Transcript Chapter 3: Supply and Demand - Vancouver Island University

Demand Estimation
and Forecasting
• Regression Analysis
• Problems in Use of Regression
Analysis
• Subjects of Forecasts
• Prerequisites of a Good Forecast
• Forecasting Techniques
Learning Objectives
• Specify components of a regression
model that can be used to estimate a
demand equation
• Interpret regression results
• Explain meaning of R2
• Evaluate statistical significance of
regression coefficients using t-test
and statistical significance of R2
using F-test
Learning Objectives
• Recognize challenges of obtaining
reliable cross-sectional and time
series data on consumer behavior
that can be used in regression models
of demand
• Understand importance of
forecasting in business
• Describe six different forecasting
techniques
Learning Objectives
• Show how to carry out least squares
projections and decompose them into
trends, seasonal, cyclical, and
irregular movements
• Explain basic smoothing methods of
forecasting, such as moving average
and exponential smoothing
Data Collection
• Data for studies pertaining to countries,
regions, or industries are readily available
and reliable.
• Data for analysis of specific product
categories may be more difficult to obtain.
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Buy from data providers (e.g. ACNielsen, IRI)
Perform a consumer survey
Focus groups
Technology: Point-of-sale, bar codes, RFID
Regression Analysis
• One use is for estimating demand
functions.
• Important terminology and concepts:
– Least Squares Regression: Y = a + bX +
e.
– Confidence Intervals.
– t-statistic.
– R-square or Coefficient of
Determination.
– F-statistic.
Regression Analysis
• Regression Analysis: A procedure
commonly used by economists to
estimate consumer demand with
available data.
– Cross-Sectional Data: provide
information on variables for a given
period of time.
– Time Series Data: give information
about variables over a number of
periods of time.
Regression Analysis
• Regression equation: linear, additive
– Y = a + b1X1 + b2X2 + b3X3 + b4X4
– Y: dependent variable, amount to be
determined
– a: constant value, y-intercept
– Xn: independent, explanatory variables, used to
explain the variation in the dependent variable
– bn: regression coefficients (measure impact of
independent variables)
Regression Analysis
• Regression Results
– Negative coefficient shows that as the
independent variable (Xn) changes, the quantity
demanded changes in the opposite direction.
– Positive coefficient shows that as the
independent variable (Xn) changes, the quantity
demanded changes in the same direction.
– Magnitude of regression coefficients is
measured by elasticity of each variable.
Regression Analysis
• Statistical evaluation of regression results
– t-test: test of statistical significance of each
estimated regression coefficient
ˆ
b
t
SE bˆ
– b: estimated coefficient
– SEb: standard error of the estimated
coefficient
– Rule of 2: if absolute value of t is greater than
2, estimated coefficient is significant at the
5% level
– If coefficient passes t-test, the variable has a
true impact on demand
Regression Analysis
• Statistical evaluation of regression results
– Coefficient of determination (R2): percentage
of variation in the dependent variable (Y)
accounted for by variation in all explanatory
variables (Xn)
• Value ranges from 0.0 to 1.0
• Closer to 1.0, the greater the explanatory power of
the regression equation
– F-test: measures statistical significance of the
entire regression as a whole (not each
coefficient)
Regression Results
• Steps for analyzing regression
results
– Check signs and magnitudes
– Compute elasticity coefficients
– Determine statistical significance
Regression Problems
• Identification Problem: The
estimation of demand may produce
biased results due to simultaneous
shifting of supply and demand curves.
• Advanced estimation techniques,
such as two-stage least squares and
indirect least squares, are used to
correct this problem.
Regression Problems
• Multicollinearity: two or more independent
variables are highly correlated, thus it is
difficult to separate the effect each has
on the dependent variable.
• Passing the F-test as a whole, but failing
the t-test for each coefficient is a sign
that multicollinearity exists.
• A standard remedy is to drop one of the
closely related independent variables from
the regression.
Problems
• Autocorrelation: also known as serial correlation,
occurs when the dependent variable relates to the
independent variable according to a certain
pattern.
• Possible causes:
– Effects on dependent variable exist that are not
accounted for by the independent variables.
– The relationship may be non-linear
• The Durbin-Watson statistic is used to identify
the presence of autocorrelation.
