Baumol argues that innovation has replaced price as the most important factor that lies behind economic growth. He suggests that even though it has been recognized that important innovations stem from small firms, individuals or entrepreneurs, the bulk of innovative activity however is carried out by large oligopolistic firms. Baumol’s argument supports Schumpeter’s distinction between entrepreneurs led and routinized innovation. Schumpeter held that technological competition was the form of competition for all types of firms but Baumol argues that it is mainly large oligopolistic firms that engage in this type of competition and according to Fagerberg (2004), this explains why in his analysis Baumol focuses mainly on oligopolistic firms.

EXPLAINING THE BAUMOL MODEL OF INNOVATION While acknowledging price competition, Baumol stresses that large corporations use innovation as the most important weapon for competition. He further explains that firms do not intend to risk too much innovation as it is expensive and can be made obsolete by rival companies. Therefore, organisations have to divide the differences through the sale of technology licenses and participation in technology sharing compact that pay huge dividend to the economy as a whole which makes innovation a routine feature of economic life.

Baumol suggests that there are five important pre-conditions for the existence of the free market economy which are oligopolistic competition this means competition among large firms where innovation is the prime weapon, routinization of innovation activities which makes them an ordinary component of the activities of a firm thereby reducing the uncertainty of the process. Productive entrepreneurship which is incentives for entrepreneurs to devote themselves to productive innovation rather than innovative rent seeking , the rule of law includes carrying out contracts and protecting contracts from illogical expropriation that is, property rights, royalties and copyright and technology selling and trading which is simply the way firms pursue opportunities for profitable dissemination of innovation (Baumol, 2002).

These pre conditions are the features of the free market economy. In other economies, they might exist in weaker forms and sometimes not exist at all. Baumol argues that these features are important for explaining the growth accomplishments of the free market.

CRITICISMS AGAINST THE BAUMOL MODEL Baumol focuses on the partnership between independent entrepreneurs who are the primary source of innovative breakthroughs in the marketplace and high tech corporations with their routinized research and development activities whose primary accomplishment has been the steady improvement of the innovative products and processes contributed by independent entrepreneurs and the vast increase in the capacity of those products and processes. According Sheshinski, (2007), the emphasis in this analysis is on the critical role of the entrepreneur.

Oligopolistic Competition refers to competition among large firms where innovation is the prime weapon, ensuring continued innovative activities and their growth. In this situation a few large firms dominate a particular market. However, it might be argued that a theory of innovation based growth needs to take into account the different types of firms that exist, their mutual interaction and the selection processes allowing some firms to grow while others may be forced out of business.

Routinization of Innovation: Innovation is one of the mechanisms of economic growth. It can be explained by repertoires and actions, the profit earning mechanism drives firms toward routinization of the innovation process, and it in turn tends to limit the resulting profits. Thus, routinization is one major means by which firms reduce the risks faced in their innovation rivalry. A considerable degree of routinization is now standard in a wide variety of firms including telecommunications, computer manufacturing and pharmaceuticals.

Technology Selling and Trading according to Baumol refers to a firm’s intentional pursuit of opportunities for profitable spreading of innovations and leasing of the right to use them that is, equilibrium between protection and diffusion and also equilibrium between first and second mover advantages. First movers have two possibilities, sell new products and the technology to develop new products, for second movers there is no incentive to steal as he is buying technology from first movers. This is very important as it reduces the problem of spillovers which tend to impede the introduction of innovations whose social benefits unlike private returns exceed their cost. However, Paul David in his theory of path dependence says that the first mover advantages matter a lot but second mover is not as important as everyone is locked-in to first movers even on the onset of new technologies and this is not consistent with the Baumol model.

Baumol also looks at the realities of the individual players in capitalism most importantly, the interplay between the small independent entrepreneur innovators and the large established corporations.

Another aspect of Baumol’s model is how risk and uncertainty is being treated. Uncertainty is an important aspect of innovation in the sense that in most cases you never know what the outcome will be, according to Baumol, innovation that shows real uncertainty is designed for small firms as large oligopolistic firms, he argues, engage in more routine type innovation, which is more predictable but according to Fagerberg (2004) he does not provide enough evidence to support this.

