ABS data set construction update

Today I met up with Gary to commence our collective construction of the ABS data set from catalogs 5204.0 and 5206.0. The panel data set is going to be constructed along:

• Time (in years)
  
• Industry
• Input variables such as capital stock, capital service, capital expenditure

Initially we were faced with a few problems in trying to work out what items we were going to include since numerous studies have elaborated on the various production inputs in different levels of detail. We have decided on including the following variables:

• Capital stock - for IT and Non-IT
• Capital service - for IT and Non-IT
• Labour productivity
• Labour hours
• Cost of employment
• Gross Value Added
• Hardware, Software (IT) expenditure and non-IT expenditure
  

We also faced problems in trying to match up these required variables with the data that the ABS has provided in these two catalogs. The fundamental difference between the two catalogs is that 5206.0 deals with data that is reported quaterly whilst 5204.0 deals with data that is reported in annually. Since the panel data set is going to need annual data we will be predominantly be using the items retrieved from 5204.0. Additionally we were slightly confused with what items in 5204.0 match up to our items especially regarding capital. However after consulting with Dr. Poon today this has been clarified. Additionally Dr. Poon has provided us with a data set up to the year 2002. This data set will not only provide us further guidance in constructing the data set but also serve as a means to use as a "test" data set, which I can use to test my AES function which i will write in R in the coming weeks.

Dr. Poon also provided us with further insight into our thesis in our brief consultation. Dr.Poon brought to my attention that I might need to obtain data on rental prices and include this in my model and calculation of AES. However I will first need to review my literature to see if previous work has included this. If they have not then the partial derivatives in the Hessian matrix (see post Test for Substitution Elasticity) will be:

• the co-efficients from the regression * [value add (output) / input of the variable]

I will continue to work on panel data set construction with my fellow peers and hope to have it almost complete by the end of the week.

Project Plan

On Thursday the 26th of July i handed in my project plan for assessment. As mentioned in my previous posts I was going to post up a copy of my plan and a Gant chart. Click on the thumbnails to view the specific details of the project plan and Gant chart.

Project Plan

GANT Chart

Tomorrow I will be meeting with two of Dr. Poon's other treatise students Gary and Nik to collate the data set that I had mentioned in my previous posts. We have all read how the data construction was done in the Parham (2001) paper and it appears to be quite straight forward. In addition to continuing the write up of my literature review and reviewing further papers, I have also spent a significant amount of time become more and more familiar with R. I am also looking into how to write functions in R as I will need to write a function using R code to implement the AES. Over the next coming days I will write more in depth about how I will go about implement AES in R and reviewing some further papers which I have found to be quite interesting.

Thesis Meeting Overview: July 23rd 2007

On Monday the 23rd of July my thesis weekly resumed with Dr. Poon and his other supervised engineering thesis students. The purpose of this meeting was to provide each other a brief overview of what we have found in our research areas. My overview was based on informing Dr.Poon, Gary and Nik about the different means where elasticity of substitution can be measured. The details of my presentation can be found in my previous posts. This was a very interesting as I became more aware of Nik's and Gary's topics. Gary gave a very interesting presentation about Fuzzy clustering and different algorithms which implement fuzzy clustering such as c-means and clustering regression. Nik gave an overview about General Additive Models (GAM).

My thesis meeting also clarified the steps we will take in finding a suitable data set for my model since our plans to obtain a particular subset of the data collected from the ABS economic activity survey fell through. Simon has proposed that as a data gathering and skills building exercise, Nik, Gary and myself to construct a data from the publicly available data from the ABS. The data to be collected is from the following catalogs:

• 5204.0 – Australian System of National Accounts
• 5206.0 – Australian National Accounts

Our task is it replicate the data collection and construction technique from the following paper:

• Parham, D., Roberts, P. & Sun, H.,'Information Technology and Australia's Productivity Surge', 2007.
  

The items that we will be extracting from catalogs 5204.0 and 5206.0 include items such as:

• Industry Value Add (output)
• Cost of Employment
• Industry Machinery

It has been agreed that we will each overview these catalogs and gain familiarity with the data construction techniques, We will then get together to aggregate our data into a single data set and will also chase up the ABS about acquiring any missing data. Additionally I am also responsible for finding and appropriate deflator for our data set. Since we have observations across time it is important to account for inflation and express the units in constant dollar terms across the time range.

