in the database) is the Armington elasticity for imports from sources k and s. Thus, we can write MSHRS (i, k, r)+ MSHRS (i, s, r)=1. from EU even though initially EU has a lower export share in USA than ROW 39 .
In the case of EU, aggregate imports increase by 0.4951 per cent, while the market shares of USA and ROW in total imports are 20 and 80 per cent respectively. The decline in 'pms' for USA (0.29 per cent) as opposed to an increase (0.1 per cent) in case of ROW translates into a relatively larger increase of exports from USA (2.1 per cent) to EU than in case of ROW (0.10 per cent) 40 .
In its own market, ROW (a composite region) supplies 52 per cent of its total import demand whereas USA and EU supply 22 and 26 per cent respectively 41 . USA and EU export respectively 73 per cent and 83 per cent of their total bilateral exports (i.e., excluding exports to the global transportation sector) to ROW whereas for ROW the intra-regional export is 49%. In ROW, USA faces competition from composite region ROW itself (supplying 52% of total imports) and EU (supplying 26% of its imports). In the post-simulation scenario, ROW experiences a rise in the market price of Stuff by 0.12%. The rise in the price of imports of composite Stuff from its own constituent regions is 0.103%. USA as the source of innovation experiences the maximum fall in the relative price of its Stuff after the HNTP shock. Now, the price of imported Stuff from USA to ROW fell by 0.283 per cent whereas it fell by 0.183 per cent in case of imports from EU. This led to a relatively larger percentage increase in export sales from USA to ROW (1.6) as compared to that in export sales from EU to ROW (1.1). On the other hand, the rise in the price of intra-regional imports from constituent regions by 0.103% causes a decline in intra-regional exports in ROW by 0.33 per cent 42 . Table 5.2.8 displays all these figures for percentage changes in bilateral export sales.  Sectoral performances are described below.

5.3.a Effects on Traded Stuff Sector
Our foregoing discussion documents that for each region, marginal productivity of 'raw' primary composite factor inputs (in conventional units), real value-added in effective units and production of Stuff go up exactly by the same percentage as the TFP improvement. Demand for real value-added measured in conventional units does not change (see row 6, Table 5.1.1). Effective price of value-added (quality-adjusted) declines in USA and EU and rises in ROW. More pronounced TFP changes lead to a more productive primary factor composite and to falling costs in USA and EU.
Stuff is produced combining the value-added composite and composite material inputs of Stuff using the Leontief technology at the top nest of the production tree (where intermediate inputs and value-added are not substitutable). Due to the expansionary effect of an increased demand, increased production of Stuff entails an equivalent increase in intermediate input demand [qf (stuff, stuff, r) ]going into its own production in each region -i.e., 2, 1.07 and 0.05% in USA, EU and ROW respectively.
The percentage falls in the price indexes for purchases of domestic Stuff as intermediate input [pfd (stuff, stuff, r) ] -0.3 per cent in USA and 0.19 per cent in EU -are relatively larger than percentage increments in price indexes of composite imports of foreign-sourced Stuff [pfm(stuff, stuff, r) ] -0.05 in USA and 0.02 in EU. Given qf (stuff, stuff, r), the decline in relative price of domestic vis-a-vis foreign sourced Stuff -0.35 per cent in USA and 0.21 per cent in EU -leads to substitution in favour of domestic intermediate Stuff. 43 Stuff [qfd (stuff, stuff, r)] i.e., 2.07 and 1.13 per cent in USA and EU respectively 44 . For demand for the composite import of Stuff [qfm(stuff, stuff, r) ], these are 1.19 (USA) and 0.604 (EU). 45 The decline in relative price of composite imports vis-a-vis domestic Stuff by 0.17 per cent in ROW results in a 0.41 per cent increase in intermediate input demand for imported Stuff whereas intermediate input demand for domestic Stuff falls by 0.01 per cent 46 . In all regions domesticallysourced Stuff has a much larger share than the foreign-sourced Stuff in its production (row 3,

5.3.b Effects on Non-traded Capital Goods Industry
The capital goods sector in GTAP is the one which does capital formation by assembling Stuffs from three regions and caters exclusively to the domestic market only. As mentioned before, the notion of TFP improvement is not valid here. However, as it assembles Armington substitutable Stuffs from domestic and two foreign sources, cost in this sector is affected by the TFP improvements in the three sources of Stuff. The logic follows from our discussion in the earlier subsection. Since it is produced using Leontief technology, the percentage increase in the demand for CGDS translates into an equivalent percentage increase in the demand for Stuff as intermediate input [qf (stuff, CGDS, r) ] -see row 6, Table  5.3.2. In all three regions, domestically sourced Stuff has a large share in CGDS production (row 4, Table 5.3.2). The falls in the price of domestic purchases of Stuff [pfd (stuff, CGDS, r) ] -0.3 per cent in USA and 0.19 per cent in EU [as compared to small rise in the price index for composite imports of Stuff -pfm(stuff, CGDS, r)in USA (0.05) and EU (0.02) ]cause the relative price of domestic vis-a-vis foreign Stuff to fall in USA and EU. As opposed to this, in the case of ROW, the increase in the relative price of domestically sourced Stuff going into production of CGDS by 0.17 per cent (row 12 minus row 13, In the case of CGDS, supply price depends on the price of intermediate input Stuff only. Since the zero-pure-profit condition requires that the price of investment goods is a weighted sum of prices of intermediate-input Stuff from the three different sources going into its production, the decline in the prices of domestically sourced Stuff in USA and EU leads to a fall in the cost of production of CGDS (row 2, Table 5.3.2). For ROW, the increase in the relative price of domestically sourced Stuff leads to an increase in the price of the investment good despite the fall in the price of composite imports. The 47 Similar calculations as shown in subsection 5.3.a yield the above numbers. increases in production of CGDS in all three regions match the corresponding increases in the demand for capital creation in every region [qcgds(r)].

