The national and regional effects of fiscal decentralisation in China

Abstract

Fiscal decentralisation has been an important part of the restructuring of China’s economy over the past three decades. Yet, there has been only limited analysis of the way in which decentralisation in China might affect variables such as welfare, output and income at the aggregate level and none at the regional level. This paper makes a start at filling this gap by analysing the aggregate and regional effects of various policies which aim to change the balance between fiscal activities of the national and regional governments. For this, we use a small theoretical model designed to capture some of the features of the Chinese economy, and we solve it numerically using a parameterisation based on Chinese data. We analyse the effects of four different shocks; all of them involve a transfer of resources to the regional governments financed by a cut in central government expenditure, but they differ in the way in which regional governments use the additional funds: (1) they adjust expenditure on the consumption good, (2) they adjust infrastructure expenditure, (3) they maximise the size of their own budget, and (4) they maximise the welfare of the representative citizen. We find that the aggregate economic effects of decentralisation depend on the precise nature of the policy and that aggregate benefits may often mask a deterioration in the inter-regional distribution of those benefits.

Appendices

Appendix 1: Definition of variables

• $V_{i} =$ Utility of the representative household, region $i$

• $V=$ National welfare

• $C_{Ai}=$ Real private consumption of agricultural output per household, region $i$

• $C_{Mi}=$ Real private consumption of manufactured good per household, region $i$

• $\mathrm{GH}_{i}=$ Real government-provided consumption per household, region $i$.

• $P=$ Price of agricultural good in terms of manufactured good

• $J_{i}=$ Real household income (net of VAT), region $i$

• $J=$ National income

• $W_{j}=$ Real wage income, sector $j$

• $\Pi H_{i}=$ Real profit distribution per household, region $i$

• $D_{j}=$ Productivity parameter, sector $j$

• $Y_{j}=$ Real output, sector $j$

• $Y=$ National output,

• $L_{j}=$ Employment, sector $j$

• $L =$ National employment

• $\Pi F_{j}=$ Firm profit, sector $j$

• $T_{v}=$ Value added tax rate

• $T_{j}=$ Output tax rate, sector$j$

• $\mathrm{TR}_{i}=$ Lump-sum transfer from the central government to regional government $i$

• $\mathrm{GRH}_{i}=$ Real regional government-provided consumption good per household, region $i$

• $\mathrm{GRF}_{i}=$ Real regional government-provided public good, region $i$

• $\mathrm{GC}_{i}=$ Real central government-provided consumption good per household in region $i$

• $\theta =$ Share of valued tax to the central government

• DECEX $=$ The regional share of aggregate government expenditure

• $\mu =$ hukou parameter

Appendix 2: Linearised version of the model

The model of Sect. 2 is linearised in terms of proportional differences by taking logarithms and differentials of each equation. The linearised form of Eqs. (1) to (19) (excluding equations (16) which are redundant) of the model is as follows, with the linearised form having the same number as the original equation but being distinguished by a prime.

The linearised utility function is:

$$\begin{aligned} v_i =\sigma _{caiv} c_{Ai} +\sigma _{cmiv} c_{Mi} +\sigma _{ghiv} gh_i \quad \quad \quad i=I, C \end{aligned}$$

(1′)

where lower-case letters represent the proportional changes (log differential) of their upper-case counterparts and

$$\begin{aligned} \sigma _{caiv} =\frac{\gamma _{Ai} C_{Ai}^{-\rho } }{\gamma _{Ai} C_{Ai}^{-\rho } +\gamma _{Mi} C_{Mi}^{-\rho } +\delta _i {\text{ GH}}_i^{-\rho } },\\ \sigma _{cmiv} =\frac{\gamma _{Mi} C_{Mi}^{-\rho } }{\gamma _{Ai} C_{Ai}^{-\rho } +\gamma _{Mi} C_{Mi}^{-\rho } +\delta _i {\text{ GH}}_i^{-\rho } },\\ \sigma _{ghiv} =\frac{\delta _i {\text{ GH}}_i^{-\rho } }{\gamma _{Ai} C_{Ai}^{-\rho } +\gamma _{Mi} C_{Mi}^{-\rho } +\delta _i {\text{ GH}}_i^{-\rho } }. \end{aligned}$$

