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Say that we are regressing consumption $C_t$ on time $Y_t$. Furthermore, suppose that both series are $I(1)$ and are co-integrated.

Given this, we set up the error correction model (ECM) as follows: $$\Delta C_t = \beta_0 + \beta_1 Y_t + \theta(C_{t-1} - \gamma_0 - \gamma_1 Y_t) + u_t$$ which is estimated using the 2-step Engle-Granger approach.

My question is: What is the economic interpretation of $\gamma_1$? Surely we cannot interpret this as the marginal propensity to consume (MPC)? I interpret it as describing the long-run equilibrium of the system.

However, I'm struggling to explain why this is the case, since mathematically: $$\gamma_1 = \frac{\partial C_t}{\partial Y_t}$$ which is exactly the definition of the MPC.

On the Wikipedia page on ECMs, they describe $\gamma_1$ as the average propensity to consume (APC), which makes a lot more sense to, but which doesn't sit well with me since mathematically: $$\text{APC} = \frac{C}{Y}$$ and clearly that is not the definition of $\gamma_1$ since: $$\frac{C}{Y} = \frac{\gamma_0}{Y} + \gamma1$$

Could someone help me sort out my confusion?

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    $\begingroup$ Economics Stack Exchange could also be a relevant place for your question. (Not sure whether that or Cross Validated is better.) $\endgroup$
    – Richard Hardy
    Commented Oct 18, 2019 at 13:52
  • $\begingroup$ Hi: are you certain that your time subscripts are correct because usually the things that are involved in the term multiplying $\theta$, in this case $C_{t-1}$ and $Y_t$, have either A) the same time subscript or B) C_t leads Y_t rather than lags it ? $\endgroup$
    – mlofton
    Commented Feb 11 at 2:17

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This is not long-run MPC - it is questionable whether long-run coefficients even bear any interpretation besides defining steady-state of system.

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  • $\begingroup$ Could you give more detail as to how your answer addresses the question. $\endgroup$
    – Michael R. Chernick
    Commented Oct 21, 2019 at 2:23

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