CLASS #6: TAXES IN THE INTERTEMPORAL MODEL: RICARDIAN EQUIVALENCE

today we will address questions like:

• How does fiscal policy affect the household's consumption decision?
• The US Government has been pressing Japan to lower taxes in order to stimulate the economy: is it a good advice?
• What is the impact of the "Fobaproa" on the economy?

Let's introduce the government into the model used in the previous class: the government collect taxes in both periods (T1 and T2) in order to finance government spending (G1 and G2)
The government has to observe an intertemporal budget constraint: the present value of government spending has to be equal to the present value of taxes collected

$$T1+\frac{T2}{1+r}=G1+\frac{G2}{1+r}$$

The government can issue debt to finance G, but it has to repay it The household's problem is the same as last time, except that now it has to pay taxes to the government:

$$max_{C1,C2} \ln (C1) + \beta \ln (C2)$$

subject to the constraint:

(1+r)(Y1+W-T1-C1)=C2-(Y2-T2)

which can be rewritten as:

$$W +Y1+\frac{Y2}{1+r}-(T1+\frac{T2}{1+r})=C1+\frac{C2}{1+r}$$

Remembering that $T1+\frac{T2}{1+r}=G1+\frac{G2}{1+r}$, let us substitute the government budget constraint into the household's budget constraint:

$$W +Y1+\frac{Y2}{1+r}-(G1+\frac{G2}{1+r})=C1+\frac{C2}{1+r}$$

or

(1+r)(Y1+W-G1-C1)=C2-(Y2-G2)

let us define the variables $Y1^*\equiv Y1-G1$ and $Y1^*\equiv Y1-G1$. The household's problem becomes:

$$max_{C1,C2} \ln (C1) + \beta \ln (C2)$$

subject to:

(1+r)(Y1^*+W-C1)=C2-Y2^*

Then the household problem is the same we studied last time with Y1^* and Y2^* instead of Y1 and Y2. And we know the solution:

$$C1= \frac{1}{1+ \beta}(W+ Y1^*+ \frac{Y2^*}{1+r})$$

$$C2= \frac{(1+r) \beta}{1+ \beta}(W+ Y1^* + \frac{Y2^*}{1+r})$$

or

$$C1= \frac{1}{1+ \beta}(W+ Y1+ \frac{Y2}{1+r} -G1 -\frac{G2}{1+r})$$

$$C2= \frac{(1+r) \beta}{1+ \beta}(W+ Y1+ \frac{Y2}{1+r} -G1 -\frac{G2}{1+r})$$

What have we learned?

• the household's consumption decisions again depend on wealth, which now includes the Present value of government spending
• an increase in government spending (no matter whether G1 or G2) induces a decrease in consumption in both periods: the household is less wealthy, as it has to pay more taxes (at some point)
• a temporary increase in G (say, war), affects consumption less than a permanent one
• in the keynesian consumption function:
  
  C=a+c(Y-T)
  
  
  a decrease in current taxes stimulates consumption. Here, the timing of taxes is irrelevant, for a given present value of government spending (RICARDIAN EQUIVALENCE)

"Real World" examples

• the crises in Japan
• the impact of "Fobaproa" on the economy: does the government commitment to pay off "bad" debt stimulate the economy?

What happens in a CLOSED ECONOMY?

In a closed economy consumption in each period has to be equal to the amount of resources available (endowment)

• RICARDIAN EQUIVALENCE still holds: the timing of taxes is irrelevant
• the timing of government spending is relevant

Does Ricardian equivalence hold in the real world?

• for Ricardian Equivalence to hold, the household must be able to borrow against its future income (Human Capital): no collateral!
• Borrowing constraints: the timing of taxes may matter
• does that alter our previous conclusions about Japan/Fobaproa?