The linearised consumption demand functions are:

$$\begin{aligned} c_{Ai} =j_i +\lambda p-\sigma _{cai} p-\sigma _{elas} p \quad i=I, C \end{aligned}$$

(2a′)

where $\sigma _{cai} =\frac{\frac{\rho }{\rho +1}}{1+P^{\frac{-\rho }{\rho +1}}(\frac{\gamma _{Mi} }{\gamma _{Ai} })^{\frac{1}{\rho +1}}},\sigma _{elas} =\frac{1}{\rho +1}$, and

$$\begin{aligned} c_{Mi} =j_i +\lambda p-\sigma _{cai} p \quad i=I,C. \end{aligned}$$

(2b′)

The linearised definitions of real household income are:

$$\begin{aligned} \sigma _{tv} t_v +j_{I} =(1-\lambda )p+\sigma _{\pi hjI} \pi h_I +\sigma _{wjI} w_I \end{aligned}$$

(3a′)

where $\sigma _{\pi hjI} =\frac{\Pi H_I }{\Pi H_I +W_I },\;\sigma _{wjI} =\frac{W_I }{\Pi H_I +W_I }, \sigma _{tv} =\frac{T_v }{1+T_v }$, and

$$\begin{aligned} \sigma _{tv} t_v +j_C =-\lambda p+\sigma _{\pi hjC} \pi h_C +\sigma _{wjC} w_C \end{aligned}$$

(3b′)

where $\sigma _{\pi hjC} =\frac{\Pi H_C }{\Pi H_C +W_C },\;\sigma _{wjC} =\frac{W_C }{IIH_C +W_C }$.

The linearised migration equilibrium condition corresponding to Eq. (4) is:

$$\begin{aligned} v_C =v_I +\mu *\mu \log \left(\frac{L_M /A_C }{L_A /A_I }\right)+\mu (n_C -n_I ) \end{aligned}$$

(4′)

where $\mu * = d\mu /\mu$ and we have used the obvious assumption that area is constant.

The linearised production functions are:

$$\begin{aligned} y_j =d_j +\alpha _{jG} grf_j +\alpha _{jL} (l_j -f_j ),\quad j=A,M. \end{aligned}$$

(5′)

The linearised profit definitions are given by:

$$\begin{aligned} \pi f_j =\sigma _{y\pi fj} y_j -\sigma _{tj} \sigma _{y\pi fj} t_j -\sigma _{w\pi fj} (w_j +l_j -f_j ) \quad j=A, M \end{aligned}$$

(6′)

where $\sigma _{y\pi fj} =\frac{(1-T_j )Y_j }{\Pi F_j },\;\sigma _{tj} =\frac{T_{j}}{1-T_j },\;\sigma _{w\pi f j} =\frac{W_j (L_j /F_j )}{\Pi F_j }$

The manufacturing sector’s profit-maximisation condition in linear form is:

$$\begin{aligned} w_M +\sigma _{tM} t_M -d_M -\alpha _\mathrm{MG} grf_M +(1-\alpha _\mathrm{ML} )(l_M -f_M )=0 \end{aligned}$$

(7a′)

and that for agriculture is given by:

$$\begin{aligned} w_A +\sigma _{tA} t_A -d_A -\alpha _\mathrm{AG} grf_A +(1-\alpha _\mathrm{AL} )(l_A -f_A )=0. \end{aligned}$$

(7b′)

The central government’s budget constraint is linearised as:

$$\begin{aligned} \begin{aligned}&\sigma _{gcIgc} (l_A +gc_I )+\sigma _{gcCgc} (l_M +gc_C )+\sigma _{gctr} (\sigma _{trtrI} tr_I +\sigma _{trtrC} tr_C )\\&\quad =\theta ^*+t_v +\sigma _{jIj} (l_A +j_I )+\sigma _{jCj} (l_M +j_C ) \end{aligned} \end{aligned}$$

