Fertility in Japan: curve-fitting the total fertility rate
This is a subsidiary page to the fertility in Japan page that discusses different models to explain the total fertility rate data in Japan (1947-200. We draw on Human Fertility Database data (data downloaded on December 2, 2013, last updated August 8, 2012). The data collected by the Human Fertility Database is based on government data collection by the government of Japan. Details about the modalities of data collection are available here.
Raw time series data
Linear model
Single straight line fit
Denote by the year. Then, the best linear fit predicting the total fertility rate in year is:
Quick summary information about the goodness of fit is below (paste from R data, needs to be converted to table):
Residuals:
Min 1Q Median 3Q Max
-0.77971 -0.19170 -0.02246 0.08087 1.59348
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 65.871500 6.016802 10.95 4.98e-16 ***
yearrange -0.032306 0.003042 -10.62 1.69e-15 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.439 on 61 degrees of freedom
Multiple R-squared: 0.649, Adjusted R-squared: 0.6433
F-statistic: 112.8 on 1 and 61 DF, p-value: 1.693e-15
The total fertility rate values, along with the residuals from this best linear fit, are below:
| Year | TFR | TFR residual from best linear fit |
|---|---|---|
| 1947 | 4.566 | 1.5934791667 |
| 1948 | 4.444 | 1.5037847542 |
| 1949 | 4.357 | 1.4490903418 |
| 1950 | 3.672 | 0.7963959293 |
| 1951 | 3.281 | 0.4377015169 |
| 1952 | 2.995 | 0.1840071045 |
| 1953 | 2.713 | -0.065687308 |
| 1954 | 2.502 | -0.2443817204 |
| 1955 | 2.383 | -0.3310761329 |
| 1956 | 2.236 | -0.4457705453 |
| 1957 | 2.058 | -0.5914649578 |
| 1958 | 2.129 | -0.4881593702 |
| 1959 | 2.061 | -0.5238537826 |
| 1960 | 2.008 | -0.5445481951 |
| 1961 | 1.963 | -0.5572426075 |
| 1962 | 1.974 | -0.51393702 |
| 1963 | 2.001 | -0.4546314324 |
| 1964 | 2.045 | -0.3783258449 |
| 1965 | 2.145 | -0.2460202573 |
| 1966 | 1.579 | -0.7797146697 |
| 1967 | 2.224 | -0.1024090822 |
| 1968 | 2.127 | -0.1671034946 |
| 1969 | 2.119 | -0.1427979071 |
| 1970 | 2.129 | -0.1004923195 |
| 1971 | 2.153 | -0.044186732 |
| 1972 | 2.138 | -0.0268811444 |
| 1973 | 2.135 | 0.0024244432 |
| 1974 | 2.04 | -0.0602699693 |
| 1975 | 1.9 | -0.1679643817 |
| 1976 | 1.84 | -0.1956587942 |
| 1977 | 1.786 | -0.2173532066 |
| 1978 | 1.774 | -0.197047619 |
| 1979 | 1.751 | -0.1877420315 |
| 1980 | 1.731 | -0.1754364439 |
| 1981 | 1.726 | -0.1481308564 |
| 1982 | 1.755 | -0.0868252688 |
| 1983 | 1.788 | -0.0215196813 |
| 1984 | 1.8 | 0.0227859063 |
| 1985 | 1.757 | 0.0120914939 |
| 1986 | 1.719 | 0.0063970814 |
| 1987 | 1.689 | 0.008702669 |
| 1988 | 1.657 | 0.0090082565 |
| 1989 | 1.576 | -0.0396861559 |
| 1990 | 1.543 | -0.0403805684 |
| 1991 | 1.537 | -0.0140749808 |
| 1992 | 1.506 | -0.0127693932 |
| 1993 | 1.464 | -0.0224638057 |
| 1994 | 1.507 | 0.0528417819 |
| 1995 | 1.426 | 0.0041473694 |
| 1996 | 1.43 | 0.040452957 |
| 1997 | 1.392 | 0.0347585445 |
| 1998 | 1.388 | 0.0630641321 |
| 1999 | 1.347 | 0.0543697197 |
| 2000 | 1.359 | 0.0986753072 |
| 2001 | 1.336 | 0.1079808948 |
| 2002 | 1.318 | 0.1222864823 |
| 2003 | 1.29 | 0.1265920699 |
| 2004 | 1.288 | 0.1568976575 |
| 2005 | 1.254 | 0.155203245 |
| 2006 | 1.313 | 0.2465088326 |
| 2007 | 1.331 | 0.2968144201 |
| 2008 | 1.36 | 0.3581200077 |
| 2009 | 1.361 | 0.3914255952 |
| Maximum | 4.566 | 1.5934791667 |
| Minimum | 1.254 | -0.7797146697 |
| Mean | 1.971047619 | -6.02692499082228E-016 |
| Median | 1.786 | -0.0224638057 |
| Standard deviation | 0.7350500406 | 0.4354673701 |
Best linear fit since 1973
The data suggest slightly different trends 1947-1961 (rapid decline), 1961-1973 (modest increase), and 1973 onward (gradual decline from replacement to ultra-low levels, with minor fluctuations). Below, we consider the best linear fit for the part of the data 1973 onward. 1973 was the last year with above-replacement fertility.
| Year | TFR | TFR residual from best linear fit |
|---|---|---|
| 1973 | 2.135 | 0.1973698435 |
| 1974 | 2.04 | 0.122667615 |
| 1975 | 1.9 | 0.0029653864 |
| 1976 | 1.84 | -0.0367368421 |
| 1977 | 1.786 | -0.0704390706 |
| 1978 | 1.774 | -0.0621412992 |
| 1979 | 1.751 | -0.0648435277 |
| 1980 | 1.731 | -0.0645457563 |
| 1981 | 1.726 | -0.0492479848 |
| 1982 | 1.755 | 4.97866287334503E-005 |
| 1983 | 1.788 | 0.0533475581 |
| 1984 | 1.8 | 0.0856453295 |
| 1985 | 1.757 | 0.062943101 |
| 1986 | 1.719 | 0.0452408725 |
| 1987 | 1.689 | 0.0355386439 |
| 1988 | 1.657 | 0.0238364154 |
| 1989 | 1.576 | -0.0368658132 |
| 1990 | 1.543 | -0.0495680417 |
| 1991 | 1.537 | -0.0352702703 |
| 1992 | 1.506 | -0.0459724988 |
| 1993 | 1.464 | -0.0676747274 |
| 1994 | 1.507 | -0.0043769559 |
| 1995 | 1.426 | -0.0650791844 |
| 1996 | 1.43 | -0.040781413 |
| 1997 | 1.392 | -0.0584836415 |
| 1998 | 1.388 | -0.0421858701 |
| 1999 | 1.347 | -0.0628880986 |
| 2000 | 1.359 | -0.0305903272 |
| 2001 | 1.336 | -0.0332925557 |
| 2002 | 1.318 | -0.0309947843 |
| 2003 | 1.29 | -0.0386970128 |
| 2004 | 1.288 | -0.0203992413 |
| 2005 | 1.254 | -0.0341014699 |
| 2006 | 1.313 | 0.0451963016 |
| 2007 | 1.331 | 0.083494073 |
| 2008 | 1.36 | 0.1327918445 |
| 2009 | 1.361 | 0.1540896159 |
| Maximum | 2.135 | 0.1973698435 |
| Minimum | 1.254 | -0.0704390706 |
| Mean | 1.5722702703 | -3.27065701849033E-015 |
| Median | 1.537 | -0.0332925557 |
| Standard deviation | 0.2305858058 | 0.0699800163 |