- Email: [email protected]
Growth effects of anticipated trade liberalization and the Baldwin multiplier
Economics Letters 59 (1998) 231–235
Growth effects of anticipated trade liberalization and the Baldwin multiplier Dirk Willenbockel* Middlesex University Business School, Queensway, Middlesex University, Enfield EN3 4 SF, UK Received 22 September 1997; accepted 4 February 1998
Abstract According to Baldwin (1992) [Baldwin, R.E., 1992. Measurable dynamic gains from trade. Journal of Political Economy 100, 162–174] trade liberalization induces a medium-run investment-led growth process. This note points out that Baldwin’s own model would actually predict a significant initial drop in investment and aggregate income, when announcement effects are taken into account. 1998 Elsevier Science S.A. Keywords: Trade policy; Growth; Economic integration; Imperfect competition JEL classification: F12; F13; F15; F43; O41
1. Introduction In two widely cited papers, Baldwin (1989), (1992) argues that conventional comparative-static approaches to the quantitative ex ante evaluation of economic integration arrangements underestimate the potential long-run effects by neglecting induced growth processes. The static efficiency gains from trade barrier reductions trigger a medium-run capital accumulation process, which ‘‘can be described in theory and measured in practice’’. While Baldwin (1989) presents his medium-run growth argument within a modified single-region Solow growth model with exogenous saving rate, Baldwin (1992) adopts a two-country intertemporal optimization framework for the same purpose. This note points out that Baldwin’s optimizing model, if taken seriously, would actually predict a significant initial drop in investment and aggregate income, when one takes into account that integration arrangements do not come as overnight surprises, but are usually announced well in advance of the actual implementation date. It is also shown that under plausible parameter values the predicted growth effect materializes only very slowly over time: in Baldwin’s medium run we are all dead.
*Tel.: 144 181 3626358; fax: 144 181 3625446; e-mail: [email protected] 0165-1765 / 98 / $19.00 1998 Elsevier Science S.A. All rights reserved. PII: S0165-1765( 98 )00039-1
D. Willenbockel / Economics Letters 59 (1998) 231 – 235
232
2. Baldwin’s model The model of Baldwin (1992) features two symmetric countries with identical tastes, technologies and initial factor endowments. Intertemporal preferences of the representative infinitely-lived consumer in each country take the iso-elastic form
s U(0) 5 ]] s 21
E C(t) `
0
(s 21 ) / s
P
1 2N e 2 r t dt , C 5 ] c i1 / (2N ) , 2N i 51
(1)
where s is the intertemporal elasticity of substitution, C is a composite defined over consumption quantities c of N domestic and N imported types of goods, and r is the subjective discount rate. The household sector supplies L s labour units at wage rate w and rents K units of non-depreciating capital at rental price r to the domestic industry sector. Capital is accumulated through purchases of a composite investment good of the same form as C. The dynamic budget constraint is
P
2N r(t) w(t) ~ 5 ]]K(t) 1 ]]L s 2 C(t) , K(0) 5 Ko , P 5 p 1i / (2N ) , K(t) P(t) P(t) i 51
(2)
where P is the consistent price index dual to C and pi is the domestic consumer price of good i. There are N symmetric oligopolistic industries in each country corresponding to the N domestic product types. Each industry is populated by m firms which act as static Cournot players. The imperfectly competitive market structure arises due to the presence of a recurrent fixed cost faced by each firm: k units of labour are required at each point in time before the first unit of output y can be produced by combining capital (k) and labour (l) according to a Cobb-Douglas technology y5 Bk a l 12 a with B5 AK b , i.e. total factor productivity is a positive function of the aggregate capital stock K5mNk. Thus investment is associated with a positive externality. Due to free entry pure profits are always zero. The presence of nontariff trade barriers (NTBs) prior to integration is entered in form of iceberg transportation costs 1 . A fraction t /(11t ) of each output unit exported melts away during shipment and the importing country receives only 1 /(11t ) units. Thus letting p* denote the price faced by the importing country per unit received, the producer price per unit exported is p* /(11t ). Since the demand elasticity perceived by the individual Cournot oligopolist is m in both the domestic and the export market 2 , profit-maximizing behaviour entails that pi 5p i* /(11t ) 5 MC(12 1 /m)21 , where MC denotes marginal production cost. Since cost conditions are identical across industries and countries are symmetric, the aggregate price index simplifies to P5pV 21 , where V :5(11t )20.5 . Nominal GDP in each country can then be expressed as PY 5 pymN 5 PV BK a L 12 a , L 5 mNl 5 L s 2 mNk .
