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Spatial perspectives of increasing freeness of trade in Lebanon

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Abstract

In this paper, we use an interregional computable general equilibrium model for Lebanon—the ARZ model—for the analysis of place-based policies in the country, in an attempt to bring additional insights to some of the proposals presented in the National Physical Master Plan of the Lebanese Territory. We apply the model to look at the ex ante potential regional implications of an increase in domestic and international integration of Lebanese regions through reductions in trade costs. The link between freeness of trade and the equilibrium distribution of activities is explored.

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Notes

  1. With less than 11,000 km\(^{2}\), Lebanon is the second smallest country in the Middle East and the Arab World (after Bahrain). Its territory represents 1/1,000th that of large countries such as the USA and Canada and 1/100th that of Egypt (NPMPLT 2005, ch. 1, p. 1).

  2. NPMPLT 2005, Introduction, p. 1.

  3. Op. cit., Introduction, p. 4.

  4. Hereafter, increase in freeness of trade and integration will be used interchangeably.

  5. ARZ is the Arabic word for cedar, the symbol of Lebanon. It is also a pseudo-acronym in Arabic standing for Analytical Regional System.

  6. To our knowledge, other sources of data are seldom incorporated in the existing modeling efforts for Lebanon (e.g. demographic and social statistics such as population, labor force and household expenditure surveys).

  7. See World Road Association (2003) for a discussion in the context of transport policies.

  8. Peter et al. (1996) and Haddad (1999).

  9. See Haddad (2012) for a detailed description of the database.

  10. Spatial friction was approximated by distance measures, calculated for each pair of origin-destination using Google Maps (see Haddad 2012).

  11. Hereafter, trade services and margins will be used interchangeably.

  12. In the case of international imported goods, the implicit trade margin may be interpreted as the costs at the port of entry, while for foreign exports it would refer to costs at the port of exit.

  13. Similarly, one can think about a flow of exports or imports.

  14. The process of calibration of trade costs assumes \(A = 1\) for all \(i,\, s\) and \(r\) in the benchmark year. Thus, \(\eta \) can be calibrated by calculating the relationship between \(m\) and \(x\) directly from the interregional input–output database.

  15. The detailed system of equations of the ARZ model is available in an “Appendix”.

  16. The system of equations provides the theoretical structure of the model. In the implementation of the ARZ model, the linearized version of the model was condensed by eliminating some equations and variables, generating a reduced version with 33,454 equations and 34,248 variables. To close the model, values for 794 variables have to be set exogenously (the number of endogenous variables must equal the number of equations). The condensation procedure, i.e., the reduction of the size of the model, is carried out by substituting out variables that are to be endogenous and are of less interest to the analysis and presentation of the simulation results, and by omitting variables that are to be exogenous and not shocked in the simulations. The nominal exchange rate was set as the numéraire.

  17. In the ARZ model we impose the assumption that margins are produced in the destination region, with the exception that margins on exports are produced in the source region.

  18. This result may be suggesting that internal trade costs are relatively more important to regional competitiveness than specific trade costs associated with international transactions in Lebanon.

  19. The regularity in the positioning of the lines in Fig. 6 is due to the model’s assumption that the price received by the producer is uniform across all customers. The assumption on zero pure profits in current production is imposed by setting unit prices received by producers equal to unit costs, while the assumption on zero pure profits in distribution is imposed by setting the prices paid by users equal to producer price plus commodity tax plus margins.

  20. Darker colors refer to higher contributions to real GRP in the context of increasing integration.

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Acknowledgments

Eduardo A. Haddad acknowledges financial support from CNPq and Fapesp; he also thanks Princeton University and Rutgers University for their hospitality.

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Appendix: The core equation system of the ARZ model

Appendix: The core equation system of the ARZ model

The functional forms of the main groups of equations of the spatial CGE core are presented in this Appendix together with the definition of the main groups of variables, parameters and coefficients.