(8′)

where

$$\begin{aligned} \sigma _{gcIgc}&= \frac{L_A {\text{ GC}}_I }{L_A {\text{ GC}}_I +L_M {\text{ GC}}_C + {\text{ TR}}_I + {\text{ TR}}_C }, \\ \sigma _{gcCgc}&= \frac{L_M {\text{ GC}}_C }{L_A {\text{ GC}}_I +L_M {\text{ GC}}_C + {\text{ TR}}_I +{\text{ TR}}_C },\\ \sigma _{gctr}&= \frac{{\text{ TR}}_I +{\text{ TR}}_C }{L_A {\text{ GC}}_I +L_M {\text{ GC}}_C +{\text{ TR}}_I +{\text{ TR}}_C },\;\sigma _{jIj} =\frac{L_A J_I }{L_A J_I +L_M J_C }, \\ \sigma _{jCj}&= \frac{L_M J_C }{L_A J_I +L_M J_C }, \theta ^*\!=\!d\theta /\theta ,\sigma _{trtrI} \!=\!\frac{{\text{ TR}}_I }{{\text{ TR}}_I + {\text{ TR}}_C },\;\sigma _{trtrC} \!=\!\frac{{\text{ TR}}_C }{{\text{ TR}}_I +{\text{ TR}}_C }. \end{aligned}$$

The regional governments’ budget constraints are linearised as:

$$\begin{aligned} \begin{aligned}&\sigma _{grhIgr} (l_A +grh_I )+\sigma _{grfAgr} grf_A -\sigma _{grtrI} tr_I\\&\quad =\sigma _{tAgr} (f_A +t_A +p-\lambda p+y_A )+\sigma _{tvIgr} (-\sigma _\theta \theta ^*+t_V +l_A +j_I ) \end{aligned} \end{aligned}$$

(9a′)

where

$$\begin{aligned} \sigma _{grhIgr}&= \frac{L_A {\text{ GRH}}_I }{L_A {\text{ GRH}}_I + {\text{ GRF}}_A -{\text{ TR}}_I },\;\sigma _{grfAgr} =\frac{{\text{ GRF}}_A }{L_A {\text{ GRH}}_I +{\text{ GRF}}_A -{\text{ TR}}_I },\\ \sigma _{grtrI}&= \frac{{\text{ TR}}_I }{L_A {\text{ GRH}}_I + {\text{ GRF}}_A -{\text{ TR}}_I },\;\sigma _\theta =\frac{\theta }{1-\theta },\\ \sigma _{tAgr}&= \frac{F_A T_A P^{1-\lambda }Y_A }{F_A T_A P^{1-\lambda }Y_A +(1-\theta )T_V L_A J_I },\;\\ \sigma _{tvIgr}&= \frac{(1-\theta )T_V N_I J_I }{F_A T_A P^{1-\lambda }Y_A +(1-\theta )T_V L_A J_I }, \end{aligned}$$

and

$$\begin{aligned} \begin{aligned}&\sigma _{grhCgr} (l_M +grh_C )+\sigma _{grfMgr} grf_M -\sigma _{grtrC} tr_C \\&\quad =\sigma _{tMgr} (f_M +t_M -\lambda p+y_M )+\sigma _{tvCgr} (-\sigma _\theta \theta ^*+t_V +l_M +j_C)\qquad \end{aligned} \end{aligned}$$

(9b′)

where

$$\begin{aligned} \sigma _{grhCgr}&= \frac{L_M {\text{ GRH}}_C }{L_M {\text{ GRH}}_C +{\text{ GRF}}_M -{\text{ TR}}_C}, \sigma _{grfMgr} \!=\!\frac{{\text{ GRF}}_M }{L_M {\text{ GRH}}_C \!+\!{\text{ GRF}}_M -{\text{ TR}}_C },\\ \sigma _{grtrC}&= \frac{{\text{ TR}}_C }{L_M {\text{ GRH}}_C \!+\! {\text{ GRF}}_M \!-\!{\text{ TR}}_C }, \sigma _{tMgr} \!=\!\frac{F_M T_M P^{-\lambda }Y_M }{F_M T_M P^{-\lambda }Y_M +(1-\theta )T_V L_M J_C },\;\\ \sigma _{tvCgr}&= \frac{(1-\theta )T_V L_M J_C }{F_M T_M P^{-\lambda }Y_M +(1-\theta )T_V L_M J_C }. \end{aligned}$$

