This sect ion out line t he det ailed st eps of t he various research approaches to be used in helping t o achieve t he research object ives of t his st udy. This includes five sect ions which are t he Dat a Source, Measurement of Variables, Model specificat ion, and t he Est imat ion st rategy.
Data Source
The st udy employed secondary macro-economic dat a t hat was downloaded from t he World Development Indicat or for t he period 1991-2018. The dat a of t he st udy was a t ime series dat a where it s observat ions were based on mult iple variables over some period of t ime and were arranged in sequent ial order. The main variables under st udy are t wo variable which is economic growt h proxy by GDP growt h (annual %) and Unemployment proxy by Unemployment , t otal (% of t he t ot al labour force). Nevert heless, t he sample of t he st udy was based on t he availabilit y of t he dat a set and t he import ance of t he chosen variables and how t hey affect each ot her.
Measurement of the variables of this study
The variables used in t his st udy were measured as; economic growt h was proxy by annual Gross Domest ic Product which is t he quant ity of economic output
how much real GDP grows from one period t o t he next . Thus, t he rat e of Real GDP is calculat ed as follows;
Current Real GDP - Previous Real GDP
Real GDP = X 100……….
(1)
Previous Real GDP
Whilst , t he Unemployment rat e proxy by Unemployment , t ot al (% of t he t otal labour force) is t he percent age of unemployed persons in t he t ot al labour force. The rat e of unemployment is t he number of persons searching for a job divided by t he t ot al labour force. Thus, t he unemployment rat e is calculat ed as follows;
Number of Unemployed Persons
Real GDP = X 100………(2)
Labour Force
Model Specification
Okun law, which explains t he link bet ween unemployment and economic growt h, was used as a t heoret ical basis. The classical t heory explains that unemployment is a short t erm condit ion which free market force will aut omat ically deal wit h it and rest ore maximum occupat ion in t he economy (Banda, Ngirande, & Hogwe, 2016) whiles t he Keynesian hold t he view that
unemployment is normally t riggered by insufficiencies in t ot al demand over specific periods wit hin t he labour market such t hat adequat e jobs are creat ed t o accommodat e people who want t o work (Keynes, 1936). The Marxist t heory also explains t hat unemployment is as a result of t he capit alist syst em where t he means of product ion are owned by t he bourgeoisie and t he prolet ariat are exploit ed t hereof t hrough alienat ion and t hat unemployment can be reduced by replacing t he capit alism wit h t he socialism (Gyang, Anzaku, &
Iyakwari, 2018).
The study, therefore, adopted Okun’s (1962) model presented by Ademola
and Badiru (2016) which int egrat ed economic growt h proxy by Annual Gross Domest ic Product as t he independent variable and Unemployment rat e proxy by Unemployment , t ot al (% of t he t ot al labour force) as t he dependent variable. The model is specified as:
Y=β0+β1Ut + εt ………...…… (3)
Hence; Y denot es t he unemployment rat e, U denot es t he economic growt h.
Modificat ion t o model (3) is as follows:
Unempl =β1 + β2 𝑅𝑔𝑑𝑝+ εt ………..……… (4)
Hence; 𝑅𝑔𝑑𝑝 denot es t he rat e of GDP growt h (independent variable),
Unempl denot es unemployment rat e (dependent variable), β1 – Paramet ers and
εt - Error t erm (whit e noise)
Therefore equat ion (2) will be log-linearized in order t o crit ically t ransform it to est imable form:
lnUnempl =β1 + β2ln𝑅𝑔𝑑𝑝+ εt ………..……… (5) The apriori expect at ions are as follows: β1 <0 (i.e. β1 is non-negat ive value)
Estimation strategy
This sect ion t alks about t he est imat ion st rat egies employed in analysing t he dat a (t ime series) t hat were ext ract ed for t he st udy. The examinat ion of t he dat a was based on t hree import ant st eps which were; st at ionarity t est ; short -run and long--run Test ; and Granger causalit y t est . First ly, t he st at ionarity test was conduct ed t o make sure all t he variables were st at ionary I(0) or at first difference I(1). Secondary, coint egrat ion t est was conduct ed t o t est t he long-run co-int egrat ion among t he variables of t he st udy and furt her proceed to t est for short -run relat ionship bet ween t he variables and finally, t he Granger causalit y t est was conduct ed t o explain t he causal relat ionship bet ween t he variables of t he st udy or causal direct ion among t he variables of t he st udy.
Unit Root Test
The unit root t est is t he principal st age in t he est imat ion procedure. It was carried out on t he variables (Unemployment and Economic growth) employed in t he st udy t o t est if t he st udy variables are st at ionary at levels I(0) or st at ionary at first difference I(1) since t here will be spurious regression results
if a non-st at ionary series dat a is regressed on anot her non-st at ionary data (Gujarat y, 2004).
The major principle underlying t he t ime series is t he st at ionary levels of t he data in quest ion. Since t he dat a (t ime series) was adopt ed t o evaluat e t he relat ionship bet ween variables for fut ure predict ion and analysis, it was, t herefore, expedient t o check whet her t he velocit y (fluct uation) was constant over a long-run, check whet her t he variance and co-variance were invariant (st ay const ant ) over t ime.
