Can Workers Predict Actual Labour Market Outcomes? | RDP 2021-08: Job Loss, Subjective Expectations and Household Spending

RDP 2021-08: Job Loss, Subjective Expectations and Household Spending 3. Can Workers Predict Actual Labour Market Outcomes?

Gabrielle Penrose and Gianni La Cava

August 2021

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3.1 Do employed workers expect to lose their jobs?

In this section, we confirm some previous research findings about worker expectations for job loss. First, we find workers typically overestimate the probability of job loss (Figure 4). This finding holds at all levels of job loss expectations, as evidenced by the actual rate of job loss being persistently below the estimated probability of job loss. While it is possible that workers may voluntarily resign in anticipation of job loss, we find that this does not explain the discrepancy, with expected job loss remaining higher than the rate of job separation on average, regardless of whether the worker voluntarily left the job or not. Expectations of job loss do appear to contain some predictive information, as they increase with the actual probability of job loss. However, the difference between estimated and actual job loss also increases with job loss expectations.

Figure 4: Job Loss Rate

By subjective probability of job loss

In Appendix A, we outline a simple model of expectations formation to more formally test the predictive ability of workers' subjective expectations. In particular, we adapt the framework of Keane and Runkle (1990) to examine whether worker expectations are fully rational, or whether their mistakes are systematic and predictable and should be accounted for when forming expectations.

The results shown in Appendix A indicate that workers have some ability to predict actual job loss in the year ahead. Indeed, subjective job loss expectations contain predictive power over and above the observed characteristics of the worker at the time of the survey. A 1 percentage point increase in the expected probability of job loss is associated with an increase of about 10 to 18 basis points in the actual probability of job loss.

But here we focus on evidence of systematic bias in forecasting future job prospects. For this, we follow a 2-stage process. First, we estimate a simple model of the ‘objective’ (or ‘true’) probability of job loss for each worker based on their own characteristics, including private information that is not observed by the researcher. Second, we compare this model-based probability estimate to the worker's subjective estimate. We then look for evidence of systematic deviations between the model-based and subjective estimates, both across workers and over time.

First, the objective probability of job loss is assumed to be given by the following model:

\begin{array}{l} y_{i t + 1}^{*} = β x_{i t} + γ x_{i t}^{*} + μ_{i t + 1} \\ y_{i t + 1} = I (y_{i t + 1}^{*} \geq 0) \end{array}

Which states that the worker's latent probability of job loss $(y_{i t + 1}^{*})$ is a function of various personal characteristics that are observed by the researcher ( x_it ), such as age, job tenure and industry of work, as well as a subset of characteristics that only the worker observes as private information $(x_{i t}^{*})$ . In practice, actual job loss (y_it+1) is observed as a binary outcome, as shown by the indicator function, I (A), that is equal to one if the statement, A, is true and is zero otherwise.

This model is estimated using a logistic regression. The observed job loss outcome is assumed to be a function of both worker characteristics observed by the researcher as well as the worker's private information, which is assumed to be captured by their subjective belief $(y_{i t}^{e})$ :

y_{i t + 1} = β x_{i t} + γ y_{i t}^{e} + μ_{i t + 1}

The predictions from the logistic regression are our proxy for the model-based or ‘objective’ probability estimates $({\hat{y}}_{i t + 1})$ .

Second, to construct estimates of forecast deviations we take the difference between the worker's subjective belief and the model-based probability estimates:

d e v i a t i o n_{i t + 1} = y_{i t + 1}^{e} - {\hat{y}}_{i t + 1} = θ_{i} + λ_{t + 1} + v_{i t + 1}

This forecast deviation is assumed to be a function of a worker fixed effect $(θ_{i})$ , a year fixed effect $(λ_{t + 1})$ and a white noise error term (v_it+1). The worker fixed effect captures the systematic ability or willingness of each worker to forecast their job market prospects a year ahead. This persistent cross-sectional variation could reflect several unobserved factors. For example, it may be due to differences in forecasting ability (e.g. economic literacy), effort or optimism.

The distribution of the estimated worker fixed effects indicates that most workers display a positive bias in that they persistently overestimate the probability of job loss, but there are some workers that persistently underestimate it (Figure 5).

Figure 5: Distribution of Job Loss Forecast Deviations

The average worker not only overestimates the probability of job loss, but the extent of this overestimation varies with aggregate labour market conditions, as shown by the time fixed effects (Figure 6). Expectations of job loss for the average worker rose by more than the model-based probability estimates during both the economic downturn in 2001 and the global financial crisis (GFC). And, since around 2013, the difference between the expected and model-based outcomes has increased compared to the period before the GFC, alongside elevated levels of job insecurity during that time (Foster and Guttmann 2018).

Figure 6: Job Loss Forecast Deviations over Time

3.2 Do unemployed workers expect to find a job?

Next, we focus on workers that are unemployed and explore the ability of their subjective expectations to predict finding a suitable job in the year ahead. This allows us to examine expectations of the duration of unemployment, which could be relevant to household spending.