The notational convention uses uppercase letters to represent the levels of the variables and lowercase for their percentage-change representation. Superscripts \((u)\), \(u = 0, 1j, 2j, 3, 4, 5\), refer, respectively, to output \((0)\) and to the five different regional-specific users of the products identified in the model: producers in sector \(j \, (1j)\), investors in sector \(j \, (2j)\), households \((3)\), purchasers of exports \((4)\), and government \((5)\); the second superscript identifies the domestic region where the user is located. Inputs are identified by two subscripts: the first takes the values \(1,\ldots , g\), for commodities, \(g + 1\), for primary factors, and \(g + 2\), for “other costs” (basically, taxes and subsidies on production); the second subscript identifies the source of the input, being it from domestic region \(b \, (1b)\) or imported \((2)\), or coming from labor \((1)\) or capital \((2)\). The symbol (\(\bullet \)) is employed to indicate a sum over an index.

Substitution between products from different regional domestic sources

$$\begin{aligned}&x_{(i(1b))}^{(u)r} =x_{(i(1{\bullet }))}^{(u)r} -\sigma _{(i)}^{(u)r} \left( p_{(i(1b))}^{(u)r} -\sum _{l\in S^{*}} {\left( {V(i,1l,(u),r)/V(i,1{\bullet },(u),r)\left( p_{(i(1l))}^{(u)r} \right) } \right) }\right) \nonumber \\&\quad i\!=\!1,\ldots ,g;\,\, b=1,\ldots ,q;\;(u)=3\hbox { and }(kj)\hbox { for }k=1\hbox { and }2\hbox { and }j=1,\ldots ,h;\nonumber \\&\quad r=1,\ldots ,R \end{aligned}$$
(1)

Substitution between domestic and imported products

$$\begin{aligned} x_{(is)}^{(u)r}&= x_{(i{\bullet })}^{(u)r} -\sigma _{(i)}^{(u)r} \left( p_{(is)}^{(u)r} -\sum _{l=1{\bullet },2} {\left( V(i,l,(u),r)/V(i,{\bullet },(u),r)\left( p_{(il)}^{(u)r} \right) \right) }\right) \nonumber \\ i&= 1,\ldots ,g;\,s=1{\bullet }\hbox { and }2;\,(u)=3\hbox { and }(kj)\hbox { for }k=1e 2\hbox { and }j=1,\ldots ,h;\nonumber \\ r&= 1,\ldots ,R \end{aligned}$$
(2)

Substitution between labor and capital

$$\begin{aligned}&x_{(g+1,s)}^{(1j)r} -a_{(g+1,s)}^{(1j)r} =\alpha _{(g+1,s)}^{(1j)r} x_{(g+1{\bullet })}^{(1j)r} -\sigma _{(g+1)}^{(1j)r} \left\{ p_{(g+1,s)}^{(1j)r} +a_{(g+1,s)}^{(1j)r}\right. \nonumber \\&\left. \quad -\sum _{l=1,2} (V(g+1,l,(1j),r) /V(g+1,{\bullet },(1j),r))\left( p_{(g+1,l)}^{(1j)r} +a_{(g+1,l)}^{(1j)r} \right) \right\} \nonumber \\&\quad j=1,\ldots ,h;\,s=1\hbox { and }2;\, r=1,\ldots ,R \end{aligned}$$
(3)

Intermediate and investment demands for composites commodities and primary factors

$$\begin{aligned} \begin{array}{l@{\quad }l} x_{(i{\bullet })}^{(u)r} =z^{(u)r}+a_{(i)}^{(u)r} &{} u=(kj) \hbox { for }k=\hbox {1 , 2 and }j=1,\ldots ,h \\ &{} \qquad \,\, \hbox { if }u=\hbox {(1}j)\hbox { then }\,i=1,\ldots ,g+2\\ &{} \qquad \,\, \hbox { if }u=(2j) \hbox { then }\, i=1,\ldots ,g; \\ &{}\qquad \,\,\, r=1,\ldots ,R \end{array} \end{aligned}$$
(4)

