Debate on NARDL( NON LINIEAR ARDL ) Mostly

Welcome To Meo School of Research Saeed A.Meo Research associate at Superior university Lahore Pakistan First of All I would like to acknowledge that I’m using the codes of NARDL provided by the father of NARDL approach ( Matthew Greenwood-Nimmo) on my email request.

In addition I would like dedicate this video to my teachers and friends most specially

Tella Oluwatoba Ibrahim, (Nigeria), Shahzad Ali(superior university), Sayed Hossain (Bangladesh ), Anees Muhammad(econometric club), Atiq Rehman(pide), Olasehinde Timilehin(Ngeria), Ch.Haqnawaz, Mahyudin Ahmad(Cambridge uk), Muili Adebayo Hamid(nageria), Hassan(Incef university),Muhammad Ilyas superior uni, salman rizavi superior uni, Matthew Greenwood-Nimmo (father of nonlinear ARDL),Shishir Shakya(Nepal), Ibn_Abdullah - PhD@INCEIF, Seye Olasehinde-Williams, Suborno Aditya ,sunita Arora(India), Idrees Aboo AbdiLlaah(nige ria) and all respected teachers.

Debate on NARDL( NON LINIEAR ARDL ) Mostly researchers ask question what is difference between ARDL and NARDL Ok let me share my thought on two basic terminologies The first one is linear relationship and second is nonlinear relationship Linear relationship Online econometric, email : [email protected]

Welcome To Meo School of Research Saeed A.Meo Research associate at Superior university Lahore Pakistan

A linear relationship is one where increasing or decreasing one variable n times will cause a corresponding increase or decrease of n times in the other variable too. In simpler words, if you double one variable, the other will double as well. Examples 

For a given material, if the volume of the material is doubled, its weight will also double. This is a linear relationship. If the volume is increased 10 times, the weight will also increase by the same factor..



The cost of objects is usually linear. If a notebook costs $1, then ten notebooks will cost $10.



The force of gravity between the earth and an object is linear in nature. If the mass of the object doubles, the force of gravity acting on it will also be double. Another example of linear relationship A relationship of direct proportionality that, when plotted on a graph, traces a straight line. In linear relationships, any given change in an independent variable will always produce a corresponding change in the dependent variable. For example, a linear relationship between production hours and output in a factory means that a 10 percent increase or decrease in hours will result in a 10 percent increase or decrease in the output Another example of linear relationship A linear relationship exists when two quantities are proportional to each other. If you increase one of the quantity, the other quantity either increases or decreases at a constant rate. For example, if you get paid $10 an hour, there is a linear relationship between your hours worked and your pay. Working another hour

Online econometric, email : [email protected]


always results in a $10 pay increase, regardless of how many hours you already worked. Non-linear relationship Most relationships in economics are, unfortunately, nonlinear. Each unit change in the x variable will not always bring about the same change in the y variable. As their name suggest, non-linear relationships are not linear, which means by doubling one variable, the other variable will not double. A nonlinear relationship is a type of relationship between two entities in which change in one entity does not correspond with constant change in the other entity. This might mean the relationship between the two entities seems unpredictable or virtually absent

NARDL The Non-linear ARDL model recently developed by Shin, Yu, and Greenwood-Nimmo 2014 uses positive and negative partial sum decompositions allowing detecting the asymmetric effects in the long and the short-term. Compared to the classical cointegration models, NARDL models present some other advantages. Firstly, they perform better for determining cointegration relations in small samples (Romilly, Song, & Liu, 2001). Secondly, they can be applied irrespective of whether the regressors are stationary at level or at the first difference (i.e. I(0) or I(1)). They cannot be applied however if the regressors are I(2).The other advantages of NARDLTherefore, the asymmetric NARDL framework of Shin et al. (2013) is particularly suitable for our research problem as it allows us not only to gauge the short- and long-run asymmetries, but also to detect hidden cointegration.. For example, a positive shock of oil prices may have a larger absolute effect in the short-run while a negative shock has a larger absolute effect in the long-run (or vice-versa).

