Palgrave Handbook of Econometrics: Applied Econometrics

B.D. McCullough 1313

50 100 150 200

–0.015

–0.01

–0.005

0.005

0.01

0.015

0.02

h = 0.01

50

2 × 10 –6

h = 0.000001

5 × 10 –6

–5 × 10 –6

–1 × 10 –6

1 × 10 –6

–1.5 × 10 –6

1.5 × 10 –6

100 150 200

Figure 28.2 Analytic minus numerical derivative fora(θ)t at various differencing intervalsh
for all 197 observations on Series A

Table 28.6 CLS benchmark – parameters

Package μφθ

Benchmark 17.093752390 0.90658703600 0.56880910281

Mathematica default 17.093753099 0.90658876305 0.56881361427

Package X 17.09375129 0.90658475 0.56880310

Package Y 17.09366504 0.90660389 0.56883103

Package Z 17.0937032318 0.90648328387 0.568536846

situation is to compare the difference between the numeric and analytic deriva-
tives (which should be close to zero) for different values ofh(it should get smaller
ashgets smaller). Both these conditions can be seen in Figure 28.2.
Having determined the benchmark coefficients and standard errors, we are now
in a position to see whether our packages can hit the benchmark. In Table 28.6 we
present default estimation for three packages that offer CLS.
Package X is the most accurate, followed by Package Y, followed by Package Z.
The first two seem to provide about four accurate digits, and the third about three