The purpose of this paper is to determine the relationship between the rate of unemployment and the rate of inflation in the US economy. It has been mainly examined in the past that the rate of unemployment is inversely proportional to the rate of inflation. The relation is stable in the short run but in the long run it is different. Many works have been done on this relation in the past and it has been listed in the literature review. Data has been collected for 40 years from 1970 to 2009 and analysis has been done to find if there is correlation between these two variables. The data has been collected from 1970 because during that period the inflation and unemployment levels were raising at the same rate in many countries including US. This was called as ‘Stagflation’ as inflation and unemployment were encountering rise in their levels which in theory opposed Phillips curve. Edmund Phelps went on to explain that in long run, there is no trade off between unemployment and inflation which got him a Nobel Prize. It was later proved that an increase in inflation can lower the unemployment in a short run temporarily but in the long run inflation has no role in controlling unemployment. This behaviour has been noted for the long run (1970-2009) and it has been proved through correlations and regression models that there is a weak correlation between unemployment and correlation.

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## Literature Review:

The relationship between the unemployment and the rate of inflation was examined by a New Zealand born economist A.W. Phillips. The economist described the statistical relationship between wage inflation and unemployment in the UK. It was found that there is an inverse relation between unemployment and inflation when the graph was plotted with inflation on Y-axis and unemployment on X-axis. Same model has been applied to other countries by different economists and the result was same when inflation was low, the unemployment was high and vice-versa. This curve obtained by the scatter of points on the graph was popularly known as Phillips curve.

In his research, Phillip found that unemployment at 5.5%, the wage inflation is zero and when unemployment at 2.5%, the price inflation is zero as the increase in wage will compensate the productivity growth.

Paul A. Samuelson and Robert M. Solow through their research on “Phillips-Curve” found that a “negative correlation between the rate of inflation and the rate of unemployment”. “The inverse relationship between inflation and unemployment was explained in terms of unemployment being a measure for the degree to which the capacity of the economy to produce output (factor employment) was utilised. When unemployment is high the excess supply of labour holds wages and prices down. When unemployment is low, excess demand will push up wages and prices more quickly. Expansionary fiscal or monetary policy would lead to an expansion of aggregate demand and more employment, but only at the price of increasing inflation” (Stratling, 2009).

Several economists assumed that the Phillips curve inferred that in the long run, at a constant rate of inflation there will be increase in the rate of unemployment. Studies in 1960 witnessed the relationship between unemployment and inflation is not what the Phillips curve recommended. Labour and companies were concerned of “real wages and real prices and not nominal ones”. “Monetarists argue that once inflation expectations are taken into account, any inflation-unemployment trade-off is only a short-term possibility” (Stratling, 2009). The inflation will be predictable and the labour and organizations will respond to increase in demand owing to a raise in money supply with price increase and supply remaining the same. High levels of inflation loads the economy with greater operation costs and which results in deformation of the industries in the region creating unemployment. Other economists believed that it is the responsibility of the government to restrain unemployment and inflation with “Keynesian policy”. “Monetary policy” should be used to pump in money into the economy which increases the GDP and reduce the unemployment rate. The unemployment factors depends on many things such as the side effects of the Vietnam War for US in 1970’s and cognisant economic policies for other countries.

The gradient of the long -run Phillips curve is correlated to inflation determination and unemployment determination as a consequence of financial blow. “The standard New Phillips curve (downward-sloping in the short run and vertical in the long run) has recognized difficulties in accounting for inflation persistence and often implies implausible impulse-response functions (IRFs) for unemployment; our Phillips curve (downward-sloping in the short, medium and long run) can generate inflation persistence and plausible unemployment IRFs” (Karanassoua et al. 2005).