Steps for NARDL



In simple, we have six steps (but major are first 4) for NARDL Step 1. In first step, we shall check unit root, the purpose of unit root test for ARDL is only to confirm that we don’t have any variable which stationary at second difference. Otherwise not need of unit root. Step 2. Generate positive and negative series for those variables for which you want to see asymmetric relationship, nonlinear relationship (suppose you wish for one variable or two or three as you wish) Step 3. Test cointegration, using bound test, with Wald test Step 4. Run NARDL , using stepwise regression under ECM Step 5. Check the asymmetries with Wald test, even from the step 4 we understand either asymmetric relationship exist or not but we can check it for further confirmation via Wald test. Step 6. Multiplier effect (sorry I’m not going to explain procedure because I don’t have idea this using EVIEWS but STATA NOTE : I followed general-to-specific approach as in all papers adopted.

Preconditions for NARDL First of all check stationary all the assumptions are same for Nonlinear ARDL as for ARDL.



Step#1 In first step we will generate first difference series of variables dependent and independents

genr de =e-e(-1) genr de =e-e(-1) genr dx =x-x(-1) genr dy =y-y(-1) genr dz =z-z(-1) Note: first of all I have created first difference series for all variables which are part of our model. Therefore you also create first difference series for all variables. Suppose my model is as follow, and the procedure is following of creating difference series. Y=f(e,x and z)



Note: in command bar type one command and then enter, again type next command again enter and so you will see new series will be generate automatically. Further if you know any other way of generating first difference series you may carry with that

Step#2 Now we shall generate a positive and negative series from an original variable let suppose I wish to generate positive and negative series for my variable “E” why I’m generating positive and negative series because of I believe that there is a nonlinear relationship between “E” and dependent variable, means I think positive change and negative change don’t effect same dependent variable. (Generate positive and negative series for those variables, which are used to subject as asymmetry variables), and the procedure is following. Generate positive and negative series for those variables ,which are used to subject as asymmetry variables(if you wish to use only one variable, and want to see asymmetry effect

then generate only for that one variable negative and positive series, what if you wish to see more than one variables effect then produce negative and positive series for other one)



genr pos =de>=0 genr depositve =pos*de genr denegative =(1-pos)*de genr epositve = @cumsum(depositve) genr enegative = @cumsum(denegative)

Generate a positive series when the first difference of variable is greater than or equal to zero (why this step because it will be used in next steps.

Now I’m generating positive series for my variable which is used to see asymmetry relationship but series will be in difference form

Note: above command is copy pate bellow intentionally so that you can copy it easily

genr pos =de>=0 genr depositve =pos*de genr denegative =(1-pos)*de genr epositve = @cumsum(depositve) genr enegative = @cumsum(denegative)

Now I’m generating negative series for my variable which is used to see asymmetry relationship but series will be in difference form

Now I’m generating partial sum from positive series which is generated in step 2

Now I’m generating partial sum from negative series which is generated in step 3

genr pos =dx>=0 genr dxpositve =pos*dx genr dxnegative =(1-pos)*dx genr xpositve = @cumsum(dxpositve) genr xnegative = @cumsum(dxnegative)



You can see here I have generated negative and positive series for two variables namely x and e ,if you wish to use only one variable as to see asymmetry relationship then no issue so it’s all up to you , Note: note again in first step we create first difference series for all the variables, we generative negative and positive series only for those variables which will be used as nonlinear.

Step#3 (NARDL ,ECM based via Step wise regression) Now we shall run stepwise regression procedure is following Go to quick ------- estimate equation------then from method--------stepl…stepwise least square or follow the following procedure I have first select dependent variable then all independent





put your equation



And ok and bellow are your results of NARDL

If the two partial sums carry the same coefficient in sign and size, the effects are symmetric. Otherwise, they are asymmetric Note: Katrakilidis and Trachanas (2012), we adopt the general-to-specific procedure to arrive at the final specification of the NARDL model by trimming insignificant lags.

