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Modeling the relationship between GDP and unemployment for Okun’s law specific to Pakistan during 1976-2010. Okun’s law postulates a negative relationship between movements of the unemployment rate and the real gross domestic product (GDP). This article investigates the link between the real GDP growth and unemployment, as described by Okun’s law. For this purpose we have used time series annual data during the period 1976 to 2010 and used unit root test and lest square method to find the relationship between GDP growth and unemployment in Pakistan. The empirical analysis shows that a rise of one percentage point of unemployment is associated with a decline of 0.36 percentage point of real GDP growth.

## I. INTRODUCTION

Okun’s law postulates a negative relationship between movements of the unemployment rate and the real gross domestic product (GDP). This empirical relationship is a major part of every traditional macro-model as the aggregate supply curve is derived by combining Okun’s law with

the Phillips curve. It is the feature of supply side in macroeconomics, as output increases in a recovery phase – unemployed workers are hired, as output falls in recession – workers are laid off from their jobs. In reality, though, Okun’s law is a statistical relationship rather than a structural feature of the economy. As with any statistical relationship, it may be subject to revisions in an ever-changing macro economy.

“In earlier studies, Okun found that the relationship was about 3 to 1: that is 1 point of unemployment for every 3 points of GDP gap. However, more recent data and more advanced econometrics techniques suggest that the 2 to 1 (or perhaps 2.5) gearing ratio between output and the unemployment rate is more representative for recent periods”. [Samuelson and Nordhaus, 15th Ed.].Irfan Lal, Sulaiman D, M. Anwer Jalil and Adnan Hussain 2010, find long run relationship between variable and error correction mechanism for short run dynamic by using co integration technique. They found that Okun’s law interpretation may not be applicable in some Asian developing countries including Pakistan.Christian Pierdzioch, Jan-Christoph Rulke and Georg Stadtmann, 2009, found a significant negative relationship between the expected growth rate of real output and change in the unemployment rate.Dany Lang and Christian de Peretti 2009 pointed out that there is a significant relationship between fluctuations in unemployment and growth, the most important past growth shock exerts an influence on the current unemployment rate.Jim Malley, Hassan Molana 2008, found that to follow the effect of typical demand side macroeconomic policies targeted at reducing unemployment depends on which state prevails, and that such policies are unlikely to yield the expected result when the economy is in a low-effort state.José Villaverde, Adolfo Maza 2008 argued that, the quantitative values of Okun’s coefficients are quite different, a result that is partially explained by regional disparities in productivity growth. These differences imply that, when it comes to policy issues, conventional aggregate demand/supply management policies should be combined with region-specific policies.Knotek (2007) pointed that there are three ways of finding the Okun’s Law. First, to captured the changes in the unemployment rate from one quarter to the next quarter i.e difference version. Second, the gap version captures unemployment to the gap between potential output and actual output, which was also applied by Thirlwall (1969) in calculating natural rate of growth and the third, the dynamic version implied the past output, current of output and past unemployment to affect the unemployment. Last but not least, the production-function version which combined the theory of production function (labour, capital and technology) with the gap version of Okun’s Law.Mohd Noor, Zaleha., Mohamed Nor, Norashidah and Abdul Ghani, Judhiana (2007)

found the existence of Okun’s law in Malaysia with coefficient of -1.75, significant at 1

percent level which is lesser than the original Okun’s law.Paramsothy Silvapulle, Imad A. Moosa, Mervyn J. Silvapulle 2004 found that the short-run effects of positive cyclical output on cyclical unemployment are quantitatively different from those of negative ones. Also proposed that the output-unemployment relationship as represented by Okun’s law is asymmetric. Leopold Soegner and Alfred Stiassny 2002 proposed that countries with a highly protected labor market actually exhibit a low reaction of employment to GDP variations (mainly due to labor hoarding), while the persistence in the unemployment rate is stronger for these countries.Lee (2000) supports the validity of Okun’s law, but not the robustness of Okun’s law application of other OECD countries, also added that the relationship of the Okun’s Law is not as robust as reported by Okun in his finding. Okun’s (1962) findings pave an important background on the analysis of the relationship between output growth and unemployment. The initial finding of Okun’s law predicts that if output were to increase by 3 percentage point, it will reduce the unemployment rate by 1 percent. This was agreed by Weber (1995) but he found smaller value of coefficient if dynamic specifications were applied.

## Model Specification

The initial form of Okun’s can be written as:

Ï‰ ( U* – U ) = ( Y – Y* ) / Y* —————————————– ( 1 )

Where U is the unemployment rate, Y is the real GDP and an asterisk represents potential or natural rate levels of the variables. The Above question states that for every percent point the unemployment is below the natural rate, GDP is Ï‰ % above potential GDP.

