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Optimality Between Time of Estimation and Reliability of Model Results in the Monte Carlo Method: A Case for a CGE Model

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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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Data availability

The data that support the findings of this study are available upon request.

Code availability

The programme codes used in the study are available upon request.

Notes

  1. The computer is equipped with an Intel Core i7 CPU and a 32GB memory.

  2. 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.

  3. The model equations used in this study is described in Appendix.

  4. 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.

  5. To maintain the accuracy of the analysis, the yield shocks in S100, S500 and S1000 are subsets of those in S2000.

  6. 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.

  7. 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.

  8. 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.

References

  • Abler, D., Rodrĭguez, A. G., & Shortle, J. S. (1999). Parameter uncertainty in CGE modeling of the environmental impacts of economics policies. Environmental and Resource Economics, 14, 75–94.

    Article  Google Scholar 

  • Armington, P. S. (1969). A theory of demand for products distinguished by place of production. International Monetary Fund Staff Paper, 16(1), 159–178.

    Article  Google Scholar 

  • Arndt, C. (1996). An introduction to systematic sensitivity analysis via gaussian quadrature. GTAP Technical Paper No. 2.

  • Devarajan, S., Lewis, J. D., & Robinson, S. (1990). Policy lessons from trade-focused, two sector models. Journal of Policy Modelling, 12(4), 625–657.

    Article  Google Scholar 

  • De Vuyst, E. A., & Preckel, P. V. (1997). Sensitivity analysis revisited: A quadrature-based approach. Journal of Policy Modeling, 19(2), 175–185.

    Article  Google Scholar 

  • Harris, R.L., and Robinson, S. (2001). Economy-wide Effects of El Niño/Southern Oscillation (ENSO) in Mexico and the Role of Improved Forecasting and Technological Change, TMD Discussion Paper No.83. (Accessed on March 1st, 2018) Available at http://www.ifpri.org/publication/economy-wide-effects-el-ni%C3%B1o-southern-oscillation-enso-mexico-and-role-improved.

  • Holton, G.A. (2014). Value-at-Risk, Theory and Practice. Second Edition. https://www.value-at-risk.net/. Accessed on 21st January, 2020.

  • Jansen, H. (2013). Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence. Reliability Engineering and System Safety, 109, 123–132.

    Article  Google Scholar 

  • Kendall, M., Stuart, A. (1973). Advanced Theory of Statistics: Inference and Relationship v. 2. Hafner Publishing.

  • Metropolis, N., & Ulam, S. M. (1949). The Monte Carlo method. Journal of the American Statistical Association, 44, 247.

    Article  Google Scholar 

  • Sassi, M., & Cardaci, A. (2013). Impact of rainfall pattern on cereal market and food security in Sudan: Stochastic approach and CGE model. Food Policy, 43, 321–331.

    Article  Google Scholar 

  • Seale, J, Regmi, A., and Bernstein, J. (2003). International evidence on food consumption patterns. USDA Technical Bulletin Number 1904

  • Stroud, A. H. (1957). Remarks on the disposition of points in numerical integration formulas. Mathematical Tables and other Aids to Computation, 11, 257–261.

    Article  Google Scholar 

  • Tanaka, T., & Hosoe, N. (2011). Does agricultural trade liberalization increase risks of supply-side uncertainty? Effects of productivity shocks and export restrictions on welfare and food supply in Japan. Food Policy, 36, 368–377.

    Article  Google Scholar 

  • Ünal, E. G., Karapinar, B., & Tanaka, T. (2018). Welfare-at-risk and extreme dependency of regional wheat yields: implications of a stochastic CGE model. Journal of Agricultural Economics, 69(1), 18–34.

    Article  Google Scholar 

  • Villoria, N. B., & Preckel, P. V. (2017). Gaussian quadratures versus Monte Carlo experiments for systematic sensitivity analysis of computable general equilibrium model results. Economic Bulletin, 37(1), 480.

    Google Scholar 

  • Wheeler, T., & von Braun, J. (2013). Climate change impacts on global food security. Science, 341(6145), 508–513.

    Article  Google Scholar 

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Correspondence to Tetsuji Tanaka.

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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.