A testing down procedure, termed as the general- to-speciﬁc procedure (Hendry, 1995), is adopted to eliminate variables which are either insigniﬁcant or economically (or theoretically) unacceptable.


Welcome To Meo School of Research Saeed A.Meo Research associate at Superior university Lahore Pakistan OUTPUT COPY PAST FROM EVIEWS. Dependent Variable: D(Y) Method: Stepwise Regression Date: 06/15/17

Time: 23:06

Sample (adjusted): 1974 2014 Included observations: 41 after adjustments Number of always included regressors: 7 Number of search regressors: 23 Selection method: Uni-directional Stopping criterion: p-value = 0.1 Variable

Coefficient

Std. Error

t-Statistic

-1103.456

722.1756

-1.527960

0.1422

Y(-1)

1.528591

0.393730

3.882330

0.0009

Z(-1)

3.307038

2.345821

1.409757

0.1740

EPOSITVE(-1)

-359.2570

150.0028

-2.395001

0.0265

ENEGATIVE(-1)

-700.1416

248.8427

-2.813591

0.0107

XPOSITVE(-1)

-4004.938

1340.942

-2.986660

0.0073

XNEGATIVE(-1)

2265.230

593.2002

-3.818660

0.0011

DZ(-1)

6.343541

1.416685

4.477736

0.0002

DY(-3)

0.498626

0.292503

1.704689

0.1037

DZ

2.953691

1.382880

2.135898

0.0452

DEPOSITVE(-3)

-1584.574

919.0621

-1.724121

0.1001

DENEGATIVE(-1)

-2491.512

744.9441

-3.344563

0.0032

DY(-2)

-1.739739

0.336550

-5.169337

0.0000

3611.912

759.0029

4.758758

0.0001

-0.963955

0.234068

-4.118275

0.0005

1749.393

849.9798

2.058158

0.0528

-2.083093

0.534505

-3.897234

0.0009

DXPOSITVE(-2)

3185.580

618.0900

5.153910

0.0000

DENEGATIVE(-2)

2788.516

972.7020

2.866773

0.0095

-461.6663

255.6860

-1.805599

0.0861

3724.146

1080.190

3.447675

0.0025

C

DXNEGATIVE(-3) DZ(-3) DXNEGATIVE(-1) DY(-1)

DXNEGATIVE DXPOSITVE(-1)

Prob.*

R-squared

0.817243

Mean dependent var

29.66630

Adjusted R-squared

0.634486

S.D. dependent var

45.90187

S.E. of regression

27.75124

Akaike info criterion

9.790989

Sum squared resid

15402.63

Schwarz criterion

10.66867


Welcome To Meo School of Research Saeed A.Meo Research associate at Superior university Lahore Pakistan Log likelihood

-179.7153

F-statistic

4.471745

Prob(F-statistic)

0.000758

Hannan-Quinn criter.

10.11059

Durbin-Watson stat

2.550126

Selection Summary Removed DXPOSITVE(-3) Removed DXNEGATIVE(-2) Removed DXPOSITVE Removed DEPOSITVE(-2) Removed DEPOSITVE Removed DEPOSITVE(-1) Removed DENEGATIVE Removed DENEGATIVE(-3) Removed DZ(-2) *Note: p-values and subsequent tests do not account for stepwise selection.

