I can't seem to find the full explanation on Log-log models (measuring elasticities).
Hypothetical model is: ln(Y) = B0 + B1 ln(X1) + B2 ln(X2 )
WithY = Wealth; X1 = Income; X2 = #money your wife spends
Hypothetical outcome: ln(Y) = -7 + 3.7 ln(X1) - 0.85 ln(X2)
Now I understand that if X1 goes up by 1 percent my Y (= wealth) will go up by 3.7 percent.
- But where do you add that 3.7 percent to? What's your starting point?
- What is the interpretation of my intercept (-7)?
- Since this is all in percentages how do I calculate the absolute value?
Thanks for the help!
So according to you.. if for example, X1 has the value of 50 and X2 of 20 I'd get:
Y = e-7 ∙ 503.7 ∙ 200.85
Y = 138.11
Since I work with a log-log model (log-linear), should this be an absolute value?
Dear Elvedin,
In log log model the coefficients such as b1, b2 show the elasticizes, you can interpret the betas just like elasticity. e.g if Qd elasticity is -1 or cross price elasticity is 3.4 etc depending upon your variables x1, x2 you can interpret.
Dear Elvedin: Here are the appropriate interpretation of your estimates:
The correct interpretation of-7 is that it reflects the mean effect of variables not included in the model. For example, the technological effect has influenced Y, on average, negatively.
For X1 - For each,1 percentage increase in X1, y increases on average or ceteris paribus by 3. 7.
For X3, an increase in X3 by a percent leads to a decrease in Y of 0.8.
Regards,
Prof. Arize
Dear my friend,
In 3conomic science, a coefficient of a log-log model represents elasticity. You can use this point for your interpretation.
Yours,
Ehsan
in log log model (statistical model)
coefficient indicates elasticities (partial ). this has some limitation. this does not reflect flexibility. example when income change elasticity of demand change for every level of income. but this model does not show that.
intercept will be EXP(B0). you have to take atilog to find it
@ Sivarajasingham
Please don't you think "ceteris paribus assumption "is missing in your write-up? From an interpretational standpoint, what limitations are we missing econometrically?
Dear Sivarajasingham
You indeed introduced an important aspect of linearity versus non-linearity of the relationship being tested. It is true that elasticity will vary along a curve (non-linear), but the log-linear model still outshines curve-linear relations (at least theoretically) because it anticipates simultaneous interactions of inputs in the production process. You can think of production as any process, including consumption or investment or trade, in which several inputs "actively" influence the output of each other in the final outcomes.
Economic analysis all over forces us to make choices, based on theory and feasibility, and each has a shortcoming. And most of these shortcomings are more entrenched in theory than in empirical observations. What we defend in theory may actually be absent in practice. Think of the consumer of cabbages in a remote village. Impose the maxims of neoclassical utility maximisation on that illiterate buyer, consider the social institutions involved, and the whole argument in the theory collapses!
I don't know what other experts think, but I feel that economics is often done at the crossroads between overthinking economic realities and underrepresenting that reality, or between underestimating agents' reality and playing the genius. Just food for thought!
MS.
Thinking about elasticity computation, here's an interesting one on how rising life expectancy (X) might affect economic growth (Y). Policy interest lies in computing life expectancy elasticity of economic growth
log Y = a + b.log X + c.( log (X) squared) + other factors
where a, b, c are the appropriately estimated regression parameter estimates.
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