  • Symbol

Sets

  • \( i,j \): commodities/sectors (other than the food composite)

  • \( r,s,r' \) : regions

  • \( h \): factors (capital, skilled labor, unskilled labor, farmland, natural resources)

  • \( nskd \): factors except unskilled labor

Endogenous variables

  • \( X_{i,r}^{p} \): household consumption

  • \( X_{i,r}^{g} \): government consumption

  • \( X_{i,r}^{v} \): investment uses

  • \( X_{i,j,r} \): intermediate uses of the ith good by the jth sector

  • \( F_{h,j,r} \): factor uses

  • \( Y_{j,r} \): value added

  • \( Z_{j,r} \): gross output

  • \( Q_{i,r} \): Armington composite good

  • \( M_{i,r} \): composite imports

  • \( D_{i,r} \): domestic goods

  • \( E_{i,r} \): composite exports

  • \( T_{i,r,s} \): inter-regional transportation from the rth region to the sth region

  • \( TT_{r} \): exports of inter-regional shipping service by the rth region

  • \( Q^{s} \): composite inter-regional shipping service

  • \( S_{r}^{p} \): household savings

  • \( S_{r}^{g} \): government savings

  • \( T_{r}^{d} \): direct taxes

  • \( T_{j,r}^{z} \): production taxes

  • \( T_{j,s,r}^{m} \): import tariffs

  • \( T_{j,r,s}^{e} \): export taxes

  • \( T_{h,j,r}^{f} \): factor input taxes

  • \( p_{i,r}^{q} \): price of Armington composite goods

  • \( p_{h,j,r}^{f} \): price of factors

  • \( p_{j,r}^{y} \): price of value added

  • \( p_{i,r}^{z} \): price of gross output

  • \( p_{i,r}^{m} \): price of composite imports

  • \( p_{i,r}^{d} \): price of domestic goods

  • \( p_{i,r}^{e} \): price of composite exports

  • \( p_{i,r,s}^{t} \): price of goods shipped from the rth region to the sth region

  • \( p^{s} \): inter-regional shipping service price in US dollars

  • \( \varepsilon_{r,s} \): exchange rates to convert the rth region’s currency into the sth region’s currency

Exogenous variables and parameters

  • \( S_{r}^{f} \): current account deficits in US dollars

  • \( FF_{h,j,r} \): factor endowment initially employed in the jth sector

  • \( TFP_{j,r} \): productivity; \( TFP_{wheat,r} \sim N\left( {1,\sigma_{r}^{2} } \right)or N\left( {1,0} \right) \)

  • \( \sigma_{r} \): standard deviation of productivity in wheat or rice sector

  • \( Z_{j,r}^{0} \): initial amount of gross output

  • \( \tau_{r}^{d} \): direct tax rates

  • \( \tau_{i,r}^{z} \): production tax rates

  • \( \tau_{i,s,r}^{m} \): import tariff rates on inbound shipping from the sth region

  • \( \tau_{i,r,s}^{e} \): export tax rates on outbound shipping to the sth region

  • \( \tau_{i,r,s}^{s} \): inter-regional shipping service requirement per unit transportation of the ith good from the rth region to the sth region

  • \( \tau_{h,j,r}^{f} \): factor input tax rates

  • 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

$$ S_{r}^{p} = s_{r}^{p} \mathop \sum \limits_{h,j} p_{h,j,r}^{f} F_{h,j,r} \quad \forall \;r. $$
(S3)
  • Value added producing firm

Factor demand function

$$ F_{h,j,r} = \left( {\frac{{b_{j,r}^{{\eta_{j}^{va} }} \beta_{h,j,r} p_{j,r}^{y} }}{{\left( {1 + \tau_{h,j,r}^{f} } \right)^{{}} p_{h,j,r}^{f} }}} \right)^{{\frac{1}{{1 - \eta_{j}^{va} }}}} Y_{j,r} \forall \;h,\;j,\;r, $$
(S4)

(Note that \( \eta_{i}^{va} = \left( {\varepsilon^{va} - 1} \right)/\varepsilon^{va} \)).

Value added production function

$$ Y_{j,r} = b_{j,r} \left( {\mathop \sum \limits_{h} \beta_{h,j,r} F_{h,j,r}^{{\eta_{j}^{va} }} } \right)^{{1/\eta_{j}^{va} }} \forall \;j,\;r. $$
(S5)
  • 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

$$ X_{i,j,r} = \frac{{\alpha x_{i,j,r} Z_{j,r} }}{{TFP_{j,r} }}\quad \forall \;i,\;j,\;r. $$
(S7)

Demand function for value added

$$ Y_{j,r} = \frac{{ay_{j,r} Z_{j,r} }}{{TFP_{j,r} }}\quad \forall \;j,\;r. $$
(S8)

Unit price function

$$ p_{j,r}^{z} = \frac{1}{{TFP_{j,r} }}\left( {\mathop \sum \limits_{i} ax_{i,j,r} p_{i,r}^{q} + ay_{j,r} p_{j,r}^{y} } \right)\quad \forall \;j,\;r. $$
(S9)
  • Government

