Functional forms of regression models

Different types of models

1. Log-linear (double-log)

2. Semilog

Log-linear (double log)

Is used to measure elasticity

Log-linear (double-log) Advantages:

1. Estimated in the same way as previous functions - in the same format

2. The hypothesis test are done in the same manner

3. Slope coefficients give the percentage change

Interpretation of log-linear (double log) - lnYt=-1.6524 + 0.3397lnXt+0.8460lnX

Intrepretation: If the total labour increases with 1%, a increase of 0.34% in GDP will occur ceteris paribus

Semilog model - Log-lin (lnY = B1+ B2X)

Y is logarithmic and X is linear

Used in growth models to determine the growth rate

Log-lin interpretation - lnUSpop = 5.3593 + 0.0107t

• Y is in log form, but not t (time)

Interpretation of B2 = B2 gives the percentage growth over time, thus population increases at an annual rate of 1.07%

Interpretation of B1 = B1 The population in the first period was 212.57 million people ( antilog of 5.3593)

Semi-log model: Lin-log

• Y is linear and x is logarithmic

Semi-log model: Lin-log - Y = B1 +B2lnX + u

• Y is not in log form, but B2 is

Semi-log model: Lin-log Interpretation - Y = -12564.8 + 1844.22lnX

Interpretation: If personal consumption expenditure increases by 1%, then average expenditure on serivces increases by 18.44 billion dollars