In order to empirically estimate Okun’s law, giving the fact that U* and Y* are difficult to estimate we will use a reduced form of the previous equation

To derive the growth rate version, we first expand equation 1:

Ï‰U* – Ï‰U = Y / Y* – Y*/ Y* —————————————– ( 2 )

Now we differentiate Eq (2) w.r.t to all variables. In order to simplify our analysis we will consider Y* as a constant, Stating the potential GDP is not changing on the short term. Thus:

Ï‰dU* – Ï‰dU – dY / Y* – dY*/ Y* —————————————– ( 3 )

Also, we assume that the change of the natural rate of unemployment dU* = 0. Using this assumption and rearranging we obtain:

dY / Y* = – Ï‰dU + dY*/ Y* —————————————— ( 4 )

The natural real GDP growth rate is usually close to the real growth rate. Therefore we can approximate dY*/Y with dY/Y. This modification can be invalidated on the short run but on the long run it is consistent. Thus

dY / Y = – Ï‰dU + dY*/ Y* ——————————————– ( 5 )

The natural real GDP growth rate is equal to the potential GDP growth rate less the product of Okun’s law coefficient and the change in unemployment rate. Using ordinary least squares Okun has obtained Ï‰ = 2 and dY* / Y* = 3. Thus potential GDP growth rate is about 3 percent points while a rise in unemployment by 1 percentage point will lower real GDP growth rate by 2 percentage points.

## Testing the Validity of Okun’s law for Pakistan

In order to empirically test Okun’s law for Pakistan, we have used annual data for real GDP growth and unemployment in the period 1973-2010. The source of the data is World Bank Dataset (WDI) and State Bank of Pakistan.

## Graph 1: Real GDP vs. Unemployment

## Graph 2 : DY/Y vs DU/U

The graph suggests that higher values of economic growth can be associated with lower values of unemployment growth rate.

To check the relationship between the growth and unemployment rate, preliminary tests were made in order to select the best regression model. First step was to test whether the variables are stationary by running ADF and PP tests. The results are shown in the Table below:

Table 1: Stationary tests for GDP growth rate (dy/y) and unemployment growth rate (du/u)

## Variable

## Test

## t-statistic

## p-value

## dy/y

## ADF

-4.639434

0.0007

## PP

-4.65725

0.0006

## du/u

## ADF

-4.932097

0.0003

## PP

-3.841364

0.0058

Both Augmented Dickey-Fuller test (ADF) and Phillips-Perron (PP) test confirmed that the variables are stationary in level. Also the dependent variable (DY/Y) the partial autocorrelation function showed dependence in the first two lags; to get better regression results we included in the regression the first two AR terms. After running several regression equations which included different lags for the unemployment growth rate it was choose the one which consider du/u (-2) based on statistically significance criterion. Therefore the equation found to describe the best relationship between the unemployment and growth rate on significance and information criteria was:

## Dependent Variable: DY/Y

Method: Least Squares

Sample (adjusted): 1977 2010

Included observations: 34 after adjustments

Convergence achieved after 12 iterations

## Variable

## Coefficient

## Std. Error

## t-Statistic

## Prob.

## C

0.028361

0.041737

0.679532

0.5020

## DU/U(-2)

-0.361528

0.381952

-0.946526

0.3514

## AR(1)

0.130541

0.198787

0.656685

0.5164

## AR(2)

-0.092076

0.289812

-0.317709

0.7529

## R-squared

0.124168

Mean dependent var

0.030317

Adjusted R-squared

0.036585

S.D. dependent var

0.237916

S.E. of regression

0.233523

Akaike info criterion

0.039058

Sum squared resid

1.635989

Schwarz criterion

0.218630

Log likelihood

3.336009

F-statistic

1.417717

## Durbin-Watson stat

## 1.987754

Prob(F-statistic)

0.256955

The coefficient of dU is around -0.36 and is statistically significant. A rise by one percentage

point of unemployment will reduce real GDP growth by 0.36 percentage points with a delay of 2

lags. The intercept can be interpreted as potential GDP growth; so the level of economic growth

which will not generate inflation is below 2.83 percentage points. The Durbin-Watson statistic is around 2 which mean that there is no autocorrelation in the residuals. The correlogram of residuals confirmed the absence of autocorrelation.

## CONCLUSION:

The importance of Okun’ law lies in its implications for economic policy. The correlation between real GDP growth and unemployment is very important for policy makers in order to obtain a sustainable rise in living standards. If the GDP growth is above its natural level, policy makers will decide not to intensively promote the creation of new jobs in order to obtain a sustainable growth rate which will not generate inflation.

The slope of unemployment in Okun’s law in around -0.36 and potential GDP growth is around

2.8 percentage points and the variables are negatively correlated as predicted by the theory. The methods used and the results presented in this paper provide insights into the effects on the unemployment rate of deviations of national output. This evidence supports the results of other authors for different series and periods, which allows us to use it as a good instrument of analysis and forecasting of the economic cycle; allows us to estimate the sacrifice rate of long run unemployment; and moreover, shows that the economic policy must focus by all means in avoiding fluctuations in growth and at the same time reducing unemployment, because this way it will stimulate growth in the long run.