The data indicate that unemployed workers typically overestimate the probability of finding a job (Figure 7). But workers that believe they have little chance of finding a job actually understate the probability of job finding. This indicates that the expectations of both employed and unemployed workers deviate from actual future labour market outcomes, on average. However, expected job finding rates do increase with actual rates, which is consistent with prior research (Spinnewijn 2015; Mueller et al 2021). More formal tests of the predictive ability of the subjective expectations of unemployed workers can be found in Appendix A.

Figure 7: Job Finding Rate

By subjective probability of finding a job given unemployed

Given the longitudinal nature of the survey, we can also examine how expectations of job finding evolve during a spell of unemployment. We find that expectations of job finding are lower the longer a worker has been unemployed (Figure 8). There are two competing explanations for this observed relationship, as discussed by Mueller et al (2021). The negative relationship between job finding expectations and duration could represent ‘true’ duration dependence, whereby unemployed respondents become increasingly discouraged the longer they are unemployed and revise down their expectations of job finding. Alternately the relationship may be due to ‘dynamic selection’, in which there is a shift in the composition of the pool of unemployed. Under dynamic selection, respondents with lower expectations of job finding remain unemployed for longer, leading to the observed relationship between unemployment duration and job finding expectations.

Figure 8: Subjective Probability of Job Finding

By duration of unemployment

We can distinguish whether the decline in expected job finding probability is due to either of these explanations by exploiting the longitudinal nature of the household survey data. If there is true duration dependence in expectations of job finding, we should observe a decline in the expected probability of job loss for a worker in a given spell of unemployment (a within-worker effect). If there is dynamic selection we should observe a decline in the expected probability of job loss across spells for different workers (a between-worker effect) (Mueller et al 2021).

To disentangle these competing explanations we estimate a regression for unemployed workers in which the dependent variable is the expected probability of finding a job and the explanatory variables are a vector of dummies for time spent unemployed (in years). By comparing the regression estimates with and without a worker fixed effect, we can gauge how expected job finding probability evolves within and between unemployed workers.

We find that the expected job finding rate declines with the length of the unemployment spell, but that this effect disappears once we include a worker fixed effect (Figure 8). This indicates that the decline in the expected probability of job finding is due to the dynamic selection effect, with a gradual shift over the duration of unemployment towards unemployed workers with lower expected probabilities of finding jobs.^[4]

3.3 Why are there differences between actual and expected job outcomes?

The systematic differences between expected and actual job outcomes could be explained by a range of factors that vary across workers, such as forecasting ability, effort or degree of optimism.

We do not pin down the mechanism that explains these differences across workers, though we provide some tentative evidence suggesting that optimism could be part of the story. Specifically, we find that workers that overestimate their probability of job loss are more likely to underestimate their probability of job finding, on average. This is based on the observation that there is a (small) negative correlation between the worker fixed effects for the rate of job loss and job finding. This could be taken as evidence that some workers are too pessimistic about their future job prospects.

However, the observed overestimates of job loss rates and underestimates of job finding rates could also be explained by ‘conservatism’ in perceptions of probability (Khaw, Stevens and Woodford 2021). Conservatism refers to the observation that individuals tend to overstate low probability events (such as losing your job), and understate high probability events (such as keeping your job). This phenomenon has been identified under numerous settings in the experimental psychology literature, but we have not seen it applied to subjective labour market expectations (Attneave 1953; Varey, Mellers and Birnbaum 1990).^[5]

We leave a more complete investigation of the mechanisms that explain these systematic deviations to future research. However, it is worth noting that predicting your future job prospects is generally a very challenging task. For instance, in estimating their probability of job loss, a worker needs to make predictions about a range of factors that are outside their control, including forecasting how economic conditions will evolve over the coming year, understanding how changes in economic conditions will affect their own firm, and subsequently predicting how much they are at risk of losing their job. In doing so, the worker may not correctly estimate the consequences of the change in economic conditions, or how the shock is distributed across firms, or how their specific job will be affected. Misspecification at any one of these points can lead to measured differences between subjective and objective (model-based) probabilities.

Moreover, an employed worker can influence their own objective probability of job loss. For example, workers that expect to lose their job have an incentive to find another job and quit before they involuntarily lose their job. This will reduce the actual probability of job loss relative to the subjective estimate (and lead to a larger positive deviation). This selection effect is partly captured by the measured difference between the subjective and objective probability of job loss shown in Figure 4. Alternatively, workers that expect to lose their job may have a greater incentive to work harder to keep it. The additional work effort may lower the actual probability of job loss relative to their subjective estimate (leading to a larger negative deviation). If individuals most at risk work harder to improve their value to the firm, the firm has less incentive to make them unemployed involuntarily.

Footnotes

This finding is also apparent in the US data (Mueller et al 2021). [4]

If conservatism fully explains the cross-sectional pattern in job loss expectations we might expect ‘mean reversion’, in which the difference between the expected and model-based estimates decreases with the level of actual job loss. Partly arguing against this interpretation, we find that the deviation between the subjective and model-based estimates of job loss increases in both the level of actual job loss and the level of expected job loss. [5]