On accuracy of survey forecasts of US mortgage spread

Figures & data

Figure 1. 30-year mortgage rate vs. 10-year Treasury rate: 1988Q1–2015Q4.

Figure 2. Mortgage spread: 1988Q1–2015Q4.

Table 1. Forecast accuracy test results: 30-year mortgage rate

Panel A. Unbiasedness test results
Row No.	f	At + f – At – 1 = α + β (Pt + f − At − 1) + ut + f				At + f − Pt + f = α′ + ut + f
		α	β	R^2	P1	α′s = ME	MAE
1	1	−0.142^a (0.045)	0.636^a(0.120)	0.16	0.001	−0.152^a (0.046)	0.413
2	2	−0.225^a (0.076)	0.464^a(0.170)	0.07	0.001	−0.274^a (0.077)	0.558
3	3	−0.317^a (0.110)	0.451^a(0.189)	0.06	0.001	−0.406^a (0.104)	0.704
4	4	−0.392^a (0.140)	0.384^a(0.208)	0.05	0.001	−0.534^a (0.126)	0.820

Panel B. Encompassing test results: At + f – At – 1 = γ0 + γ^B (Pt + f – At − 1) + γ^R (Rt + f – At − 1) + ut + f
	f	γ0	γ^B	γ^R	R^2
5	1	−0.069 (0.046)	−0.060 (0.168)	0.970^a(0.188)	0.28
6	2	−0.151^a(0.087)	0.069 (0.223)	0.723^a(0.301)	0.14
7	3	−0.243^a(0.123)	0.197 (0.254)	0.611^a(0.278)	0.11
8	4	−0.356^a(0.151)	0.292 (0.263)	0.294 (0.259)	0.06

Notes: A_t + f and A_t − 1 are the actual 30-year mortgage rates for, respectively, quarters t + f and t − 1, and P_t + f (R_t + f) is the Blue Chip (random walk) forecasts of A_t + f made in quarter t; f is the forecast horizon. ME is the mean forecast error, and MAE is the mean absolute forecast error. The correct (Newey–West) standard errors are in parentheses. P1 is the p-value for testing the joint null hypothesis of unbiasedness (α = 0 and β = 1). The sample periods for f = 1, 2, 3, and 4 are, respectively, 1988Q2–2015Q1, 1988Q3–2015Q2, 1988Q4–2015.3, and 1989Q1–2015Q4, with 108 observations for each forecast horizon. Superscript “a” indicates significance at the 10% or lower level of significance.

Table 2. Forecast accuracy test results: 10-year Treasury rate

Panel A. Unbiasedness test results
Row No.	f	At + f − At − 1 = α + β (Pt + f – At − 1) + ut + f				At + f – Pt+f = α′ + ut + f
		α	β	R^2	P1	α′ = ME	MAE
1	1	−0.159^a (0.053)	0.640^a(0.137)	0.13	0.001	−0.179^a(0.053)	0.477
2	2	−0.241^a (0.085)	0.456^a(0.173)	0.05	0.001	−0.307^a(0.086)	0.620
3	3	−0.358^a (0.118)	0.527^a(0.190)	0.07	0.001	−0.455^a(0.112)	0.775
4	4	−0.447^a (0.146)	0.469^a(0.200)	0.06	0.001	−0.600^a(0.131)	0.891

Panel B. Encompassing test results: At+f – At – 1 = γ0 + γB (Pt + f – At-1) + γR (Rt+f – At-1) + ut+f
	f	γ0	γ^B	γ^R	R^2
5	1	−0.079 (0.054)	−0.155 (0.225)	1.032^a(0.261)	0.23
6	2	−0.174^a(0.092)	0.080 (0.220)	0.620^a(0.302)	0.09
7	3	−0.294^a(0.127)	0.300 (0.237)	0.483^a(0.256)	0.09
8	4	−0.409^a(0.150)	0.239 (0.244)	0.257 (0.250)	0.06

Notes: See the notes in Table 1. A_t + f and A_t − 1 are the actual 10-year Treasury rates for, respectively, quarters t + f and t − 1, and P_t + f (R_t + f) is the Blue Chip (random walk) forecasts of A_t + f made in quarter t. Superscript “a” indicates significance at the 10% or lower level of significance.

