<p>Im trying to replicate the forecasts of this VECM model presented by the bank of canada in <a href="http://www.bankofcanada.ca/wp-content/uploads/2010/08/adam-final.pdf" rel="nofollow noreferrer">The M1 Vector-Error-Correction Model:
Some Extensions and Applications</a> </p>

<p>Context (from page 24 in the pdf).</p>

<blockquote>
  <p><strong>Details of the Adjusted-M1 VECM</strong><br><br>
  Step 1: Estimating long-run money demand and the money gap
  The Johansen-Juselius methodology is used to test for the existence of a
  unique long-run cointegrating relationship between money, inflation, output,
  and interest rates (non-seasonally adjusted data). The model is an errorcorrection
  model because deviations of money demanded from money
  supplied (the money gap) are assumed to be corrected in the long run. The
  model has the form
  $$\Delta X=\Gamma(L)\Delta X_t+DZ_t+\alpha \beta^{'}[X_{t-1},D80a_{t-1}]$$
  , (A1)
  where
  $X_t= [M1_t, CPI_t, Y_t , RONf_t]$</p>
  
  <p>$RONf_t$= <strong>level of “policy-free” overnight interest
  rate</strong> =$RONf_t- \epsilon_t$</p>
  
  <p>$\epsilon_t$ is the residual from the interest rate equation(A8)</p>
  
  <p>$M1_t$=log level of adjusted M1<br>
  $Y_t$= log level of real output<br>
  $CPI_t$= log level of the consumer price index<br>
  $Zt$= [constant, 3 seasonal dummies, output gap$_{t–1}$, log(exchange
  rate) from $t$ to $t–3$, $USCP90_t$
   rate, $D80b^* \Delta NPNt$
  , $D80a_t$]</p>
  
  <p>$...$</p>
</blockquote>

<p>Im just wondering, how does the bank of Canada define output $Y_t$? do they mean GDP?</p>

CC BY-SA 3.0
2017-10-26T00:29:14.010Z
For me it's a bit hard to understand your question without going through the full paper: maybe you could make it more reader friendly by posting the full question here  (including the formula), or indicating in which page we can find the model part where you have doubts?
JoaoBotelho
CC BY-SA 3.0
2017-10-26T02:43:23.283Z
@JoaoBotelho better?
EconJohn
CC BY-SA 3.0
2017-10-26T13:34:31.677Z
Perfect @EconJohn! 
The paper itself seems to refer other sources for the definition of output, such as «Hendry, S. 1995. “Long-Run Demand for M1.” Bank of Canada Working Paper No. 95–11.» and https://www.researchgate.net/publication/4905980_%27A_Semi-Structural_Method_to_Estimate_Potential_Output_Combining_Economic_Theory_with_a_Time-Series_Filter_The_Bank_of_Canada%27s_New_Quarterly_Projection_Model_Part_4%27
Did you take a look there?
JoaoBotelho
CC BY-SA 3.0
2017-10-29T17:23:30.997Z
@JoaoBotelho I have, It doesn't seem to mention the definition there.
EconJohn
<reference-request><monetary-policy><applied-econometrics>
How does the bank of Canada define "output"
EconJohn
# How does the bank of Canada define "output"

(Asked by: username_0 on 2017-10-25)

Im trying to replicate the forecasts of this VECM model presented by the bank of canada in [The M1 Vector-Error-Correction Model:
Some Extensions and Applications](http://www.bankofcanada.ca/wp-content/uploads/2010/08/adam-final.pdf)

Context (from page 24 in the pdf).

> **Details of the Adjusted-M1 VECM**  
>   
> Step 1: Estimating long-run money demand and the money gap
> The Johansen-Juselius methodology is used to test for the existence of a
> unique long-run cointegrating relationship between money, inflation, output,
> and interest rates (non-seasonally adjusted data). The model is an errorcorrection
> model because deviations of money demanded from money
> supplied (the money gap) are assumed to be corrected in the long run. The
> model has the form
> $$\Delta X=\Gamma(L)\Delta X\_t+DZ\_t+\alpha \beta^{'}[X\_{t-1},D80a\_{t-1}]$$
> , (A1)
> where
> $X\_t= [M1\_t, CPI\_t, Y\_t , RONf\_t]$
>
> $RONf\_t$= **level of “policy-free” overnight interest
> rate** =$RONf\_t- \epsilon\_t$
>
> $\epsilon\_t$ is the residual from the interest rate equation(A8)
>
> $M1\_t$=log level of adjusted M1  
> $Y\_t$= log level of real output  
> $CPI\_t$= log level of the consumer price index  
> $Zt$= [constant, 3 seasonal dummies, output gap$\_{t–1}$, log(exchange
> rate) from $t$ to $t–3$, $USCP90\_t$
> rate, $D80b^\* \Delta NPNt$
> , $D80a\_t$]
>
> $...$

Im just wondering, how does the bank of Canada define output $Y\_t$? do they mean GDP?

**Tags:** reference-request, monetary-policy, applied-econometrics
> **Comments:**
> **username_1**: For me it's a bit hard to understand your question without going through the full paper: maybe you could make it more reader friendly by posting the full question here  (including the formula), or indicating in which page we can find the model part where you have doubts?  
> **username_0**: @JoaoBotelho better?  
> **username_1**: Perfect @EconJohn!  The paper itself seems to refer other sources for the definition of output, such as «Hendry, S. 1995. “Long-Run Demand for M1.” Bank of Canada Working Paper No. 95–11.» and https://www.researchgate.net/publication/4905980_%27A_Semi-Structural_Method_to_Estimate_Potential_Output_Combining_Economic_Theory_with_a_Time-Series_Filter_The_Bank_of_Canada%27s_New_Quarterly_Projection_Model_Part_4%27 Did you take a look there?  
> **username_0**: @JoaoBotelho I have, It doesn't seem to mention the definition there.  

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## 0 answers