Also, Baumol sees innovation as demand driven to minimize cost of production and create products to meet the market demand with the aim of maximizing profit, however, Mowery and Rosenberg see innovation as demand driven, driven by routines but also supply constrained that is, by the supply of knowledge and one has to invest in prepositional knowledge as they are connected together which could lead to highly routinized process.

Baumol also looks at innovation from micro level and how it is driven by the fact that actors can compete in the market.

Baumol also asserts that if all benefits were captured by innovators, then the labor force would be permanently “condemned to extremely low nutritional and educational levels.” However, the argument overlooks the fact that with given resource endowments, innovation raises the amount of social product available for distribution and hence by Say’s Law aggregate demands (Scherer, 2002),

CONCLUSION In all, Baumol’s model is really original and it centers on the free market innovation being the main driver of economic growth in a capitalist economy, although, he did not really define competition nor did he address consideration of transaction cost. His work could also be criticized as he concentrated on large oligopolistic firms and not the smaller firms

## Correlation between productivity and gdp in the uk

The numbers of Gross domestic product (GDP) are generally used to evaluate the overall performance of a country’s economy. To take a closer look, it shows that productivity enhancements are the primary source for supporting economic growth (Mckinsey, 2002). Productivity is generally defined as output per unit of input and is an essential indicator of using resources efficiently (Phelps, 2010). In the long-term, it also is a signal of underlying economic growth potential. It reflects the efficiency of labour market which interacts with the changes in production and output (Myers, 2009). Furthermore, a fall in GDP growth will unavoidably have an incidental impact on growth of productivity. The timing of reflection the changes depends on the situation in the labour market. Although GDP growth can drop quite rapidly, and sometimes suddenly, companies tend to delay the action of lay off workers or decrease hour worked, namely, the action of diminishing the amount of labour employed behinds of a drop GDP growth. The hour worked are likely to be reduced more quickly than amount of hiring staff, as a result, there is a lag compared with the change of GDP growth (Myers, 2009)

There are two factors influence the per capita of GDP which are employment levels and labour productivity. Employment levels refer to the ratio of the actively labour force involved in economic activities and the average hour worked. In the other hand, labour productivity is the output produced by per unit of labour. To sustain the growth of GDP per capita, labour productivity must increase. For example, when a company improves its output per unit of labour that allows this company to obtain more profits, and have the ability to pay higher salaries to employees. This surplus will be directed back to the economy by increased consumer expenditure, higher exports, and more business investment. Consequently, the increasing in productivity leads to GDP increased (Mckinsey, 2002).

Both the information of Gross Value Added (GVA) per hour worked and per worker measures are used to compare GDP growth with productivity growth. From 25 years data, it indicates that productivity growth is very little lag behind to respond the changes in GDP growth (Myers, 2009). From this finding, it shows a relatively sensitive and flexible between labout market and the changes in output growth. For example, when the labour market is rigid and output ran down, it is difficult to hire properly skilled and experienced staff and to reduce work hours or lay off staff. Also, the growth rate of productivity tends to decline in front of the fall in output growth in economy downturn, but increase ahead of rise in output growth when economy recovers (Myers, 2009).

The trend of growth implies the underlying growth potential of the economy that outside the cyclical influences. It is a main determinant of the long-term growth rate of an economy, and acts as the base in deciding the growth of per capita income and the direction of living standards. Although short term causes may influence the growth of GDP and the living standards, in the long-term, it underpins the potential growth of the economy that resolve the wealth and prosperity of a country and living standard. To estimate the trend growth, it is based on the average growth rate between the start and the end of economic cycle, the productivity growth, average hour worked, the employment rate and the adult population are also included (Myers, 2009).

The Higher productivity not only directly enriches national welfare; it also enhances the competitive abilities of companies and national economies, allowing growth without inflation, and creating a financial platform for social spending. Eventually, productivity is the only sustainable factor for job creation (Mckinsey, 2002).