The definition of the decentralisation measure is linearised as:

$$\begin{aligned} \begin{aligned} decex&=\sigma _{dergrf A} grf_A +\sigma _{dergrh I} (l_A +grh_I )+\sigma _{dergrf M} grf_M +\sigma _{dergrh C} (l_M +grh_C )\\&\quad -\sigma _{dengrf A} grf_{I\backslash A} -\sigma _{dengrh I} (l_A +grh_I )-\sigma _{dengrf M} grf_M -\sigma _{dengrh C} (l_M +grh_C)\\&\quad -\sigma _{dengc I} (l_A +gc_I )-\sigma _{dengc C} (l_M +gc_C ) \end{aligned} \end{aligned}$$

(10′)

where $\sigma _{dergrfA} =\frac{GRF_A }{GRF_A +L_A GRH_I +GRF_M +L_M GRH_C }$

$$\begin{aligned} \sigma _{dergrhI}&= \frac{L_A {\text{ GRH}}_I }{{\text{ GRF}}_A +L_A {\text{ GRH}}_I +{\text{ GRF}}_M +L_M {\text{ GRH}}_C }\\ \sigma _{dergrfM}&= \frac{{\text{ GRF}}_M }{{\text{ GRF}}_A +L_A {\text{ GRH}}_I +{\text{ GRF}}_M +L_M {\text{ GRH}}_C}\\ \sigma _{dergrhC}&= \frac{L_M {\text{ GRH}}_C }{{\text{ GRF}}_A +L_A {\text{ GRH}}_I +{\text{ GRF}}_M +L_M {\text{ GRH}}_C }\\ \sigma _{dengrfA}&= \frac{GRF_A }{{\text{ GRF}}_A +L_A {\text{ GRH}}_I +{\text{ GRF}}_M +L_M {\text{ GRH}}_C +L_A {\text{ GC}}_I +L_M {\text{ GC}}_C }\\ \sigma _{dengrhI}&= \frac{L_{A}^*GRH_{I} }{{\text{ GRF}}_A +L_A {\text{ GRH}}_I +{\text{ GRF}}_M +L_M {\text{ GRH}}_C +L_A {\text{ GC}}_I +L_M {\text{ GC}}_C }\\ \sigma _{dengrfM}&= \frac{{\text{ GRF}}_M }{{\text{ GRF}}_A +L_A {\text{ GRH}}_I +{\text{ GRF}}_M +L_M {\text{ GRH}}_C +L_A {\text{ GC}}_I +L_M {\text{ GC}}_C }\\ \sigma _{dengrhC}&= \frac{L_M {\text{ GRH}}_C }{{\text{ GRF}}_A +L_A {\text{ GRH}}_I +{\text{ GRF}}_M +L_M {\text{ GRH}}_C +L_A {\text{ GC}}_I +L_M {\text{ GC}}_C }\\ \sigma _{dengcI}&= \frac{L_A {\text{ GC}}_I }{{\text{ GRF}}_A +L_A {\text{ GRH}}_I +{\text{ GRF}}_M +L_M {\text{ GRH}}_C +L_A {\text{ GC}}_I +L_M {\text{ GC}}_C }\\ \sigma _{dengcC}&= \frac{L_M {\text{ GC}}_C }{{\text{ GRF}}_A +L_A {\text{ GRH}}_I +{\text{ GRF}}_M +L_M {\text{ GRH}}_C +L_A {\text{ GC}}_I +L_M {\text{ GC}}_C } \end{aligned}$$

