What are the 5 steps in demand estimation?
- identification of variables
- collection of data
- specification of the demand model
- estimation of the parameters of the model
- development of forecasts based on the model
Linear*
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Multiplicative*
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Simple linear regression assumptions**
- Y is a random variable whose distribution depends on the value of X, which is measured without error
- There is a linear relationship between the expected value of Y and each possible value of X…i.e. E(Y|X) = a + BX
- The actual value of Y associated with each value of X is some of E(Y|X) and a stochastic error term E…i.e. Y = E(Y|X) + E = a + BX + E
- The error term has the following properties for all observations: **
Simple regression model*
Q = a + BP + E
What does R^2 mean in simple regression?
That the model explains XX% of the total variation of Q
What does the F significance in simple regression tell us?
We are essentially XX% sure the model predicts better than the sample mean of Q
T-statistics, how to find* and what it tells us.
t = ( B - Bb) / se
2 sided: |t-stat| > critical value = reject Ho
1 sided: t-stat < -critical value, if hypothesizing ‘-‘ coefficient
Multiple linear regression (assumptions continued)
- The number of observations (n) must exceed the number of parameters to be estimated (m+1)
- There is no exact linear relationship among any of the independent variables
Multiple linear regression*
Q = a + B1P + B2Y + B3T + E
could have 3 different prices instead of time and income affecting it
Multiple linear regression elasticity of demand*
E(Q,P) = (dQ/dP) * (P/E(Q|P)) = B1 * (P/E(Q|P))
Multiplicative exponential model*
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Semilogarithmic model*
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Reciprocal model*
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Polynomial model*
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Exponential smoothing*
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Autocorrelation
Error terms are correlated over time, space, etc
- Parameter estimates are unbiased, but estimates of standard error are biased we lose efficiency
Heteroscedasticity
Error terms do not have constant variance
- parameter estimates are unbiased, but estimates of se are biased we lose efficiency
Measurement error
Random errors in measuring an explanatory variable or the dependent variable
- if measurement errors are correlated with an explanatory variable regression results are biased
- measurement errors in dependent variable are reflected in se of error term
Multicollinearity
A high degree of correlation among explanatory variables
- results are not biases, but its difficult to sort out effects of each variable
- overall, model has good explanatory power, but few explanatory variables are statistically significant
Simultaneous equation relationships
The dependent variable and one or more explanatory variables are simultaneously determined - i.e. price and quantity are simultaneously determined in a supply-demand system
- challenge is to recognize interdependence, then specify a model that takes it into account. adding other demand-supply shifters in one way to address this
RMSE****
Standard deviation - always pos***
What is the main difference between the linear and growth model?
linear shows a constant unit change, growth shows a % change