Table 3. Forecast accuracy test results: Mortgage spread

Panel A. Unbiasedness test results
Row No.	f	At+f – At-1 = α + β (Pt+f – At-1) + ut+f				At+f –Pt+f =α‘ + ut+f
		α	β	R^2	P1	α‘ = ME	MAE
1	1	0.030 (0.018)	1.134^a(0.261)	0.23	0.223	0.027 (0.020)	0.148
2	2	0.045 (0.028)	1.399^a(0.290)	0.32	0.137	0.033 (0.029)	0.179
3	3	0.066 (0.041)	1.370^a(0.355)	0.28	0.150	0.049 (0.039)	0.199
4	4	0.104^a(0.046)	1.655^a(0.372)	0.38	0.049	0.066 (0.045)	0.219

Panel B. Encompassing test results: At + f − At – 1 = γ0 + γ^B (Pt + f − At − 1) + γ^R (Rt + f  − At − 1) + ut + f
	f	γ0	γ^B	γ^R	R^2
5	1	0.029 (0.018)	0.738^a(0.372)	0.505^a(0.207)	0.28
6	2	0.044 (0.027)	1.327^a(0.340)	0.109 (0.217)	0.31
7	3	0.065^a(0.036)	1.227^a(0.389)	0.293 (0.219)	0.28
8	4	0.103^a(0.046)	1.605^a(0.412)	0.120 (0.197)	0.38

Notes: See the notes in Table 1. A_t + f and A_t − 1 are the actual mortgage spreads for, respectively, quarters t + f and t − 1, and P_t+f (R_t + f) is the Blue Chip (random walk) forecast of A_t + f made in quarter t. Superscript “a” indicates significance at the 10% or lower level of significance.

Table 4. Contingency table

	Actual
	Upward	Downward
Correct directional predictions	n1: ΔAt + f (+) & ΔPt + f (+)	n2: ΔAt + f (−) & ΔPt + f (−)
Incorrect directional predictions	n3: ΔAt + f (+) & ΔPt + f (−)	n4: ΔAt + f (−) & ΔPt + f (+)

Notes: With Aw_t measuring the most recent rate known at the time of the survey, ΔA_t + f = (A_t + f − Aw_t) is the actual change, and ΔP_t + f = (P_t+f  − Aw_t) is the predicted change. The sign (+) represents an upward move, and the sign (−) represents a downward move in the series. The numbers of correct (incorrect) sign predictions are n₁ and n₂ (n₃ and n₄). As such, the sample size is n (=n₁ + n₂ + n₃ + n₄).

Table 5. Directional accuracy test results

Row No.	f	Correct		Incorrect		πAll	πUp	πDown	P2
		n1	n2	n3	n4
30-year mortgage rate
1	1	26	22	18	42	0.44	0.59	0.34	–
2	2	31	24	12	41	0.51	0.72	0.37	–
3	3	28	23	9	48	0.47	0.76	0.32	–
4	4	24	22	8	54	0.43	0.75	0.29	–
10-year Treasury rate
5	1	29	15	16	48	0.41	0.64	0.24	–
6	2	38	21	6	43	0.55	0.86	0.33	–
7	3	31	18	6	53	0.45	0.84	0.25	–
8	4	28	20	6	54	0.44	0.82	0.27	–
Mortgage spread
9	1	35	34	22	17	0.64^b	0.61	0.67	0.570
10	2	32	42	21	13	0.69^b	0.60	0.76	0.073
11	3	30	42	26	10	0.67^b	0.54	0.81	0.003
12	4	25	40	33	10	0.60^b	0.43	0.80	0.001

Notes: See the notes for Table 4. The overall directional accuracy rate is π_All = (n₁ + n₂)/n, the proportion of correctly predicted upward moves is π_Up = n₁/(n₁ + n₃), and the proportion of correctly predicted downward moves is π_Down = n₂/(n₂ + n₄). Superscript “b” indicates that the p-values of Fisher’s exact test and the chi-square tests with and without Yate’s continuity correction are all below 0.10, and thus the null hypothesis of no directional association between the actual and predicted change is rejected. P2 is the chi square test p-value for examining the null hypothesis of “no asymmetry,” which is defined as the proportion of incorrectly predicted upward moves (1 − π_Up) equals the proportion of incorrectly predicted downward moves (1 − π_Down).