STO5 Two-country storage-trade model
Model close to Miranda and Glauber (1995). Countries and are indicated by the subscript . When variables corresponding to both countries appear in the same equation, the foreign country is indicated by the subscript .
Contents
Model's structure
Response variables Storage (), Planned production (), Price () and Export ().
State variable Availability ().
Shock Productivity shocks ().
Parameters Unit physical storage cost (), Depreciation share (), Interest rate (), Scale parameter for the production cost function (), Inverse of supply elasticity (), Demand price elasticity (), Scale parameter for demand function (), Trade cost () and Tariff ().
Equilibrium equations
For and :
Transition equation
For :
Writing the model
The model is defined in a Yaml file: sto5.yaml.
Create the model object
Mu = [1 1]; sigma = [0.05 0; 0 0.05]; model = recsmodel('sto5.yaml',struct('Mu',Mu,'Sigma',sigma^2,'order',7));
Deterministic steady state (different from first guess, max(|delta|)=0.31777) State variables: Aa Ab ______ ______ 1.0402 1.0567 Response variables: Sa Sb Ha Hb Pa Pb Xa Xb __ __________ ______ ______ ______ ______ ________ __ 0 8.4168e-19 1.0402 1.0567 1.2178 1.3178 0.078829 0 Expectations variables: EPa EPb EPea EPeb ______ ______ ______ ______ 1.2178 1.3178 1.2178 1.3178
Define approximation space
[interp,s] = recsinterpinit(15,0.73*model.sss,2*model.sss);
Find a first guess through the perfect foresight solution
interp = recsFirstGuess(interp,model,s,model.sss,model.xss,struct('T',5));
Solve for rational expectations
[interp,x] = recsSolveREE(interp,model,s);
Successive approximation Major Minor Lipschitz Residual 0 0 7.73E-01 (Input point) 1 1 0.8943 2.14E-01 2 1 0.9616 9.75E-02 3 1 0.7867 7.31E-02 4 1 0.6319 4.34E-02 5 1 0.6484 1.69E-02 6 1 0.7361 4.49E-03 7 1 0.7768 1.00E-03 8 1 0.7905 2.10E-04 9 1 0.7945 4.32E-05 10 1 0.7958 8.82E-06 11 1 0.7962 1.80E-06 12 1 0.8031 3.74E-07 13 1 0.9038 8.46E-08 14 1 1.0000 0.00E+00 Solution found - Residual lower than absolute tolerance
Simulate the model
[~,~,~,stat] = recsSimul(model,interp,model.sss(ones(1E4,1),:),100);
Statistics from simulated variables (excluding the first 20 observations): Moments Mean StdDev Skewness Kurtosis Min Max pLB pUB __________ __________ _________ ________ _______ ________ _______ ___ Aa 1.0615 0.056021 0.079139 3.0594 0.82001 1.342 NaN NaN Ab 1.0588 0.053172 0.0023208 3 0.78352 1.3038 NaN NaN Sa 0.021354 0.02686 1.7747 6.5435 0 0.26334 20.218 0 Sb 0.0014208 0.0049854 6.2295 57.578 0 0.11381 70.087 0 Ha 1.0406 0.005748 -1.4948 5.0673 1.0027 1.0463 0 0 Hb 1.0574 0.0054542 -1.5047 5.0917 1.0214 1.0628 0 0 Pa 1.2222 0.17537 1.5246 6.0402 0.90647 3.1226 0 0 Pb 1.3242 0.17191 1.5469 6.4956 0.99882 3.2159 0 0 Xa 0.077861 0.038788 0.33209 2.6835 0 0.26816 0.15363 0 Xb 0.00016171 0.00086318 23.532 798.22 0 0.061958 44.815 0 Correlation Aa Ab Sa Sb Ha Hb Pa Pb Xa Xb _________ _________ _________ _________ ________ ________ ________ ________ ________ _________ Aa 1 -0.032507 0.68347 -0.084515 -0.64564 -0.64578 -0.66163 -0.66965 0.52251 -0.20812 Ab -0.032507 1 0.53128 0.52702 -0.605 -0.60358 -0.63603 -0.63559 -0.84956 0.1135 Sa 0.68347 0.53128 1 0.1961 -0.98168 -0.98219 -0.65901 -0.67349 -0.182 -0.060681 Sb -0.084515 0.52702 0.1961 1 -0.36548 -0.36373 -0.21845 -0.22125 -0.4213 0.07748 Ha -0.64564 -0.605 -0.98168 -0.36548 1 0.99999 0.68427 0.6972 0.24316 0.055652 Hb -0.64578 -0.60358 -0.98219 -0.36373 0.99999 1 0.68284 0.69585 0.24239 0.05576 Pa -0.66163 -0.63603 -0.65901 -0.21845 0.68427 0.68284 1 0.99549 0.15623 0.10826 Pb -0.66965 -0.63559 -0.67349 -0.22125 0.6972 0.69585 0.99549 1 0.15001 0.047489 Xa 0.52251 -0.84956 -0.182 -0.4213 0.24316 0.24239 0.15623 0.15001 1 -0.16019 Xb -0.20812 0.1135 -0.060681 0.07748 0.055652 0.05576 0.10826 0.047489 -0.16019 1 Autocorrelation T1 T2 T3 T4 T5 __________ _________ _________ _________ _________ Aa 0.22939 0.02947 -0.010715 -0.01749 -0.020583 Ab -0.028468 -0.024722 -0.01517 -0.012473 -0.012601 Sa 0.1978 0.022797 -0.011241 -0.017322 -0.018987 Sb 0.0060039 -0.016106 -0.014682 -0.013809 -0.01206 Ha 0.18214 0.019869 -0.011336 -0.017478 -0.018262 Hb 0.18243 0.01992 -0.011329 -0.017489 -0.018273 Pa 0.10913 0.0078086 -0.013164 -0.016746 -0.016546 Pb 0.11533 0.0090659 -0.013051 -0.016779 -0.016571 Xa -0.030315 -0.026361 -0.015005 -0.011474 -0.013226 Xb -0.0053893 -0.011814 -0.013243 -0.01292 -0.013993
References
Miranda, M. J. and Glauber, J. W. (1995). Solving stochastic models of competitive storage and trade by Chebychev collocation methods. Agricultural and Resource Economics Review, 24(1), 70-77.