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## Vector Error Correction Model (VECM)

• Topics of Today’s exercise
• VECM, Lag Length Selection,
• Granger Causality Test, Impulse Response Function

In this lab exercise, we will again use the data from lab4 for testing long run relation-

ship for taylor’s rule and uncovered interest rate parity. The US interest rate data is

Data Files We will again focus on the following six variables with in-sample data

set to 1990Q1 to 2019Q4:

1 GDP_new GDP total Canadan GDP v41881478

2 NHOUSE_P_CAN New housing price index v111955442

3 TBILL_3M US Treasury bills (3 months)

4 TBILL_3M Treasury bills (3 months) v122541

6 CPI_ALL_NF Consumption price index (CPI) (all)

1. Report Summary Statistics

Summary Statistics

1. Estimate a VAR(2) Model with all six variables in stationary form

1. Lag Length Selection using AIC and SC

What is the optimal lag length?

1. Report Granger Causality Test

Should we drop any of the variables in the system? Does inflation Granger cause GDP to change?

1. Estimate the VECM using the optimal lag length from Q3.

This model is not optimal. We need to run through a series of cointegration test before finalizing the model.

6. Johansen test for number of cointegrating vectors with no constant but trend in the CE.

Johansen (trace) test for Rank(P) = 0

H0: r = 0                H0: r > 0

Level of significance = 5%                                   N =

Johansen (Trace) stat =                             p-value =

Conclusion:

Repeat for Rank(P) = 1

H0: r = 1                H0: r > 1

Level of significance = 5%                                   N =

Johansen (Trace) stat =                             p-value =

Conclusion:

Johansen Max test for Rank(P) = 0

H0: r = 0                H0: r =1

Level of significance = 5%                                   N =

Johansen (max) stat =                               p-value =

Conclusion

H0: r = 1                H0: r =2

Level of significance = 5%                                   N =

Johansen (max) stat =                               p-value =

Conclusion

1. Report the summary table for Johansen tests for all five specifications

What is the best model for the data based on AIC?

1. Impulse Responses on GDP from 1sd tbill shock with the ordering as

GDP, Inflation, FX, tbill, US_tbill

What is 1 sd tbill shock?

What is the impact on GDP for 1 month =      4 month =             12 month=

GRAPH and Table

Repeat with this ordering

CAN_GDP, IPP, Inflation, US_GDP, OIL

GRAPH and Table

What is the impact on GDP for 1 month =       4 month =             12 month=

1. Forecast GDP growth for the next two years and graph the actual and forecasted data.