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Stata Technical Bulletin
STB-48
Goodman, A., and S. Webb. 1994. For Richer, for Poorer. The Changing Distribution of Income in the United Kingdom, 1961-91. Commentary No.
42, Institute for Fiscal Studies, London. Abridged version in: Fiscal Studies 15: 29-62.
Jenkins, S. P. 1991. The measurement of income inequality. In Economic Inequality and Poverty: International Perspectives, ed. L. Osberg. Armonk
NY: M. E. Sharpe.
Jenkins, S. P. and P. Van Kerm. 1995. Accounting for inequality trends: decomposition analyses for the UK, 1971 -86. Economica 62: 29-63.
——. 1997. Trends in real income in Britain: a microeconomic analysis. Empirical Economics 22: 483-500.
——. 1999. sg107: Generalized Lorenz curves and related graphs. Stata Technical Bulletin 48: 25-29.
Lambert, P. J. 1993. The Distribution and Redistribution of Income: A Mathematical Analysis. 2d ed. Manchester University Press: Manchester and
New York.
Sen, A. K. 1976. Real national income. Review of Economic Studies 43: 19-39.
Shorrocks, A. F. 1982a. Inequality decomposition by factor components. Econometrica 50: 193-212.
——. 1982b. The impact of income components on the distribution of family incomes. Quarterly Journal of Economics 98: 311-326.
——. 1984. Inequality decomposition by population subgroups. Econometrica 52: 1369-1388.
Whitehouse, E. 1995. sg30: Measures of inequality. Stata Technical Bulletin 23: 20-23. Reprinted in Stata Technical Bulletin Reprints, vol. 4,
pp. 146-150.
sg105 Creation of bivariate random lognormal variables
Stephen P. Jenkins, University of Essex, UK, [email protected]
Description
mkbilogn is a program for the creation of bivariate random normal variables. More precisely it creates random variables, Xi
and X2, drawn from a bivariate lognormal distribution defined as follows. Xi and X2 are such that, as n —> oo,æɪ = Iog(Xi)
and X2 = Iog(X2) are bivariate normal distributed with means mi, and rn2, standard deviations si, and s2, and correlation r.
The parameters of the distribution can be optionally chosen by the user, or default to the values specified below.
The program applies methods proposed in the Stata FAQ archive:
http://www. st at a.c om∕support/f aqs∕st at/mvnorm.html
Syntax
mkbilogn varl var2 [, r(#) ml(#) sl(#) m2(#) s2(#)]
Options
r(#) correlation of IirOrarl) and Iirarar2); default is .5.
ml(#) mean of Iiι(varΓ); default is 0.
sl(#) standard deviation of Iirar ar 1); default is 1.
m2(#) mean of Iirarar2) ; default is 0.
s2(#) standard deviation of Iirarar2); default is 1.
Example
. clear
. set obs IOOOO
obs was 0, now 10000
. mkbilogn yl y2t r(.3) ml(l) sl(2) m2(3) s2(4)
Creating 2 r.v.s Xl X2 s.t. xl=log(Xl)t x2=log(X2) are bivariate
Normal with mean(xl) = 1 ; mean(x2) = 3 ; s.d.(xl) = 2 ;
s.d.(x2) = 4 ; corr(xltx2) = .3
. generate Iyl = ln(yl)
. generate ly2 = ln(y2)