(3)
Firms hire capital up to the point where 1 2
See Willenbockel (1994) pp. 120–1 for further discussion of the rationale for this strategy to model cost-increasing NTBs. It is assumed that the individual firm does not perceive to have an influence on the aggregate price index P.
D. Willenbockel / Economics Letters 59 (1998) 231 – 235
r(t) K(t) 1 5 Va BS]]D S1 2 ]D . S D S1 2 ]m1 D ⇔ ]] m P(t) L(t)
r(t) k(t) ]] 5 a B ]] p(t) l(t)
a 21
233
a 21
(4)
The optimal household consumption path must obey
S
D
~ C(t) r(t) ]] 5 s ]] 2 r . C(t) P(t)
(5)
Due to the investment externality, the steady-state capital stock K* under decentralized decisionmaking is not pareto-optimal. Using hat notation to indicate proportional changes, the steady-state effect of a small change in t on aggregate capital stock and GDP is given by
S
1 1 1 ˆ , Yˆ * 5 ]]]] Kˆ * 5 ]]]]V Vˆ 5 Vˆ 1 ]] 2 1 12a 2b 12a 2b a 1b
D
21
Vˆ .
(6)
The far RHS of Eq. (6) decomposes the total effect on long-run GDP into the ‘‘static’’ effect, which would occur without change in the capital endowment (see Eq. (3)), and the dynamic medium-run ‘‘Baldwin multiplier’’ effect. Baldwin cites econometric evidence suggesting a range of 0.22–0.58 for the aggregate capitaloutput elasticity a 1 b. He then concludes on basis of Eq. (6) that conventional comparative-static ex ante assessments of trade liberalization initiatives, which do not account for induced growth, underestimate the medium-run effect on GDP by at least 25% and perhaps by nearly 140%.3 The dynamic model can be expressed as a nonlinear differential equation system in the logs of K and C (normalizing L to unity for notational convenience): d ln K ]] 5 e ln V 1(a 1 b 21) ln K 2 e ln C 2ln K , dt
(7)
d ln C ]] 5 (1 2 1 /m)sa e ln V 1(a 1 b 21) ln K 2 sr . dt
(8)
Linearizing Eq. (7) and Eq. (8) by a Taylor series expansion around the steady state, we obtain an approximation of the form dz(t) / dt5 Az(t)1Bu(t), where z(t)5[ln(K(t) /K*), ln(C(t) /C*)], u(t)5 ln(V (t) /V *),
A 5
r (a 1 b ) ]]]] (1 2 1 /m)a sr (a 1 b 2 1)
3
2r r ]]]] ]]]] (1 2 1 /m)a , B 5 (1 2 1 /m)a . 0 sr
4
3
4
Since det(A),0, its eigenvalues have alternating signs and the system is saddlepoint-stable. 3
In a recent critical note on Baldwin’s analysis, Mazumdar (1996) uses a traditional two-sector growth model to point out that the presence of a static real income gain is not sufficient for the occurence of a medium-run growth effect. See Willenbockel (1997) for a generalized restatement of this point and further comment on Baldwin’s argument.
234
D. Willenbockel / Economics Letters 59 (1998) 231 – 235
3. Dynamic adjustment to a liberalization shock Starting from an initial long-run equilibrium, an unanticipated permanent reduction in t raises the return to capital above the time preference rate and induces an investment-led medium-run growth process. Fig. 1 shows the adjustment paths of consumption and capital to a trade liberalization shock which raises V by 2.5%. The paths are computed by application of the Buiter (1984) solution method to the linearized model. In line with Baldwin (1992), the assumed parameter values are a 50.3, b 50.2, r 50.05, s 50.1 or 0.5, k 50.001 and N510. In this case, the long-run capital stock rises by 5%. The speed of convergence to the new steady state is governed by the stable eigenvalue of the Jacobian A and depends in particular on the magnitude of the intertemporal substitution elasticity between present and future consumption s. The lower s, the stronger is households’ inclination to smooth out consumption over time and thus the higher is the initial boost to consumption in response to the productivity shock. Correspondingly, the strength of the initial investment effect and hence the convergence speed of capital stock and GDP are positively related to s. With s 50.1 4 , 50% of the total capital stock adjustment is completed within 146 years while for s 50.5 the half-life of convergence is around 34 years. Now large-scale integration arrangements, like the Single European Market programme to which Baldwin applies his framework, are generally announced well in advance of their actual implementation. Hence it appears reasonable to relax the assumption that the integration scheme catches agents by surprise in t50. The scenario depicted in Fig. 2 introduces an implementation lag of 5 years: In t50, the authorities credibly commit themselves to lift NTBs from t55 onwards. Households immediately revise their consumption plans upward in anticipation of the rise in expected future income, and in the phase between announcement and implementation aggregate capital stock and GDP decline. The stronger agents’ preferences for a stable consumption path over time, the more pronounced is the initial disinvestment effect. Note that due to the positive investment externality, the
Fig. 1. Response to an unanticipated trade liberalization shock.