• To correct autocorrelation consider:
– Transforming the data into a different order of
magnitude
– Introducing leading or lagging data
An Example
• Use a spreadsheet to estimate the
following log-linear demand function.
ln Qx  0   x ln Px  e
Summary Output
Regression Statistics
Multiple R
0.41
R Square
0.17
Adjusted R Square
0.15
Standard Error
0.68
Observations
41.00
ANOVA
df
Regression
Residual
Total
Intercept
ln(P)
SS
1.00
39.00
40.00
MS
F
3.65
18.13
21.78
Coefficients Standard Error
7.58
1.43
-0.84
0.30
3.65
0.46
t Stat
5.29
-2.80
Significance F
7.85
0.01
P-value
0.000005
0.007868
Lower 95%
Upper 95%
4.68
10.48
-1.44
-0.23
Interpreting the
Regression Output
• The estimated log-linear demand function
is:
– ln(Qx) = 7.58 - 0.84 ln(Px).
– Own price elasticity: -0.84 (inelastic).
• How good is our estimate?
– t-statistics of 5.29 and -2.80 indicate that the
estimated coefficients are statistically
different from zero.
– R-square of .17 indicates we explained only 17
percent of the variation in ln(Qx).
– F-statistic significant at the 1 percent level.
Subjects of Forecasts
• Gross Domestic Product (GDP)
• Components of GDP
– E.g. consumption expenditure, producer
durable equipment expenditure,
residential construction
• Industry Forecasts
– Sales of products across an industry
• Sales of a specific product
Prerequisites of a Good
Forecast
• A good forecast should:
– be consistent with other parts of the
business
– be based on knowledge of the relevant
past
– consider the economic and political
environment as well as changes
– be timely
Forecasting Techniques
• Factors in choosing the right
forecasting technique:
– Item to be forecast
– Interaction of the situation with the
characteristics of available forecasting
methods
– Amount of historical data available
– Time allowed to prepare forecast
Forecasting Techniques
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Expert opinion
Opinion polls and market research
Surveys of spending plans
Economic indicators
Projections
Econometric models
Forecasting Techniques
• Qualitative forecasting is based on
judgments of individuals or groups.
• Quantitative forecasting utilizes
significant amounts of prior data as a basis
for prediction.
• Naïve forecasting projects past data
without explaining future trends.
• Causal (or explanatory) forecasting
attempts to explain the functional
relationships between the dependent
variable and the independent variables.
Forecasting Techniques
• Expert opinion techniques
– Jury of executive opinion: Forecasts
generated by a group of corporate executives
assembled together. The major drawback is
that persons with strong personalities may
exercise disproportionate influence.
– The Delphi Method: A form of expert opinion
forecasting that uses a series of questions and
answers to obtain a consensus forecast, where
experts do not meet.
Forecasting Techniques
• Opinion polls: Sample populations are surveyed to
determine consumption trends.
– may identify changes in trends
– choice of sample is important
– questions must be simple and clear
• Market research is closely related to opinion
polling.
– Market research will indicate “not only why the
consumer is or is not buying, but also who the consumer
is, how he or she is using the product, and what
characteristics the consumer thinks are most important
in the purchasing decision.”
Forecasting Techniques
• Surveys of spending plans: seek
information about “macro-type” data
relating to the economy.
• Consumer intentions
– Survey of Consumers, Survey Research Center,
University of Michigan
– Consumer Confidence Survey, The Conference
Board
• Inventories and sales expectations
Forecasting Techniques
• Economic Indicators: A barometric
method of forecasting designed to
alert business to changes in economic
conditions.
– Leading, coincident, and lagging
indicators
– One indicator may not be very reliable,
but a composite of leading indicators
may be used for prediction.
Forecasting Techniques
• Leading Indicators predict changes in future economic
activity
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Average hours, manufacturing
Initial claims for unemployment insurance
Manufacturers’ new orders for consumer goods and materials
Vendor performance, slower deliveries diffusion index
Manufacturers’ new orders, nondefense capital goods
Building permits, new private housing units
Stock prices, 500 common stocks
Money supply, M2
Interest rate spread, 10-year Treasury bonds minus federal
funds
– Index of consumer expectations
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Forecasting
Techniques
Coincident Indicators identify peaks and troughs in economic
activity
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Employees on nonagricultural payrolls
Personal income less transfer payments
Industrial production
Manufacturing and trade sales
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Average duration of unemployment, weeks
Ratio, manufacturing and trade inventories to sales
Change in labor cost per unit of output, manufacturing (%)
Average prime rate charged by banks
Commercial and industrial loans outstanding
Ratio, consumer installment credit outstanding to personal income
Change in consumer price index for services
• Lagging Indicators confirm upturns and downturns in economic
activity
Forecasting Techniques
• General rule of thumb: if, after a
period of increases, the leading
indicator index sustains three
consecutive declines, a recession (or
a slowing) will follow.