Once we have aggregated and formed our data set we will each use this data set in our respective projects where hopefully we can find interesting results which we can use to assist the other in their project. Our next meeting is to be held Wednesday next week. I am also required to provide another brief presentation as to how I am going to go about measuring and estimating AES for the panel data set.

The meeting deliverables are:

• Construct the ABS data set
• Provide and overview to my fellow peers on how I will go about implementing AES using R and other tools
  

Test for Substitution Elasticity

The following is a brief overview of the presentation that I will be giving in my thesis meeting today.

What is Partial Elasticity?

Partial Elasticity of Substitution is the proportional change in the ratio of the use of two inputs brought about by a change in the relative price ratio for these two inputs. Since my thesis topic is concerned with a production function with multiple input factors we must use a measure that considers the multi-factor case. The main measures that I have come across my research are the Allen Partial Elasticity of Substitution (AES) and Morishima elasticity of substitution (MES).

What is AES?

AES is defined as the percentage change in the ratio of the quantity of two factors to the percentage change in their price ration allowing all other factors to adjust to their optimal level (Hitt 2005). AES tends to be usually measured via cost functions but a lot the research I have undertaken has used various production functions to measure it. As noted by Chambers (1988) AES is defined by:

Where: x_i x_j, are the inputs we wish to see if they are complements or substitutes
f_i is the first order partial derivative of our production function with respect to x_i .
F is the bordered Hessian Matrix:

F_ij is the cofactor associated with f_ji
If σ_ij > 0 than the two inputs are substitutes if σ_ij >0 then the are complements

What is MES?

MES measure the relative input changes as opposed to AES which measures the absolute input changes. MES can be re-expressed in terms of AES.

Where: σ_ij^A and σ _jj^A are Allen elasticities of substitution.

It should be noted that unlike AES which is symmetrical MES is asymmetric. Furthermore if inputs are classified as substitutes under Allen’s measure they are substitutes under Morishima’s measure. However if the inputs are classified as complements under Allen’s measure they are not necessarily compliments under Morishima’s measure. Hence it is important to note that MES has a bias towards treating the inputs as substitutes and AES is biased towards treating them as compliments.

Production Functions Used

Reviewing the literature I have found various production functions have been used in testing the elasticity of substitution for the various factor inputs. They are:

• Cobb Douglas Production Function
• Translog Production Function
• CES- Translog Production Function

The majority of the literature do not use the Cobb Douglas production function when estimate the Allen partial elasticity of substitution since its function constrains the substitution elasticities to be unity (Dewan et al. 1997). Consequently the Translog and CES-Translog production function tend be more readily used.

Statistical Tests

Since the substitution elasticities calculated are highly non-linear in their parameters the means and standard errors are approximated via various techniques these are:

• Bootstrapping
• Monte Carlo Simulation
• Dividing the sample into different sub-sample and then estimating the separate production functions for each sample.

For the first two methods standard one tailed statistical test apply. However if the latter method is applied then the distributions of substitution of elasticities for each sub-sample are then compared using distribution fee statistical tests which are:

• Median Test
• Wilcoxon Rank Test.

After my meeting I will write more in depth of any additional deliverables.

Update on the ABS Data request

The ABS got in contact with me on Thursday. Unfortunately the news was not the best. The consultant had informed me that the data I was requesting from the Economic and Activity Survey would not be available for purchase. This is because items such as Computer Software Expensed are not collected annually but every four years. As a result the data is not of a quality that can be used to do statistical analysis upon. The consultant did point me however to two surveys that could be of use. They are:

• 8126.0 - Information and Communication Technology, Australia, 2004-05, for items related to IT and communications.
  
• 8155.0 - Australian Industry, 2004-05, for items such as operating income etc.

The data for these items are available for previous and may prove useful for my thesis. I have contacted Dr. Poon about this matter and he has informed me that we will discuss this in our next Meeting on Monday the 23rd of July. Hopefully this problem in obtaining the data that Dr. Poon would have liked me to obtain will not pose a big problem in the continuing progress of my thesis.

