Middle East Technical University

Department of Economics

Estimation of Import Regression for

Canada (1975-2014)

Garay Garayli

1846534

Literature Review

The balance of international payments, generally known as Balance of payments (BOP) is a

statement that indicates the transactions between the country and the rest of the worlds

Imported and exported goods have always been crucial components for governments.

Difference between value of Exported and Imported goods represent balance of trade of that

country. The higher the value of imports enter to country with respect to export the more

negative that country’s balance of payments. Imports depend from income of that country and

from exchange rate.

According to Cathy L. Jabara the relationship between exchange rate and imported goods is

crucial to understand the nature of imported goods as well as the behavior of CPI which

further directly affect GDP. Exchange rate changes affect the price of imported goods. With

rise in value of domestic currency decrease price of imported goods which increase amount

of import to the country. According to macroeconomic theory GDP should affect Import in a

positive way whereas Real Exchange Rate should demonstrate negative relationship.

In article ‘How Do Exchange Rates Affect Import Prices? Recent Economic Literature and

Data Analysis’ in ‘Estimates of Exchange Rate Pass-through–Foreign Exporters’ part author

approves that import function explanatory variables should be exchange rate and output.

Estimation of import regression will help us to understand how import changes with respect

to the changes in macroeconomic variables GDP and exchange rate in terms of consistency of

each model.

Statistical Review

As it was obvious from Literature Review part that we should further overlook effect of GDP

and exchange rate on Import in order to analyze Import Regression. Thence construct import

regression as follows:

IMi= β0 + β1GDP+ β2REER+ui

IM: Import

GDP: Gross Domestic Product

REER: Real Exchange Rate

Ŷ: fitted values obtained from the regression of IM on GDP and REER(which

will be used in Ramsey Reset Test)

Import is dependent variable where GDP and REER are independent variables. In addition ,

β0 is an intercept term (constant) where β1 and β2 represents slope terms.We assume that

Gauss-Markov assumptions are valid for this multipple regression.

Model Estimation and Hypthohesis Testing

According to macroeconomic theory, I estimated my first model as follows:

(M1) IMi= β0 + β1GDPi-β2REERi+ui

IMi=132238401100.1947+0.296642GDPi-1206543237.024449REERi

(4.319175) (48.59623) (-3.783443)

R2=0.985176 SSR= 1.51*1022 AIC=50.37069 SBC=50.49736

Theory consistency hold for this model cause model is linear model.The estimation result

shows that there is negative relationship between real exchange rate and import which is

consistent with macroeconomic theory and literature review. One unit increase in GDP leads

to approximately 0.2996 unit increase in import and one unit increae in real exchange rate

leads to 1206543237 unit decreae in import.

In order to checked statistical aviability of this model we should to test coefficents indivually

and jointly.

1) Individual significance

t-test.

H0: β0=0 : Intercept term is individually insignificant

H0: β0≠ 0 : Intercep term is individually significant

|tβ0|=|4.319175|>|ttable|=2.021 Reject H0

Intercept term is Individually Significat

H0: β1=0 : Slope term(β1) is individually insignificant

H0: β1≠ 0: Slope term (β1) is individually significant

|tβ1|=|48.59623|>|ttable|=2.021 Reject H0

Slope term(β1) is Individually Significat

H0: β2=0 : Slope term(β2) is individually insignificant

H0: β2≠ 0: Slope term(β2) is individually insignificant

|tβ2|=|3.783443|>|ttable|=2.021

Slope term(β2) is Individually Significat

2) Joint Significance:

Restricted Model:IM= β0+ui

H0: β1= β2=0

H1: at least one differs than zero

F=R2u*(n-k-1)/(1-R2

u)

F=0.985176*37/0.014824*2=1229.493> F2, 370.05

H0 is rejected at 95 % significance level. Therefore model is overall significant.

Approximately 98 % of variations in Import are explained by GDP and real exchange

rate.Even if coefficent of determination is quite high there is no Multicollinearity problem

because Variance Indicator Factor (VIF) is equal to 1.015530 which is smaller than 10 and

the model is significant which can conclude that model is valid statistically and

economically.To checked whether regression in it’s true form or not we will use Ramsey

Reset Test.

(M2) IMi= β0 + β1GDPi-β2REERi+ β3 ŷ2 + β4 ŷ3 + ui2

IM=671897767775.96-0.073729GDP + 288754637.28REER + (4.17E-12) ŷ2 - (4.04E-24) ŷ3

(2.089188) (-1.178789) (0.746369) (5.747188) (-51.387551)

R2=0.992615 SSR=7.54*1021 F=1176.043 AIC=49.77395 SBC=49.98506

By Using Ramsey Reset Test we will ,whether there specification error or not.