The linearised equations for the empire-building assumption:

$$\begin{aligned} \sigma _{ngrhI} l_A =-\sigma _{grhI} grh_I \end{aligned}$$

(11a′)

$$\begin{aligned} \sigma _{ngrhC} l_M =-\sigma _{grhC} grh_C \end{aligned}$$

(11b′)

where

$$\begin{aligned}&\sigma _{ngrhI} =\frac{L_A \frac{\partial {\text{ GRH}}_I }{\partial {\text{ GRF}}_A }}{L_A \frac{\partial {\text{ GRH}}_I }{\partial {\text{ GRF}}_A }+{\text{ GRH}}_I \frac{\partial L_A }{\partial {\text{ GRF}}_A }},\;\sigma _{grhI} =\frac{{\text{ GRH}}_I \frac{\partial L_A }{\partial {\text{ GRF}}_A }}{L_A \frac{\partial {\text{ GRH}}_I }{\partial {\text{ GRF}}_A }+{\text{ GRH}}_I \frac{\partial L_A }{\partial {\text{ GRF}}_A }}\\&\sigma _{ngrhC} =\frac{L_M \frac{\partial {\text{ GRH}}_C }{\partial {\text{ GRF}}_M }}{L_M \frac{\partial {\text{ GRH}}_C }{\partial {\text{ GRF}}_M }+{\text{ GRH}}_C \frac{\partial L_M }{\partial {\text{ GRF}}_M }},\;\sigma _{grhC} =\frac{{\text{ GRH}}_C \frac{\partial L_M }{\partial {\text{ GRF}}_M }}{L_M \frac{\partial {\text{ GRH}}_C }{\partial {\text{ GRF}}_M }+{\text{ GRH}}_C \frac{\partial L_M }{\partial {\text{ GRF}}_M }} \end{aligned}$$

$$\begin{aligned} gh_I =\sigma _\mathrm{GHMI} c_\mathrm{MI} +\sigma _\mathrm{GHAI} c_\mathrm{AI} \end{aligned}$$

(11c′)

$$\begin{aligned} gh_C =\sigma _\mathrm{GHMC} c_\mathrm{MC} +\sigma _\mathrm{GHAC} c_\mathrm{AC} \end{aligned}$$

(11d′)

where

$$\begin{aligned} \sigma _\mathrm{GHMI}&= \frac{\gamma _\mathrm{MI} \frac{\partial C_\mathrm{MI} }{C_\mathrm{MI} }/\frac{\partial {\text{ GRH}}_I }{{\text{ GRH}}_I }C_\mathrm{MI}^{-\rho } }{\gamma _\mathrm{MI} \frac{\partial C_\mathrm{MI} }{C_\mathrm{MI} }/\frac{\partial {\text{ GRH}}_I }{{\text{ GRH}}_I }C_\mathrm{MI}^{-\rho } +\gamma _\mathrm{AI} \frac{\partial C_\mathrm{AI} }{C_\mathrm{AI} }/\frac{\partial {\text{ GRH}}_I }{{\text{ GRH}}_I }C_\mathrm{AI}^{-\rho } }\\ \sigma _\mathrm{GHAI}&= \frac{\gamma _\mathrm{AI} \frac{\partial C_\mathrm{AI} }{C_\mathrm{AI} }/\frac{\partial {\text{ GRH}}_I }{{\text{ GRH}}_I }C_\mathrm{AI}^{-\rho } }{\gamma _\mathrm{MI} \frac{\partial C_\mathrm{MI} }{C_\mathrm{MI} }/\frac{\partial {\text{ GRH}}_I }{{\text{ GRH}}_I }C_\mathrm{MI}^{-\rho } +\gamma _\mathrm{AI} \frac{\partial C_\mathrm{AI} }{C_\mathrm{AI} }/\frac{\partial {\text{ GRH}}_I }{{\text{ GRH}}_I }C_\mathrm{AI}^{-\rho } }\\ \sigma _\mathrm{GHMC}&= \frac{\gamma _\mathrm{MC} \frac{\partial C_\mathrm{MC} }{C_\mathrm{MC} }/\frac{\partial {\text{ GRH}}_C }{{\text{ GRH}}_C }C_\mathrm{MC}^{-\rho } }{\gamma _\mathrm{MC} \frac{\partial C_\mathrm{MC} }{C_\mathrm{MC} }/\frac{\partial {\text{ GRH}}_C }{{\text{ GRH}}_C }C_\mathrm{MC}^{-\rho } +\gamma _\mathrm{AC} \frac{\partial C_\mathrm{AC} }{C_\mathrm{AC} }/\frac{\partial {\text{ GRH}}_C }{{\text{ GRH}}_C }C_\mathrm{AC}^{-\rho } }\\ \sigma _\mathrm{GHAC}&= \frac{\gamma _\mathrm{AC} \frac{\partial C_\mathrm{AC} }{C_\mathrm{AC} }/\frac{\partial {\text{ GRH}}_C }{{\text{ GRH}}_C }C_\mathrm{AC}^{-\rho } }{\gamma _\mathrm{MC} \frac{\partial C_\mathrm{MC} }{C_\mathrm{MC} }/\frac{\partial {\text{ GRH}}_C }{{\text{ GRH}}_C }C_\mathrm{MC}^{-\rho } +\gamma _\mathrm{AC} \frac{\partial C_\mathrm{AC} }{C_\mathrm{AC} }/\frac{\partial GRH_C }{GRH_C }C_{AC}^{-\rho } } \end{aligned}$$