Data description and collection In this paper, it intends to explore the correlation and regression between productivity and GDP in UK. The two variables come from different database but from the same organization which is Office for National Statistics (ONS). The data of ‘Manufacturing output per filled job, unit wage costs and productivity jobs’ is related to the UK manufacturing sector. The output per filled job is the proportion of Index of Production and productivity jobs in manufacturing industry. The major area for the data collection is at UK. This data is released monthly and quarterly by ONS. The quarterly data for manufacturing could trace back to Q4 1954 (Great Britain. Office for National Statistics, 2009).

The Office for National Statistics (ONS) preliminary estimates for gross domestic product (GDP) including steady price gross value added (GVA) data of UK. Data are separated by division of industry. The main region of GDP data is collected from UK and the GDP data is released by quarterly. In this paper, the GDP data will be used from Q1 1985 to Q4 2009. The quarterly GDP growth rates of last quarter of previous year are used to analyze the quarterly productivity growth rate of last quarter of previous year in UK, finding out the relationship with these two variables. These two statistics are produced by following high professional principles and announced base on the arrangements permitted by the UK Statistics Authority (Great Britain. Office for National Statistics, 2010).

Analysis Scatter diagrams pattern To analyze the relationship between two quantitative variables, the scatter plot is used to graphically represent the relationship between two variables (Groebner et al, 2008). The scatter diagrams help to examine the data graphically and draw the initial conclusion about the possible relationship between variables. On Figure 1, the scatter diagrams show the positive relationship between quarterly GDP growth and quarterly productivity growth. It should be possible to estimate productivity growth by given GDP growth forecasts.

Figure 1: Scattergrams

3.2 Correlation Correlation coefficient The correlation coefficient determines the relative strength of a linear relationship between two numerical variables. The values of the correlation coefficient range from -1 for a perfect negative correlation to 1 for a perfect positive correlation. The value of correlation coefficient is closer to 1 or -1, and then the linear relationship between the two variables is stronger. The exiting of a strong correlation does not mean there is a causation effect. It only shows the tendencies presented in the data (Berenson et al, 2009).

It shows that quarterly GDP growth has the relation with quarterly productivity growth. Also, r=0.7394 indicates the two variables have strong relation.

Confidence intervals for the correlation coefficient FISHER

w

Correlation coefficient (r)

0.7394

0.9492

sample size (n)

100

standard deviation

0.1015

95% confidence interval

from

0.6353

0.7503

To

0.8171

1.1481

Figure 2: Confidence intervals for the correlation coefficient

Based on sample data to make an inference about a population value of the correlation coefficient, The Fisher’s transformation is used. It is a formula which firstly transform the value r to a value of w, that is approximately normally distributed with variance (n is the sample size). And finally, transform back to values for r (Jessop, 2010).

The mean for the normal distribution:

0.9492

The standard deviation is ==0.1015

The 95% confidence interval for w is

0.7503 to 1.1481

Then use FISHERINV to get the corresponding values of r:

w = 0.7503 ® r = FISHERINV (0.7503) = 0.6353

and w = 1.1481 ® r = FISHERINV (1.1481) = 0.8171

The 95% confidence interval for the population correlation is from 0.6453 to 0.8171.

3.3 Regression model Simple linear regression model There are two parameters which are slope and intercept composed the linear model. A linear model has the form y = a bx which describes how the mean value of y is related to x.

a is the intercept, the value of y when x=0.

b is the slope, the change in y when x increases by 1.

To present linear regression, it is y=intercept (slope * x) = a bx

a= intercept

-0.1546

b = slope

0.1365

y = -0.1546 0.1365 x

Figure 3: Linear regression

The slope is 0.1365; it means that for each increase of 1 unit in x, the mean value of y is estimated to increase by 0.1365 units. It could be assumed that if quarterly GDP growth rate increases 5% then estimate the productivity growth will be 0.5279.

inference: regression analysis SUMMARY OUTPUT

Regression Statistics

Multiple R

0.7394

R Square

0.546712

Adjusted R Square

0.542087

Standard Error

0.270283

Observations

100

ã€€ Coefficients

Standard Error

T Stat

P-value

Lower 95%

Upper 95%

Intercept

-0.15458

0.040204

-3.84488

0.000214

-0.23436

-0.0748

X

0.136474

0.012553

10.8719

1.57E-18

0.111563

0.161385

Figure 4: Summary output

The overall model performance of regression statistics is showed on Figure 4. The Multiple R represents correlation coefficient of two variables which are quarterly GDP growth and quarterly productivity growth and the number is 0.7394. The amount of observations, which is the sample size, is 100, checking the table of 5% risk of incorrectly concluding non-zero population correlation, the number is 0.197. The value of sample CORREL, which is 0.7394, is larger than 0.197. It concludes that in the population CORREL is non-zero correlation. That is to say, there is a relation between the two variables (Jessop, 2010).

