Incomplete Information

Incomplete information emphasizes the observation that in the real world, in contrast to perfectly competitive model assumptions, no agent has full information as to other agents’ budgets, preferences, resources, or technologies, not to mention their plans for the future and numerous other factors that affect prices in markets.

Real business investment is one area where incomplete information is most obvious. A firm may find that it needs to adjust its capital stock to achieve a level of capital consistent with a new level of expected output. Since the costs of a full adjustment and the cost of making a mistake may be very high, a firm will pursue a policy of partial adjustments. In our analysis, this may give rise to a distributed lag process in a series such as capital investment. Incomplete information also leads to a bias in thinking called the hindsight bias. Sometimes called the “I-knew-it-all-along” effect, the tendency is to see past events as being predictable at the time those events happened.

Currently, there are two other fields where incomplete information is having a significant impact on current economic activity. First, in labor markets, both potential workers and potential employers face incomplete information barriers regarding job opportunities and the location of skilled workers to fill those jobs. One sign of these information barriers is exhibited in the sharp peaks and valleys of the unemployment rate in Figure 3.6. Both potential employers and employees face significant search costs to find a match.⁷ The gap between job searchers and employers looking to fill a vacancy is illustrated in Figure 3.7. For a given vacancy rate on the y-axis, there has been a clear outward shift in the unemployment rate during the current cycle.

A classic example of incomplete information is when an important variable is missing from the model. For example, the Taylor (1993) rule suggests inflation and the unemployment rate (or output) are two key determinants of the federal funds rate, or short-term interest rates.⁸ If we were to model the fed funds rates and include only the inflation rate as a determinant, we would likely see an autocorrelation problem. The estimated results including the confidence interval would be unreliable.⁹ That said, the missing variable is often unknown or unobserved. That is, in the above example, we know the unemployment rate is missing from the model and that would be considered a known unknown. Known unknowns are not the only case of missing variables and the other, more complicated, example would be an unknown unknown case—a variable is missing and we do not know what is missing. One major reason of this unknown unknown scenario is that economies are complex and evolve over time and the relationships between variables also evolve. A good example of this is the Phillips curve relationship between unemployment and inflation.¹⁰ If we model inflation using the Phillips curve and utilize the unemployment rate as predictor, then that model may produce autocorrelation. In this case, we are following the economic theory, no known unknowns, but economies also evolve and introduce the problem of unknown unknowns. For example, between May 2012 and January 2016, the unemployment rate dropped from 8.2 percent to 4.9 percent, but the personal consumption expenditures (PCE) deflator stayed below the Federal Open Market Committee’s (FOMC) target of 2 percent for the entire period—the longest period of below 2 percent inflation in several decades. That suggests we need to include more variables (e.g., interest rates, oil prices, a measure of overall economic activity) to improve model fit in an attempt to address the unknown unknown problem.

Another possible source of incomplete information is the missing observations problem, where a data set contains missing values. The missing observations problem may lead to measurement errors and inconsistent results—see Chapter 9 of Kmenta (1971) for more detail. Another source of missing observations, typically for time series data, is due to the selection of the time span. That is, if we were to estimate the Taylor rule using the post-1990s era only, we would get different results from the pre-1990s era. The past three recoveries are considered “jobless” by some observers and the inflation rate, on average, was much lower compared to the pre-1990s—again economies evolve over time. Furthermore, we are not sure whether the future will be like the 1990s or closer to the 1980s. Therefore, to avoid incomplete information we should use the entire data set.

Incomplete information is also a problem when decision makers attempt to assess the state of the economy and the behavior of other economic agents in response to economic events. For example, we note the sometimes surprising reactions of financial markets to an economic data release that would appear very positive for the economy, but the market reaction is negative. One only has to experience a few releases of the Employment Situation report and the subsequent market reaction to appreciate the problem. In this case, what we are witnessing is the release of an economic number, such as employment, that is positive but that is not as positive as the market had expected. The difference between expected and actual will generate the market response. In addition, implications for inflation from a rapidly expanding economy and the revisions to expectations for monetary policy moving forward can weigh on financial markets.