Demand function for government consumption

$$ X_{i,r}^{g} = \frac{{\iota_{i,r} }}{{p_{i,r}^{q} }}\left( {T_{r}^{d} + \mathop \sum \limits_{h,j} T_{h,j,r}^{f} + \mathop \sum \limits_{j} T_{j,r}^{z} + \mathop \sum \limits_{j,s} T_{j,s,r}^{m} + \mathop \sum \limits_{j,s} T_{j,r,s}^{e} - S_{r}^{g} } \right)\quad \forall \;i,\;r. $$
(S10)

Direct tax revenue

$$ T_{r}^{d} = \tau_{r}^{d} \mathop \sum \limits_{h,j} p_{h,j,r}^{f} F_{h,j,r} \quad \forall \;r. $$
(S11)

Production tax revenue

$$ T_{j,r}^{z} = \tau_{j,r}^{z} p_{j,r}^{z} Z_{j,r} \quad \forall \;j,\;r. $$
(S12)

Import tariff revenue

$$ T_{j,s,r}^{m} = \tau_{j,s,r}^{m} \left[ {\left( {1 + \tau_{j,s,r}^{e} } \right)\varepsilon_{s,r} p_{j,s,r}^{t} + \tau_{j,s,r}^{s} \varepsilon_{USA,r} p^{s} } \right]^{{}} T_{j,s,r} \quad \forall \;j,s,r. $$
(S13)

Export tax revenue

$$ T_{j,r,s}^{e} = \tau_{j,r,s}^{e} p_{j,r,s}^{t} T_{j,r,s} \quad \forall \;j,r,s. $$
(S14)

Factor input tax revenue

$$ T_{h,j,r}^{f} = \tau_{h,j,r}^{f} p_{h,j,r}^{f} F_{h,j,r} \quad \forall \;h,j,r. $$
(S15)

Government savings function

$$ S_{r}^{g} = s_{r}^{g} \left( {T_{r}^{d} + \mathop \sum \limits_{h,j} T_{h,j,r}^{f} + \mathop \sum \limits_{j} T_{j,r}^{z} + \mathop \sum \limits_{j,s} T_{j,s,r}^{m} + \mathop \sum \limits_{j,s} T_{j,r,s}^{e} } \right)\quad \forall \;r. $$
(S16)
  • Investment

Demand function for commodities for investment uses

$$ X_{i,r}^{v} = \frac{{\lambda_{i,r} }}{{p_{i,r}^{q} }}\left( {S_{r}^{p} + S_{r}^{g} + \varepsilon_{USA,r} S_{r}^{f} } \right)\quad \forall \;i,\;r. $$
(S17)
  • Armington composite good producing firm

Composite good production function

$$ Q_{i,r} = \gamma_{i,r} \left( {\delta_{i,r}^{m} M_{i,r}^{{\eta_{i} }} + \delta_{i,r}^{d} D_{i,r}^{{\eta_{i} }} } \right)^{{1/\eta_{i} }} \quad \forall \;i,\;r, $$
(S18)

(Note that \( \eta_{i} = \left( {\varepsilon - 1} \right)/\varepsilon \)).

Composite import demand function

$$ M_{i,r} = \left( {\frac{{\gamma_{i,r}^{{\eta_{i} }} \delta_{i,r}^{m} p_{i,r}^{q} }}{{p_{i,r}^{m} }}} \right)^{{\frac{1}{{1 - \eta_{i} }}}} Q_{i,r} \quad \forall \;i,\;r. $$
(S19)

Domestic good demand function

$$ D_{i,r} = \left( {\frac{{\gamma_{i,r}^{{\eta_{i} }} \delta_{i,r}^{d} p_{i,r}^{q} }}{{p_{i,r}^{d} }}} \right)^{{\frac{1}{{1 - \eta_{i} }}}} Q_{i,r} \quad \forall \;i,\;r. $$
(S20)
  • Import variety aggregation firm

Composite import function

$$ M_{i,r} = \omega_{i,r} \left( {\mathop \sum \limits_{s} \kappa_{i,s,r} T_{i,s,r}^{{\varpi_{i} }} } \right)^{{1/\varpi_{i} }} \quad \forall \;i,\;r $$
(S21)

Import demand function

$$ T_{i,s,r} = \left( {\frac{{\omega_{i,r}^{{\varpi_{i} }} \kappa_{i,s,r} p_{i,r}^{m} }}{{\left( {1 + \tau_{i,s,r}^{m} } \right)\left[ {\left( {1 + \tau_{i,s,r}^{e} } \right)\varepsilon_{s,r} p_{i,s,r}^{t} + \tau_{i,s,r}^{s} \varepsilon_{USA,r} p^{s} } \right]^{{}} }}} \right)^{{\frac{1}{{1 - \varpi_{i} }}}} M_{i,r} \quad \forall \;i,s,r $$
(S22)
  • Gross output transforming firm

CET transformation function

$$ Z_{i,r} = \theta_{i,r} \left( {\xi_{i,r}^{e} E_{i,r}^{{\varphi_{i} }} + \xi_{i,r}^{d} D_{i,r}^{{\varphi_{i} }} } \right)^{{1/\varphi_{i} }} \quad \forall \;i,r. $$
(S23)

(Note that \( \varphi_{i} = \left( {\varepsilon_{i} + 1} \right)/\varepsilon_{i} \)).

