Quantifying aviation- tourism relations: an introduction to elasticity using least – squares
Exercises:
Answers to exercises should be submitted via Moodle as part of Assignment. The answers should not be more than one -page in length (per Unit).
Income is one of the most significant factor s determining air travel and tourism demand. Data in Table 1 can be segmented into two groups: one with high levels of income and the other lower levels of income. Based on theory, we might expect that the two groups have different elasticity.
Figure: Distribution of demand by income group
Data are available on Moodle (excel format).
1. Calculate the Pearson’s correlation coefficient between air travel cost and demand contained in Table. Calculate the correlation coefficient betwee n air travel cost and demand for each income group. Thus, three correlation coefficients should be reported : (a) air travel cost and demand; (b) air travel cost and demand (higher income group); (c) air travel cost an d demand (lower income group).
Interpret the coefficients – what do they mean?
2. What are your expectations about the elasticity of two income groups? Relatively more elastic or inelastic? Explain your answer.
3. Calculate the slope of the ‘line of best fit ’ for each market segment (higher income and lower income) . Calculate the constant price elasticity of demand for two income groups and provide a brief interpretation of the results.
0 2 4 6 8
log(quantity)
4 5 6 7 8
log(price)
Higher income group Lower income group
Slope of lower income group data Slope of higher income group data
4. Briefly explain what factors other than price and income might change the values of these elasticities.
5. Your colleague asks to borrow the elasticity estimate for a different task. In particular the colleague would like to use this information to predict the impact of carbon tax of $10/ticket. In particular the colleague is in terested in the effect of the $10 carbon tax on the demand for passenger air travel by small and medium businesses. What cautions must be exercised when using your elasticity estimates?
6. Your colleague is aware of these cautions and carefully applies your elasticity to the carbon tax problem. What is the effect of $10 tax per ticket on demand? Suggest other wa ys of segmenting the dataset to obtain more realistic elasticity estimates.
• Why is it necessary to specify a random component in a model of linear relationship?
• What is the meaning of random?
• Why is ‘slope of the line’ an important information to be estimated from regression analysis?
• What is the least-squares estimator? Why is it called ‘least-squares’?
• What is the difference between ‘r’ (the correlation coefficient) and ‘r-squared’?
When reading this extract, pay attention to the following:
• What is a specification error?
• What is a measurement error?
• What are the five assumptions concerning the error term?
• What are the implications of the violation of all or some of these assumptions?
• Why is it (sometimes) useful to logarithmically transform data? Use concepts such as R -squared and standard error s to answer this question. As will be seen, logarithmic tran sformation has a convenient property in terms of elasticity.
This is discussed in the following section.
• What are the common sources of measurement errors in computing airfare elasticities of tourism demand? (p.30)
• What are the various ways in which analysts can partially overcome measurement errors ? What are the advantages and limitations of these approaches (p.31 -34)?
Essential Readings:
Lewis-Beck, M. (1980) Applied Regression Sage Publications – Reading 2,3 & 5 McKillup, S. (2007) “Statistics Explained, An Introductory Guide for Life Scientists” pp.175 -185 – Reading 1
Seetaram, N (2010) Computing airfare elasticities or opening pandora’s box? Research in Transport Economics 26:27-36 – Reading 4
References:
You may wish to consult the following statistics and econometrics resources:
McClave, J., Dietrich, F., Sincich, T. (1997) Statistics, 7th ed Prentice Hall
Wooldridge, J. (2005) Introductory Econometrics, SouthWestern.