R square is the coefficient of determination in regression analysis. It means the ratio of the total variation in the dependent variable can be explained by its relative independent variable (Groebner et al, 2008). R Square is 0.5467. It means 54.67% of the variation in the quarterly productivity growth data for this sample can be explained by the linear relationship between quarterly productivity growth and quarterly GDP growth (Groebner et al, 2008).

Adjusted R Square specifies the sample size and is a better way to estimate the population. In a simple regression analysis, adjusted (Jessop, 2010).

Standard Error is the standard deviation of the residuals and is a compute of the level of variation in variable y remains cannot be accounted by the model (Jessop, 2010). An inference of the population standard deviation of residuals is

Standard error

That = 0.2703 as shown in the output.

The second part of the output shows the estimates for intercept and slope. The value for slope is 0.1364. The 95% confidence interval estimate of the population slop coefficient is from 0.1116 to 0.1614. It concludes that a 1 unit increase in GDP growth will result in an increase between 0.1116 and 0.1614 units of productivity growth (Groebner, 2008). While this interval does not include the value 0, it concludes that the slope is non-zero (Jessop, 2010). It can be sure that there is a positive slope but are uncertain of the extent. Also, the value of standard error indicates the variation of the slope value from sample to sample. If the standard error of the slope is large, the value of slope will be variable. The regression output in figure 4 shows the standard error is 0.0126, so that, the slope values will be less variable and the sample regression lines will cluster closely around the true population line (Jessop, 2010).

Moreover, the very small P-value associated with the t test for significance. Given the level of significance =0.05, the decision of whether to reject can be made as

Reject , if p-value <

Because the p-value = 1.57E-18<=0.05, it rejects and conclude that there is a significant relationship between quarterly GDP growth and quarterly productivity growth (Anderson et al, 2003).

Significance tests The significance test of the correlation coefficient and the regression coefficient are developed from the sample data which point estimates of the population correlation coefficient and the true regression coefficients for the population that are subject to sampling error. Therefore, it needs a test procedure to determine whether the coefficient is statistically significant. Moreover, the test for the simple linear regression slope coefficient is equal to the test for the correlation coefficient. That is when the correlation between variable x and variable y is found significant, and then the regression slope coefficient will also be significant (Groebner et al, 2008).

Correlation significance test The correlation coefficient computed from 100 sample data is a point estimate of the population correlation coefficient. Although the correlation coefficient of 0.7394 seems high, compare to 0, it is subject to sampling error. The formal hypothesis-testing procedure is needed to determine whether the linear relationship between GDP growth and productivity growth is significant.

The null and alternative hypotheses to be tested are:

(no correlation)

(correlation exists)

=0.05

represents the population correlation coefficient. It is must to test whether the sample data support or refute the null hypothesis. The test procedure utilizes the t-test statistic.

Test statistic for correlation

Where: t = number of standard errors r is from 0

r = sample correlation coefficient

n = sample size

df = n-2

The calculated t-value is

= 10.8719

Decision rule:

If t > t 0.025 = 1.9845, reject Ho

If t < -t 0.025 = -1.9845, reject Ho

Otherwise, do not reject Ho

Because 10.8719 > 1.9845, reject Ho. Based on the sample evidence, it concludes that there is a significant, positive linear relationship in the population between quarterly GDP growth and quarterly productivity growth.

