ECO 550 Chapter 4—Estimating Demand

Chapter 4—Estimating Demand

MULTIPLE CHOICE
    
1.    Using a sample of 100 consumers, a double-log regression model was used to estimate demand for gasoline.  Standard errors of the coefficients appear in the parentheses below the coefficients.

Ln Q = 2.45 -0.67 Ln P + . 45 Ln Y  - .34 Ln Pcars
                                (.20)        (.10)        (.25)
    
Where Q is gallons demanded, P is price per gallon, Y is disposable income, and Pcars is a price index for cars.  Based on this information, which is NOT correct?
a.    Gasoline is inelastic.
b.    Gasoline is a normal good.
c.    Cars and gasoline appear to be mild complements.
d.    The coefficient on the price of cars (Pcars) is insignificant.
e.    All of the coefficients are insignificant.

2.    In a cross section regression of 48 states, the following linear demand for per-capita cans of soda was found:  Cans = 159.17 – 102.56 Price + 1.00 Income + 3.94Temp

     Coefficients    Standard Error    t Stat
Intercept    159.17    94.16    1.69
Price    -102.56    33.25    -3.08
Income    1.00    1.77    0.57
Temperature    3.94    0.82    4.83

    R-Sq = 54.1%     R-Sq(adj) = 51.0%

From the linear regression results in the cans case above, we know that:
a.    Price is insignificant
b.    Income is significant
c.    Temp is significant
d.    As price rises for soda, people tend to drink less of it
e.    All of the coefficients are significant

3.    A study of expenditures on food in cities resulting in the following equation:
    Log E = 0.693 Log Y + 0.224 Log N
where E is Food Expenditures; Y is total expenditures on goods and services; and N is the size of the family. This evidence implies:
a.    that as total expenditures on goods and services rises, food expenditures falls.
b.    that a one-percent increase in family size increases food expenditures .693%.
c.    that a one-percent increase in family size increases food expenditures .224%.
d.    that a one-percent increase in total expenditures increases food expenditures 1%. 
e.    that as family size increases, food expenditures go down.

    4.    All of the following are reasons why an association relationship may not imply a causal relationship except:
a.    the association may be due to pure chance
b.    the association may be the result of the influence of a third common factor
c.    both variables may be the cause and the effect at the same time
d.    the association may be hypothetical
e.    both c and d

5.        In regression analysis, the existence of a significant pattern in successive values of the error term constitutes:
a.    heteroscedasticity
b.    autocorrelation
c.    multicollinearity
d.    nonlinearities
e.    a simultaneous equation relationship

    6.    In regression analysis, the existence of a high degree of intercorrelation among some or all of the explanatory variables in the regression equation constitutes:
a.    autocorrelation
b.    a simultaneous equation relationship
c.    nonlinearities
d.    heteroscedasticity
e.    multicollinearity

    7.    When using a multiplicative power function (Y = a X1b1 X2b2 X3b3) to represent an economic relationship, estimates of the parameters (a, and the b's) using linear regression analysis can be obtained by first applying a ____ transformation to convert the function to a linear relationship.
a.    semilogarithmic
b.    double-logarithmic
c.    reciprocal
d.    polynomial
e.    cubic

    8.    The correlation coefficient ranges in value between 0.0 and 1.0.
a.    true
b.    false

    9.    The coefficient of determination ranges in value between 0.0 and 1.0.
a.    true
b.    false

    10.    The coefficient of determination measures the proportion of the variation in the independent variable that is "explained" by the regression line.
a.    true
b.    false

11.    The presence of association between two variables does not necessarily imply causation for the following reason(s):
a.    the association between two variables may result simply from pure chance
b.    the association between two variables may be the result of the influence of a third common factor
c.    both variables may be the cause and the effect at the same time
d.    a and b
e.    a, b, and c

    12.    The estimated slope coefficient (b) of the regression equation (Ln Y = a + b Ln X) measures the ____ change in Y for a one ____ change in X.
a.    percentage, unit
b.    percentage, percent
c.    unit, unit
d.    unit, percent
e.    none of the above

    13.    The standard deviation of the error terms in an estimated regression equation is known as:
a.    coefficient of determination
b.    correlation coefficient
c.    Durbin-Watson statistic
d.    standard error of the estimate
e.    none of the above