Imperfect Information: Data Revisions and Data Quality

Second, the case of imperfect information—information that does not precisely reflect reality—is often faced by decision makers. The challenge is faced all the time because so much economic information comes via initial surveys of activity that are frequently revised, sometimes significantly, as further information is gathered. Initial estimates of retail sales, GDP, employment, and capital goods orders are more often than not revised from their initial released number.

For many, house hunting is daunting because of the uncertainty on pricing. In fact, many of us will sometimes ask—why is this house so cheap? In credit, there are the issues of adverse selection and moral hazard as well as questions on the quality of bank capital in the United States, Europe, and China. Finally, there are always questions on the quality of corporate profits and analysts are always asking for more details, suggesting that there is still information that remains to be found that could improve the quality of earnings estimates.

What about the cost of labor? In recent years, decision makers have had many different measures of labor costs, as illustrated in Figure 3.8. First, there is the traditional average hourly earnings series that is released along with the nonfarm payroll report at the start of each month. A second release is the wages and salaries series that is part of the personal income report. Finally, there is the employment cost index, which provides a summary of the wages, salaries, and benefit changes that accrue to workers.

Economic variables that we model are presumed to influence, or at least represent, the actual economy. However, we often receive new information (note the revision of GDP estimates we witnessed for the first quarter of GDP in 2014 and 2015) such that the initial information imperfectly represents the real economic situation. Lucas has made the case for imperfect information on prices, whether a relative price change compared to other competitors or an absolute change for all competitors.¹³ If a firm perceives that the price change is relative (greater demand for its products), then that firm may alter its production schedules. Although a firm may actually be misreading the data, the firm will pursue a departure from previous output schedules. For any decision maker the critical question becomes: how much of our macro data reflect actual activity as opposed to our perceptions of what activity we believe to be happening?

Imperfect information: Dealing with the Problem of Measurement Error

There are several potential sources of imperfect information resulting in unreliable conclusions. In most cases, imperfect information would lead to autocorrelation or nonstationary problems, and results are unreliable in either case; see Silvia et al. (2014) for more detail.

Here, we examine the problem of imperfect information by comparing the Standard & Poor’s (S&P) 500 index and nonfarm payrolls. A common measurement error is that an analyst may utilize the level form of the variables in regression/correlation analysis. Many time series variables are nonstationary at their level form. The common estimation method utilized by analysts is the ordinary least squares (OLS) model, which assumes the underlying data set is stationary.¹⁴ If the data are nonstationary at the level form, then using OLS on that data set would produce spurious results; that is, it would tend to suggest a very strong relationship (denoted by a very high R-squared value), even though there is no meaningful relationship between the variables. In our example, both the S&P 500 index and nonfarm payrolls are nonstationary at level form and using that form of the variables, we obtain a very high R-squared value of 0.89 (Figure 3.9). The difference form (month-over-month percent change in this case) of a series, however, is usually stationary and, therefore, is better suited for regression analysis. Using the difference form of the S&P 500 index and nonfarm payrolls, we obtained a lower, but more reliable R-squared of 0.01 (Figure 3.10). Therefore, measurement error (wrong functional form) can lead to a completely wrong conclusion.

The OLS regression is a simple and widely utilized method of estimation and forecasting. A typical OLS model consists of a dependent variable (left-hand side variable) and one or more independent variables (right-hand side variables). The OLS method is simple because of several limitations. First, OLS only estimates a statistical association between the variables of the model and does not identify the statistical causal relationship. Second, to generate out-of-sample forecasts of the dependent variable, we need out-of-sample values of the right-hand side (independent) variables. Third, we cannot include too many variables because we would reduce our degrees of freedom and/or introduce multicollinearity problems. Fourth and finally, since the OLS is a single equation (only one dependent variable), it is unable to capture the underlying structure of an economy and may suffer model specification issues and provide unreliable results.

