ORDINARY LINEAR REGRESSION: Given Yi: (y1, y2, ..., yn) dependent variable and Xi: (x1, x2, ..., xn). The simple linear regression of Y and X is simply Y = a + bX where the parameter b explains the relationship between Y and X. This measurement is a measure of direct linear relationship between Y and X.
TOBIT REGRESSION: In TOBIT, the measured relationship is not b. Tobit assumes that there is a latent relationship between non-negative Y and X which may be measured by Y* = a + BX + ui where ui is normally distributed. Y* is not observable whereas in the prior case of ordinary regression Y is observable. Moreover, B could not accurately be estimated by Y = a = bX because the slope would be underestimated and the intercept would be over-estimated. The argument in TOBIT is that using Y*, the estimated B is more accurate.
In micro-finance efficiency measurement studies, one may look into NPL (non-Performing Loans) rate. Say Y = NPL observed over series of period, t1, t2, ..., T and X observed is series of economic indicators Xe1, Xe2, ..., XeE . Simple regression model Y = a + bXe could tell us about direct linear relationship between NPL in micro-finance and the observable Xei. However, using Y* modeling, we may obtain information about latent interaction that contributed to NPL which is not readily observable through Y and Xei. This method is advantageous especially if we deal with secondary data and want to see latent effect between variables---which is not readily observable by the available secondary data (X, Y).
REFERENCE: Tobin, James (1958). "Estimation of relationships for limited dependent variables". Econometrica 26 (1): 24–36. doi:10.2307/1907382. NOT FREE.
See attached articles for later works that are freely accessible online.
Thank you so much for your reply.
Actually i am trying to use tobit regression in finding determinants of efficiecny of indian microfinance institutions. firstly i have calculated efficiency score of microfinance institutions and in second stage using efficiency score as a dependent variable. in few papers researchers argued that efficiency score is a censored data so use tobit regression and other (john Mcdonald) said use OLS. so please tell me which method shall i use in second stage to to find determinants.
Using tobit method in post dea analysis can provide a biaised results. The best approach is the Simar and wilson (2007) procedure truncated whish is based on a bootstrapping approach. Here is the command: simarwilson depvar indepvars [if] [in] [weight], [options]
Dear Swati Chauhan ,
efficiency measures in bounded between 0 and 1, it means that this variable is bounded NOT censored.
for your propose, I'd recommend you using four models simultaneously:
Fractional regression models (Best model)
ordinary least square
Simar and Wilson's approach (2007)
robust regression
non of these models are perfect, but are more perfect than Tobit model.
Bests...
Paul Louangrath Sir, can we apply tobit regression on sample size of 25 companies? Please Reply.
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In tobit regression modeling, the error term must be normally distributed. If a sample size of 25 could allow you to verify the distribution of the error term then it should be alright. However, as a caveat, a general minimum sample size is n = 30. Then again, for distribution verification of non-time series, Anderson-Darling go as low as n = 5. This depends on the type of data you are working with. Since the test statistic employs the maximulum likelihood, even with a sample of 25 as observed data set, you can use Monte Carlo simulation to simulate the likely outcome.
REFRENCESS:
Amemiya, Takeshi (1984). "Tobit models: A survey". Journal of Econometrics. 24 (1–2): 3–61. doi:10.1016/0304-4076(84)90074-5.
Amemiya, Takeshi (1985). "Tobit Models". Advanced Econometrics. Oxford: Basil Blackwell. pp. 360–411. ISBN 0-631-13345-3.
Gouriéroux, Christian (2000). "The Tobit Model". Econometrics of Qualitative Dependent Variables. New York: Cambridge University Press. pp. 170–207. ISBN 0-521-58985-1.
Using tobit method in post dea analysis can provide a biaised results. The best approach is the Simar and wilson (2007) procedure truncated whish is based on a bootstrapping approach. Here is the command: simarwilson depvar indepvars [if] [in] [weight], [options]
Continuous variables that are bounded in nature are generally addressed using Tobit models or censored regressions, or truncated models. Tobit regressions are suitable for settings in which the dependent variable is bounded at one of the extremes, presents positive mass of observations at that extreme, and is unbounded otherwise. If the variable is bounded between 0 and 1 inclusive; it cannot take values greater than one or less than zero. A proportion is bounded between 0 and 1, means that the effect of explanatory variables tends to be non-linear, and the variance tends to decrease when the mean gets closer to one of the boundaries. The fractional response model (FRM) represents a viable solution to address many of the econometric limitations that are found in the nonlinear solutions currently utilized to model continuous bounded dependent variables. Usually from fractional response models the bounds are natural bounds, such as a proportion. If the 0 to 1 coding arbitrary, the use of FRM may not be right. You may try with a linear model estimated by OLS. and compare the coefficients to the average partial effects from the fractional response model.