Summary and Conclusion
In this paper, embodied technology spillovers through bilateral trade linkages have been analyzed within the GTAP framework. The analysis is embedded in a setup where each region produces a traded Stuff along with a non-traded capital good. However, the Armington assumption of product differentiation by origin opens the scope for international trade in the sourcespecific Stuff. Embodied technology spillover occurs via bilateral trade in Stuff between source (viz., USA) and destination (viz., EU and ROW). Absorption capacity (AC) and structural congruence (SS) jointly determine a capture-parameter which, together with the trade volume, endogenize the spillover coefficient.
We considered an exogenous 2% value-added augmenting TFP shock in the source country USA. Following the shock, the higher value of the capture parameter in EU allows this region to realise a high percentage of the potential productivity improvement, whereas ROW experiences a relatively less pronounced TFP improvement despite a larger proportional stimulus in imports from USA than that from EU.
In the GTAP's standard medium-run closure, the regional composition of global nett investment is unaltered by the shock and capital stock in use is also unchanged. Given this closure, the shock generates relative price divergences and consequent inter-regional competition effects. A changing composition of demand in the private and public sector and of the sectors producing Stuff and capital goods shape the profile of aggregate demand. The TFP shock leads to an increase in the marginal productivity (in conventional units) of the 'raw' primary factor composite in all three regions whilst the effective price of value-added (quality-adjusted) declines in USA and EU. Owing to the Armington structure and identical Armington elasticities across uses and regions, the relatively larger percentage falls in the price indexes for the purchases of domestically sourced Stuff as compared to the percentage rises in the price indexes of composite imports of foreign-sourced Stuff, resulted in substitution in favour of domestic Stuff in USA and EU. On the other hand, the decline in the relative price of foreign composite imports and an increase in the price of domestic Stuff in ROW causes substitution in favour of imported Stuff. Given the expansionary effects due to increased general activity levels, changes in the price relativities between regions alter the trading conditions. Divergences between the export supply price of Stuff in the regions and its average world price have led to changes in regional terms of trade. Thus, the rise in the price of Stuff in ROW erodes its competitive edge in the global market for Stuff. In particular, a decline in the price of exports in USA and EU translated into a larger percentage expansion of exports from USA and EU to ROW than that from ROW to both of these regions. ROW loses its export share in its own market. With no scope for inter-generic-commodity competition, the terms-of-trade effect predominantly reflects the export price effect.
Given the general-equilibrium relative price effects, a higher percentage increase in the value of exports than in the value of imports in both USA and EU has caused their initial trade deficits to decline. For ROW, the TFP shock causes the value of imports to rise by a larger proportion than that of its exports leading to a fall in its initial trade surplus. Thus, trade creation between the regions is manifest as an increase in bilateral and global trade volumes. However, in the case of the composite region ROW, the loss in competitiveness has caused trade diversion and a resultant loss in the export share in its own market 48 .
This effect is coupled with the regional investment allocation mechanism. ROW having obtained the highest proportional allocation of the global supply of investible funds according to the base−case proportions, experiences a relatively larger increase in demand for gross domestic capital formation than that do USA and EU. Given the constant budget share in regional income, real nett savings increased by less than the real gross investment in ROW whereas the reverse is the case with USA and EU. ROW, having generated an insufficient increase in real savings to finance the new capital formation, has to depend on capital inflows from abroad manifest as an equivalent fall in its trade surplus. By contrast, USA and EU generate an improvement in their trade balances, leading to lower deficits.
The simulations in this paper are meant to be illustrative only since the size and location of the productivity shock was arbitrary, as were the numerical values of the parameters affecting absorptive capacity and structural similarity. Policy conclusions must await the moblilization of realistic data. 48 Under the GTAP conventions, non-zero tariffs and trade flows can exist in the diagonal positions of bilateral matrices in the case of regions which are composites of countries or of smaller regions.

APPENDIX
In this appendix, we document the aggregation method, set definitions, parameter settings and associated files as used in the implementation of a one-sector, three-region macro model. The economic model is the one described in Hertel (ed.) (1997), with some additional equations, coefficients, and variables as described in the main text.

