3.1 The Data: Michigan/SRC
The household-based survey data used in the current analysis are that complied by the SRC for the USA. The samples for the SRC are statistically designed to be representative of all US households, excluding those in Alaska and Hawaii. Each month, a minimum of 500 interviews is conducted by telephone.2
The exact wordings of the surveys conducted by the SRC that we are concerned with are:
Indices are then calculated by computing the relative scores; the percentage of individuals giving favorable replies minus the percentage giving unfavorable replies. The compiled indices, essentially, reflect the forecast of the majority surveyed, which we use as a proxy for the representative household's subjective expectations and perceived good and bad news regarding the macroeconomy. The sample covers the period from January 1978 to November 2005.
The question is framed and indices are compiled indicating that households have clear distinctions between perceived favorable (good) and unfavorable (bad) news. Households may experience both good and bad news concurrently. For instances, they may perceive good news regarding employment but bad news regarding interest rate. They may not necessarily cancel each other out and together form perceived aggregate news about the aggregate economy.
Such perceived news may not reflect households views about which specific phase the aggregate economy is currently experience, i.e. recessionary or boom. It would be assuming unrealistic expertise on the part of households. It may be more reasonable to assume that they reflect households' perceived ‘turning points’ in the aggregate economy. They are similar to judgmental or directional forecasts.3 So if they have heard recently of any good (bad) changes to the aggregate economy, they would anticipation an upturn (downturn). Within this context, news could be more (less) favorable reflecting momentum, i.e. acceleration (deceleration). For example, when households expect interest rates to fall and would perceive this as good news for the aggregate economy, expecting an upturn. However, interest rates fall by smaller amount than expected, say by 0.25 per cent instead of 0.5 per cent. This could be conceived as less favorable news (as opposed to no fall or rise in interest rates which would be bad news) as the economy may not accelerate as much.
Figure 1 depicts the individual variables, while Table 1 the relevant statistics.
Table 1 contains the basic parameters of the statistical distributions of the households' expectations, good and bad news. When measuring the variability, of variables, the range and standard deviation of the variables shows that the least amount of variability is in the good news followed by bad news. The highest amount of variation is found in the households' expectations of the macroeconomy. The households' expectations of the macroeconomy exhibits negative skewness. Negative values for the skewness indicate that observations are skewed leftwards, or that the left tail is heavier than the right tail. The indication here is that there were more episodes of downward spikes than upward spikes in the indices of households' expectations of the macroeconomy. For both good and bad news we find that the indices exhibit positive skewness, an indication that more episodes of upward spikes (episodes of rising indices) than negative ones. Kurtosis measures whether the price distribution is peaked or flat in comparison with a normal distribution. Data sets with low kurtosis tend to have a flat top near the mean instead of sharp peaks which characterizes higher kurtosis values. Good news tends to have a high kurtosis indicating large movements in the indices were common. In comparison, bad news and the households' expectations of the macroeconomy tend to display relatively smaller movements in indices during the period under consideration.
A battery of unit root tests is conducted to test whether the variables displayed any stochastic trends. The standard ADF test suggests that the data are stationary as we can reject the null hypothesis of a unit root in the variables. This result is reinforced with the results obtained employing the ERS and PN tests due to Elliot et al. (1996) and Perron and Ng (1996) respectively. We can conclude that the variables employed in this study are stationary.
3.2 Econometric Methodology
The structural change, or regime switching behavior, could be captured using smooth transition regression models. The regime-switching issue depicted in equation (6), allowing for structural change, can be generalized as follows:
where wt is the vector of explanatory variables and st are distinct transition variables. The transition variables are depicted as a logistic function:
Specifying the transition variables as a logistic function (as it is a monotonically increasing function of st) enables us to capture any effect on how households form expectations that are due to a change to either types of news or a specific event. Hence, shift the relative weights given to these perceived news and the rate of absorption. The switch between the two regimes F(st) = 0 and F(st) = 1 is captured by the parameter γ. It can be smooth (for relatively small γ) or abrupt, similar to a threshold (large γ). The location of the switch, or transition, between the two regimes is given by the threshold parameter τ. We closely follow the TV-STAR model, with one transition introduced by Lundbergh et al. (2003). Hence, the non-linear model capturing changes to the relative weights given the two types of news and speed of updating is as follows:
The rest of the section considers the estimation and implications of both the relationship between households' subjective expectations and perceived news, i.e. the linear and non-linear models respectively.
As indicated in the theoretical model, subjective expectations are determined positively with good news and inversely with bad news.
