Question

consider the following regression

ln(GDP) = 0.80 + 0.70 ln (M2V) + 0.10 ln (debt)

where GDP = Gross National Product

M2V = velocity of money

debt = National debt

choose the correct interpretation of the coefficient of debt

		if debt increase by 1 unit, GDP will increase by 0.10 units, assuming all other variables remain constant.
		if debt increases by 1 unit, GDP will increase by 0.10 %, assuming all other variables remain constant.
		if debt increases by 1%, GDP will increase by 0.10 %, assuming all other variables remain constant.
		if debt increases by 1%, GDP will increase by 10%, assuming all other variables remain constant.

consider the following regression

ln(GDP) = 4.68 + 1.5 (M2V) + 0.0007 saving

where GDP = Gross National Product

M2V = velocity of money

Saving = National Saving

choose the correct interpretation of the coefficient of debt

		if M2V increase by 1 unit, GDP will increase by 1.5 units, assuming all other variables remain constant.
		if M2V increases by 1 unit, GDP will increase by 1.5%, assuming all other variables remain constant.
		if M2V increases by 1 unit, GDP will increase by 150%, assuming all other variables remain constant.
		if M2V increases by 1% unit, GDP will increase by 1.5%, assuming all other variables remain constant.

Answer 1

ln(GDP) = 0.80 + 0.70 ln (M2V) + 0.10 ln (debt)

Assuming Current GDP = GDP1

debt = debt1

When all other variables remain constant,

= 0.80 + 0.70 ln (M2V) + 0.10 ln (debt1) ----------------- Equation (1)

After Change

GDP = GDP2

debt = debt2

When all other variables remain constant,

ln(GDP2) = 0.80 + 0.70 ln (M2V) + 0.10 ln (debt2)   ----------------- Equation (2)

Solving  Equation (2) - Equation (1)

ln(GDP2) -  ln(GDP1) = { 0.80 + 0.70 ln (M2V) + 0.10 ln (debt2) } - {0.80 + 0.70 ln (M2V) + 0.10 ln (debt1) }

ln(GDP2) -  ln(GDP1) = 0.10 ln (debt2) -  0.10 ln (debt1)

ln (GDP2/GDP1) = 0.1 ln (debt2 / debt1)

1% increase debt,  debt2 = 1.01  debt1

ln (GDP2/GDP1) = 0.1 ln (1.01) = 0.1 * 0.009950

(GDP2/GDP1) = e ^ (0.0009950) (Applying reverse log both side)

(GDP2/GDP1) = 1.000995495

(GDP2  - GDP1)/  GDP1 = 0.000995495   = 0.09954% ~ 0.01%

Change in GDP 0.01%

So,

Ans : if debt increases by 1%, GDP will increase by 0.10 %, assuming all other variables remain constant.