Significant test of the regression slope Commonly, the sample regression slope is not likely equal to the true population slope. To determine if the population regression slope coefficient is 0 or not, the test of significance of the simple linear regression slope coefficient is used. A slope of 0 indicates that the relationship between x and y variables is not linear. That is, in this linear form, independent variable x will neither explain any variation in the dependent variable y, nor useful in predicting the dependent variable. If the linear relationship is significant, then the hypotheses of regression slope is 0 should be rejected. However, the estimated regression slope coefficient is calculated from sample data, it is subject to sampling error. Therefore, even though estimated regression slope coefficient is not 0, it is necessary to determine if the difference from 0 is greater than would mainly be attributed to sampling error (Groebner et al, 2008)

The null and alternative hypotheses to be tested at the 0.05 level of significance are:

=0.05

Simple linear regression test statistic for test of the significance of the slope

Where: = sample regression slope coefficient

= hypothesized slope (usually=0)

=estimator of the standard error of the slope

The calculated t is

==10.8719

Decision rule:

If , reject

If , reject

Otherwise, do not reject

Because of 10.8719 > 1.9845, null hypothesis should rejected and conclude that the true slope is not 0. Therefore, the simple linear relationship that utilizes the independent variable, quarterly GDP growth, is helpful to explain the variation in the dependent variable, quarterly productivity growth (Greobner, 2008).

Conclusion To find out the relation between quarterly GDP growth and quarterly productivity growth, the analysis of correlation, regression models and the test of significant are used. From the analysis results, it shows that quarterly GDP growth has the relation with quarterly productivity growth.

The correlation coefficient of these two variables is 0.7394; it indicates the strength of relation between them. Also, it is possible to forecast quarterly productivity growth by given the quarterly growth rate of GDP. However, the correlation coefficient only implies the tendency of the data. It is not support the cause and effect relationship. The Fisher’s transformation is based on sample data to make an inference of the correlation coefficient value of a population. The 95% of confidence intervals for correlation coefficient of the population is from 0.6353 to 0.8171.

The linear regression model develops the equation of y = -0.1546 0.1365 x. The number of slope, which is 0.1365, represents when GDP growth increases per 1 unit, the mean value of productivity growth will be increased by 0.1365 units. From the summary output of regression analysis, the 100 sample size shows the risk of incorrectly concluding non-zero population correlation is lower and the relation between these two variables are significant. R square suggests the variation in the dependent variable can be explained by independent variable. The portion of productivity growth can be explained by GDP growth is 54.67%. Moreover, the number of slope is 0.1365; the 95% confidence interval forecast of the population slop coefficient is between 0.1116 and 0.1614. It shows a positive slope but unsure of the extent. The small number of standard error, which is 0.0126, suggests that the slope values will be less variable and the sample regression lines will come together around the true population line. The small number of p-value related with t test for significance, it concludes that there is a significant relationship between quarterly GDP growth and quarterly productivity growth.

From correlation significance test and the regression slope significant test, it comes out the same results which are a significant positive linear relationship between quarterly GDP growth with quarterly productivity growth. And the quarterly GDP growth is helpful to explain the variation in quarterly productivity growth.

Reflection This paper analyzes the relationship between quarterly GDP growth and quarterly productivity growth. The numbers of quarterly growth rate came from the comparison with the same quarter of previous year. Moreover, the sample data focused on manufacturing section in UK.

Research shows that the production industries, such as manufacturing, construction, distribution, hotels and catering sector and transport and communication, have more elastic in the downturn in terms of productivity growth. This partially reflects a more moderate drop in output growth in production sector; also, it takes more time to modify the arrangement of labour input than some other sectors (Myers, 2009). If the sample data came from other non-production industries, the result might different.

The coefficient of determination, which is 54.67%, shows the proportion of variation in productivity growth can be explained by GDP growth. Namely, there are other factors might influence the productivity growth. Productivity is the ratio of output to the input of labour. The hours worked is used to measure of labour input rather than the numbers of employees. The output is influenced by many elements such as the resources of capital equipment, new technologies, and management practices that are outside of worker’s influence.

Moreover, the economic status might have different level of impacts on productivity growth. During economic recession, productivity growth would not go down as much as output growths in theory, because companies laid off the least productive employees first and retained the more productive employees. Likewise, in economic upturn, productivity growth is expected to be lower than output growth. Because when more employees are recruited, the skill and experience level of the incremental employees decline, and so does their potential of productive (Myers, 2009). The future research could emphasize on discovering other factors which are impacts on productivity growth and analyze the relationship among variables.

[casanovaaggrev]