Measurement Error?
- Do we care about measurement error?
- We can think systematically about it…
- If we can assume that, on average, it’s zero and has constant variance:
- As in, errors \(e_t \sim (0,\sigma^2)\).
- Then on average, errors random, noise, over longer term can be ignored.
- If, however, there is serial correlation, if mean non-zero:
- Suggests there are systematic errors being made.
- Can get GDP revisions (full) history:
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -0.04 -0.01 0.00 0.00 0.01 0.04 68846
- Distribution of revisions from first release appears stable.
- What is likelihood of different sizes of adjustment?
revisions <- as.numeric(as.vector(t(gdpr.g1[-1,-1])))
revisions <- revisions[is.na(revisions)==F]
pcs <- data.frame("percentiles"=quantile(revisions,seq(0,1,0.01)))
library(knitr)
kable(pcs, format = "markdown")
| 0% |
-0.0391679 |
| 1% |
-0.0272120 |
| 2% |
-0.0230263 |
| 3% |
-0.0203457 |
| 4% |
-0.0179335 |
| 5% |
-0.0159794 |
| 6% |
-0.0149120 |
| 7% |
-0.0144557 |
| 8% |
-0.0136929 |
| 9% |
-0.0129356 |
| 10% |
-0.0122505 |
| 11% |
-0.0118399 |
| 12% |
-0.0113726 |
| 13% |
-0.0108127 |
| 14% |
-0.0102547 |
| 15% |
-0.0096976 |
| 16% |
-0.0091805 |
| 17% |
-0.0086457 |
| 18% |
-0.0081625 |
| 19% |
-0.0078756 |
| 20% |
-0.0075355 |
| 21% |
-0.0070509 |
| 22% |
-0.0065821 |
| 23% |
-0.0062307 |
| 24% |
-0.0057092 |
| 25% |
-0.0052178 |
| 26% |
-0.0048487 |
| 27% |
-0.0045424 |
| 28% |
-0.0042716 |
| 29% |
-0.0039756 |
| 30% |
-0.0036748 |
| 31% |
-0.0033048 |
| 32% |
-0.0030348 |
| 33% |
-0.0027570 |
| 34% |
-0.0025005 |
| 35% |
-0.0021907 |
| 36% |
-0.0019497 |
| 37% |
-0.0016368 |
| 38% |
-0.0013289 |
| 39% |
-0.0010441 |
| 40% |
-0.0007798 |
| 41% |
-0.0005221 |
| 42% |
-0.0002947 |
| 43% |
-0.0000820 |
| 44% |
0.0000000 |
| 45% |
0.0001888 |
| 46% |
0.0003889 |
| 47% |
0.0005767 |
| 48% |
0.0007945 |
| 49% |
0.0009589 |
| 50% |
0.0011102 |
| 51% |
0.0012934 |
| 52% |
0.0015093 |
| 53% |
0.0017026 |
| 54% |
0.0019898 |
| 55% |
0.0022062 |
| 56% |
0.0023460 |
| 57% |
0.0025110 |
| 58% |
0.0027470 |
| 59% |
0.0029331 |
| 60% |
0.0031541 |
| 61% |
0.0033199 |
| 62% |
0.0035536 |
| 63% |
0.0037157 |
| 64% |
0.0039335 |
| 65% |
0.0041517 |
| 66% |
0.0043267 |
| 67% |
0.0045760 |
| 68% |
0.0048992 |
| 69% |
0.0051691 |
| 70% |
0.0054170 |
| 71% |
0.0057042 |
| 72% |
0.0060557 |
| 73% |
0.0064294 |
| 74% |
0.0068203 |
| 75% |
0.0071686 |
| 76% |
0.0074656 |
| 77% |
0.0080468 |
| 78% |
0.0084892 |
| 79% |
0.0088702 |
| 80% |
0.0092537 |
| 81% |
0.0097983 |
| 82% |
0.0106153 |
| 83% |
0.0113474 |
| 84% |
0.0120416 |
| 85% |
0.0128854 |
| 86% |
0.0136546 |
| 87% |
0.0145962 |
| 88% |
0.0152511 |
| 89% |
0.0162666 |
| 90% |
0.0171879 |
| 91% |
0.0183868 |
| 92% |
0.0195124 |
| 93% |
0.0207788 |
| 94% |
0.0218054 |
| 95% |
0.0235918 |
| 96% |
0.0259986 |
| 97% |
0.0276709 |
| 98% |
0.0296740 |
| 99% |
0.0327496 |
| 100% |
0.0436356 |
- From looking at the distribution:
- 43% chance of downward revision, 57% chance of upward.
- Only about a 1–2% chance of revision of +0.03.
- About 6–7% chance of revision >+0.02.
- Biggest ever negative revision 0.04, so no chance of negative growth.
- Hence more than 50/50 chance consensus was right all along…
