§19 IS-LM and Expectations

Overview

• Main idea:
  • The basic IS-LM model over-weights the present.
  • In practice, expectation about future conditions play a big role in the decisions of all economic actor’s (consumers, firms, government, foreigners…).
• Steps:
  • Consumption and investment decisions.
  • IS-LM with expectations.

Consumption

• Consumption decisions depend not only on a person’s current income but also on his or her expected future income and on financial wealth.

  • Permanent income theory of consumption (Friedman);
  • Life-cycle theory of consumption (Modigliani).

• Total wealth:

  • Financial wealth: value of all assets minus debt (EPDV);
  • Human wealth: EPDV of labor income.

• In principle:

  $$C_t = C(TotalWealth_t)$$

• In practice:

  $$C_t = C(TotalWealth_t, Y_t - T_t); \quad C_1 > 0, C_2 > 0$$

• Permanent (persistent) versus temporary changes in income.

Investment

• Investment decisions depend on current and expected profits and on current and expected real interest rates.

  • The decision, e.g., on whether to buy a machine or not must compare the price of the machine with the EPDV of the profits it will generate.

• Depreciation

  • How long will the new machine last?
  • A reasonable assumption is geometric depreciation: a machine that is new this year is worth only $(1 - \delta)$ machines next year, $(1 - \delta)^2$ machines two years from now, and so on.

• The PV of Expected Profits

  $$\begin{aligned} V_t \ &= \ \frac{\Pi_{t+1}^{e}}{1 + r_t} + (1 - \delta) \frac{\Pi_{t+2}^{e}}{(1 + r_t)(1 + r_{t+1}^{e})} + \cdots \\&\quad + (1 - \delta)^{n-1} \frac{\Pi_{t+n}^{e}}{(1 + r_t)(1 + r_{t+1}^{e}) \cdots (1 + r_{t+n-1}^{e})} + \cdots \end{aligned}$$

• The decision, e.g., on whether to buy a machine or not must compare the price of the machine with the EPDV of the profits it will generate

  • Suppose the price of the machine is 1…

• In principle:

  $$I_t = I(V_t)$$

• In practice:

  $$\begin{aligned}I_t \ &= \ I(V_t, \Pi_t); \quad I_1 > 0, I_2 > 0 \\&= \ I\left(V_t, \Pi\left(\frac{Y_t}{K_t}\right)\right) \\&\approx \ I(V_t, Y_t)\end{aligned}$$

• Again, persistently higher profits matter more than transitory ones.

• Same holds for interest rates.

IS-LM with Expectations

• Basic IS

  $$\begin{aligned}Y \ &= \ C(Y - T) + I(Y, r) + G_t \\ &= \ A(Y, T, r, G); \quad A_1, A_4 > 0, A_2, A_3 < 0\end{aligned}$$

• A short-cut to an IS-LM model with expectations (same signs for current and expected variables)

  $$Y = A(Y, T, r, G, Y^{'e}, T^{'e}, r^{'e}, G^{'e})$$

• LM is the same as before: $r$

— Apr 27, 2025

§19 IS-LM and Expectations by Lu Meng is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Permissions beyond the scope of this license may be available at About.