4
This is the value selected by Baldwin (1992) himself with reference to the evidence presented by Hall (1988).
D. Willenbockel / Economics Letters 59 (1998) 231 – 235
235
Fig. 2. Response to an anticipated trade liberalization shock.
temporary drop of the capital stock is not merely a pareto-efficient response to the anticipated future integration shock. To conclude: Baldwin (1992) argues that trade liberalization not only generates static efficiency gains but also raises the long-run capital stock and hence induces an extra dynamic output effect. He derives a simple multiplier formula which allows to ‘‘measure’’ the size of this dynamic effect on steady-state income, yet this formula provides no information about the speed of convergence to the new steady state implied by the underlying dynamic model. As shown above, Baldwin’s own analytic framework would predict that the dynamic effect evolves only very gradually over the decades. Moreover, once implementation lags are taken into account, the model would actually predict an initial negative investment effect as a direct consequence of optimal consumption smoothing behaviour. These facts should be taken into account when interpreting estimates of aggregate dynamic integration effects along Baldwin’s lines.
References Baldwin, R., 1989. The growth effects of 1992, Economic Policy No. 9, 247–281. Baldwin, R.E., 1992. Measurable dynamic gains from trade. Journal of Political Economy 100, 162–174. Buiter, W.H., 1984. Saddlepoint problems in continuous time rational expectations models: A general method and some macroeconomic examples. Econometrica 52, 665–680. Hall, R.E., 1988. Intertemporal substitution in consumption. Journal of Political Economy 96, 339–357. Mazumdar, J., 1996. Do static gains from trade lead to medium-run growth?. Journal of Political Economy 104, 1328–1337. Willenbockel, D., 1994. Applied General Equilibrium Modelling: Imperfect Competition and European Integration. John Wiley, Chichester. Willenbockel, D., 1997. On measurable dynamic effects of integration. Middlesex University School of Economics Discussion Paper No. 32.
Growth effects of anticipated trade liberalization and the Baldwin multiplier Dirk Willenbockel* Middlesex University Business School, Queensway, Middlesex University, Enfield EN3 4 SF, UK Received 22 September 1997; accepted 4 February 1998
Abstract According to Baldwin (1992) [Baldwin, R.E., 1992. Measurable dynamic gains from trade. Journal of Political Economy 100, 162–174] trade liberalization induces a medium-run investment-led growth process. This note points out that Baldwin’s own model would actually predict a significant initial drop in investment and aggregate income, when announcement effects are taken into account. 1998 Elsevier Science S.A. Keywords: Trade policy; Growth; Economic integration; Imperfect competition JEL classification: F12; F13; F15; F43; O41
1. Introduction In two widely cited papers, Baldwin (1989), (1992) argues that conventional comparative-static approaches to the quantitative ex ante evaluation of economic integration arrangements underestimate the potential long-run effects by neglecting induced growth processes. The static efficiency gains from trade barrier reductions trigger a medium-run capital accumulation process, which ‘‘can be described in theory and measured in practice’’. While Baldwin (1989) presents his medium-run growth argument within a modified single-region Solow growth model with exogenous saving rate, Baldwin (1992) adopts a two-country intertemporal optimization framework for the same purpose. This note points out that Baldwin’s optimizing model, if taken seriously, would actually predict a significant initial drop in investment and aggregate income, when one takes into account that integration arrangements do not come as overnight surprises, but are usually announced well in advance of the actual implementation date. It is also shown that under plausible parameter values the predicted growth effect materializes only very slowly over time: in Baldwin’s medium run we are all dead.
