Econ 75 (econometrics) Group Assignment
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Prepared by: John Amorante A Bao :: Economics Department of Xavier University-Ateneo de Cagayan :: 19th Sept 2008
GROUP ONE
The Phillips curve says that the rate of change of money wages is a function of the reciprocal of the unemployment rate. Specifically, let wt = money wage rate in year t ut = unemployment rate in year t w − w t −1 %∆w t = t × 100 = percentage rate of w t −1 change in the wage rate The Phillips curve is given by 1 + et ut where it is hypothesized that β1 < 0 and β2 > 0. Using the observations on aggregate data given in the file phillips.xls: a Find least squares estimates for β1 and β2. b Test whether there is a relationship between %∆w and (1/u). c Draw a graph of the estimated relationship with u on the horizontal axis and %∆w on the vertical axis. d Find the estimate for the “natural rate of unemployment” (the natural rate of unemployment is the rate for which %∆w = 0). e Find estimates for d(%∆w)/du when u = 1 and when u = 3. f When does a change in the unemployment rate have the greatest impact on the rate of change in wages? When does it have the smallest? g What is the economic meaning of β1 and what is suggested by its estimate b1? h Find 95 percent interval estimates for β1 and β2. %∆w t = β1 + β 2
A functional form that has been popular for estimating expenditure functions for commodities is wfood = β1 + β2ln(totexp) + e a Estimate this function for households with one child and households with two children. Report and comment on the results. b It can be shown that expenditure elasticity for food is given by β + β 2 [ln(totexp) + 1] η= 1 β1 + β 2 ln(totexp) Find estimates of this elasticity for one- and twochildren households, evaluated at average total expenditure in each case. Do these estimates suggest food is a luxury or a necessity? (Are the elasticities greater than one or less than one?)
The file london.xls is a cross section of 1,519 households drawn from the 1980-1982 British Family Expenditure Surveys. Data have been selected to include only households with one or two children living in Greater London. Self-employed and retired households have been excluded. The data were used by: Richard Blundell, Alan Duncan, and Krishna Pendakur, “Semiparametric Estimation and Consumer Demand,” Journal of Applied Econometrics, Vol. 13, No. 5, 1998, pp. 435-462. List of variables wfood wfuel wcloth walc wtrans
= budget share for food expenditure = budget share for fuel expenditure = budget share for clothing expenditure = budget share for alcohol expenditure = budget share for transportation expenditure wother = budget share for other expenditures totexp = total household expenditure (rounded to the nearest 10 UK pounds sterling) income = total net household income (rounded to the nearest 10 UK pounds sterling) age = age of household head nk = number of children
GROUP TWO
The file london.xls is a cross section of 1,519 households drawn from the 1980-1982 British Family Expenditure Surveys. Data have been selected to include only households with one or two children living in Greater London. Self-employed and retired households have been excluded. The data were used by: Richard Blundell, Alan Duncan, and Krishna Pendakur, “Semiparametric Estimation and Consumer Demand,” Journal of Applied Econometrics, Vol. 13, No. 5, 1998, pp. 435-462. List of variables wfood wfuel wcloth walc wtrans
= budget share for food expenditure = budget share for fuel expenditure = budget share for clothing expenditure = budget share for alcohol expenditure = budget share for transportation expenditure wother = budget share for other expenditures totexp = total household expenditure (rounded to the nearest 10 UK pounds sterling) income = total net household income (rounded to the nearest 10 UK pounds sterling) age = age of household head nk = number of children
The budget share of a commodity, say fuel, is defined as expediture on fuel wfuel = total expenditure A functional form that has been popular for estimating expenditure functions for commodities is wfuel = β1 + β2ln(totexp) + e a Estimate this function for households with one child and households with two children. Report and comment on the results. b It can be shown that expenditure elasticity for fuel is given by β + β 2 [ln(totexp) + 1] η= 1 β1 + β 2ln(totexp) Find estimates of this elasticity for one- and twochildren households, evaluated at average total expenditure in each case. Do these estimates suggest fuel is a luxury or a necessity? (Are the elasticities greater than one or less than one?)
