Fortran Toolkit

`olsreg`

subroutine olsreg(coeffs,yvar,xvar1,xvar2,...,xvar8,w,mask,table,stds)
  implicit none
  real(kind=8) , intent(out)            :: coeffs(:)
  logical      , intent(out) , optional :: stds(:)
  real(kind=8) , intent(in)             :: yvar(:)
  real(kind=8) , intent(in)             :: xvar1(:)
  real(kind=8) , intent(in) , optional  :: xvar2(:),xvar3(:),...,xvar8(:)
  real(kind=8) , intent(in) , optional  :: w(:)     
  logical      , intent(in) , optional  :: mask(:)
  logical      , intent(in) , optional  :: table

This subroutine returns the OLS coefficients from a linear regression model:

\[\texttt{yvar} = \beta_0 + \beta_1 \cdot \texttt{xvar1} + \beta_2 \cdot\texttt{xvar2} + ... + \beta_8 \cdot\texttt{xvar8} + u\]

The subroutine allows up to 8 explanatory variables. The subroutine automatically includes a constant terms if size(coeffs) equals n+1, where n is the number of explanatory variables. The user can supply a vector of weights, w of the same size as yvar. If not supplied, the program assums uniform weigthing.

The user can also supply a mask to compute the impose a condition. The input mask is a logical array of the same size of yvar. For example:

call olsreg(coeffs,yvar,xvar1,xvar2,mask = xvar1.gt.0.0d0 .and. xvar2.lt.5.0d0)

This code computes the OLS coefficients from a linear regression of yvar on xvar1 and xvar2 conditional on xvar1 being positive and xvar2 being smaller than 5. If coeffs is of size 3, the model includes a contant term so that $\texttt{coeffs} = (\beta_0,\beta_1,\beta_2)$. If the size of coefs is 2, then the returned vector is $\texttt{coeffs} = (\beta_1,\beta_2)$.

Finally, the variable table controls the output of the subroutine. If table is .false. (or missing), the subroutine returns the coefficients in the vector coeffs. If table is .true., the subroutine prints a regression table with the coefficients and some additional statistics (t-stats, R-squared, etc).

Internal dependencies: error, varmean, varvar, inverse, transmat, diag

Example

Imagine we have three vectors (x0, x1, x2, x3) each with 100 normal random numbers (all with mean zero). And we define a vector y such that

\[\texttt{y} = 0.10 + \texttt{x0} + 0.7\cdot\texttt{x1} - 0.5\cdot \texttt{x2} + 0.2\cdot\texttt{x3}\]

We want to estimate the following regression model

\[\texttt{y} = \beta_0 + \beta_1 \cdot \texttt{x1} + \beta_2 \cdot\texttt{x2} + \beta_3 \cdot\texttt{x3} + u\]

To do so we first define a vector coeffs of dimension 4 and the run:

real(kind=8) :: coeffs(4)

call olsreg(coeffs,y,x1,x2,x3)

! coeffs = (/ 0.1000 , 0.7265 , -0.4519 , 0.2535 /)

if we add a vector of dimension 4 to stds, the subroutine also returns the standard deviations of the coefficients:

real(kind=8) :: coeffs(4)
real(kind=8) :: stds(4)

call olsreg(coeffs,y,x1,x2,x3,stds=stds)

! coeffs = (/ 0.1000 , 0.7265 , -0.4519 , 0.2535 /)
! stds   = (/ 0.0311 , 0.0839 , 0.0664 , 0.0526 /)

If we specify table = .true., the command prints the following:

call olsreg(coeffs,y,x1,x2,x3,table=.true.)

! Output:
!
!                               Number of variables =       4
!                            Number of observations =     100
!                      Number of valid observations =     100
!                                         R-squared =  0.6240
!                                Adjusted R-squared =  0.6122
!   
! -----------------------------------------------------------
!                beta     sd(b)      minb      maxb    t-stat
! -----------------------------------------------------------
! Constant     0.1000    0.0311    0.0390    0.1610    3.2141
! Var 1        0.8205    0.0839    0.6560    0.9850    9.7767
! Var 2       -0.4489    0.0664   -0.5791   -0.3187    6.7593
! Var 3        0.1603    0.0526    0.0571    0.2635    3.0456
! -----------------------------------------------------------

If we want to run the same regression model without a constant, we just define the vector coeffs to have dimension 3.

real(kind=8) :: coeffs(3)

call olsreg(coeffs,y,x1,x2,x3)

! coeffs = (/ 0.7265 , -0.4519 , 0.2535 /)

call olsreg(coeffs,y,x1,x2,x3,table=.true.)

! Output:
!   
!                               Number of variables =       3
!                             Number of observatios =     100
!                       Number of valid observatios =     100
!                                         R-squared =  0.5997
!                                Adjusted R-squared =  0.5915
!   
! -----------------------------------------------------------
!                beta     sd(b)      minb      maxb    t-stat
! -----------------------------------------------------------
! Var 1        0.8205    0.0879    0.6483    0.9927    9.3379
! Var 2       -0.4489    0.0695   -0.5852   -0.3126    6.4560
! Var 3        0.1603    0.0551    0.0523    0.2683    2.9089
! -----------------------------------------------------------

Note: the R-squared in a regression without a constant term is not well defined. This subroutine deals with this issue as Stata does. See the following thread for a discussion on this.

Foortran Toolkit

olsreg

`olsreg`