Household demands for composite commodities

$$\begin{aligned} V(i,{\bullet },(3),r)(p_{(i{\bullet })}^{(3)r}\!+\!x_{(i{\bullet })}^{(3)r} )&\!=\! \gamma _{_{(i)} }^r P_{(i{\bullet })}^{(3)r} Q^{r}(p_{(i{\bullet })}^{(3)r} \nonumber \\&+\,x_{(i{\bullet })}^{(3)r})\!+\!\beta _{(i)}^r \!\left( C^{r}\!-\!\sum _{j\in G} \gamma _{(j)}^r P_{(i{\bullet })}^{(3)r} Q^{r}\left( p_{(i{\bullet })}^{(3)r} \!+\!x_{(i{\bullet })}^{(3)r} \right) \right) \! \nonumber \\&i=1,\ldots ,g;\,r\!=\!1,\ldots ,R \end{aligned}$$
(5)

Purchasers’ prices related to basic prices and margins (trade costs)

$$\begin{aligned} \begin{aligned}&V(i,s,(u),r)p_{(is)}^{(u)r} =(B(i,s,(u),r)+\sum _{m\in G} {M(m,i,s,(u),r)p_{(m1)}^{(0)r} } , \\&i=1,\ldots ,g;\,(u)=(3),\,(4),\hbox { (5)} \hbox { and }(kj)\hbox { for }\,k=1,\,2\hbox { and } \\&j=1,\ldots ,h;\,s=1b,\,2\hbox { for }\,b=1,\ldots ,q \\&r=1,\ldots ,R \end{aligned} \end{aligned}$$
(6)

Foreign demands (exports) for domestic goods

$$\begin{aligned}&\left( x_{(is)}^{(4)r} -fq_{(is)}^{(4)r} \right) =\eta _{(is)}^r \left( p_{(is)}^{(4)r} -e-fp_{(is)}^{(4)r} \right) , \nonumber \\&i=1,\ldots ,g ;s=1b, 2\hbox { for }\,b=1,\ldots ,q\hbox {;}r=1,\ldots ,R \end{aligned}$$
(7)

Government demands

$$\begin{aligned}&x_{(is)}^{(5)r} =x_{({\bullet }{\bullet })}^{(3)r} +f_{(is)}^{(5)r} +f^{(5)r} +f^{(5)}\nonumber \\&i=1,\ldots ,g; \quad s=1b,2 \hbox { for } b=1,\ldots ,q; r=1,\ldots ,R \end{aligned}$$
(8)

Margins demands for domestic goods

$$\begin{aligned} x_{(m1)}^{(is)(u)r} =x_{(is)}^{(u)r} +a_{(m1)}^{(is)(u)r} \quad \begin{array}{l} m,i=1,\ldots ,g; \\ (u)=(3),(4b)\hbox { for }\,b=1,\ldots ,r,\hbox { (5) and }(kj)\hbox { for }\,k=1,\,2; \\ j=1,\ldots ,h\hbox {; }s=1b,\,2\hbox { for }\,b=1,\ldots ,r; \\ r=1,\ldots ,R \\ \end{array} \end{aligned}$$
(9)

Demand equals supply for regional domestic commodities

$$\begin{aligned} \sum _{j\in H} Y(l,j,r)x_{(l1)}^{(0j)r}&= \sum _{u\in U} {B(l,1,(u),r)x_{(l1)}^{(u)r} \,}\nonumber \\&+\sum _{i\in G} {\sum _{s\in S} {\sum _{u\in U} {M(l,i,s,(u),r)x_{(l1)}^{(is)(u)r} } } }\nonumber \\&l=1,\ldots ,g;\,r=1,\ldots ,R \end{aligned}$$
(10)

Regional industry revenue equals industry costs

$$\begin{aligned} \sum _{l\in G} Y(l,j,r)\left( p_{(l1)}^{(0)r} +a_{(l1)}^{(0)r} \right)&= \sum _{l\in G*} {\sum _{s\in S} {V(l,s,(1j),r)\left( p_{(ls)}^{(1j)r} \right) ,} } \nonumber \\&j=1,\ldots ,h; \quad r=1,\ldots ,R \end{aligned}$$
(11)

Basic price of imported commodities

$$\begin{aligned}&p_{(i(2))}^{(0)} =p_{(i(2))}^{(w)} -e+t_{(i(2))}^{(0)},\quad i=1,\ldots ,g \end{aligned}$$
(12)