The Phillips curve plays a pivotal role in the area of macroeconomics and in the formation of monetary policies framed by the respective governments. Economists look upon the negative correlation between the rate of inflation and the rate of unemployment in Phillips curve as precise and consistent relation to price rise. Research by economists such as Lipsey suggested that “the rate of change of unemployment also has an effect upon inflation in addition to the effect of the level of unemployment” and Gordon highlighted the function of demand increase in determining inflation (Guha and Visviki, 2001). Generally all the previous research concentrates on the “level effects” rather than “rate of change of effects”. In the research conducts by Guha and Visviki (2001), the result from the study states that “US job growth is more important than the unemployment rate in determining inflation”. The relation between the variables job growth and inflation is found to have greater impact than the current variables. After the post-war era in US, employment growth has a greater enduring authority on price rise following the effect of job loss and the control of unemployment on price rise is little. In the past 10 years, it has been observed that inflation being at its lowest levels, the rate of unemployment has remained low as well.

The Phillips curve is a simple equation that interprets “the impulse-response function of inflation to a monetary shock into the impulse-response function of unemployment to that shock; thus the monetary shock is substituted out in deriving the relation between inflation and unemployment. This curve cannot portray the interplay between money growth and nominal frictions, which is the focus of our analysis” (Karanassou et al., 2008).

## Data Description and Data Collection:

The United States has been selected to find the correlation of unemployment and inflation. As US is the world’s largest economy with more than $14 trillion in 2009 which is 3 times larger than Japan.

The two variables considered for this study are unemployment and inflation.

Inflation is computed by Consumer Price Index (CPI) method. It is a measure assessing the average cost of goods bought by consumers. It is a price change for steady lot of goods from one time to another in the same region.

Unemployment is the number of people who are unemployed at a given period of time. The number is determined every month by the Bureau of Labor Statistics (BLS) of the U.S. Department of Labor.

The data for unemployment has been collected from United States Department of Labor, Bureau of Labor Statistics. The data has been considered for 40 years from 1970 to 2009 can be found in the Appendix. The unemployment in 1970 was around 4 million which was the minimum in the sample size of 40. The highest number of unemployment was recorded in the year 2009 with more than 14 million.

The data for inflation has been collected from the US Inflation Calculator website. The data has been considered for 40 years from 1970 to 2009. The rate of inflation in 1970 was 5.7%. The rate of inflation was recorded negative in 2009 with -0.4% and the maximum inflation was recorded in the year 1980 with 13.5%.

The mean, median, mode and standard deviation can be found in the table.

## Correlation Analysis:

Hypothesis: There is a weak relation between unemployment and inflation (inversely proportional).

Dependent variable (DV): Inflation

Independent variable (IV): Unemployment

Data of the two variables (unemployment and inflation) are plotted as points on a graph. The graph obtained is called as scatter gram. To determine whether there is an evidence of the relation between the two variables, we calculate the correlation coefficient. “The correlation coefficient is a number which describes the extent to which the pattern of points is linear” (Jessop, 2010). By using the excel sheet and applying the function CORREL, we get CORREL = -0.2901

“A correlation coefficient is a “ratio” not a percent” (Higgins, 2005).

When CORREL is negative, it implies that it is a downward sloping straight line pattern.

As we can see from the graph, a downward sloping pattern has been observed which means a negative correlation has been determined. As the rate of inflation increases, the unemployment decreases. “The degree to which any pattern of points corresponds to the ideal of a perfect linear relation is described by the average value of the product. This is called correlation coefficient” (Jessop, 2010).

With the help of correlation, we can determine whether the variables are correlated or not i.e. we can say that the greater the number of unemployment the less will be the rate of inflation. But we cannot conclude that unemployment causes inflation or vice-versa. This correlation helps us to recognize that a prototype exists but not why the pattern exists. We will look into this issue in the latter sections.

Therefore we have found correlation coefficient (r) = 0.290

When considered hypothesis test for CORREL, we find that the absolute value of sample CORREL (r = 0.290) is smaller than 0.312. As the sample size of population is 40 and 95% confidence interval is considered we get value of 0.312 from the table.

The absolute value of r is not greater than the tabulated value; this implies that there is a weak correlation.

To find the confidence intervals for r, we use FISHER function to find the mean (w) for the normal distribution.

W = FISHER (0.290) = 0.299

This is the mean for the normal distribution.

