Abstract
Computable general equilibrium (CGE) is one of the most frequently utilised macroeconomic models in policy decision-making processes. Economists introduced a stochastic concept to deterministic CGE models using the Monte Carlo (MC) method to identify the effects of climate change or extreme weather patterns that have exacerbated global food insecurity. However, a weakness of the MC method is its time-consuming process to approximate probability distributions with a considerable number of randomised draws. Modellers have unavoidably to face a trade-off between the duration of computation and the accuracy of a model’s results. This paper explores an optimal balance point between the two elements in CGE analysis. Assuming that 2000 repetitive simulations create adequately precise simulation outcomes, we compare model results from 100, 500 and 1000 iterations with those from 2000 repetitive calculations. We found that 1000-time iterations indicate highly credible outcomes, 500-time simulations can function well; however, with moderate accuracy, whereas 100-time calculations are apparently insufficient to obtain reliable outcomes.
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The data that support the findings of this study are available upon request.
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The programme codes used in the study are available upon request.
Notes
The computer is equipped with an Intel Core i7 CPU and a 32GB memory.
The desired samples are 4852 for equivalent variation. In our experiments, we look into various variables including producer prices, which are directly affected by TFP exogenous shocks. Hence, the desired sample size is estimated as large as 206,914.
The model equations used in this study is described in Appendix.
Even though FAOSTAT provides a much longer time series, we concentrated on the period between 1992 and 2017 since the former Soviet Union regions such as Russia do not have production and land area data older than 1992.
To maintain the accuracy of the analysis, the yield shocks in S100, S500 and S1000 are subsets of those in S2000.
We use the standard t-test as the methodology. To guarantee the robustness of the results, the Welch t-test, Anova F-test and Welch F-test are also applied to the difference in mean tests. The results of these tests are similar to the t-test and the results can be obtained from the authors upon request.
The Wilcoxon test was used in this study. The results are robust to the Chi-square test, Kruskal-Wallis test and Van der Waerden test for difference in medians. For the sake of brevity, these results are not reported here.
Bartlett’s test for differences in standard deviations was applied in the analysis. In addition, similar results were obtained by using a standard F-test, Siegel-Tukey test, Levene’s test and the Brown-Forsythe test. These results can be obtained from the authors upon request.
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Appendix: Algebraic description of the model
Appendix: Algebraic description of the model
A full specification of the standard CGE used in the analysis is as follows.
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Symbol
Sets
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\( i,j \): commodities/sectors (other than the food composite)
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\( r,s,r' \) : regions
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\( h \): factors (capital, skilled labor, unskilled labor, farmland, natural resources)
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\( nskd \): factors except unskilled labor
Endogenous variables
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\( X_{i,r}^{p} \): household consumption
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\( X_{i,r}^{g} \): government consumption
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\( X_{i,r}^{v} \): investment uses
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\( X_{i,j,r} \): intermediate uses of the ith good by the jth sector
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\( F_{h,j,r} \): factor uses
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\( Y_{j,r} \): value added
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\( Z_{j,r} \): gross output
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\( Q_{i,r} \): Armington composite good
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\( M_{i,r} \): composite imports
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\( D_{i,r} \): domestic goods
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\( E_{i,r} \): composite exports
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\( T_{i,r,s} \): inter-regional transportation from the rth region to the sth region
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\( TT_{r} \): exports of inter-regional shipping service by the rth region
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\( Q^{s} \): composite inter-regional shipping service
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\( S_{r}^{p} \): household savings
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\( S_{r}^{g} \): government savings
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\( T_{r}^{d} \): direct taxes
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\( T_{j,r}^{z} \): production taxes
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\( T_{j,s,r}^{m} \): import tariffs
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\( T_{j,r,s}^{e} \): export taxes