The definition of national output is linearised as:

$$\begin{aligned} y=\sigma _{yyA} (f_A +y_A )+\sigma _{yyM} (f_M +y_M ) \end{aligned}$$

(12′)

where $\sigma _{yyA} =\frac{Y_A }{Y_A +Y_M },\;\sigma _{yyM} =\frac{Y_M }{Y_A +Y_M }$, and we assume that $\lambda =\sigma _{yyA}$.

The definition of national income is linearised as:

$$\begin{aligned} j=\sigma _{nIj} (j_I +l_A )+\sigma _{nCj} (j_C +l_M ) \end{aligned}$$

(13′)

where $\sigma _{nIj} =\frac{L_A J_I }{L_A J_I +L_M J_C },\;\sigma _{nCj} =\frac{L_M J_C }{L_A J_I +L_M J_C }$.

The definition of national welfare is linearised as:

$$\begin{aligned} v=\sigma _{nIv} (v_I +l_A -n)+\sigma _{nCv} (v_C +l_M -n) \end{aligned}$$

(14′)

where $\sigma _{nIv} =\frac{L_A V_I }{L_A V_I +L_M V_C },\;\sigma _{nCv} =\frac{L_M V_C }{L_A V_I +L_M V_C }$.

The definition of $GH_{i}$ is linearised as:

$$\begin{aligned} gh_i =\sigma _{grhigh} grh_i +\sigma _{gcigh} gc_i \quad i=I,C \end{aligned}$$

(15′)

where $\sigma _{grhigh} =\frac{GRH_i }{GH_i },\;\sigma _{gcigh} =\frac{GC_i }{GH_i }$.

Equations (16), the goods markets clearing conditions, are dropped from the model due to the redundancy result explained in Sect. 2.

The profit distribution conditions can be linearised to give:

$$\begin{aligned} f_A +\pi f_A =l_A +\pi h_I , \end{aligned}$$

(17a′)

$$\begin{aligned} f_M +\pi f_M =l_M +\pi h_C. \end{aligned}$$

(17b′)

The balance of trade condition in linear form is:

$$\begin{aligned} l_M +p+c_{AC} =l_A +c_{MI}. \end{aligned}$$

(18′)

The national employment constraint results in the following linearised condition:

$$\begin{aligned} \sigma _{nI} l_A +\sigma _{nC} l_M =l \end{aligned}$$

(19′)

where $\sigma _{nI} =L_A /L,\sigma _{nC} =L_M /L$.

Appendix 3: Calibrating the linearised model

The linearised model contains a number of parameters which have to be evaluated before the model can be put to work to simulate the effects of various shocks. These parameters fall into two groups. The first are parameters which appear in model relationships; $\gamma _{ji},\delta _{i}$ and $\rho$ appear in the utility function (1) and $\alpha _{jG}$ and $\alpha _{jL}$ appear in the production function (5). The remainder, on the other hand, are linearisation parameters which are all shares of some sort.

