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
retrieved from US Federal Reserve at St. Louis https://fred.stlouisfed.org.
Data Files We will again focus on the following six variables with in-sample data
set to 1990Q1 to 2019Q4:
D1: Canada Data file (CAN_Big_Data.csv)
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
5 realUSDCAD Exchange rate CADUSD v37426 v111666275
6 CPI_ALL_NF Consumption price index (CPI) (all)
- Report Summary Statistics
Summary Statistics
| Mean | S.D. | Min | Max | |
|---|---|---|---|---|
| Real GDP | ||||
| Housing Price | ||||
| Tbill | ||||
| US Tbill | ||||
| FX | ||||
| Inflation |
- Estimate a VAR(2) Model with all six variables in stationary form
- Lag Length Selection using AIC and SC
What is the optimal lag length?
- Report Granger Causality Test
Should we drop any of the variables in the system? Does inflation Granger cause GDP to change?
- 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
- Report the summary table for Johansen tests for all five specifications
What is the best model for the data based on AIC?
- 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=
- Forecast GDP growth for the next two years and graph the actual and forecasted data.