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\( T_{h,j,r}^{f} \): factor input taxes
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\( p_{i,r}^{q} \): price of Armington composite goods
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\( p_{h,j,r}^{f} \): price of factors
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\( p_{j,r}^{y} \): price of value added
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\( p_{i,r}^{z} \): price of gross output
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\( p_{i,r}^{m} \): price of composite imports
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\( p_{i,r}^{d} \): price of domestic goods
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\( p_{i,r}^{e} \): price of composite exports
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\( p_{i,r,s}^{t} \): price of goods shipped from the rth region to the sth region
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\( p^{s} \): inter-regional shipping service price in US dollars
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\( \varepsilon_{r,s} \): exchange rates to convert the rth region’s currency into the sth region’s currency
Exogenous variables and parameters
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\( S_{r}^{f} \): current account deficits in US dollars
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\( FF_{h,j,r} \): factor endowment initially employed in the jth sector
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\( TFP_{j,r} \): productivity; \( TFP_{wheat,r} \sim N\left( {1,\sigma_{r}^{2} } \right)or N\left( {1,0} \right) \)
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\( \sigma_{r} \): standard deviation of productivity in wheat or rice sector
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\( Z_{j,r}^{0} \): initial amount of gross output
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\( \tau_{r}^{d} \): direct tax rates
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\( \tau_{i,r}^{z} \): production tax rates
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\( \tau_{i,s,r}^{m} \): import tariff rates on inbound shipping from the sth region
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\( \tau_{i,r,s}^{e} \): export tax rates on outbound shipping to the sth region
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\( \tau_{i,r,s}^{s} \): inter-regional shipping service requirement per unit transportation of the ith good from the rth region to the sth region
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\( \tau_{h,j,r}^{f} \): factor input tax rates
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Household
$$ \left( {{\text{Utility}}\;{\text{function:}}UU_{r} = \mathop \prod \limits_{i} X_{i,r}^{{p\alpha_{i,r} }} \quad \forall \;r} \right). $$(S1)$$ X_{i,r}^{p} = \frac{{\alpha_{i,r} }}{{p_{i,r}^{q} }}\left( {\mathop \sum \limits_{h,j} p_{h,j,r}^{f} F_{h,j,r} - T_{r}^{d} - S_{r}^{p} } \right)\quad \forall i,r $$(S2)
Savings function
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Value added producing firm
Factor demand function
(Note that \( \eta_{i}^{va} = \left( {\varepsilon^{va} - 1} \right)/\varepsilon^{va} \)).
Value added production function
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Gross output producing firm
$$ \left( {{\text{Production}}\;{\text{function}}:Z_{j,r} = TFP_{j,r} \hbox{min} \left( {\left\{ {\frac{{X_{i,j,r} }}{{ax_{i,j,r} }}} \right\}_{i} ,\frac{{Y_{j,r} }}{{ay_{j,r} }}} \right)\quad \forall \;j,\;r} \right). $$(S6)
Demand function for intermediates
Demand function for value added
Unit price function
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Government
Demand function for government consumption
Direct tax revenue
Production tax revenue
Import tariff revenue
Export tax revenue
Factor input tax revenue
Government savings function
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Investment
Demand function for commodities for investment uses
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Armington composite good producing firm
Composite good production function
(Note that \( \eta_{i} = \left( {\varepsilon - 1} \right)/\varepsilon \)).
Composite import demand function
Domestic good demand function
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Import variety aggregation firm
Composite import function
Import demand function
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Gross output transforming firm
CET transformation function
(Note that \( \varphi_{i} = \left( {\varepsilon_{i} + 1} \right)/\varepsilon_{i} \)).
Composite export supply function
Domestic good supply function
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Export variety producing firm
Composite export transformation function
Export supply function
Balance of payments
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Inter-regional shipping sector
Inter-regional shipping service production function
Input demand function for international shipping service provided by the rth country
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Market-clearing conditions
Commodity market
Factor markets
Labor market
Foreign exchange rate arbitrage condition
Inter-regional shipping service market
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Tanaka, T., Guo, J., Hiyama, N. et al. Optimality Between Time of Estimation and Reliability of Model Results in the Monte Carlo Method: A Case for a CGE Model. Comput Econ 59, 151–176 (2022). https://doi.org/10.1007/s10614-020-10080-8
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DOI: https://doi.org/10.1007/s10614-020-10080-8