A Quick Explanation of Recent NARDL - Hassan

5/21/2017

A Qui ck Expl anati on of Recent N AR DL - Hassan

Hassan

 A Quick Explanation of Recent NARDL Twee Tw eett

Folllow @b Fol @born orneo eote temp mpllat ates es

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The News of a positiv e change change in the character character of a villain villain (did  (did something very good) of your area may surprise you, but his negative change may not. These two sides si des of changes do not not have an uniform uniform impact on you. Again, think t hink of a very moral person you like. His negative change may shock you but his posit positive ive change won’t. These two changes in opposite directions (positive and negative) do not have the same power to move you, in both examples. And the effects are not really symmetric or equivalent; they are asymmetric or non-equivalent. Asymmetry is one type of non-linearity. The asymmetries and other other forms of non-linearity are also frequent in economic variables. For example, an increase (positive change) in oil price is said to have stronger effect on particular macroeconomic variables than decrease (negative change). In fact, ‘’nonlinearity is endemic within the social sciences and that asymmetry is fundamental to the human condition’’ Shin et al. (2014)

 A conven conventional tional time series regression regression model c ontain ontains s constant parameter parameters s and assumes t hat a chang change e in i n explanatory explanatory variable has the same effect over time which may not be appropriate in all cases as shown in the oil example earlier.  Again, the pop popular ular cointegration cointegration tecniques tecniques such as EG-ECM, VECM, Boun Bound d testing t esting etc. imply a c onstan onstantt spee speed d of  adjustment ( i.e a constant ECT) to long-run equilibrium after a shock (change). But this dos not hold true always when there is market frictions. (see G Dufrénot, V Mignon 2012). Estimating a relationship which possibly has asymmetry with symmetric sy mmetric technique tec hniques s seems unfair and may leads one to some serious inappropriate inappropriate policy conclusions c onclusions (Enders 2014)). Since the conventiona cointeration test doesn’t allow one to capture the asymmetries in macroeconomic variables. variable s. Vario Various techniques have hav e been intr oduced oduced so far to account this asy mm mmet etr  r y,  y,  Threshold ECM, Smooth transition regression ECM. Markov-switching ECM etc. But the recent NARDL or Non-linear Autoregressive Model proposed by shin et al (2014) incorporate asymmetries both in the long run and in short run relationships, and at the same time, it captures the asymmetries in the dynamic dynamic adjustment. Moreover Moreover,, it allows the regressors regressors of mixed order  of I(0) and I(1).

An illustration:  illustration:   If inflation rate rises in a country you may expect that the domestic foods becomes expensive and there will be a tendency to import foods from foreign countries. The relationship is positive. Again if inflation rate falls the consumers find domestic foods cheaper and people reduce buying foreign foods, the food imports decline (positive relationship). Although in both cases the food imports  imports  react positively to the inflation rate, are the magnitudes of  reactions same in both cases ? maybe not; maybe food import import response more to positive positi ve change or otherwise. A t ime series regression specification with a constant parameter will tell us that the reaction is same in both direction. Here comes the NARDL. NARDL (also other asymmetric regression techniques) explicitly distinguishes the reactions of both directions. I denote food import by food t  and inflation rate by INF t,  intercept by C and residuals by Ut.  For simplicity, ignore the other regressors that may influence the food import. The simple OLS two-variable model takes the following form: Foodt=C+βINFt + U t.

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5/21/2017

A Quick Explanation of Recent NARDL - Hassan

To capture the possible asymmetric effects of inflation on food import NARDL technique decomposes the inflation rate series into two parts 1)partial sum of positive change in inflation rate denoted by INF t+ and 2) partial sum of positive change in inflation rate denoted by INF t- and include both of them as separate regressors in the model and the model becomes:

Foodt=C+ β1 INFt+ + β2  INFt - + Ut.

Clearly, this is now a three-variable OLS model. If we now represent this equation in (linear) ARDL model proposed by pesaran et. Al (2001) the final model takes the form as show in picture below. The model shown in the picture is the general form of NARDL. (Non linear   Autoregressive Distributed Lag Model. See the explanation of each term i n the picture below.