We undertake a number of restrictions tests, which are found in Table 3.
Table 3. Restrictions Test (Linear Model)
| Null hypothesis || F statistic [p value] |
| ||9.87 [0.00]**|
| ||0.059 [0.80]|
| ||7.01 [0.00]**|
As outlined in the theoretical section we are interested in the relative weights, or importance, given to respective news. We, therefore, not only consider whether subjective expectations are correlated with the two types of news but also their relative impacts. The two types of restrictions test, i.e. joint hypothesis and the sum of coefficients tests, relate respectively to the necessary and sufficient conditions to establishing the relationship between subjective expectations and perceived news. The necessary condition establishes whether subjective expectations and news are correlated, which they are.4 The latter test relates directly to determining the relative importance given to either type of news. The restriction that the sum of the coefficients of the bad news equal to zero cannot be rejected. The corresponding F tests on the other coefficients, and , are clearly rejected.5 This implies that and are non-zero while is not significantly different from zero. This clearly suggesting that little, or negligible, importance (weight) is given to bad news. The speed of updating is also slow, approximately around 4 per cent of new news is updated each period.
As discussed in the previous section the linear relationship can be extended to capture structural change, distinguishing between periods when there are negative and positive shocks to the respective news and specific events. These non-linear extensions are investigated using the linear model and estimates as the base. The non-linear relationship is estimated following the TV-STAR model:
where the transition variables (st) used are either ΔNG, ΔNB or time.
In the first instances, it would be useful to examine how the respective transition variables evolve diagrammatically, i.e. how smooth is the transition from one regime to the other and the size of the threshold.
Table 4. Non-linear Model (Equation(11))
| Variables || Model 1 || Model 2 || Model 3 |
| Coefficient [t ratio] || Coefficient [t ratio] || Coefficient [t ratio] |
| Regime 1 || || || |
| ||0.758 [4.449]||0.665 [7.111]||0.674 [6.808]|
| ||−0.924 [3.079]||−0.223 [1.821]||−0.206 [1.643]|
| ||−0.328 [1.305]||−0.277 [2.705]||−0.334 [3.113]|
| ||−0.843 [7.058]||−0.611 [8.882]||−0.562 [8.274]|
| ||0.670 [4.574]||0.410 [3.808]||0.332 [3.628]|
| ||0.088 [0.720]||0.176 [1.966]||0.211 [2.797]|
| ||0.650 [6.740]||0.650 [11.187]||0.643 [10.814]|
| ||0.108 [1.065]||0.160 [2.436]||0.196 [2.850]|
| ||0.171 [1.584]||0.066 [1.107]||0.104 [1.640]|
| ||−0.025 [0.260]||−0.057 [0.941]||−0.019 [0.311]|
| ||−0.052 [0.556]||0.065 [1.040]||−0.028 [0.446]|
| ||0.000 [0.001]||0.082 [1.722]||0.077 [1.649]|
| Regime 2 || || || |
| ||0.622 [5.865]||0.638 [1.352]||0.795 [3.203]|
| ||−0.500 [3.119]||−0.654 [1.320]||−0.687 [2.042]|
| ||0.044 [0.284]||0.380 [0.738]||0.702 [2.388]|
| ||−0.472 [6.357]||−0.448 [2.018]||−0.643 [3.073]|
| ||0.207 [1.931]||0.391 [1.317]||0.630 [2.260]|
| ||0.279 [3.158]||0.045 [0.145]||0.218 [1.042]|
| ||0.672 [10.491]||0.824 [4.222]||0.654 [5.073]|
| ||0.178 [2.344]||0.006 [0.028]||0.030 [0.213]|
| ||0.061 [0.910]||0.051 [0.222]||−0.208 [1.460]|
| ||−0.057 [0.831]||0.438 [1.701]||0.068 [0.475]|
| ||0.027 [0.389]||−0.341 [1.563]||0.144 [0.989]|
| ||0.078 [1.542]||−0.087 [0.721]||−0.047 [0.461]|
| st || || || Time |
| γ ||500.000 [0.001]||10.066 [0.925]||21.660 [1.280]|
| τ ||−1.899 [2.913]||8.837 [8.746]||0.848 [47.519]|
|Diagnostics tests [p values]|| || || |
|Additional non-linearity test for transition variable|| || || |
The estimates for the respective models and corresponding restrictions tests are outlined in Tables 4 and 5.