*Tel.: 144 181 3626358; fax: 144 181 3625446; e-mail: [email protected] 0165-1765 / 98 / $19.00 1998 Elsevier Science S.A. All rights reserved. PII: S0165-1765( 98 )00039-1
D. Willenbockel / Economics Letters 59 (1998) 231 – 235
232
2. Baldwin’s model The model of Baldwin (1992) features two symmetric countries with identical tastes, technologies and initial factor endowments. Intertemporal preferences of the representative infinitely-lived consumer in each country take the iso-elastic form
s U(0) 5 ]] s 21
E C(t) `
0
(s 21 ) / s
P
1 2N e 2 r t dt , C 5 ] c i1 / (2N ) , 2N i 51
(1)
where s is the intertemporal elasticity of substitution, C is a composite defined over consumption quantities c of N domestic and N imported types of goods, and r is the subjective discount rate. The household sector supplies L s labour units at wage rate w and rents K units of non-depreciating capital at rental price r to the domestic industry sector. Capital is accumulated through purchases of a composite investment good of the same form as C. The dynamic budget constraint is
P
2N r(t) w(t) ~ 5 ]]K(t) 1 ]]L s 2 C(t) , K(0) 5 Ko , P 5 p 1i / (2N ) , K(t) P(t) P(t) i 51
(2)
where P is the consistent price index dual to C and pi is the domestic consumer price of good i. There are N symmetric oligopolistic industries in each country corresponding to the N domestic product types. Each industry is populated by m firms which act as static Cournot players. The imperfectly competitive market structure arises due to the presence of a recurrent fixed cost faced by each firm: k units of labour are required at each point in time before the first unit of output y can be produced by combining capital (k) and labour (l) according to a Cobb-Douglas technology y5 Bk a l 12 a with B5 AK b , i.e. total factor productivity is a positive function of the aggregate capital stock K5mNk. Thus investment is associated with a positive externality. Due to free entry pure profits are always zero. The presence of nontariff trade barriers (NTBs) prior to integration is entered in form of iceberg transportation costs 1 . A fraction t /(11t ) of each output unit exported melts away during shipment and the importing country receives only 1 /(11t ) units. Thus letting p* denote the price faced by the importing country per unit received, the producer price per unit exported is p* /(11t ). Since the demand elasticity perceived by the individual Cournot oligopolist is m in both the domestic and the export market 2 , profit-maximizing behaviour entails that pi 5p i* /(11t ) 5 MC(12 1 /m)21 , where MC denotes marginal production cost. Since cost conditions are identical across industries and countries are symmetric, the aggregate price index simplifies to P5pV 21 , where V :5(11t )20.5 . Nominal GDP in each country can then be expressed as PY 5 pymN 5 PV BK a L 12 a , L 5 mNl 5 L s 2 mNk .
(3)
Firms hire capital up to the point where 1 2
See Willenbockel (1994) pp. 120–1 for further discussion of the rationale for this strategy to model cost-increasing NTBs. It is assumed that the individual firm does not perceive to have an influence on the aggregate price index P.
D. Willenbockel / Economics Letters 59 (1998) 231 – 235
r(t) K(t) 1 5 Va BS]]D S1 2 ]D . S D S1 2 ]m1 D ⇔ ]] m P(t) L(t)
r(t) k(t) ]] 5 a B ]] p(t) l(t)
a 21
233
a 21
(4)
The optimal household consumption path must obey
S
D
~ C(t) r(t) ]] 5 s ]] 2 r . C(t) P(t)
(5)
Due to the investment externality, the steady-state capital stock K* under decentralized decisionmaking is not pareto-optimal. Using hat notation to indicate proportional changes, the steady-state effect of a small change in t on aggregate capital stock and GDP is given by
S
1 1 1 ˆ , Yˆ * 5 ]]]] Kˆ * 5 ]]]]V Vˆ 5 Vˆ 1 ]] 2 1 12a 2b 12a 2b a 1b
D
21
Vˆ .
(6)
The far RHS of Eq. (6) decomposes the total effect on long-run GDP into the ‘‘static’’ effect, which would occur without change in the capital endowment (see Eq. (3)), and the dynamic medium-run ‘‘Baldwin multiplier’’ effect. Baldwin cites econometric evidence suggesting a range of 0.22–0.58 for the aggregate capitaloutput elasticity a 1 b. He then concludes on basis of Eq. (6) that conventional comparative-static ex ante assessments of trade liberalization initiatives, which do not account for induced growth, underestimate the medium-run effect on GDP by at least 25% and perhaps by nearly 140%.3 The dynamic model can be expressed as a nonlinear differential equation system in the logs of K and C (normalizing L to unity for notational convenience): d ln K ]] 5 e ln V 1(a 1 b 21) ln K 2 e ln C 2ln K , dt
(7)
d ln C ]] 5 (1 2 1 /m)sa e ln V 1(a 1 b 21) ln K 2 sr . dt
(8)
Linearizing Eq. (7) and Eq. (8) by a Taylor series expansion around the steady state, we obtain an approximation of the form dz(t) / dt5 Az(t)1Bu(t), where z(t)5[ln(K(t) /K*), ln(C(t) /C*)], u(t)5 ln(V (t) /V *),
A 5
r (a 1 b ) ]]]] (1 2 1 /m)a sr (a 1 b 2 1)
3
2r r ]]]] ]]]] (1 2 1 /m)a , B 5 (1 2 1 /m)a . 0 sr
4
3
4
Since det(A),0, its eigenvalues have alternating signs and the system is saddlepoint-stable. 3
In a recent critical note on Baldwin’s analysis, Mazumdar (1996) uses a traditional two-sector growth model to point out that the presence of a static real income gain is not sufficient for the occurence of a medium-run growth effect. See Willenbockel (1997) for a generalized restatement of this point and further comment on Baldwin’s argument.