The standard deviation is 1/sqrt (40-3) = 0.164

The 95% confidence interval for w is

0.299 + (1.96*0.164) = 0.620

0.299 – (1.96*0.164) = -0.022

Now using FISHERINV to get the corresponding values of r:

W = -0.022 => r = FISHERINV (-0.022) = -0.022

W = 0.620 => r = FISHERINV (0.620) = 0.551

Therefore the 95% confidence interval for the population correlation is from -0.022 to 0.551.

## Regression Analysis:

The Regression analysis is a “Statistical tool for the investigation of relationships between variables and to determine the causal effect of one variable upon another. It assesses the statistical significance of the estimated relationships” (Sykes, 2000).

The straight line obtained from the graph is expressed by equation:

The equation obtained from the straight line is y = -0.0005x + 7.9857

Which implies slope = – 0.0005

And intercept = 7.9857

## Overall Model Performance:

## Multiple R:

Multiple R is the correlation coefficient (CORREL) = 0.2901.

From the table for the hypothesis test for CORREL, with a risk of error of 5%, a value less than 0.312, we cannot validate that population CORREL is non zero, alternatively putting in other words, we can reject the hypothesis test for CORREL.

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The CORREL tells us “whether two variables are related to one another, whether the relationship is positive or negative and how large the relationship is. It also gives us details about how accurately the variation in one variable is proportional to the change in the other variable” (Higgins, 2005).

## R Square:

To convert the correlation coefficient into percentage we have to square the correlation coefficient i.e multiply it by r and the obtained value is called “Coefficient of Determination”.

“The coefficient of determination tells you the percentage of variability in one variable that is directly related to variability in the other variable” (Higgins, 2005).

In our case: we have R Square = 0.0842 => 8.42%

In other words, large correlation coefficient means strong relationship which in turn results in high R Square value. High R Square signifies “more variance accounted for and allows better, more accurate, predictions about one variable based on knowledge of the other”.

This implies 8.42% of variance in inflation is explained by unemployment.

## Adjusted R Square:

Adjusted R square considers the total sample size of the population and an improved estimation of R Square. As we can see that the Adjusted R Square has further been reduced to 6.01%. This means that 6.01% of variance in inflation is explained by unemployment. This might not be considered significant.

## Parameter estimates:

We obtained the equation: y = -0.0005x + 7.9857

Slope: -0.0005

Intercept: 7.9857

## t Stat:

t Stat is “estimated coefficient divided by its own standard error”

It is used to examine whether the hypothesis that the value of the slope is non-zero. If the slope is non zero there exists a relation between the variables. Considering 5% risk of error, we get the tabulated value 2.776 from the t distribution. From what we get the t Stat value -1.868, it is less than 2.776 which deduces that the relation is not significant. In other words “the variable is NOT a significant predictor of the dependent variable BEYOND the sample. However, as the model is a good fit with the sample – it does not detract from its value within the sample, it only affects generalisability outside the sample” (talkstats website).

## P-value:

If 5% risk of error is not considered then the P-value tells us that there is risk of 6.9% if we reject the hypothesis that slope of population is zero.

“The p-value is the probability of observing a t-stat that large or larger in magnitude given the null hypothesis that the true coefficient value is zero. If the p-value is greater than 0.05; which occurs roughly when the t-stat is less than 2 in absolute value, it means that the coefficient may be only “accidentally” significant” (duke.edu).

## Confidence Interval:

The 95% confidence interval for the variable in the sample population is between -0.0010 and 0.0000. The interval consists of value zero therefore the slope of the equation can also be a zero.

## Conclusion:

From the analysis, we can see that 95% confidence interval for the population correlation is from -0.022 to 0.551. This implies that r could be positive or negative. As all the correlation coefficients have to be in the range from +1 to -1, the analysis is correct.

The CORREL value of +1 gives us positive relationship between the two variables and -1 gives us negative correlation between the two variables.

The behaviour of CORREL value fluctuating between positive and negative is explained in detail as there are many factors other than inflation which causes unemployment.

The dependent variable inflation has a positive relationship between the rates of money growth. “In the model of aggregate demand and aggregate supply, increases in the money supply shift the aggregate demand curve to the right and thus force the price level upward. Money growth thus produces inflation” (web-books). There are other factors which influence the inflation other than the growth of the money but this may affect inflation on a short term basis.

