# Interpretation of ECM coefficients

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?

• Economics Stack Exchange could also be a relevant place for your question. (Not sure whether that or Cross Validated is better.) Commented Oct 18, 2019 at 13:52
• 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 ? Commented Feb 11 at 2:17

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

• Could you give more detail as to how your answer addresses the question. Commented Oct 21, 2019 at 2:23