Hence, t he st udy used bot h Augment ed Dickey-Fuller (ADF) unit root t est by Dickey and Fuller (1979) and t he Perron (PP) unit root t est by Phillips-Perron (1988) t o t est and confirm t he st at ionarity of t he variables (Unemployment and Economic growt h) at levels and at first levels. Bot h t he Augment ed Dickey-Fuller (ADF) unit root t est and t he Phillips-Perron (PP) unit root t est would t est t he alt ernat ive hypot hesis against t he null hypot hesis to check whet her t he dat a (t ime series) employed were non-st at ionary.
Accept ing or reject ing t he null hypot hesis depends on t he t -t est of t he lags and t he t -st atistics. If t he t -t est of t he lags is a lesser amount of t han t he crit ical point t he null hypot hesis of a presence of unit root is accept ed.
The Autoregressive Distributed Lagged (ARDL) cointegration framework
Coint egrat ion is t he second st age of t he est imat ion procedure. It was execut ed out t o explain t he long-t erm relat ionship bet ween variables of t his
st udy (t he rat e of Unemployment and Economic growt h rat e). Series of lit erat ure in t he field of economics has employed t he Johansen coint egrat ion approach in est imat ing t he long-run relat ionship of variables. Most researchers have argued t hat t his is t he best when it comes t o dealing wit h I(1) variables.
On t he ot her hand, researches by earlier scholars int roduced Aut oregressive Dist ribut ed Lags (ARDL) which has become an alt ernat ive in at t empting coint egrat ion issue. These scholars believe t hat the ARDL approach has so many benefit s t hat out weigh t he benefit of t he Johansen co-int egrat ion.
However, t his st udy employed a coint egrat ion met hod acknowledged as t he
“Autoregressive Distributed Lag (ARDL) bound test. The reasons for employing
t he ARDL bound t est are; The ARDL coint egrat ion procedure is comparat ively more efficient when t he size of t he dat a of t he st udy is small. This st udy dat a of st udy covers t he period of 1991t o 2018 inclusive. Thus, t he whole dat a set for t he st udy is 27 which are quit e good considering t he scope and nat ure of t he st udy; and also, t he ARDL model will enable t he ordinary least square (OLS) t echnique t o est imat e t he coint egrat ion once t he lag of t he model is ident ified. This makes t he ARDL approach very t he best model in t his case and;
Finally, t he ARDL met hod does not need t he pret est ing of t he variables of t he st udy involved in t he met hod for unit root s as compared t o ot her met hods such as t he Johansen approach. It is expedient t o apply t he Johansen t echnique when t he variables of t he st udy are st at ionary at levels I(0) but when all variables are st at ionary at first difference I(1) or t he variables are at a
combinat ion of st at ionary at t he level I(0) and st at ionary at first difference I(1), t he ARDL model is t he best .
ARDL model uses just t wo st eps in it s est imat ion. First ly, t he F-t est is employed to decide t he incidence of long-t erm relat ionship bet ween variables under st udy.
Secondary, we approximat e t he short run error correct ion model.
ARDL Bounds test
This t est was done following t wo main procedures. The first procedure was to est imat e t he ARDL equat ion by using t he ordinary least squares est imat or in ot her t o check if t here exist s a long-t erm relat ionship among t he variables of t he st udy. The F-t est is t hen conduct ed for t he combined significance with respect t o t he elast icit y const ant s of variables at t heir lagged st at e.
We check t he null hypot hesis in cont radict ion of t he alt ernat ive hypot hesis as follows:
𝐻0= 𝛿𝑜 𝐻1 ≠ 𝛿0
The crit ical values give rise t o t he t est for coint egrat ion when t he variables of t he st udies are st at ionary at levels I(0) or st at ionary at first difference I(1). There is an assumpt ion on t he lower bound value in t hat the order of combinat ion of t he explanat ory variable is zero, or I(0) wit h t he order of int egration of t he upper bound being one, I(1). The following int erpret ation is given;
1) When t he F calculat ed is more t han t he higher bound, we conclude that t here is co-int egrat ion bet ween t he t wo variables of t he st udy. Then, we discard t he null hypot hesis of no relat ionship bet ween t he variables of t he st udies.
2) When t he F calculat ed drops lower t han t he lesser bound figure, t hen we cannot discard t he null hypot hesis of no relat ionship among t he variables of t he st udies.
3) When t he F calculat ed falls bet ween t he t wo bounds t hat are lower and upper bound, t here is no conclusive decision whet her t he variables of t he st udies are coint egrat ed or not .
Imperat ively, we have t o proceed wit h t he bound t est , we impose a rest rict ion on t he ARDL t o approximat e t he long-t erm relat ionship bet ween t he dependent and independent variables of t he st udies.
Test for Causality
Test for causalit y is t he final st age of t he est imat ion procedure. It was carried out t o inspect t he causal relat ionship bet ween t he t wo variables (t he rat e of unemployment and economic growt h rat e). The st udies employed Engle &
Granger (1989), Granger causalit y t est t o know causal relat ionship among t he t wo variables of t he st udy, whet her one variable direct ly causes t he ot her variable or none of t he variables has an influence on t he ot her.
ANALYSIS OF DATA