Data for more than 150 countries have been collected for a period of 30 years which shows a positive relationship between the inflation and rate of money supply.

The variation in unemployment can manipulate inflation in 2 distinct ways. The difference of the real amount of unemployment from its normal limits can give rise to “inflationary pressures”. On the other hand “the variation of the growth rate of the variable from its long run equilibrium growth rate can also affect inflation” (Guha and Visviki, 2001).

The Phillips curve recommends that more the employment in the country the more will be the rate of inflation. At any point of time, there will be unemployment which is not because of inflation but of the other factors such as structural and frictional unemployment. “When the rate of unemployment is below the non-accelerating-inflation rate of unemployment (NAIRU), then the demand puts pressure on wages to rise faster than productivity. When the unemployment rate is above the NAIRU, the lack of demand leads to wages rising more slowly than productivity (or even falling). At the NAIRU, any wage increases are off-set by increases in productivity” (Stratling, 2009).

The experiment with the Phillips curve for US was stable for the year in 1980s and beginning of 1990s to forecast the inflation. The same was not true for the last decade. The unemployment levels began to fall in late 1990s without change in inflation. NAIRU is variable for US and the reasons for it could be less possible salary level, trade unions and the automation of industries driven by computers. It has been observed that during the period when there was high economic growth, there were advancements in the health care industries which contributed to the US imports being low. “The reason that most inflation models have not managed to accurately predict inflationary movements in the 1990s is that they have not taken into account a very important determinant of price changes: the rate of job growth” (Guha and Visviki, 2001).

The rate of inflation was high in 1970s in US because of the Vietnam war and oil price increase in OPEC member countries. After this there was deflation known as “Volker deflation” followed by recession. According to Russell and Banerjee (2008) “positive supply shock will initially increase both inflation and the unemployment rate leading to a positive short-run relationship. A supply shock to unemployment is likely to take a very long time to dissipate due to transaction costs, retraining, and the rigidity of human and physical capital”. But in the long run this relation is different.

The practical study by Abraham and Shimer (2002) and Valletta (1999) says that for the increase in unemployment is the result of ‘changes in women’s labour force attachment’ and ‘changes in the incidence and duration of permanent job loss that relate to declining job security’ (Valletta, 2005).

Unemployment is always there in any country because of ‘structural and frictional unemployment’. Structural unemployment is disparity of the attributes of a demand and attributes of the supply for job. Frictional unemployment occurs when a person shifts from one occupation to another for his own priorities.

Other factors for unemployment in US are increase in population, competition that US firms face from other countries, technological advancement causing job losses, recession, seasonal jobs, minimum wage programme, outsourcing to other countries, multitasking of jobs carried by single person.

Supply of money plays an important role in the cause of inflation. Keynesian suggests that the inflation is because of three main reasons – Demand-Pull inflation (increase in demand for goods is greater than the supply of goods, Cost-Push inflation (drop in supply because of external factors) and Built-in inflation. The rate of economic growth also influences inflation.

## Reflection:

The analysis of correlation and regression models between the two variables helped in understanding the statistical significance associated with the variables. The analysis of the 40 years data assisted in providing evidence based on theories by noted economists. Initially there was a great deal of difficulty in assessing the accuracy of the data collected. Other factors affecting unemployment and inflation were considered as the correlation of the two variables was found to be weak. A lot of effort was put on gathering information about the causes of inflation and unemployment between the time intervals. The analysis of Phillips curve is different for short term and long term. This added a lot of complexity in giving an explanation about the change in behaviour of the Phillips curve. The direct correlation would have been an easy one to solve and to present an analysis. But I thought unemployment and inflation would give me a challenging task, I chose these variables. The positive correlation between the inflation and the money supply could have better explained the cause and effect on the economy. The example provided a detailed statistical analysis for the controversial variables. The Phillips curve has to be explained in two parts i.e. the long run Phillips curve and the short run Phillips curve. This is my personal learning after referring to lot of literature and doing research about Phillips curve.