The budget share of a commodity, say food, is defined as expediture on food wfood = total expenditur e
GROUP THREE
GROUP FOUR
Problem 1: Consider the food expenditure and income data, i.e., file fdexin.xls. List of variables
Prepared by: John Amorante A Bao :: Economics Department of Xavier University-Ateneo de Cagayan :: 19th Sept 2008
yt xt
= food expenditure = weekly income
yt x and x *t = t . 100 100 b Estimate the following models and discuss the similarities and differences in the results: i Regress y on x ii Regress y on x* iii Regress y* on x iv Regress y* on x* a
Using your computer software (Excel®), create the variables y *t =
Problem 2: Does an increase in the concentration on arsenic in drinking water lead to an increase in the concentration of arsenic in toenails? These concentrations were measured in 15 wells and in toenail clippings from 15 corresponding people. The measurements in parts per million appear in the file arsen.xls. Let y = toenail concentration and x = water concentration. a Plot the following observations: i y against x ii ln(y) against ln(x) iii y against ln(x) iv ln(y) against x ln = natural logarithm Based on these plots, what functional form would you choose for relating y to x? Choose from listed in part (a). b
Estimate the following equations: i yt = β1 + β2xt + et ii ln(yt) = α1 + α2ln(xt) + et iii yt = λ1 + λ2ln(xt) + et iv ln(yt) = θ1 + θ2xt + et Report the results. Does the level of arsenic in the water appear to influence the level of arsenic in the toenails?
GROUP FIVE
You wish to investigate how dietary habits change with age. In the file diet.xls you have observations on the following variables for 314 individuals: AGE: age in years FIBER: grams of fiber consumed per day CALORIES: number of calories consumed per day CHOL: cholesterol consumed in mg per day FAT: grams of fat consumed per day Estimate four equations with fiber, calories, cholesterol, and fat as the dependent variables and age as the explanatory variable. Report the results and explain what you have discovered. Do you think age is a good predictor for dietary intake?
GROUP ONE
The Phillips curve says that the rate of change of money wages is a function of the reciprocal of the unemployment rate. Specifically, let wt = money wage rate in year t ut = unemployment rate in year t w − w t −1 %∆w t = t × 100 = percentage rate of w t −1 change in the wage rate The Phillips curve is given by 1 + et ut where it is hypothesized that β1 < 0 and β2 > 0. Using the observations on aggregate data given in the file phillips.xls: a Find least squares estimates for β1 and β2. b Test whether there is a relationship between %∆w and (1/u). c Draw a graph of the estimated relationship with u on the horizontal axis and %∆w on the vertical axis. d Find the estimate for the “natural rate of unemployment” (the natural rate of unemployment is the rate for which %∆w = 0). e Find estimates for d(%∆w)/du when u = 1 and when u = 3. f When does a change in the unemployment rate have the greatest impact on the rate of change in wages? When does it have the smallest? g What is the economic meaning of β1 and what is suggested by its estimate b1? h Find 95 percent interval estimates for β1 and β2. %∆w t = β1 + β 2
A functional form that has been popular for estimating expenditure functions for commodities is wfood = β1 + β2ln(totexp) + e a Estimate this function for households with one child and households with two children. Report and comment on the results. b It can be shown that expenditure elasticity for food is given by β + β 2 [ln(totexp) + 1] η= 1 β1 + β 2 ln(totexp) Find estimates of this elasticity for one- and twochildren households, evaluated at average total expenditure in each case. Do these estimates suggest food is a luxury or a necessity? (Are the elasticities greater than one or less than one?)
