The logit model has very similar properties, but had the early advantage of being easily differentiable.
There are more versions of these models to explain more complicated choices.
The logit model has very similar properties, but had the early advantage of being easily differentiable.
There are more versions of these models to explain more complicated choices.
A basic supply and demand model nicely illustrates the main concepts. There are two curves in the model, and a regression tries to fit one line to the data.
Details:
Here is how both curves shifting generates the data. Shifts in either curves change both price and quantity.
Exclusion restrictions that cause a given variable to shift just one curve help to identify the other curve.
Indirect least squares shows how we can recover estimates of the structural parameters from the reduced form parameters if exogenous variables are excluded from some equations.
If an equation is identified, we can calculate consistent parameter estimates using two-stage least squares.
The classic example of heteroskedasticity of a know form and the classic correction:
Avoiding obvious heteroskedasticity is often a matter of using a sensible functional form.
Using logarithms is also a common way to avoid obvious heteroskedasticity.
The ARCH model, which envisions serial correlation in the error variance, has been very popular in explaining volatility clustering in the financial markets.
The Cochrane-Orcutt estimation procedure alternates between estimating rho and estimating beta until the process converges.
The Durbin-Watson statistic is very nearly equal to 2(1-rho), where rho is the correlation between the current and lagged error residual.
A lagged dependent variable can induce dynamics very similar to those created by serially correlated errors. Distinguishing between the models is very difficult in practice.
Log scales are used for sound levels (decibels) and hurricane strengths. They also make sense for income.
How to construct normally distributed random numbers from uniformly distributed random numbers:
To justify these calculations
we need these assumptions and conclusions
The derivation looks something like this:
If the errors are serially correlated the derivation above is invalid because the covariance terms do not equal zero.
The bottom line is that the standard calculations assume that the errors are serially independent and, therefore, that the covariance terms can be dropped. If the errors are serially correlated, the formula for the standard error is wrong. Given that serial correlation tends to be positive, the standard error formula leaves out positive terms, causing the calculated result to be too small and causing the t ratio to be too large.
We can apply these ideas to the production functioin example.