Composite export supply function

$$ E_{i,r} = \left( {\frac{{\theta_{i,r}^{{\varphi_{i} }} \xi_{i,r}^{e} \left( {1 + \tau_{i,r}^{z} } \right)p_{i,r}^{z} }}{{p_{i,r}^{e} }}} \right)^{{\frac{1}{{1 - \varphi_{i} }}}} Z_{i,r} \quad \forall \;i,r. $$
(S24)

Domestic good supply function

$$ D_{i,r} = \left( {\frac{{\theta_{i,r}^{{\varphi_{i} }} \xi_{i,r}^{d} \left( {1 + \tau_{i,r}^{z} } \right)p_{i,r}^{z} }}{{p_{i,r}^{d} }}} \right)^{{\frac{1}{{1 - \varphi_{i} }}}} Z_{i,r} \quad \forall \;i,r. $$
(S25)
  • Export variety producing firm

Composite export transformation function

$$ E_{i,r} = \varsigma_{i,r} \left( {\mathop \sum \limits_{s} \rho_{i,r,s} T_{i,r,s}^{{\phi_{i} }} } \right)^{{1/\phi_{i} }} \quad \forall \;i,r. $$
(S26)

Export supply function

$$ T_{i,r,s} = \left( {\frac{{\varsigma_{i,r}^{{\phi_{i} }} \rho_{i,r,s} p_{i,r}^{e} }}{{p_{i,r,s}^{t} }}} \right)^{{\frac{1}{{1 - \phi_{i} }}}} E_{i,r} \quad \forall \;i,r,s. $$
(S27)

Balance of payments

$$ \begin{aligned} & \mathop \sum \limits_{i,s} \left( {1 + \tau_{i,r,s}^{e} } \right)\varepsilon_{r,USA} p_{i,r,s}^{t} T_{i,r,s} + S_{r}^{f} + \varepsilon_{r,USA} \left( {1 + \tau_{TRS,r}^{z} } \right)p_{TRS,r}^{z} TT_{r} \\ & \quad = \mathop \sum \limits_{i,s} \left[ {\tau_{i,s,r}^{s} p_{{}}^{s} \varepsilon_{USA,USA} + \left( {1 + \tau_{i,s,r}^{e} } \right)p_{i,s,r}^{t} \varepsilon_{s,USA} } \right]T_{i,s,r} \quad \forall \;r. \\ \end{aligned} $$
(S28)
  • Inter-regional shipping sector

Inter-regional shipping service production function

$$ Q^{s} = c\mathop \prod \limits_{r} TT_{r}^{{\chi_{r} }} $$
(S29)

Input demand function for international shipping service provided by the rth country

$$ TT_{r} = \frac{{\chi_{r} }}{{\left( {1 + \tau_{TRS,r}^{z} } \right)^{{}} \varepsilon_{r,USA} p_{TRS,r}^{z} }}p^{s} Q^{s} \quad \forall \;r. $$
(S30)
  • Market-clearing conditions

Commodity market

$$ Q_{i,r} = X_{i,r}^{p} + X_{i,r}^{g} + X_{i,r}^{v} + \mathop \sum \limits_{j} X_{i,j,r} \quad \forall \;i,r. $$
(S31)

Factor markets

$$ FF_{nuskd,j,r} = F_{nuskd,j,r} \quad \forall \;j,r. $$
(S32)

Labor market

$$ \mathop \sum \limits_{j} FF_{unskilled,j,r} = \mathop \sum \limits_{j} F_{unskilled,j,r} \quad \forall \;r. $$
(S33)
$$ p_{unskilled,j,r}^{f} = p_{unskilled,i,r}^{f} \quad \forall \;i,j,r. $$
(S34)

Foreign exchange rate arbitrage condition

$$ \varepsilon_{r,r'} \cdot \varepsilon_{r',s} = \varepsilon_{r,s} \quad \forall \;r,r',s. $$
(S35)

Inter-regional shipping service market

$$ Q^{s} = \mathop \sum \limits_{i,r,s} \tau_{i,r,s}^{s} T_{i,r,s} . $$
(S36)

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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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