Note: I am following same procure as followed by M A T T H E W G R E E N W O O D - N I M M O in his paper title as Asymmetric Cointegrating Relationships, Asymmetric Dynamic Multiplier s, Nonlinear ARDL (NARDL) ECM-based Estimation and Tests, Nonlinear Unemployment-Output Relationship. If you wish to download code for NARDL please search this link from official site of M A T T H E W G R E E N W O O D - N I M M O link is here: http://www.greenwoodeconomics.com/publications.html

Note :The existing literature regarding asymmetric cointegration is dominated by three types of nonlinear models, all derived from the basic linear Error Correction Model (ECM(Author: Rania Jammazi Amine Lahiani Duc Khuong Nguyen, 2014)

If you wish to copy above command you can from below. d(y) c y(-1) z(-1) epositve(-1) enegative(-1) xpositve(-1) xnegative(-1) dy(-1 to -3) dz(-0 to -3) depositve(-0 to -3) denegative(-0 to -3) dxpositve(-0 to -3) dxnegative(-0 to -3)

Note: note we are going to run above regression under error correction model that’s why first variable is in difference form in above box. further changing will be in option tab and all the detail of option tab is blow.



Step#4 Now we shall confirm either cointegration exist or not if cointegration exists then we shall carry estimation otherwise not, so procedure of cointegration is following And we shall check cointegration via wald test ,go to view of resulted window of NARDL ,Coefficient diagnostic and then wald test.


Welcome To Meo School of Research Saeed A.Meo Research associate at Superior university Lahore Pakistan I have start from c(2), the reason is that at c(1) we have constant

F statistics calculated value

Note:

based on the estimated NARDL, we perform a test for the presence of cointegration among the Variables using a bounds testing approach of Pesaran et al. (2001) and Shin et al. (2011).



Note here our calculated f statistics values is greater than as compare to upper bound value at 5% level of significance ,If you wish to download these critical value you can from Google.as we have total three regressors that’s why I selected K 3. Our calculated value of bound test is 10.25 and upper bound value at 5% level of significance is 4.35 hence we shall reject null hypothesis of no cointegration and say there is cointegration. Step#5 Deriving long run coefficients The procedure for the deriving long run coefficients is adopted from the procedure adopted by

Matthew Greenwood-Nimmo “Modelling Asymmetric Cointegration and Dynamic

Multipliers in a Nonlinear ARDL Framework” and all other good paper published in good journals follows same


procedure


Ok let’s calculate long run coefficient for

Calculate your long run coefficient like this via wald test and if you wish you can through calculation, not if you are calculating long run coefficient via wald test then procedure is same ,view, coefficient diagnostic and then wald test. Long run coefficient of z(-1)1

=

Long run coefficient of epositive(-1)=

-c(3)/c(2)=0 (-2.163454) -c(4)/c(2)=0

Long run coefficient of enegative (-1)=

-c(5)/c(2)=0

Long run coefficient of xpositive (-1)=

-c(6)/c(2)=0

Long run coefficient of xnegative(-1)=

-c(7)/c(2)=0

(235.0248)

(1481.907)

Note: at c(1) we have constant and c(2) is conversion coefficient so divide all your long run coefficients with c(2) or conversion coefficient and put – at first of c(2), c(3) , c(4) , c(5) and c(6) Step #6 Testing

the presence of asymmetry:

We will check asymmetry with the help of wald test Asymmetry meaning not equal means now I’m going to see either the positive and negative series effect on dependent variable is same or there is difference as from coefficient value calculated above for long

11

Note: for z(-1) I have put c(3) because of z(-1) is at c(3) and divide all coefficients with c(2)


Welcome To Meo School of Research Saeed A.Meo Research associate at Superior university Lahore Pakistan run coefficient it is clear that coefficient are not same but we further confirm asymmetry with the help of wald test; I will put



Note: In particular, the long-run symmetry can be tested by using a Wald test of the null hypothesis

Null hypothesis: there is no asymmetry Alternative: there is asymmetry Here our probability value is insignificant so we shall accept null hypothesis of no asymmetry means there is no inequality, coefficients are same Kindly do same procedure for the other variables if you used as Good luck ……………



BEST PAPERS ON NONLINEAR ARDL  What drives housing price dynamics in Greece: New evidence from asymmetric ARDL Cointegration

 Modelling Asymmetric Cointegration and Dynamic Multipliers in a Nonlinear ARDL Framework