Cost of constructing units of capital for regional industries

$$\begin{aligned}&V({\bullet },{\bullet },(2j),r)\left( p_{(k)}^{(1j)r} -a_{(k)}^{(1j)r} \right) =\sum _{i\in G} {\sum _{s\in S} {V(i,s,(2j),r)\left( p_{(is)}^{(2j)r} +a_{(is)}^{(2j)r} \right) } } ,\nonumber \\&j=1,\ldots ,h;\,r=1,\ldots ,R \end{aligned}$$
(13)

Investment in period T

$$\begin{aligned}&X_{(g+1,2)}^{(1j)r} (1)x_{(g+1,2)}^{(1j)r} (1)=X_{(g+1,2)}^{(1j)r} (1-\delta _j )x_{(g+1,2)}^{(1j)r} +Z^{(2j)r} z^{(2j)r}\nonumber \\&\,j=1,\ldots ,h;\quad r=1,\ldots ,R \end{aligned}$$
(14)

Capital stock in period \(T+1\)—comparative statics

$$\begin{aligned} x_{(g+1,2)}^{(1j)r} (1)=x_{(g+1,2)}^{(1j)r} \quad j=1,\ldots ,h;\,r=1,\ldots ,R \end{aligned}$$
(15)

Definition of rates of return to capital

$$\begin{aligned} r_{(j)}^r =Q_{(j)}^r \left( p_{(g+1,2)}^{(1j)r} -p_{(k)}^{(1j)r} \right) ,\quad j=1,\ldots ,h;\,r=1,\ldots ,R \end{aligned}$$
(16)

Relation between capital growth and rates of return

$$\begin{aligned} r_{(j)}^r -\omega \!=\! \varepsilon _{(j)}^r \left( x_{(g+1,2)}^{(1j)r} -x_{(g+1,2)}^{({\bullet })r} \right) \! +\! f_{(k)}^{(2j)r} ,\quad j=1,\ldots ,h;\,r=1,\ldots ,R\qquad \quad \end{aligned}$$
(17)

Other definitions in the CGE core include: import volume of commodities, components of regional/national GDP, regional/national price indices, wage settings, definitions of factor prices, employment aggregates, and accounting identities.

1.1 Variables

Variable

Index ranges

Description

\(x_{(is)}^{(u)r}\)

\(\begin{array}{l} \left( u \right) \,=\,\left( 3 \right) ,\,\left( 4 \right) ,\,\left( 5 \right) ,\,\left( 6 \right) \hbox { and} \\ \left( {kj} \right) \hbox { for}\, k= 1,2\, \hbox { and}\, j= 1,\ldots ,h; \\ \hbox {if }\left( u \right) \,=\,\left( {1j} \right) \, \hbox {then}\, i= 1,\ldots ,g + 2; \\ \hbox {if }\left( u \right) \ne \left( {1j} \right) \hbox { then}\, i = 1,\ldots ,g; \\ s=1\hbox {b},2\,\mathrm{for}\, { b} = 1,\ldots ,q;\, \hbox { and}\, i = 1,\ldots ,g\, \hbox {and} \\ s= 1, 2,3\,\hbox { for}\, i= g+1 \\ r= 1,\ldots ,R \\ \end{array}\)

Demand by user (u) in region r for good or primary factor (is)

\(p_{(is)}^{(u)r} \)

\(\begin{array}{l} \left( u \right) \,=\,\left( 3 \right) ,\,\left( 4 \right) ,\,\left( 5 \right) ,\,\left( 6 \right) \hbox { and} \\ \left( {kj} \right) \hbox { for}\, k = 1,2 \,\hbox { and}\, j = 1,\ldots ,h; \\ \hbox {if }\left( u \right) \,=\,\left( {1j} \right) \, \hbox {then} \,i= 1,\ldots ,g + 2; \\ \hbox {if }\left( u \right) \ne \left( {1j} \right) \hbox { then}\, i = 1,\ldots ,g; \\ s =1b,2\hbox { for}\, b = 1,\ldots ,q; \,\hbox { and}\, i = 1,\ldots , g \,\hbox {and} \\ s = 1, 2,3\hbox { for}\, i =g+1 \\ r = 1,\ldots ,R \\ \end{array}\)

Price paid by user (u) in region r for good or primary factor (is)

\(x_{(i{\bullet })}^{(u)r} \)

