Estimate of an Appropriate Demand Equation for QLEIS, Term Paper Example

Introduction

The demand function for leisure price in Ruritania can be estimated through various tests. The regression statistics are used to define the variables in the demand function equation. The price for leisure keeps fluctuating depends on several factors such as the weather pattern. The validity of the equation is tested in the structural stability.  The seasonality describes the expected changes in the coefficients of the equation.

The price of a commodity is inversely proportional to the demand.  The higher the price, the lower the demand and vice versa. The gradient of the line is negative hence verifying the inverse proportionality nature of the line.

Initial Predictions

The equation gives the true situation because the total number of the units is proportional to their price. The gradient of the line gives the rate of increase in units the customers are willing to buy. The line is straight from the origin. The change in demand curve from 1987 to 2016 is due to the changes in the customer purchasing power or increase in quality of the products. Driving forces which increased the demand for the products was the feasibility study carried out in 1987 and the findings implemented in 2016.

Price of Coffee (PCOFF)

Driving forces which increased the demand for the products was the feasibility study carried out in 1987 and the findings implemented in 2016. The clients have their taste of the products produced hence the demand increased.

Price of Beer (PBEER) and Price of Wine (PWINE)

The convergence of the beer prices encouraged the investors to increase the production of the wine. The food companies opted for the beer due to its low price. The exchange stockpiles for the wine type grew by 72% in 2012 which translated to 2.6 million bags each with the weight of 132.0 pounds. On the other hand, the inventories for the wine type decreased by 55% within the same period. Some of the food companies swapped the beer with the wine due to the effect of the global commodity index.

Index of all other prices (PALLOTH)

Global Coffee organizations predicted a rise in the demand for the coffee beans by 6% in 2016. It was due to the increase in the consumption of the coffee by approximately 1%. The climatic conditions were predicted to reduce the rate of robusta production in Vietnam regions due to lack of enough rains. The production of Arabica beans was expected to increase in Brazil. The change in the quantity of production was expected to affect the price gap immensely. The diagram below illustrates the trend of the coffee market from 2012 to 2016.

Income (INCOME)

For instance, the prices of coffee rose up by 13% in 2012 due to the increase in the demand for the commodity. The prices for the coffee beans rose in the markets. On the other hand, the prices of Arabica coffee went down in the same year due to the hard economic times in countries. The prices for the of coffee were close to each other due to the fluctuations in the demand and effect of economic factors. The average gap between the prices of them and the coffee was about $1.0972 in 2014.

Price Function Estimation

The equation of the line is as shown in the equation below.

Y= -66.0x + 300

The stock which is more related to the market index is stock A because it has a defined correlation coefficient. The proxy for risk-free rate gives the comparison for the items in the stock and prices.  The choice leads to a proper analysis of the same values hence the regression analysis gives accurate coefficient.

Identification of the Functional Form

The equation for the data is tested using the following equations.

The linear equation used in the has several coefficients and variables.

Linear 

Regarding the log-linear algebraic equation, the terms are as follows:

Regarding the reciprocal form, the equation is as follows

The functional form of the equation has the useful properties. For the sake of simplicity, the linear functional form is used in textbooks and other functional forms such as the log-linear. The form of the equation allows for the change of the prices and detecting the demand of the coefficients. The appropriate form is chosen according to the demand variation. The diagnostic tests are carried out to determine the boundary conditions of the equations. The elasticity of the demand depends on the confidence of the equation. The equations can be summarised in the following table.

The diagnostic tests follow the general progress of the functions. The tests done include the white test and the Ramsey RESET test. The log-linear and reciprocal functions passed the tests. One of the equations should be chosen depending on the auto-correction results. The reciprocal function has the advantage of elastic explicitly since the coefficient depends on the reciprocal coefficient. The economic data for the PLEIS chooses follows the log form of the equation.

Preferred Model

The initial unrestricted general model has several variables which are not significant. The model for the variables has some multi-collinearity. The explanatory were highly collinear. The multicollinearity increases with coefficients. The log-linear equation has the RESET test investigation specification. The method of stepwise regression will eliminate the variables by the ascending significance order.

Slutsky Equation

The term s represents the income from the leisure time. The Slutsky equation increases the price of leisure by 1%.  1.3% of the income represents some of the substitution consumers. -.043% comes from the decreased real consumer purchasing power. The income for effect works in the different direction to bring down the inferior services offered in the leisure time. The leisure time is taken as a priority for different people.

Additional Tests

Covariance is a function of variance while correlation is a function of the change in y-axis and x-axis.

The table below shows the covariance and correlation of 2010 and 2012 respectively.

The patterns in the graphs can be explained using the statistics since they follow the normal distribution.

Tabulation of the dates when the two market indices move in opposite direction

Two stocks A and B and d their daily prices (Pa and Pb) from 2017-01-01 to present

Histogram for the two series respectively.

Structural Stability

The time series data is plotted on the graph to come up with the changing mechanism for the structure of the equation. The structural change inflates the number of the factors identified in the usual information provided. The log form of the equation gives the estimation of the regression results. The equations used in the stability analysis are as shown in the expressions below.

The data is as shown in the figure below.

Seasonality

The seasonality exists in the data given in the data set for the PLEISURE prices. The model given might fail to reflect the real-life patterns. Price for the leisure is affected by the changes in the climate and weather. The location for the Ruritania has minute changes in the climate hence there are very little fluctuations in the prices. The seasonality is examined by using the regression model and avoiding the dummy variable. The dummies are added as in the following expressions.

The table below summarizes the dummy testing for various seasons.

The stock which is more related to the market index is stock A because it has a defined correlation coefficient.

Compute the correlation between each stock and the S&P 500 Index

The stock which is more strongly related to the market index is the stock C. The values have a well-defined correlation.

Presentation and Interpretation of Preferred Model

Compute the daily return series from the daily price data

Literature Tie-in

So far, the demand function for Pleisure in Ruritania is estimated to be linear log function. Since the analysis by the choice of the preferred regression model is restricted to the given data, there might exist other factors influencing Ruritanian P-leisure demand: relative income, dietary culture, changes in age distribution and etc. the expressions used include the following.

Works Cited

Baltagi, Badi. Econometric analysis of panel data. John Wiley & Sons, 2017.

Harris, Lawrence, and Eitan Gurel. “Price and volume effects associated with changes in the S&P 500 list: New evidence for the existence of price pressures.” The Wall Street Journal 41.4 (2012): 1-10.