 Nonlinear ARDL Approach, Asymmetric Effects and the J-Curve  New Evidence on Asymmetric Gasoline Price Responses  Price Transmission in the Swedish Pork Chain: Asymmetric nonlinear ARDL  Price Transmission in the Swedish Pork Chain: Asymmetric non linear ARDL  Exchange rate nonlinearities in EMU exports to the US  Title: A wavelet-based nonlinear ARDL model for assessing the exchange rate pass through to crude oil prices

 Oil and food prices in Malaysia: a nonlinear ARDL analysis  Investor emotional biases and trading volume’s  asymmetric response: A non-linear ARDL approach tested in S&P500 stock... Appendix Note this highlighted discussion is not a part of NARDL I m just tryi ng to share with you what is logic behind the setting which we done in above screenshot. For the Uni-directional and Stepwise methods you may specify the direction of the method using the Forwards and Backwards radio buttons. These two methods allow you to provide a Stopping Criteria using either a p-value or t-statistic tolerance for adding or removing variables. You may also choose to stop the procedures once they have added or removed a specified number of You may also set the maximum number of steps taken by the procedure. To set the maximum number of additions to the model, change the Forwards steps, and to set the maximum number of removals, change the Backwards steps. You may also set the total number of additions and removals. In general it is best to leave these numbers Online econometric, email : [email protected]


at a high value. Note, however, that the Stepwise routines have the potential to repetitively add and remove the same variables, and by setting the maximum number of steps you can mitigate this behavior. The Swapwise method lets you choose whether you wish to use Max R-squared or Min Rsquared, and choose the number of additional variables to be selected. The Combinatorial method simply prompts you to provide the number of additional variables. By default both of these procedures have the number of additional variables set to one. In both cases this merely chooses the single variable that will lead to the largest increase in Rsquared

Example of 5 regressors As an example we use the following code to generate a workfile with 40 independent variables (X1–X40), and a dependent variable, Y, which is a linear combination of a constant, variables X11–X15, and a normally distributed random error term. Given this data we can use a forwards stepwise routine to choose the “best” 5 regressors, after the constant, from the group of 40 in XS. We do this by entering “Y C” in the first Specification box of the estimation dialog, and “XS” in the List of search regressors box. In the Stopping Criteria section of the Options tab we check Use Number of Regressors, and enter “5” as the number of regressors. Estimating this specification yields the results:



The top portion of the output shows the equation specification and information about the stepwise method. The next section shows the final estimated specification along with coefficient estimates, standard errors and t-statistics, and p-values. Note that the stepwise routine chose the “correct” five regressors, X11–X15. The bottom portion of the output shows a summary of the steps taken by the selection method. Specifications with a large number of steps may show only a brief summary

Uni-directional-Forwards The Uni-directional-Forwards method uses either a lowest p-value or largest tstatistic criterion for adding variables. The method begins with no added regressors. If using the p-value criterion, we select the variable that would have the lowest p-value were it added to the



regression. If the p-value is lower than the specified stopping criteria, the variable is added. The selection continues by selecting the variable with the next lowest pvalue, given the inclusion of the first variable. The procedure stops when the lowest p-value of the variables not yet included is greater than the specified forwards stopping criterion, or the number of forward steps or number of added regressors reach the optional user specified limits. If using the largest t-statistic criterion, the same variables are selected, but the stopping criterion is specified in terms of the statistic value instead of the p-value. Uni-directional-Backwards The Uni-directional-Backwards method is analogous to the Uni-directionalForwards method, but begins with all possible added variables included, and then removes the variable with the highest p-value. The procedure continues by removing the variable with the next highest p-value, given that the first variable has already been removed. This process continues until the highest p-value is less than the specified backwards stopping criteria, or the number of backward steps or number of added regressors reach the optional user specified limits. The largest tstatistic may be used in place of the lowest p-value as a selection criterion.