A.1 Set Modifications
Text file SET1BY3.TXT written in the WINGEM text editor is used in running the MODHAR program interactively to create SET1BY3.HAR file.   For our purpose, three different header array (.HAR) files are created for each of the three regions as sources of invention. These files corresponding to three individual sources viz., USA, EU and ROW are SRCUSA.HAR, SRCEU.HAR, and SRCROW.HAR respectively. This is useful for implementing these regions as different sources of invention. These files are created by running MODHAR on a TEXT file named SETINFO.TXT describing the name of each of these regions separately. In the TABLO file, the logical file name (SETINFO) associated with these files is declared as

FILE SETINFO
#The File containing Sources of Innovations. # ; By choosing the name of the header array file (.HAR) relevant for our simulation corresponding to the logical name SETINFO in the Command file (.CMF), one can implement the simulation for a specific source of invention. In the current treatment, set SRC contains USA (as the only source of innovation) and the set REG_NOT_SRC (generated directly by TABLO-see below) contains the destinations EU and ROW and therefore, we select SRCUSA.HAR as the SETINFO file in the CMF file.
Modification in the SET specifications in the TABLO file is given in

A.2 Appended Variables and Equations Ψ
The equation that has been appended and implemented in our analysis is described in the text (vide Sections 2.2b and 4.1 in the text). Apart from these, we defined the following variables and equations: VARIABLE(All,r,REG) Tec_Chg(r); !Value-added-share weighted Value-added Augmenting Technical change! EQUATION E_Tec_Chg (All,r,REG) Tec_Chg(r)=sum(j,PROD_COMM,(VA_Share(j,r)*ava(j,r))); VARIABLE(All,r,REG) NA_gdpfc(r) # Value of Nominal GDP at factor cost#; EQUATION E_NA_gdpfc !Nominal value of GDP at factor cost! (All,r,REG) Sum(i,ENDW_COMM, VOA(i,r)) * NA_gdpfc(r) = Sum(i,ENDW_COMM,(VOA(i,r)*[qo(i,r)+ps(i,r)])); Ψ A complete list of variables including those appended are not provided here for want of space; those are available from author on request.

A.3 Additional Parameters:
The additional parameters in the original TABLO file are COEFFICIENT (all, s, REG_NOT_SRC) HK (s) !The Destination-specific Human Capital Index parameter! COEFFICIENT (all, r, SRC) (all, s, REG_NOT_SRC ) SS (r,s) !The Binary Structural similarity Index parameter in the Spillover function !
The values of these parameters are chosen arbitrarily in the parameter file viz., AGPAR1X3.DAT for this aggregation.
COEFFICIENT (ALL,r,REG) SHSAVE(r) !Share of Nominal net SAVE in INCOME-for each region!; FORMULA (ALL, r, REG) SHSAVE (r)=SAVE(r)/INCOME(r); COEFFICIENT (All,r,REG) SH_SAVGLBINV(r) !Share of Nominal net SAVE in GLOBINV-for each region!; FORMULA (All, r, REG) SH_SAVGLBINV(r)=SAVE(r)/GLOBINV; COEFFICIENT WORLDVKB # Aggregate over Beginning-of-period Capital Stock of all Regions#; FORMULA WORLDVKB=Sum(r, REG, VKB(r)); COEFFICIENT (All,r,REG) SH_REGVKB(r) !Share of Regional VKB in GLOBAL VKB as a whole!; FORMULA (All, r, REG) SH_REGVKB(r)=VKB(r)/WORLDVKB; COEFFICIENT (All,r,REG) CONV_RATIO(r) !It is the conversion ratio from NET to GROSS investment--not the same as GRNETRATIO (r)!; CONV_RATIO (r)=NETINV(r)/REGINV(r); The first one in Box 1 corresponds to Equation (2.4) and the second one to Equation (2.7a) as documented in section 2 in the text. They have three subscripts corresponding to i∈TRAD_COMM, r∈SRC, s∈REG_NOT_SRC. VXWD(i,r,s) is the value of exports of traded commodity i from r to s evaluated at world prices. VOW(i,s) is the value of output in s evaluated at world prices, too. Ratio of these two gives the index for embodied technology spillovers from r to s via trade (E rs ). SPLCOEFFT measures the value of actual spillovers to recipients s [γ s (E rs , θ s )] depending on the values of HK(s) and SS(r,s). The first two coefficients in Box 2 are appended in the existing national accounts reporting module for sake of facilitating the computations of some macroeconomic variables. These two define the gross national expenditure (GNE) and GDP at factor cost for each region. The third one defines the share of each value-adding sector (in our case, it is Stuff) in the region wise aggregate value-added. This has been added to capture the effect of value-added augmenting technical change in a particular sector on its share in value-added. In other words, the product of this share and the magnitude of value-added augmenting technical progress yields the region-wide technical change variable [Tec_Chg(r)]. The coefficients SHPRIVX, SHGOVX, and SHSAVE calculate the shares of each categories of income-use in regional nominal income. All these coefficients are added for computational conveniences.

A.5 Encoded Computer Model and Software
The economic theory underlying the GTAP model is encoded in TABLO language based on FORTRAN programme. The model that we have used for

A.7 List of GTAP variables for current implementation
The list of GTAP variables including those appended are provided below.