The Bayesian Vector Autoregression (BVAR) model, on the other hand, addresses the issues mentioned above. The BVAR approach can be utilized to test causal relationships between variables of interest (Granger causality). The BVAR model does not require future values of the right-hand side variables to generate out-of-sample forecasts for target variables. In addition, the BVAR approach allows us to include many variables in the model and hence permits us to include more information than the OLS model. Finally, the BVAR method improves upon the single-equation approach into a system of equations (several dependent variables) and can better capture the underlying structure of an economy. In general, the BVAR approach is more flexible and should be utilized to test causal relationships as well as generate forecasts.

Information Dynamics: Information Can Change in the Future—Out-of-Sample Forecast Errors

Third, information is also dynamic over time. For example, information on the pace of economic growth and job creation over time is revised and this changed perspective leads to alternative decisions or decisions that are regretted and would have been different if economic agents did indeed have perfect foresight. In war, it is said that battle plans change after the first shot. In business, the introduction of New Coke was met with an immediate negative reaction that marketing executives completely failed to anticipate.¹⁵ Many times, government rules on land use or flood plains can change after a developer or homeowner has bought a piece of real estate.¹⁶

Credit decisions can be turned on their head by court decisions on municipal bankruptcies, rule of law in corporate bankruptcies and federal mandates, or simply a rewriting of federal/state laws that upset the previously understood relationship between creditors and debtors. Finally, recent years have witnessed significant shifts in sovereign government commitments to exchange rate regimes and trading agreements, as a new political leadership assumes leadership after an election.

Forecast errors tend to increase with the forecast horizon—the longer the forecast horizon, the larger the forecast error. This can be illustrated by the forecast variance of the canonical autoregressive model of order one (AR[1] model). For tractability, we assume there is no drift term (constant). An AR(1) model is given as follows¹⁷:

Where X_t is the time series being studied and ε_t is the independent and identically distributed error term with mean zero and variance of σ2. The l-step ahead value of our series is given by recursively stepping forward in the model as follows:

The expected value of this series is given below, as the error terms drop out.

The variance of this forecast, however, is fully dependent on the variance of the error terms. Note that the error of our forecast will be given as the difference of the actual value (X_T+l) and the expected value, which simplifies to the cumulative error:

Now this seems like an ugly equation to work with. This is why the assumption of i.i.d. error terms is useful. This means that whenever a ≠ b. Therefore, most terms in the above equation drop out. We can simplify further to:

Note that, as one would expect, variance is monotonically increasing the further out into the future we are forecasting. That said, the concavity of the error is dependent on the value of β. If β < 1, the series is mean reverting, and the standard deviation of the forecast is concave down. If the series is not mean reverting, however, and β > 1, then the standard deviation is concave up, and therefore our forecasts will be poor.

There are several reasons behind the larger forecast errors for longer forecast horizons (Figure 3.11). For instance, the cumulative chance of a shock (in policies or consumer/investor behavior for example) increases with time. In addition, the objective function of other players may change over time, thereby complicating economic decisions. European governments can quickly shift to tighter fiscal policy—as we saw post-2009. Foreign governments can quickly shift exchange rate policy. Domestically, regulators can alter the direction of policy and rules over time. This problem is compounded with changes in political party leadership. At the state/local level, changes in land use policy after property has been bought for development affects the planned development and therefore limits economic development in many local areas. As a result, in contrast to the model that assumes that the objective functions of economic agents do not change over time, the reality is that change is constant on the part of decision makers and the rules they promote. New information and rules alter the payoffs and the expected rates of return on investment in equipment and workers. This uncertainty regarding future policy changes will tend to reduce long-term investment in equipment and the hiring of workers. The time horizon for all economic decisions is shortened given the risk/uncertainty of future political/policy change.