The file london.xls is a cross section of 1,519 households drawn from the 1980-1982 British Family Expenditure Surveys. Data have been selected to include only households with one or two children living in Greater London. Self-employed and retired households have been excluded. The data were used by: Richard Blundell, Alan Duncan, and Krishna Pendakur, “Semiparametric Estimation and Consumer Demand,” Journal of Applied Econometrics, Vol. 13, No. 5, 1998, pp. 435-462. List of variables wfood wfuel wcloth walc wtrans
= budget share for food expenditure = budget share for fuel expenditure = budget share for clothing expenditure = budget share for alcohol expenditure = budget share for transportation expenditure wother = budget share for other expenditures totexp = total household expenditure (rounded to the nearest 10 UK pounds sterling) income = total net household income (rounded to the nearest 10 UK pounds sterling) age = age of household head nk = number of children
GROUP TWO
The file london.xls is a cross section of 1,519 households drawn from the 1980-1982 British Family Expenditure Surveys. Data have been selected to include only households with one or two children living in Greater London. Self-employed and retired households have been excluded. The data were used by: Richard Blundell, Alan Duncan, and Krishna Pendakur, “Semiparametric Estimation and Consumer Demand,” Journal of Applied Econometrics, Vol. 13, No. 5, 1998, pp. 435-462. List of variables wfood wfuel wcloth walc wtrans
= budget share for food expenditure = budget share for fuel expenditure = budget share for clothing expenditure = budget share for alcohol expenditure = budget share for transportation expenditure wother = budget share for other expenditures totexp = total household expenditure (rounded to the nearest 10 UK pounds sterling) income = total net household income (rounded to the nearest 10 UK pounds sterling) age = age of household head nk = number of children
The budget share of a commodity, say fuel, is defined as expediture on fuel wfuel = total expenditure A functional form that has been popular for estimating expenditure functions for commodities is wfuel = β1 + β2ln(totexp) + e a Estimate this function for households with one child and households with two children. Report and comment on the results. b It can be shown that expenditure elasticity for fuel is given by β + β 2 [ln(totexp) + 1] η= 1 β1 + β 2ln(totexp) Find estimates of this elasticity for one- and twochildren households, evaluated at average total expenditure in each case. Do these estimates suggest fuel is a luxury or a necessity? (Are the elasticities greater than one or less than one?)
The budget share of a commodity, say food, is defined as expediture on food wfood = total expenditur e
GROUP THREE
GROUP FOUR
Problem 1: Consider the food expenditure and income data, i.e., file fdexin.xls. List of variables
Prepared by: John Amorante A Bao :: Economics Department of Xavier University-Ateneo de Cagayan :: 19th Sept 2008
yt xt
= food expenditure = weekly income
yt x and x *t = t . 100 100 b Estimate the following models and discuss the similarities and differences in the results: i Regress y on x ii Regress y on x* iii Regress y* on x iv Regress y* on x* a
Using your computer software (Excel®), create the variables y *t =
Problem 2: Does an increase in the concentration on arsenic in drinking water lead to an increase in the concentration of arsenic in toenails? These concentrations were measured in 15 wells and in toenail clippings from 15 corresponding people. The measurements in parts per million appear in the file arsen.xls. Let y = toenail concentration and x = water concentration. a Plot the following observations: i y against x ii ln(y) against ln(x) iii y against ln(x) iv ln(y) against x ln = natural logarithm Based on these plots, what functional form would you choose for relating y to x? Choose from listed in part (a). b
Estimate the following equations: i yt = β1 + β2xt + et ii ln(yt) = α1 + α2ln(xt) + et iii yt = λ1 + λ2ln(xt) + et iv ln(yt) = θ1 + θ2xt + et Report the results. Does the level of arsenic in the water appear to influence the level of arsenic in the toenails?
GROUP FIVE
You wish to investigate how dietary habits change with age. In the file diet.xls you have observations on the following variables for 314 individuals: AGE: age in years FIBER: grams of fiber consumed per day CALORIES: number of calories consumed per day CHOL: cholesterol consumed in mg per day FAT: grams of fat consumed per day Estimate four equations with fiber, calories, cholesterol, and fat as the dependent variables and age as the explanatory variable. Report the results and explain what you have discovered. Do you think age is a good predictor for dietary intake?
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