    14.    In testing whether each individual independent variables (Xs) in a multiple regression equation is statistically significant in explaining the dependent variable (Y), one uses the:
a.    F-test
b.    Durbin-Watson test
c.    t-test
d.    z-test
e.    none of the above

    15.    One commonly used test in checking for the presence of autocorrelation when working with time series data is the ____.
a.    F-test
b.    Durbin-Watson test
c.    t-test
d.    z-test
e.    none of the above

    16.    The method which can give some information in estimating demand of a product that hasn’t yet come to market is:
a.    the consumer survey
b.    market experimentation
c.    a statistical demand analysis
d.    plotting the data
e.    the barometric method

    17.    Demand functions in the multiplicative form are most common for all of the following reasons except:
a.    elasticities are constant over a range of data
b.    ease of estimation of elasticities
c.    exponents of parameters are the elasticities of those variables
d.    marginal impact of a unit change in an individual variable is constant
e.    c and d

    18.    The Identification Problem in the development of a demand function is a result of:
a.    the variance of the demand elasticity
b.    the consistency of quantity demanded at any given point
c.    the negative slope of the demand function
d.    the simultaneous relationship between the demand and supply functions
e.    none of the above

    19.    Consider the following linear demand function where QD = quantity demanded, P = selling price, and Y = disposable income:

          QD = 36 2.1P + .24Y

The coefficient of P (i.e., 2.1) indicates that (all other things being held constant):
a.    for a one percent increase in price, quantity demanded would decline by 2.1 percent
b.    for a one unit increase in price, quantity demanded would decline by 2.1 units
c.    for a one percent increase in price, quantity demanded would decline by 2.1 units
d.    for a one unit increase in price, quantity demanded would decline by 2.1 percent
e.    none of the above

20.    Consider the following multiplicative demand function where QD = quantity demanded, P = selling price, and Y = disposable income:

The coefficient of Y (i.e., .2) indicates that (all other things being held constant):
a.    for a one percent increase in disposable income, quantity demanded would increase by .2 percent
b.    for a one unit increase in disposable income, quantity demanded would increase by .2 units
c.    for a one percent increase in disposable income quantity demanded would increase by .2 units
d.    for a one unit increase in disposable income, quantity demanded would increase by .2 percent
e.    none of the above

    21.    One shortcoming of the use of ____ in demand analysis is that the participants are generally aware that their actions are being observed and hence they may seek to act in a manner somewhat different than normal.
a.    market experiments
b.    consumer clinics
c.    statistical (econometric) methods
d.    a and b
e.    none of the above

    22.    The constant or intercept term in a statistical demand study represents the quantity demanded when all independent variables are equal to:
a.    1.0
b.    their minimum values
c.    their average values
d.    0.0
e.    none of the above

    
23.    Novo Nordisk A/S, a Danish firm, sells insulin and other drugs worldwide. Activella, an estrogen and progestin hormone replacement therapy sold by Novo-Nordisk, is examined using 33 quarters of data
Y = -204 + . 34X1 - .17X2
                (17.0)     (-1.71)
Where Y is quarterly sales of Activella, X1 is the Novo’s advertising of the hormone therapy, and X2 is advertising of a similar product by Eli Lilly and Company, Novo-Nordisk’s chief competitor. The parentheses contain t-values. Addition information is: Durbin-Watson = 1.9 and R2 = .89.

Using the data for Novo-Nordisk, which is correct?
a.    Both X1 and X2 are statistically significant.
b.    Neither X1 nor X2 are statistically significant.
c.    X1 is statistically significant but X2 is not statistically significant.
d.    X1 is not statistically significant but X2 is statistically significant.
e.    The Durbin-Watson statistic shows significant problems with autocorrelation

24.    In which of the following econometric problems do we find Durbin-Watson statistic being far away from 2.0?
a.    the identification problem
b.    autocorrelation
c.    multicollinearity
d.    heteroscedasticity
e.    agency problems

25.    When there is multicollinearity in an estimated regression equation,
     a.    the coefficients are likely to be small.
     b.    the t statistics are likely to be small even though the R2 is large.
     c.    the coefficient of determination is likely to be small.
    d.    the problem of omitted variables is likely.
    e.    the error terms will tend to have a cyclical pattern.