Analysis Paralysis

Too much information can be a problem. For both public and private decision makers, too many guidelines and economic indicators can actually stifle decision making. The perceived cost of making a decision exceeds the benefits that could be gained by enacting some decision. Decision makers often seek the optimal or perfect solution to a problem as they rightly fear the costs of a wrong decision, leading to over analysis. That said, no action is often more costly than many suboptimal actions. This is a problem today in several areas. First, in monetary policy, as we have cited before, there are several economic guidelines (multiple measures of labor slack and inflation) such that so much information may stymie any future decision making by often suggesting contradictory assessments of the economic situation. This uncertainty often prompts cautious responses—overly cautious policy may be too late. In addition, financial institutions face numerous regulators (Federal Reserve, Securities and Exchange Commission, Federal Deposit Insurance Corporation, and the Comptroller of the U.S. Treasury), each with their own set of priorities. In the face of many possible disparate regulatory signals, in the private sector, both financial institutions and nonfinancial corporations, rather than moving forward by putting cash to use, these institutions simply sit on the cash waiting for further information. In a similar way, private nonfinancial firms face similar problems with the multiple information guideposts on taxes and public spending decisions. In each case the quantity of information and analysis overwhelms the decision-making process and thereby inhibits an economic agent from making a decision.

In addition, when public policy makers do act, their decisions may create the impression that there is some special piece of information available to them, not available to the private sector, such that the private sector asks itself—what are we missing?¹⁸

Bounded Rationality

Herbert A. Simon commented that the rationality of individuals is limited by the information they have, the cognitive limitations of their minds, and the finite amount of time they have to make a decision.¹⁹ This is the reality of making decisions on production, hiring, and allocating credit in real time. This leads many decision makers to be satisficers—not optimizers with complex mathematical models. Households apply their rationality only after having greatly simplified the choices available. Households, firms, and even public policy makers lack the ability and resources to arrive at the optimal solution.

Decision makers pick a stopping point—they do not seek all the information that might be available. However, the particular stopping point differs among individuals. As a result, the perfectly rational decisions assumed in economic models are often not feasible in practice even with perfect information because of the finite computational resources and time available for making them.

Our evaluation of economic activity and the impact of public or private sector actions must begin with the recognition that the costs of gathering, processing and disseminating information provides an incentive to limit the time spent in these efforts. In fact, the complexity of the situation may limit, rather than expand, the information process. In real time, actions must be taken despite the complexity, as in Captain Mancuso’s need to send a message without gathering information and checking his Morse code. Decision makers simply are unable to process and compute the expected utility of every alternative action. Deliberation costs might be high, and they are often concurrent with economic activities also requiring attention so decision makers have limits on time and the ability to process information.

Information Asymmetry

Here, we focus on decisions in transactions where one party has more, or better, information than the other. There are three situations that produce results that are contrary to the idealized results of the perfectly competitive market model: adverse selection, moral hazard, and the principal-agent problem.²⁰

Adverse selection arises when one party to the agreement lacks critical information while negotiating an agreed contract. This problem often arises in financial services when a loan is being made and complete information about the credit history and the motivations of the borrower are unknown. Other situations of adverse selection include used cars and home purchases—consider the canonical market for lemons.²¹

Moral hazard arises when one party lacks critical information about performance of the agreed-upon transaction or lacks the ability to retaliate for a breach of the agreement. Households/firms may behave more recklessly after becoming insured, but the insurer cannot effectively retaliate against the insured in the short run during the term of the current contract. Only in the long run can the insurer deny to renew—but even here that ability is sometimes prohibited. Furthermore, the riskiest individuals are more likely to buy insurance and insurance companies often cannot discriminate due to the force of law. We can see this in the market for health insurance where younger, healthier people are less likely to buy medical insurance compared to older, less healthy people.²²

In the case of the principal-agent problem, there is an information asymmetry where agents have more information and the principal cannot directly ensure that the agent is always acting in the principal’s best interests. In the most common situation, corporate management acts as agent and shareholders are the principal.²³ In another case, politicians are the agent and voters are the principal. The information asymmetry therefore has significant private-sector implications with respect to the incentives for corporate management, where maximizing shareholder value may not be the driving principle for management, and it is therefore difficult to determine if management is truly maximizing profits—a basic tenet of microeconomic theory about the firm. In public policy, do politicians support policy actions to actually maximize economic growth or are decisions on policy, such as a fiscal stimulus, directed more toward ensuring their own reelection rather than public benefit?