\(\begin{array}{l} \left( u \right) \,=\,\left( 3 \right) \,\hbox { and }\,\left( {kj} \right) \hbox { for}\, k = 1,2 \hbox { and} \\ j = 1,\,\ldots ,h. \\ \hbox {if }\left( u \right) \,=\,\left( {1j} \right) \hbox { then}\, i= 1,\,\ldots ,g + 1; \\ \hbox {if }\left( u \right) \ne \left( {\hbox {1j}} \right) \hbox { then}\, i= 1,\,\ldots ,g \\ r = 1,\ldots ,R \\ \end{array}\)

Demand for composite good or primary factor i by user (u) in region r

\(a_{(g+1,s)}^{(1j)r} \)

\(\begin{array}{l} j = 1,\,\ldots , h \,\mathrm{and}\, s = 1, 2,3 \\ r = 1,\ldots , R \\ \end{array}\)

Primary factor saving technological change in region r

\(a_{(i)}^{(u)r} \)

\(\begin{array}{l} i = 1,\ldots ,g,\,\left( u \right) \,=\,\left( 3 \right) \hbox { and }\left( {kj} \right) \hbox { for}\, k = 1,2\,\\ \hbox {and}\quad j = 1,\ldots , h \\ r = 1,\ldots , R \\ \end{array}\)

Technical change related to the use of good i by user (u) in region r

\(C^{r}\)

 

Total expenditure by regional household in region r

\(Q^{r}\)

 

Number of households

\(z^{(u)r}\)

\(\begin{array}{l} \left( u \right) \,=\,\left( {kj} \right) \hbox { for}\, k = 1,2 \,\hbox { and}\, j = 1,\,\ldots , h \\ r = 1,\ldots , R \\ \end{array}\)

Activity levels: current production and investment by industry in region r

\(fq_{(is)}^{(4)r} \)

\(\begin{array}{l} i = 1, \ldots , g; s =1b, 2\,\mathrm{for} \,b = 1, \ldots , q \\ r = 1,\ldots , R\\ \end{array}\)

Shift (quantity) in foreign demand curves for regional exports

\(fp_{(is)}^{(4)r} \)

\(\begin{array}{l} i = 1,\,\ldots , g; s =1 b, 2 \hbox { for}\, b = 1,\,\ldots ,q \\ r = 1,\ldots , R \\ \end{array}\)

Shift (price) in foreign demand curves for regional exports

\(e\)

 

Exchange rate

\(x_{(m1)}^{(is)(u)r} \)

\(\begin{array}{l} m,i = 1,\ldots , g; s=1b, 2\, \hbox {for}\, b = 1,\ldots , q \\ \left( u \right) \,=\,\left( 3 \right) ,\,\left( 4 \right) ,\,\left( 5 \right) \hbox { and} \\ \left( {kj} \right) \hbox { for}\, k = 1, 2\, \hbox {and} j= 1,\,\ldots ,h \\ r= 1,\ldots ,R \\ \end{array}\)

Demand for commodity (m1) to be used as a margin to facilitate the flow of (is) to (u) in region r

\(a_{(m1)}^{(is)(u)r} \)

\(\begin{array}{l} m, i= 1,\ldots ,g; s=1b, 2 \hbox { for}\, b = 1,\ldots , q \\ \left( u \right) \,=\,\left( 3 \right) ,\,\left( 4 \right) ,\,\left( 5 \right) \hbox { and} \\ \left( {kj} \right) \hbox { for}\, k = 1, 2 \,\hbox {and} j = 1,\,\ldots ,h \\ r = 1,\ldots ,R \\ \end{array}\)

Technical change related to the demand for commodity (m1) to be used as a margin to facilitate the flow of (is) to (u) in region r

\(x_{(i1)}^{(0j)r} \)

\(\begin{array}{l} i= 1,\ldots ,g; j= 1,\ldots ,h \\ r= 1,\ldots ,R \\ \end{array}\)

Output of domestic good i by industry j

\(p_{(is)}^{(0)r} \)

\(\begin{array}{l} i = 1,\ldots ,g; s =1b, 2 \hbox { for}\, b = 1,\ldots , q \\ r = 1,\ldots ,R \\ \end{array}\)