The long run coefficients:  We can calculate the long run coefficient of INF+t by dividing the the negative of the coefficient of INF +t , θ+ by the coefficient of Food t-1 , ρ, and the the long run coefficient of INF - t by dividing the negative of the coefficient of INF -t , θ- by the coefficient of Food t-1 , ρ (-θ+ / ρ) and (-θ- / ρ) are the long run coefficients of of INFt+ and INFt- , respectively. The summation notation Σ implies that NAR DL consider inclusion of differenced variables into model upto some lags. For example, in case of ∆Foodt-1, NAR DL considers the incusion of its first lagged term upto maximum lag you

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5/21/2017

A Quick Explanation of Recent NARDL - Hassan

choose, if appropriate. And in case of ∆INF -t it consider the the inclusion of its zero lag (∆INF -t itself) upto the maximum lag you choose, if appropriate.

Asymmetric Cointegration test:  A long run relationship or c ointegration is present if  the joint null hypothesis, ρ =θ+ = θ- =zero is rejected. The critical value are the same critical values for ARDL.

Testing Symmetry: Clearly, if the long-run coefficients (-θ+ / ρ)  and (-θ- / ρ) are not same then there is

asymmetry in the long run. So we test the null hypothesis of (-θ+ / ρ) = (-θ- /  ρ). If the null is rejected then there is an evidence of long-run asymmetry in the model.

To estimate NARDL, follow these steps:

Steps:

Step 1. Perform unit root tests to justify that non of the variables are I(2). Step 2. Generate INFt  and INFt    from INFt  Step 3. Run the Non linear ECM under NARDL Step 4. Test the ‘non linear cointegration’ test with F‑test  Step 5. check the asymmetries.

See my another post on estimating Nonlinear ARDL (NARDL) with Eviews.

NARDL With Eviews

Shin et al. (2104): http://hassanhaniif.blogspot.sg/2017/03/NARDL1.html

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A Quick Explanation of Recent NARDL - Hassan

Researchgate link

https://www.researchgate.net/publication/228275564_Modelling_Asymmetric_Cointegration_and_Dynamic_  Multipliers_in_a_Nonlinear_ARDL_Framework

Some papers which applied NARDL:

1. Abdlaziz, Rizgar Abdlkarim, Khalid Abdul Rahim, and Peter Adamu. "Oil and Food Prices Cointegration Nexus for Indonesia: A Nonlinear ARDL Analysis." International Journal of Energy Economics and Policy 6.1 (2016). 2. Ndoricimpa, Arcade. "Analysis of asymmetries in the nexus among energy use, pollution emissions and real output in South Africa." Energy (2017). 3. Zhang, Zan, Su-Ling Tsai, and Tsangyao Chang. "New Evidence of Interest Rate Pass-through in Taiwan: A Nonlinear Autoregressive Distributed Lag Model." Global Economic Review   (2017): 1-14.

References:

1. Dufrénot, Gilles, and Valérie Mignon. Recent developments in nonlinear cointegration with

applications to macroeconomics and finance. Springer Science & Business Media, 2012. link 2.

Enders, Walter. App lied Econometric Time Series. Hoboken: W iley, 2015. Print.

3. Pesaran, M. Hashem, Yongcheol Shin, and Richard J. Smith. "Bounds testing approaches to the

analysis of level relationships." Journal of applied econometrics 16.3 (2001): 289‐326. link 4. Shin, Y., Yu, B., Greenwood‐Nimmo, M.J., 2014. Modelling Asymmetric Cointegration and Dynamic Multipliers in a Nonlinear ARDL Framework. In William C. Horrace and Robin C. Sickles (Eds.), Festschrift in Honor of Peter Schmidt: Econometric Methods and Application, pp. 281‐314. New York (NY): Springer Science & Business Media. link

Eviews official website: http://www.eviews.com/home.html

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