ABS data gathering and update on progress

Since my last post I have been reviewing the papers i have found and have started to write my literature review. As mentioned in my previous post we have collectively decided with Dr. Poon that we will aim to have this finished by the end of the month. Reviewing my progress so far, I am definitely on track to meet this milestones deadline and may even be able to start the model building earlier than i anticipated.

I also contacted the ABS today with regards to obtaining a quote for the data from the Economic and Activity Survey. The individual which i spoke with was very helpful and within 24 hours an information consultant will contact me to inform me not only how much the data will cost but also the level of detail of the data. I will be writing more about this shortly in my next post.I have also started my detailed engineering plan which is due Friday the 27th of July. Once i have a fairly complete project plan I will post up a screen shot of the GANT chart.

Over the next coming days I will continue to work on my literature review and my presentation next week to my fellow peers where I will be presenting the different techniques where elasticity of substitution and complementarities can be measured.

Thesis Meeting: July the 9th 2007

On Monday a meeting was held with Dr. Poon and my fellow colleagues to discuss our progress in research what the deliverables will be for the next few week. We all gave updates on where we were in terms of our research and Dr. Poon was please with our progress.

One of my tasks will be to obtain data from the Australian Bureau of Statistics (ABS) that will be used in my model to estimate the complementarities between hardware and software. The data to be obtained will be from the Economic Activity Survey, from 1998 to 2007. Whilst a lot of the literature I have found does advocate the use of firm level data, Dr. Poon has advised me that the ABS most likely will not provide this level of detail. He has suggests that I ask the ABS for data broken up by firm size i.e. small, medium and large. Whilst this level of detail is not the most desirable form it will still serve the purpose of treatise well in examining the complementarities between hardware and software. The items from the survey which I am required to obtain data for are:

• Employment
• Income from Services
• Sale of Goods
• Total Income
• Labour Costs
• Purchases
• Telecommunication Services
• Computer Software Expensed
• Training Services provided by other businesses
• Other Management and Administrative services
• Reported operating profit or loss before tax
• Inventories
• Derived items
• Capital expenditure and disposal of assets including computer software capitalised and computers and computer peripherals
• Capitalised wages and salaries and purchases of materials for capital work.

In addition to obtaining the data, I have been researching additional papers related to my topic to determine my motivation and definitions of my thesis. I have found in excess of 40 papers and am still researching for additional papers. I am currently going through the papers that I have found to determine which are the most relevant to my topic. I will continue this activity over the coming 2 weeks. I have also received notification from the library that the Chambers text book I have requested is available for pick up and I will collect this today to continue my research into substitution elasticities.

Dr Poon has also provided me with four additional papers for me to read, however I had already come across most of them through my research. These papers are :

• Fernadez, W., Gregor, S., Martin, M., Stern, S. & Vitale, Michael. ‘Identifying the Key Strategies in the Realization of Value from Information Technology’, 2007.
• Fernandez, W. ,Gregor, S., Holtham, D,. Martin, M., Stern, S., Pratt, G. & Vitale, M., ‘Achieving Value from ICT: key management strategies’, Department of Communications, Information Technology and the Arts, ICT Research Study, Canberra, 2004.
• Mittal, N. & Nault, B.R., ‘Investments in Information Technology: Indirect Effects and Information Technology Intensity’, Haskayne School of Business: University of Calgary Canada, 2006.
• Dewan, S. 'The Subsitution of Information Technology for Other Factors of Production: A Firm Level Analysis', (2006) 43 Management Science 1660-16.
  

Dr. Poon for our next meeting would also like us to prepare a 15 minute presentation on a particular area that is inline with the research and literature reviewing that we are currently completing. My presentation will focus on the different testing methods of substitution elasticity that I have come across my research.

Our next meeting is scheduled to be early on in the first week of semester 2. My goals and aims I wish to achieve by the next meeting are:

• Obtain a quote on the data to be obtain from the ABS
• Continue to develop core skills using R
• Continue further research int the testing methods of substitution of elasticity
• Complete my thesis project plan