Imperfect Decision Making

In policy making, the problem of imperfect information arises in two distinct paths. First, while there is one monetary policy, we often hear from several different members of the FOMC that create different impressions for the direction of policy. Second, currently the FOMC is following a broad set of labor market indicators to determine the direction of policy. Although this may enhance policy, the information problem is that a central bank that follows multiple labor market indicators sends a confusing signal to the private-sector investor. As the adage goes, a man with one clock will know what time it is, but a man who has two clocks is never sure. This policy-making problem is further complicated by the initial unemployment rate guidepost of 6.5 percent being replaced by the emphasis on a wider range of labor market indicators. This problem is also present when several different inflation guidelines shift between core and overall inflation, consumer price index (CPI), and PCE inflation—once again, too many clocks.

Cognitive Bias

Even with the proper information, the decision maker has biases that will often not produce an optimal solution. The decision maker employs his or her own subjective social reality, not the objective input of relevant information that would lead most other people to pursue a different decision path. Judgments deviate from the optimum, so it becomes increasingly difficult to judge the range of outcomes and their possibilities. This situation often arises when investors seek to evaluate the strategy of corporate leadership and that strategy of introducing new products/prices or acquisitions appears confused and without a clear path forward. These cognitive biases include the confirmation bias, framing, and the sunk cost bias.²⁴

All of these biases introduce challenges to the assumption of rationality. The price one paid for a good or asset should not be relevant when it comes to selling the good or asset. That said, one must not look far to find someone who is reluctant to sell an asset for less than what they paid for it, even though this is an arbitrary delineation because the purchase prices is a sunk cost. Anchoring biases are also present throughout economics. While the ratio of home prices to income was roughly constant for several decades, this relationship was forgotten during the run-up to the Great Recession, where home prices grew rapidly (Figure 3.12). People began to believe that the recent trend would continue indefinitely. Analysts failed to consider the implications for a decline in home prices and largely ignored that possibility.

Rational Ignorance

Rational ignorance occurs when the cost of educating oneself on an issue exceeds the potential benefit of that education.²⁵ In this case, the decision maker comes to a rational decision that the cost of educating oneself on an issue outweighs any potential benefits; therefore, it is irrational for a decision maker to waste time pursuing additional information. That is, once the marginal cost of searching for information exceeds the marginal benefit of obtaining that information, it would be irrational to continue searching. For example, consumers have limited time, so visiting another store to possibly find a better price may not be worth the time. Now, of course, consumers will use the Internet to search for better prices or product information to lower the marginal cost of information.

This can also be seen in politics. Small groups who derive substantial benefits from a policy are incentivized to lobby hard for that policy. Policy makers may implement the policy, even if it is costly to the public, because the cost would be spread among a large group of people and be relatively small. It would often be irrational for voters to learn the specifics of each issue in an election from a purely economic standpoint, as the expected benefit of this is minuscule. The probability that an individual vote will matter is small and even if that vote is persuasive, the policies the voters advocate are not necessarily what will be made into law.

Heuristics

Heuristics are often employed by economic agents, where households and firms employ experience-based techniques for problem solving, learning, and discovery, which gives a solution that is not guaranteed to be optimal. Here, exhaustive searching for, and processing of, information is impractical. Heuristic methods are employed to speed up the process of finding a satisfactory solution via mental shortcuts to ease the cognitive load of making a decision. In other contexts, we can refer to rules of thumb, educated guesses, intuition, working backward, or trial and error. With rational ignorance, where it is impractical to gain all the information, heuristics are often employed.

Prospect Theory

Under prospect theory, households make decisions based on the potential value of losses and gains rather than the final expected outcome, and then people evaluate their prospects (these losses and gains) using certain heuristics rather than precise economic models.²⁶ Our focus here is the way people choose between probabilistic alternatives that involve risk, where the probabilities of outcomes are known. This involves a two-step process. First, households order outcomes and match outcomes that are perceived to be equivalent. Then households set a reference point and then consider lesser outcomes as losses and greater ones as gains. This involves considering the entire distribution of outcomes from a decision rather than simply looking at the expected value. Because agents in an economy are typically risk averse, we must consider all possible outcomes, not solely the mean. In the traditional capital asset pricing model, notice how the undiversifiable risk influences the expected return of a stock. That is, investors require a higher expected return because of the increased risk to the downside.