H0: β3 = β4= 0

H1: at least one differs than zero

Restricted model: IMi= β0 + β1GDPi + β2REERi + ui

Unrestricted model: β0 + β1GDPi-β2REERi+ β3 ŷ2 + β4 ŷ3 + ui2

By using F test we conclude that F calculated which obtained from this test 1176.043 is

greater than corresponding value from F table. Due to Reject H0 ,there specification error in

model 1.

In order to avoid specification error we should test different type of models.

(M3) lnImi= γ0+ γ1lnGDP+ γ2lnREER+ui3

lnImi=5.615646+0.830011lnGDPi-0.458941nREERi

(3.769880) (23.52338) (-2.221819)

R2=0.943327 SSR=0.781469 F=307.9537 AIC= -0.947582 SBC= -0.820916

This model is different than others with double-log.1 % increase in GDP causes 0.83%

increase in Import.Similarly, 1 % decline in Real Exchange Rate leads to 0.45 % increase in

Imports. Both slope terms and intercept term statistically significant. Model is overall

significant, also.Whether R2 of Model 3 less than M1, Akaike and Schwarz quite low in this

Model which refering clue about appropriate model.VIF value of this model is 1.057133

which refer about absence of Multicollinearity problem.

(M4) lnIMi= α0 + α1lnGDPi + α2REERi + ui4

lnIMi=4.040234+0.829683lnGDPi-0.005305REER

(3.911183) (23.58803) (-2.276861)

R2=0.943660 SSR=0.776882 F=309.8632 AIC= -0.953469 SBC= -0.826803

Sign of Real Exchange Rate and logarithmic form GDP demonstrate theoretically consistent

model.Increase 1 % in GDP leads to increase 0.83 % in import which demonstrate Income

Elasticity of Import. However one unit increase of Real Exchange Rate decrease Import 0.05

percent. All coefficients of regression are statistically significant. 94.3660% of variations in

Import are explained by GDP and Real Exchange Rate.In addition, M4 is jointly

signifcant.Variance Indactor Factor is equal to 1.056717 which is less than 10 which means

there is no Multicollinearity problem for M4.Akaike and Schwarz less than compare to third

model which refer about better model.

(M5) lnIMi= θ0+ θ1GDP- θ2lnREER+ui5

lnImi=29.80039+0.00000000000105GDPi-1.001729lnREERi+ui5

(46.65149) (34.43123) (-7.122397)

R2=0.972633 SSR=0.377371 F=657.4906 AIC=-1.675528 SBC=-1.548862

Intercept and both slopes terms of Model 5 are individually significant and overall

significant.Sign of Real Exchange Rate is mention about consistency of theory.The 1 unit

increase in GDP leads to 0.00000000000105 % increase in Imports. According to model 5

income elasticity of Import is almost unitary elastic because second slope coefficient is equal

to 1.001729. We can check whether Import is unitary elastic by testing H0: θ2= 0. After

testing the corresponding restriction we reject the null hypothesis which means not unitary

elastictic however elastic. Akaike and Schwarz less than all models above with same

dependent variable (lnIMi) which is talk about most preferable model. Even if determination

of coefficients high ,individuall and overall significance of model shows no Multicollinearity

problem of model.In addition ,VIF value equal to 1.014903.

(M6)IMi= λ0+ λ1lnGDPi+ λ2lnREER+ui6

IMi= -5982073471511.994+224165648750.6412lnGDPi+32292303269.44715lnREERi

(-9.846584) (15.57697) (0.383309)

R2=0.872732 SSR=1.30*1023 F=126.8628 AIC=52.52075 SBC=52.64742

According to this model there is positive relationship between Real Exchange Rate and

Imports which is not true in macroeconmic theory. Whether λ0 and λ1 are individually

significant λ2 is not. Model6 is overall significant. Approximately 87% of variations in Import

are explained by GDP and Real Exchange Rate. Whether λ2 is not statistically significant

there is no multicollinearity problem due to VIF value is 1.057133. In terms of AIC and

Schwarz model is not appropriate also.

(M7)IMi=p0+p1GDPi+p2lnREERi+ui7

IMi=503473302460.5477+0.296695GDPi-106805645635.1961lnREERi

(3.937960) (48.65848) (-3.794210)

R2=0.985200 SSR=1.51*1022(1.51E+22) F=1231.477 AIC=50.36911 SBC=50.49577

1% increase in Real Exchange Rate cause to decline in Imports 106805645635.1961 units.

