Question

For each of the models below, provide me with:

1. The functional form used (log-log, lin-lin, lin-log or log-lin)
2. Where the coefficients in bold is an elasticity, a semi-elasticity or none of them
3. The interpretation of the coefficient in bold, i.e. “if X (say the variable name) increases by 1 unit (or 1 %) then Y (say the variable name) increases (or decreases) by --- unit (or %)”.  

Model 1: ln (YIELDi) = 0.56 + 0.76 x RAINFALL - 2.24 x TEMPERATURE + ui

Model 2: YIELDi = 0.58 + 0.79 x RAINFALL - 2.20 x TEMPERATURE + ui

Model 3: YIELDi = 0.64 + 1.02 x ln (RAINFALL) - 2.15 x ln (TEMPERATURE) + ui

Model 4: ln (YIELDi) = 0.66 + 0.68 x ln(RAINFALL) - 1.80 x ln (TEMPERATURE) + ui

Answer 1

i) Model 1

The functional form used here is log-lin because all the regressors X are linear but Y has log attached to it.

Model 2

The functional form used here is lin-lin because all the regressors X are linear and Y is linear too.

Model 3

The functional form used here is lin- log because all the regressors X have log attached with them but Y is linear.

Model 4

The functional form used here is log- log because all the regressors X have log attached with them and even theresponse has log with it.

ii) As none of the coefficients are in Bold i'll interpret of all those in next part

iii) Model 1

if rainfall increases by 1 unit then ln(Yeild) increases by 0.76 unit”.  

if temperature increases by 1 unit then ln(Yeild) decreases by 2.24 units”

Model 2

if rainfall increases by 1 unit then Yeild increases by 0.79 unit”.

if temperature increases by 1 unit then Yeild decreases by 2.20 unit”.

Model 3

if ln(rainfall) increases by 1 unit then Yeild increases by 1.02 units”.

if ln(temperature) increases by 1 unit then Yeild decreases by 2.15 units” .

Model 4

if ln(rainfall) increases by 1 unit then ln(Yeild) increases by 0.68 units”.

if ln(temperature) increases by 1 unit then ln(Yeild) decreases by 1.80 units” .