A Simple Ecological Monetary Macroeconomic Model

Abstract

This chapter first reviews the various functions and limitations of economic modeling, before introducing SIM-E, a simple ecological monetary macroeconomic SFC model with 16 equations aligned with the basic monetary principles outlined in the previous chapters. SIM-E can be implemented with the help of a spreadsheet, and permits to highlight the ripple effects of outside money creation on the real and monetary spheres of the economy, as well as on a simplified representation of the Earth System. Finally, the case study section guides students to develop their own spreadsheet simulations, with the objective of initiating a model-based climate policy discussion in the classroom.

Appendix: Calculating of the Steady State in SIM-E

The stationary state of the model is defined as a situation where flows and stocks cease to change. In the excel spreadsheet, the stationary state is achieved after 40 numerical iterations. In this appendix, we show how to calculate analytically the value of GDP, disposable income, consumption, monetary wealth in the stationary state.

1.1 Calculation of Steady-State GDP

In a steady state, tax revenues are equal to government expenditures: there is neither a budget surplus nor a budget deficit. This implies that the money supply stabilizes, since in this case, there is neither net creation nor destruction of currency. This balanced budget condition implies the following equality (omitting suffixes):

$$ G={T}^{\ast }=\theta .W.{N}^{\ast }=\theta .{Y}^{\ast } $$

This is equivalent to: ${Y}^{\ast }=\frac{G}{\theta }$. Therefore, the stationary income Y* is equal to 20/0.2 = 100 as in Table 7.4.

1.2 Calculation of Steady-State Disposable Income and Consumption

In the steady state, the government budget is in equilibrium, and households cease to accumulate new savings. Therefore, consumption is equal to total disposable income:

$$ \varDelta {H}_h^{\ast }=Y{D}^{\ast }-{C}^{\ast }=0 $$

Which implies that:

$$ Y{D}^{\ast }={C}^{\ast } $$

(7.19)

Using the value of the steady-state GDP:

$$ {Y}^{\ast }=\frac{G}{\theta}\leftrightarrow G={Y}^{\ast }.\theta $$

(7.20)

Inserting Eq. (7.6) of the model into (7.19):

$$ {C}^{\ast }=w{N}_s-{T}_s $$

(7.21)

Inserting Eqs. (7.12) and (7.5) of the model into (7.21):

$$ {C}^{\ast }={Y}^{\ast }-{T}_s $$

Given Eqs. (7.4) and (7.7) of the model we know that:

$$ {T}_s={T}_d=\theta .w{N}_s $$

Which given Eq. (7.12) of the model and (7.20), can be written:

$$ {T}_s={T}_d=\theta .{Y}^{\ast }=G $$

Using Eq. (7.12) of the model and (7.21) we get:

$$ {C}^{\ast }={Y}^{\ast }-{T}_s=\frac{G}{\theta }-G=\frac{G\left(1-\theta \right)}{\theta } $$

Therefore, in the stationary state we obtain:

$$ Y{D}^{\ast }={C}^{\ast }=\frac{G.\left(1-\theta \right)}{\theta } $$

Given the parameters of the model: $Y{D}^{\ast }=\frac{20.\left(1-0.2\right)}{0.2}=80$

We thus retrieve the results obtained with the spreadsheet simulations shown in Table 7.4.

1.3 Calculation of the Steady-State Monetary Wealth

At the stationary state, both the stock of public debt and the stock of household savings stop growing (since net money issues are zero). Therefore, H = H₋₁ (monetary wealth is stable) and YD^∗ = C^∗ (households consume their disposable income). Considering Eq. (7.7) of the model: C_D = α₁. Y_D + α₂. H₋₁

$$ {H}^{\ast }=\left\{\frac{\left({C}_D-{\alpha}_1.Y{D}^{\ast}\right)}{\alpha_2}\right\} $$

$$ {H}^{\ast }=\left\{\frac{\left(1-{\alpha}_1\right)}{\alpha_2}\right\}.Y{D}^{\ast }={\alpha}_3.\frac{G.\left(1-\theta \right)}{\theta } $$

With ${\alpha}_3=\frac{\left(1-{\alpha}_1\right)}{\alpha_2}$. Given the numerical values assigned to the differentparameters we obtain ${\alpha}_3=\frac{0.4}{0.4}=1$ so H^∗ = YD^∗ = 80. We thus retrieve theresults of the spreadsheet simulations shown in Table 7.4.

Activities

Mini-Case Using the model SIM-E

• 1. Explain why the sums of each row and column of the transaction matrix of SIM-E are all zero?

• 2. Why is net government spending (i.e. government spending G superior to tax revenue T) equal to net money creation? How does it impact the monetary wealth of the private sector?

• 3. Inspect the first 11 equations in the model. Create a table that sorts these equations into two categories: accounting equations and behavioral equations. Explain the meaning of each equation in the second column of the table.

• 4. Activate the iterative calculation function on your spreadsheet software and download the ‘SIM-E.xls’ spreadsheet from www.pocfin.kedgebs.com. Make sure you understand the meaning of each cell in the spreadsheet. Then answer the following questions:

  • a. In your own words, explain the mechanisms by which an increase in net public spending of 20 affects the financial wealth of the private sector, consumption, disposable income, national income and climate.

  • b. Holding everything else constant, change the model parameter values in Table 7.1 separately as requested below:

    • Simulation 1: Tax rate increase: T goes from 20% to 50%

    • Simulation 2: Increase in government spending: G goes from 20 to 50

    • Simulation 3: Decrease in the propensity to consume out of accumulated savings: α2 decreases from 0.4 to 0.3

      • Each simulation will automatically change the model’s output. After each new simulation, export each output chart into a separate word document.

      • Inspect these charts and describe the response of financial wealth, consumption, disposable income, national income. Discuss the response of climate in each scenario, and explain the underlying mechanisms.

      • What lessons can you draw from these simulations regarding the relationship between the model’s climate and economic outcomes?

• 5. Return to the baseline simulation in which government spending increases to 20 in the first year. Based on your understanding of how the model works, identify a policy scenario which may permit to reaching both climate and economic objectives and implement it in the model. Then, answer the following questions in less than 1000 words:

  • a. Compare and contrast real-world climate policies implemented by countries of your choice with your proposed simulated policy.

  • b. What are the main limits to your simulations? Are there any effects and mechanisms potentially critical but not included in the model?

  • c. If you were to develop an improved version of SIM-E, what new mechanisms would you include in priority and why?

  • d. According to you, under which conditions can economic models serve as a useful guide to policy-making?