This Model is overall significant besides all coefficents are individually significant.There is

no such problem like M6.Sign of coefficents is consistent with Macroeconomic theory.Even

similar to Model 6 Akaike and Schwarz values are high which refer about not an appropriate

model. Even is R2 high enough VIF value is 1.014903 which demonstrate no

Multicollinearity.This model aslo valid statistically and economically.

(M8) IMi= δ0+δ1lnGDP+ δ2REER+ui8

IMi=-5860239397914.341+223983596986.1628lnGDPi+314637062.7810084REERi

(-13.86163) (15.55941) (0.329928)

R2=0.872602 SSR=1.30*1023 F=126.7138 AIC=52.52178 SBC=52.64845

Real Exchange Rate coefficient not consistent with macroeconomic theory in Model8. In

addition δ2 is statistically insignificant whether δ0 and δ1 individually significant.Despite this

factors, Model 8 is overall significant Model. Compare to all other models biggest AIC and

SBC observe in Model 8 which refer to least reliable with respect to above models with same

dependent variables(IMi). Besides , inconsistent sign and absence of reliability ,least

coefficient of determination observe in Model 8 ,which is obviously not good model compare

to above models.Variance Indicator Factor value is 1.056717 which has no Multicollinearity

problem.

(M9) lnIMi= 𝜺0+ 𝜺1GDP+ 𝜺2REER+ui8

IMi=26.31376+0.00000000000105GDPi-0.011265REERi

(170.6303) (34.10366) (-7.012945)

R2=0.972141 SSR=0.384146 F=645.5691 AIC= -1.657735 SBC= -1.531069

Model 9 is theory consistent model contrary to Model 8 and Model 6. Model 9 is statisticaly

signifcant both individually and overall. 1 unit increase in Real Exchange Rate leads to

0.011265 % decrease in Import. 97.2141% of variations in Import are explained by GDP and

Real Exchange Rate.VIF value is 1.015530 which means there is no multicollinearity in

Model 9. This Model AIC and SBC quite low which imply about appropriate model but

Model 5 AIC and SBC lower than Model 9.

According to all analyzes above the best model is 4th Model with R2=0.943660 and with

low(AIC= -0.953469 SBC= -0.826803) Akaike and Schwarz values.In addition,all examines

about show that fourth model is best describe consistency of theory with appropriate AIC

,SCB and R2 values. Increase 1 % in GDP leads to increase 0.83 % in import which

demonstrate Income Elasticity of Import.However one unit increase of Real Exchange Rate

decrease Import 0.05 percent. By overlooking graph below it is obvious that Actual and Fitted

values move together which also mentions about appropriate model.

Furthermore , if Ramsey Reset Test is applied to the model which demonstrate that if there is

non-linearity in model or not.With applying Ramsey Reset Test we can conclude that there is

non linearity and F value showing the significance of coefficients of fitted values is the

smallest in model 4 . This situation leads to conclude that model 4 approximates to the most

appropriate model faster than other models.To see whether Canada affected by the global

-.4

-.2

.0

.2

.4 25.0

25.5

26.0

26.5

27.0

27.5

5 10 15 20 25 30 35 40

Residual Actual Fitted

financial crisis in 2008 or not ,we should test Chow Test.By overlooking Chow Breaking test

we could conclude that there was no structural break (2008) in Canada.

Conclusion

Due to Ramsey Reset test we conclude that there is specification error in 4th Model. Even if

Model 6 and 8 are valid statistically they are not theory consistent and not valid economicly.

As macroeconomic theory mentioned there should be positive relationship between GDP and

Import ,a negative relationship between Real Exchange Rate and Import.We expected these

relationship due to macroeconomic theory which was mention in literature review part. This

fact is consistent with our choosen model.Besides consistency of theory ,our model

appropriate for econometrics comparisons and model selections.As it is showed above,R2

high enough,model in it’s logarithmic form and Information Criteria test have lower values in

Model 4 which have same dependent variables (lnImi). Individuall and overall significance of

model shows no Multicollinearity problem of model with VIF value equal to 1.056717.

Furtermore, in fourth model it is possible to calculate income elasticity of import which again

mention about best economic model.

References

http://data.worldbank.org/country/canada

http://stats.oecd.org/

http://www.worldbank.org/en/country/canada

Colleen Gorman (2007). AN ECONOMIC ANALYSIS OF THE EFFECTS OF

EXCHANGE RATE REGIMES ON INTERNATIONAL TRADE

Cathy L. Jabara (October 2009). How Do Exchange Rates Affect Import Prices?

Recent Economic Literature and Data Analysis

https://www.usitc.gov/publications/332/ID-21_revised.pdf