• Economic indicators have predicted
each recession since 1948.
Forecasting Techniques
• Economic Indicators Drawbacks
– Leading indicator index has forecast a
recession when none ensued.
– A change in the index does not indicate
the precise size of the decline or
increase.
– The data are subject to revision in the
ensuing months.
Forecasting Techniques
• Trend projections: A form of naïve
forecasting that projects trends
from past data without taking into
consideration reasons for the change.
– Compound growth rate
– Visual time series projections
– Least squares time series projection
Forecasting Techniques
• Compound growth rate: Forecasting by
projecting the average growth rate of the
past into the future.
– Calculate the constant growth rate using
available data, then project this constant
growth rate into the future.
– Provides a relatively simple and timely forecast
– Appropriate when the variable to be predicted
increases at a constant percentage
Forecasting Techniques
• General compound growth rate formula:
E = B(1+i)n
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E = final value
n = years in the series
B = beginning value
i = constant growth rate
Forecasting Techniques
• Visual Time Series Projections:
plotting observations on a graph and
viewing the shape of the data and any
trends.
Forecasting Techniques
• Time series analysis: A naïve method of
forecasting from past data by using least
squares statistical methods.
• Data collected of a number of periods
usually exhibit certain characteristics:
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Trends
Cyclical fluctuations
Seasonal fluctuations
Irregular movements
Forecasting Techniques
• Time Series Analysis Advantages
– easy to calculate
– does not require much judgment or
analytical skill
– describes the best possible fit for past
data
– usually reasonably reliable in the short
run
Forecasting Techniques
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Yt = f(Tt, Ct, St, Rt)
Yt = Actual value of the data at time
t
Tt = Trend component at t
Ct = Cyclical component at t
St = Seasonal component at t
Rt = Random component at t
Additive form: Yt = Tt + Ct + St + Rt
Multiplicative form: Yt =
(Tt)(Ct)(St)(Rt)
Forecasting Techniques
• Must decompose the time series into
its four components
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Remove seasonality
Compute trend
Isolate cycle
Cannot do anything with random
component
Forecasting Techniques
• Seasonality: need to identify and
remove seasonal factors, using
moving averages to isolate those
factors.
• Remove seasonality by dividing data
by seasonal factor
Forecasting Techniques
• Trend Line: use least squares method
• Possible best-fit line styles:
– Straight Line: Y = a + b(t)
– Exponential Line: Y = abt
– Quadratic Line: Y = a + b(t) + c(t)2
• Choose style with a balance of high
R2 and high t-statistics
Forecasting Techniques
• Cycle and Random Elements
– Random factors cannot be predicted and
should be ignored
– Isolate cycle by smoothing with a moving
average
Forecasting Techniques
• Smoothing Techniques
– Moving Average
– Exponential Smoothing
• Work best when:
– No strong trend in series
– Infrequent changes in direction of
series
– Fluctuations are random rather than
seasonal or cyclical
Forecasting Techniques
• Moving Average: average of actual past
results used to forecast one period ahead
Et+1 = (Xt + Xt-1 + … + Xt-N+1)/N
• Et+1 : forecast for next period
• Xt, Xt-1 : actual values at their respective
times
• N: number of observations included in
average
Forecasting Techniques
• Exponential Smoothing: allows for
decreasing importance of information in
the more distant past, through geometric
progression
Et+1 = w·Xt + (1-w) · Et
• w: weight assigned to an actual observation
at period t
Forecasting Techniques
• Econometric Models: causal or
explanatory models of forecasting
– Regression analysis
– Multiple equation systems
• Endogenous variables: comparable to
dependent variables of single-equation
model, but may influence other endogenous
variables
• Exogenous variables: from outside the
system, truly independent variables