Consider a closed economy with private household consumption and investment given by
(1) C = c0+c1·YD
(2) I = ̄ι0+ ̄ι1·Y
where disposable income YD is given by: YD = Y − T , c0 and ̄ι0 are autonomous consumption and investment spending, c1 and ̄ι1 are the marginal propensity to consume and to invest and c1 + ̄ι1 < 1. Government spending G is exogenously given by G ̄.
Assume that the government considers two distinct forms of taxation:
Case (i) A lump-sum taxation: A lump-sum tax is a special way of taxation where the government collects a fixed amount of taxes of each entity (taxpayer) independent of the entity’s income, revenues, etc. This gives rise to the following expression for taxes T:
T = T ̄
where T ̄ is some exogenously given amount of taxes.
Case (ii) An income taxation: An income tax is a tax imposed on an entity (taxpayer) that varies
with the respective income. This gives rise to the following expression for taxes T:
T=τ·Y; where τ ∈ (0, 1) is the income tax rate.
Theoretical tasks
- (2 Pts) Derive the goods market multiplier for Case (i).
- (2 Pts) Provide an answer to the following question: How does the fact that investment reacts to changes in output – captured the parameter ̄ι1 in equation (2) – affect the size of the goods market multiplier?
- Optional: (2 Pts) Derive the goods market multiplier for Case (ii).
- Optional: (2 Pts) Provide an answer to the following question: Which of the two forms of taxation gives rise to the highest effectiveness of government spending?
Empirical tasks
Each of you chooses one specific country for the macroeconomic analysis — mention the country you have chosen.
- Collect annual data on (i) GDP, (ii) private household consumption, (iii) investment1, (iv) the unemployment rate and provide scatter plots2 for the following:
(a) (2 Pts) the unemployment rate (on the y-axis; values in percent) and the growth rate of GDP (on the x-axis; values in percent).
(b) (2 Pts) the change in consumption (on the y-axis) and the change in GDP (on the x-axis).
(c) (2 Pts) the change in investment (on the y-axis) and the change in GDP (on the x-axis).
where the change in consumption (∆Ct) refers to the difference in consumption in year t relative to its value of the previous year (t − 1): ∆Ct = Ct − Ct−1. The same applies for the change in investment and GDP.
- (2 Pts) What empirical relation can you identify between the unemployment rate and the GDP growth rate? Assume that the GDP growth rate increases, what does the empirical evidence imply for the unemployment rate in this case? Consider the scatter-plot of exercise (of question 5a) to this purpose.
- (1 Pt) What is the negative empirical relationship between the unemployment rate and the GDP growth rate referred to as in macroeconomics?
- (2 Pts) Equation (1) assumes that consumption reacts to changes in income. This is captured by the parameter c1 which gives rise to a positive relation between consumption (C) and output (GDP, Y ). Can you find empirical evidence in the data in favour of this? Consider your scatter-plot (of question 5b) to this purpose and provide arguments in favour or against.
- (2 Pts) Equation (2) assumes that investment reacts to changes in income. This is captured by the parameter ̄ι1 which gives rise to a positive relation between investment (I) and output (GDP, Y ). Can you find empirical evidence in the data in favour of this? Consider your scatter-plot (of question 5c) to this purpose and provide arguments in favour or against.
- (2 pts) Given your empirical findings in questions 8 and 9, which overall conclusion can you draw from this for the fiscal spending multiplier as identified in question 1?
in case of the IMF and
in case of the World Bank.
- There are, though, many other sources to access and download data of your country, as for instance: National Central Banks, National Statistical Authorities, etc.