234
D. Willenbockel / Economics Letters 59 (1998) 231 – 235
3. Dynamic adjustment to a liberalization shock Starting from an initial long-run equilibrium, an unanticipated permanent reduction in t raises the return to capital above the time preference rate and induces an investment-led medium-run growth process. Fig. 1 shows the adjustment paths of consumption and capital to a trade liberalization shock which raises V by 2.5%. The paths are computed by application of the Buiter (1984) solution method to the linearized model. In line with Baldwin (1992), the assumed parameter values are a 50.3, b 50.2, r 50.05, s 50.1 or 0.5, k 50.001 and N510. In this case, the long-run capital stock rises by 5%. The speed of convergence to the new steady state is governed by the stable eigenvalue of the Jacobian A and depends in particular on the magnitude of the intertemporal substitution elasticity between present and future consumption s. The lower s, the stronger is households’ inclination to smooth out consumption over time and thus the higher is the initial boost to consumption in response to the productivity shock. Correspondingly, the strength of the initial investment effect and hence the convergence speed of capital stock and GDP are positively related to s. With s 50.1 4 , 50% of the total capital stock adjustment is completed within 146 years while for s 50.5 the half-life of convergence is around 34 years. Now large-scale integration arrangements, like the Single European Market programme to which Baldwin applies his framework, are generally announced well in advance of their actual implementation. Hence it appears reasonable to relax the assumption that the integration scheme catches agents by surprise in t50. The scenario depicted in Fig. 2 introduces an implementation lag of 5 years: In t50, the authorities credibly commit themselves to lift NTBs from t55 onwards. Households immediately revise their consumption plans upward in anticipation of the rise in expected future income, and in the phase between announcement and implementation aggregate capital stock and GDP decline. The stronger agents’ preferences for a stable consumption path over time, the more pronounced is the initial disinvestment effect. Note that due to the positive investment externality, the
Fig. 1. Response to an unanticipated trade liberalization shock.
4
This is the value selected by Baldwin (1992) himself with reference to the evidence presented by Hall (1988).
D. Willenbockel / Economics Letters 59 (1998) 231 – 235
235
Fig. 2. Response to an anticipated trade liberalization shock.
temporary drop of the capital stock is not merely a pareto-efficient response to the anticipated future integration shock. To conclude: Baldwin (1992) argues that trade liberalization not only generates static efficiency gains but also raises the long-run capital stock and hence induces an extra dynamic output effect. He derives a simple multiplier formula which allows to ‘‘measure’’ the size of this dynamic effect on steady-state income, yet this formula provides no information about the speed of convergence to the new steady state implied by the underlying dynamic model. As shown above, Baldwin’s own analytic framework would predict that the dynamic effect evolves only very gradually over the decades. Moreover, once implementation lags are taken into account, the model would actually predict an initial negative investment effect as a direct consequence of optimal consumption smoothing behaviour. These facts should be taken into account when interpreting estimates of aggregate dynamic integration effects along Baldwin’s lines.
References Baldwin, R., 1989. The growth effects of 1992, Economic Policy No. 9, 247–281. Baldwin, R.E., 1992. Measurable dynamic gains from trade. Journal of Political Economy 100, 162–174. Buiter, W.H., 1984. Saddlepoint problems in continuous time rational expectations models: A general method and some macroeconomic examples. Econometrica 52, 665–680. Hall, R.E., 1988. Intertemporal substitution in consumption. Journal of Political Economy 96, 339–357. Mazumdar, J., 1996. Do static gains from trade lead to medium-run growth?. Journal of Political Economy 104, 1328–1337. Willenbockel, D., 1994. Applied General Equilibrium Modelling: Imperfect Competition and European Integration. John Wiley, Chichester. Willenbockel, D., 1997. On measurable dynamic effects of integration. Middlesex University School of Economics Discussion Paper No. 32.