Table 5. Restrictions Tests (Non-linear Model)
| Null hypothesis || Model 1 || Model 2 || Model 3 |
| F statistic || F statistic || F statistic |
| [p value] || [p value] || [p value] |
| Regime 1 || || || |
| Regime 2 || || || |
As with the linear model previously, we focus on the restrictions test. In particular, the restrictions tests that establishes the relative weight (or importance) given to good and bad news, i.e. the sum of the coefficients equal to zero, is reported here.6 Regime 1 of Model 1 captures the subjective expectations–news relationship when good news is worsening due to negative shocks, which are moderate to large. Now some importance is given to bad news. Table 6 outlines the calculated values from estimated equation (11).
Table 6. Estimates of, and
| || Model 1 || Model 2 || Model 3 |
| Regime 1 || || || |
| Regime 2 || || || |
Nevertheless, relative weight given to bad news is approximately half that given to good news . The absorption rate is slow and approximates the linear model at around 0.05. In the case when good news is improving or worsening by amounts less than 2 units, i.e. Regime 2, the relationship reflects the linear case, where no weight is given to bad news.
We saw earlier that in the case of changes to bad news (Model 2), the switch between regimes only takes place when bad news worsens considerably, as suggested by the estimated threshold 8.837. Regime 1 captures the relationship during periods of improving bad news (ΔNB < 0) and modest worsening. Conversely, Regime 2 captures periods when bad news is worsening considerably (ΔNB > 8.837). In Regime 1, the relationship mimics the linear model. However, in Regime 2 the subjective expectation–news relationship is depicted as an autoregressive process. Households do not update their subjective expectations when bad news is worsening considerably.
Turning to Model 3, which incorporates the time transition variable, there are distinct regimes before and after September 2001 (see Fig. 4). This captures the impact of the September 11 terrorists attack. Prior to September 2001, i.e. Regime 1, households form subjective expectations consistent with the linear model. Little or no relative weight is given to bad news and the speed of updating subjective expectations is slow, around 4 per cent is absorbed each period. This is in sharp contrast to the post-September 2001 period. Here some relative importance is given to bad news . Nevertheless, it is still less than a quarter of the relative weight given to good news. The most interesting feature of this regime is the absorption rate is now considerably faster . Households update their subjective expectations nine times faster since September 2001.
The diagnostics indicate no evidence of parameter non-constancy for all three models. However, it is notable that the model where the change in bad news is the transition variable (Model 2) does not account for all features of the households' subjective expectations-news relationship. There is evidence of parameter instability remaining in the non-linear specifications at the 5 per cent significance. This is not found for Models 1 and 3.
3.4 Discussion of Results
The estimates of both the linear and non-linear models provide strong evidence that it is good news that matters overwhelmingly when households form subjective expectations about the aggregate economy. The only times when some weight, or importance, is given to bad news is during Regime 1 of Model 1 and Regime 2 of Model 3. That is during periods when good news is worsening and in the aftermath of September 11. But in both cases, the importance given to bad news is considerably less than that given to good news. Households' ignoring bad news is consistent with cognitive dissonance and/or overconfidence. A good example of ‘ostrich behavior’ is found in Regime 2 of Model 2. When bad news increases, or worsens, by large amounts households no longer absorb or update their subjective expectations.
In an important recent paper Brunnermeier and Parker (2006) put forward a model of household subjective beliefs, distinguishing between ‘optimal’ and ‘objective’ expectations. They argue that households ‘having their expectations about the future not affect their current felicity is inconsistent’, as ‘agents care in the present about utility flows that are expected in the future in defining what beliefs are optimal’ (pp. 1093–1094). Hence, households prefer to more positive, or optimistic, outlook of the future. Even in the case of the aggregate economy and, therefore, ignore or give less importance to bad news.
The rate of absorption, or speed of updating, subjective expectations due to perceived news is slow. Only between 5 and 3 per cent of changes to news are updated each period. As discussed previously the speed of updating does not just reflect imperfect observation of news pertaining to the aggregate economy but also cost of thinking when news is observed. This is especially important when the news is as perceived by households, reflecting subjectivity and choice of signals. Nevertheless, during periods of adverse uncertainty the absorption rate increases considerably as indicated by the difference before and after September 2001. This is consistent with Akerlof et al. (1996, 2000), where they argue that ignorance would be more costly for households during periods of bad news. Here, we see that only the face of extremely bad or adverse news are households more willing to incur transactions cost and update their aggregate or macro information set. Similar to Carroll (2003) a larger volume of news leads to higher absorption.