Basic price of good \(i\) in region r from source s

\(p_{(i(2))}^{(w)} \)

i = 1,...,g

USD c.i.f. price of imported commodity i

\(f_{(k)}^{(2j)r} \)

\(\begin{array}{l} j = 1,\ldots , h \\ r = 1,\ldots ,R \\ \end{array}\)

Regional-industry-specific capital shift terms

\(x_{(g+1,2)}^{(1j)r} (1)\)

\(\begin{array}{l} j = 1,\ldots , h \\ r = 1,\ldots ,R \\ \end{array}\)

Capital stock in industry j in region r at the end of the year, i.e., capital stock available for use in the next year

\(p_{(k)}^{(1j)r} \)

\(\begin{array}{l} j = 1,\ldots , h \\ r = 1,\ldots , R \\ \end{array}\)

Cost of constructing a unit of capital for industry j in region r

\(f_{(is)}^{(5)r} \)

\(\begin{array}{l} i = 1,\,\ldots , g; s =1 b,2\,\hbox { for}\, b = 1,\ldots ,q \\ { r} = 1,\ldots ,{ R} \\ \end{array}\)

Commodity and source-specific shift term for government expenditures in region r

\(f^{(5)r}\)

r = 1,...,R

Shift term for government expenditures in region r

\(f^{(5)}\)

 

Shift term for government expenditures

\(\omega \)

 

Overall rate of return on capital (short-run)

\(r_{(j)}^r \)

\(\begin{array}{l} j = 1,\ldots , h \\ r = 1,\ldots ,R \\ \end{array}\)

Regional-industry-specific rate of return

1.2 Parameters, Coefficients and Sets

Symbol

Description

\(\sigma _{(i)}^{(u)r} \)

Parameter: elasticity of substitution between alternative sources of commodity or factor i for user (u) in region r

\(\sigma ^{(0j)r}\)

Parameter: elasticity of transformation between outputs of different commodities in industry j in region r

\(\alpha _{(g+1,s)}^{(1j)r} \)

Parameter: returns to scale to individual primary factors in industry j in region r

\(\beta _{(i)}^r \)

Parameter: marginal budget shares in linear expenditure system for commodity i in region r

\(\gamma _{(i)}^r \)

Parameter: subsistence parameter in linear expenditure system for commodity i in region r

\(\varepsilon _{(j)}^r \)

Parameter: sensitivity of capital growth to rates of return of industry j in region r

\(\eta _{(is)}^r \)

Parameter: foreign elasticity of demand for commodity i from region r

\(B(i,s,(u),r)\)

Input–output flow: basic value of (is) used by (u) in region r

\(M(m,i,s,(u),r)\)

Input–output flow: basic value of domestic good m (m = trade) used as a margin to facilitate the flow of (is) to (u) in region r

\(V(i,s,(u),r)\)

Input–output flow: purchasers’ value of good or factor i from source s used by user (u) in region r

\(Y(i,j,r)\)

Input–output flow: basic value of output of domestic good i by industry j from region r

\(Q_{(j)}^r \)

Coefficient: ratio, gross to net rate of return

G

Set: \(\{1,2, {\ldots }, g\}\), g is the number of composite goods

G*

Set: \(\{1,2, {\ldots }, g+1\},\, g+1\) is the number of composite goods and primary factors

H

Set: \(\{1,2, {\ldots },\, h\}\), h is the number of industries

U

Set: \(\{(3), (4), (5), (6), (k j)\,\hbox { for }\, k \!=\! 1, 2\,\hbox { and}\, j = 1, {\ldots }, h\}\)

U*

Set: \(\{(3),{ (k j)} \text {for} k = 1, 2\,\hbox { and}\, j = 1, {\ldots }, h\}\)

S

Set: \(\{1, 2, {\ldots }, r+1\}, r+1\) is the number of regions (including foreign)

S*

Set: \(\{1, 2, {\ldots },r\}\), r is the number of domestic regions

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Haddad, E.A. Spatial perspectives of increasing freeness of trade in Lebanon. Ann Reg Sci 53, 29–54 (2014). https://doi.org/10.1007/s00168-014-0615-3

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