How do firms form inflation expectations? Empirical evidence from the United States

Figures & data

Figure 1. The actual inflation and firms’ inflation expectations in the United States. Source: Authors’ calculation.

Table 1. Stationarity tests for inflation expectations and actual inflation.

Unit root test method	Inflation Expectation		Actual Inflation
	Firm	Household
ADF	−3.5977 (0.0064)	−3.7190 (0.0225)	−3.3955 (0.0119)
PP	−4.4274 (0.0003)	−5.3151 (0.0001)	−4.8671 (0.0001)

Note: This table summarises the stationarity test results of inflation expectations of firms and households and the actual inflation. ADF denotes the augmented Dickey–Fuller (ADF) unit root test and PP denotes the Phillips and Perron’s test. The sample period is November 1993 to June 2018.

Source: Authors’ calculation.

Table 2. Maximum likelihood estimates for households and firms with the naïve expectation, adaptive expectation, and VAR model.

	Panel A	Panel B	Panel C
	Households (1978.1-2018.06)	Households (1993.11-2018.06)	Firms (1993.11-2018.06)
${\mathit{MSE}}_{j,t-\Delta \mathrm{t}}^{\delta =1}$	0.0333 (0.0001)	0.0127 (0.0247)	0.1857 (0.0000)
${\mathit{MSE}}_{j,t-3\Delta \mathrm{t}}^{\delta =0.9}$	0.1348 (0.0000)	0.1035 (0.0000)	0.1019 (0.0000)
$C_N$	0.0000	0.0000	0.0000
$C_A$	26.7892 (0.0030)	12.9568 (0.0015)	−143.9588 (0.0006)
$C_V$	−19.3604 (6.2542)	−16.5925 (5.3600)	−150.9925 (0.1017)

Note: $C_N,$ $C_A,$ and $C_V$ represent the costs of naïve, adaptive, and VAR predictors, respectively. Standard errors in parentheses.

Source: Authors’ calculation.

Figure 2. The proportions of the Naïve Expectation, Adaptive Expectation, and VAR model for households (January 1978 to June 2018). Source: Authors’ calculation.

Figure 3. The proportions of the Naïve Expectation, Adaptive Expectation, and VAR model for households (November 1993 to June 2018). Source: Authors’ calculation.

Figure 4. The proportions of the Naïve Expectation, Adaptive Expectation, and VAR model for firms (November 1993 to June 2018). Source: Authors’ calculation.

Table 3. Maximum likelihood estimates for households and firms with alternative predictor sets.

	Panel A: ${\mathcal{H}}_1$	Panel B: ${\mathcal{H}}_2$
${\mathit{MSE}}_{j,t-\Delta \mathrm{t}}^{\delta =1}$	1.0941 (0.0002)	0.1902 (0.0002)
${\mathit{MSE}}_{j,t-3\Delta \mathrm{t}}^{\delta =0.9}$	2.3054 (0.0000)	0.0265 (0.0003)
$C_A$	0.0000	0.0000
$C_V$	71.6187 (0.0084)	221.7275 (0.0521)
$C_R$	71.6476 (18.1267)	\
$C_H$	\	254.9286 (72.4513)

Note: $C_A,$ $C_V,$ $C_R,$ and, $C_H$ represent the costs of the Adaptive Expectation, VAR model, the Rational Expectation, and the Heterogeneous Static Expectation, respectively. Standard errors in parentheses.

Source: Authors’ calculation.

Figure 5. The proportions of the Adaptive Expectation, VAR model, and the Rational Expectation for firms (November 1993 to June 2018). Source: Authors’ calculation.

Figure 6. The proportions of the Adaptive Expectation, VAR model, and the Heterogeneous Static Expectation for firms (November 1993 to June 2018). Source: Authors’ calculation.