Homework 8: Introduction to consumption theory, a unit root process, and the error correction model.

This week’s homework should give you a gentle introduction to consumption theory. We’ll start by reading Angus Deaton’s lecture on Modigliani’s life-cycle theory of consumption. Next, we’ll estimate a very simple Keynesian consumption function for Australia.

Question 1

You should start by reading the paper “Franco Modigliani and the Life Cycle Theory of Consumption” by Angus Deaton.

  1. Briefly, what is Modigliani’s life-cycle theory of consumption? For an individual, draw someone’s consumption schedule over their life. Now draw their wealth over their life. At which periods are they saving and dissaving?
  2. What effects do population growth and economic growth have on savings rates?
  3. In the Modigliani model, do consumers consume from current income?
  4. What is the impact in the model of an increase in transitory income?
  5. What are the implications of the theory for savings rates over the economic cycle?

Question 2

From ABS Catalogue 5204.0 Table 2, create a new spreadsheet. This should contain Household Final Consumption Expenditure and GDP, both in chain volume measures. Also include a date column, in yyyy-mm-dd format.

Data preparation:

  1. Save the file as a .csv file and read it into R.
  2. Create the following new columns: logs of consumption and GDP, lagged values of both of these logs, and first differences of both contemperaneous and lagged log series.

Hints:

# To create a lagged value, you can use

mydata <- mydata %>% 
  mutate(myvariablelagged = lag(myvariable))

# To create a differenced series, you need to append a NA on the beginning of the differenced series (which is shorter than the full dataset)
mydata <- mydata %>% 
  mutate(myvariable.diff = c(NA, diff(myvariable)))

Modelling

  1. Plot consumption and GDP on the same plot. Are they stationary variables?
  2. Run a linear model for the logged values \(C_{t} = \beta_0 + \beta_1 C_{t-1} + \epsilon_t\). What is the value of \(\beta_1\)? Is this a unit root series? (if you are feeling keen, you can look up how to perform unit root tests, and do so with an increased number of lags)
  3. Run a forecasting linear model of the logged values \(C_{t} = \beta_0 + \beta_1 Y_{t-1} + \epsilon_t\). Extract the residuals from the model, add them as a new column to the data frame, and plot them over time. Do they appear to be stationary? If a residual is high in a given period, does this appear to indicate lower residuals in the future?
  4. Create a new column of lagged residuals from the model.
  5. Build a (linear) model for changes in log consumption. The left hand side of this model should be differenced log consumption at \(t\). On the right hand side should be lagged changes in log consumption (which capture “momentum”), and changes in log GDP at \(t\) (which captures a shift in GDP that could be affecting contumption). What are the coeffients? What interpretation do you give to them?
  6. Build the same model again, but this time including the lagged residuals from the the model in step 3. What is the coefficient on this term? What interpretation do you give to it?
  7. What do you estimate to be the marginal propensity to consume?