The model parameters were evaluated as follows. For the parameters of the utility function, we broadly followed the method set out in Mansur and Whalley (1984) in which the substitution elasticity $\sigma = 1/(1+\rho )$ is derived from the equation:

$$\begin{aligned} \sigma =\frac{\eta _i -\gamma _{i}^{\sigma }}{1-\gamma _{i}^{\sigma }} \end{aligned}$$

where $\eta _i$ is the (uncompensated) own-price elasticity, values for which were derived as averages from Table 4 in Mansur and Whalley, and $\gamma _i^\sigma$ can be derived from ratios of consumption expenditure and our assumption that $\gamma _{Ai} +\gamma _{Mi} + \delta _{i}= 1$.

The manufacturing sector production parameters, $\alpha _\mathrm{MG}$ and $\alpha _\mathrm{ML}$, were calibrated as follows. Using the firm’s first-order condition for profit-maximisation, Eq. (7a), and the assumption that the firm can choose the government expenditure to maximize profit, we can write:

$$\begin{aligned}&\alpha _\mathrm{ML} =\frac{W_M L_M }{Y_M (1-T_M )},\text{ and}\\&\alpha _\mathrm{MG} =\frac{{\text{ GRF}}_M }{Y_M (1-T_M )} \end{aligned}$$

and use data for the wage bill, government infrastructure expenditure and manufacturing output net of tax to compute the parameters.

Since we assume that firms in the interior region (the agricultural sector) pay all workers the average product rather than their marginal product, we cannot use the profit-maximisation condition to derive production parameters for agricultural sector. Instead, we rely on previous work which has estimated agricultural production functions of the Cobb-Douglas type from which we obtain parameter values. In particular, we use a value of 0.25 for the labour parameter $(\alpha _\mathrm{AL})$ and 0.35 for the land parameter $(1- \alpha _\mathrm{AL}-\alpha _\mathrm{GL})$, based on values reported in Fan (1991) and use the constant-returns-to-scale assumption to derive a value of 0.4 for the government expenditure parameter $( \alpha _\mathrm{GL})$.

The linearisation parameters can be evaluated directly from their definitions, given values for $P,\theta ,\mu ,IIH_i ,W_j ,T_v ,T_j ,Y_j ,\Pi F_j ,L_j ,\mathrm{GC}_i ,J_i ,\mathrm{GRH}_i ,\mathrm{GRF}_i ,\mathrm{GH}_i$and $\mathrm{TR}_{i}$. We normalise $P$ at unity and also set the immigration parameter, $\mu$, at unity; $\theta$ is set at 0.75 to reflect the current division of VAT revenue between the central and regional governments. We then use these assumed values and the data for $C_{i}, \mathrm{GRH}_{i},\mathrm{GRF}_j ,\mathrm{GC}_i ,L_j ,W_j ,\mathrm{TR}_i$ together with the model definitions to calculate the value of all other variables. The use of the model definitions ensures that the parameter values used in the simulations are consistent with the model constraints.

We therefore need data for two regions, the interior and the coast, for the variables $C_i ,\mathrm{GRH}_i ,\mathrm{GRF}_j ,\mathrm{GC}_i ,L_j ,W_j ,\mathrm{TR}_i$. The data we use are based on those for the Chinese provinces which we have allocated to the two regions as follows. The coastal region consists of Beijing, Tianjin, Hebei, Guangdong, Hainan, Shandong, Fujian, Zhejiang, Jiangsu, Shanghai, Liaoning and Guangxi with the remaining provinces being allocated to the interior region. The interior therefore consist of: Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan, Sichuan, Chongqing, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, Tibet, Xinjiang. A map of the two regions is provided in Fig. 1.

For each region, we use data averaged over the 7-year period 2000–2006 to avoid cyclical influences on the share parameters. All the data come from China Statistics Year Book (SSB, various issues) except for data on area used to compute population density for the migration equilibrium condition, Eq. (4′), which come from China Civil Affairs Statistical Yearbook 2005 (State Statistical Bureau 2005).