26.    When two or more "independent" variables are highly correlated, then we have:
a.    the identification problem
b.    multicollinearity
c.    autocorrelation
d.    heteroscedasticity
e.    complementary products

27.    Which is NOT true about the coefficient of determination?
a.    As you add more variables, the R-square generally rises.
b.    As you add more variables, the adjusted R-square can fall.
    c.    If the R-square is above 50%, the regression is considered significant.
d.    The R-square gives the percent of the variation in the dependent variable that is explained by the independent variables.
e.    The higher is the R-square, the better is the fit.

PROBLEMS

    1.    Phoenix Lumber Company uses the number of construction permits issued to help estimate demand (sales). The firm collected the following data on annual sales and number of construction permits issued in its market area:

    No. of Construction    Sales
Year    Permits Issued (000)    (1,000,000)
        
2003    6.50    10.30
2004    6.20    10.10
2005    6.60    10.50
2006    7.30    10.80
2007    7.80    11.20
2008    8.20    11.40
2009    8.30    11.30

(a)    Which variable is the dependent variable and which is the independent variable?
(b)    Determine the estimated regression line.
(c)    Test the hypothesis (at the .05 significance level) that there is no relationship between the variables.
(d)    Calculate the coefficient of determination. Give an economic interpretation to the value obtained.
(e)    Perform an analysis of variance on the regression including an F-test (at the .05 significance level) of the overall significance of the results.
(f)    Suppose that 8,000 construction permits are expected to be issued in 2010. What would be the point estimate of Phoenix Lumber Company's sales for 2010?

    2.    Lenny's, a national restaurant chain, conducted a study of the factors affecting demand (sales). The following variables were defined and measured for a random sample of 30 of its restaurants:

Y    = Annual restaurant sales ($000)
X1    = Disposable personal income (per capita) of residents within 5 mile radius
X2    = License to sell beer/wine (0 = No, 1 = Yes)
X3    = Location (within one-half mile of interstate highway--0 = No, 1 = Yes)
X4    = Population (within 5 mile radius)
X5    = Number of competing restaurants within 2 mile radius

The data were entered into a computerized regression program and the following results were obtained:

MULTIPLE R    .889
R-SQUARE    .79
STD. ERROR OF EST.    .40

ANALYSIS OF VARIANCE
                
    DF    Sum Squares    Mean Sqr.    F-Stat
Regression    5    326.13    65.226    18.17
Error    24    86.17    3.590    
Total    29    412.30        

Variable    Coefficient    Std. Error    T-Value
            
Constant          .363          .196    1.852
X-1              .00275              .00104    2.644
X-2    76.65    93.70      .818
X-3    164.3        235.4          .698
X-4              .00331              .00126    2.627
X-5    46.2      12.1      3.818  

Questions:

(a)    Give the regression equation for predicting restaurant sales.
(b)    Give an interpretation of each of the estimated regression coefficients.
(c)    Which of the independent variables (if any) are statistically significant at the .05 level in "explaining" restaurant sales?
(d)    What proportion of the variation in restaurant sales is "explained" by the regression equation?
(e)    Perform an F-test (at the .05 significance level) of the overall explanatory power of the regression model.

    3.    The following demand function has been estimated for Fantasy pinball machines:

          QD = 3,500  40P + 17.5Px + 670U + .0090A + 6,500N

where    P = monthly rental price of Fantasy pinball machines
    Px = monthly rental price of Old Chicago pinball machines (their largest competitor)
    U = current unemployment rate in the 10 largest metropolitan areas
    A = advertising expenditures for Fantasy pinball machines
    N = fraction of the U.S. population between ages 10 and 30

(a)    What is the point price elasticity of demand for Fantasy pinball machines when P = $150, Px = $100, U = .12, A = $200,000 and N = .35?
(b)    What is the point cross elasticity of demand with respect to Old Chicago pinball machines for the values of the independent variables given in part (a)?

    4.    Given the following demand function:
          Q = 2.0 P1.33 Y2.0 A.50

where    Q = quantity demanded (thousands of units)
    P = price ($/unit)
    Y = disposable income per capita ($ thousands)
    A = advertising expenditures ($ thousands)

determine the following when P = $2/unit, Y = $8 (i.e., $8000), and A = $25 (i.e., $25,000)

(a)    Price elasticity of demand
(b)    The approximate percentage increase in demand if disposable income percentage increases by 3%.
(c)    The approximate percentage increase in demand if advertising expenditures are increased by 5 percent.