What is an Autonomous Expenditure?

An autonomous expenditure describes the components of an economy’s aggregate expenditure that are not impacted by that same economy’s real level of income. This type of spending is considered automatic and necessary, whether occurring at the government level or the individual level. The classical economic theory states that any rise in autonomous expenditures will create at least an equivalent rise in aggregate output, such as GDP, if not a greater increase.

Understanding Autonomous Expenditure

An autonomous expenditure obligation must be met regardless of income. It is considered independent in nature, as the need does not vary with incomes. Often, these expenses are associated with the ability to maintain a state of autonomy. Autonomy, in regard to nations, includes the ability to be self-governing. For individuals, it refers to the ability to function within a certain level of societally acceptable independence.

To be considered an autonomous expenditure, the spending must generally be deemed necessary to maintain a base level of function or, in an individual sense, survival. Often, these expenses do not vary regardless of personal disposable income or national income. Autonomous expenditure is tied to autonomous consumption, including all of the financial obligations required to maintain a basic standard of living. All expenses beyond these are considered part of induced consumption, which is affected by changes in disposable income.

In cases in which personal income is insufficient, autonomous expenses still must be paid. These needs can be met through the use of personal savings, consumer borrowing mechanisms such as loans and credit cards, or various social services.

Autonomous Expenditures and Income Levels

While the obligations that qualify as autonomous expenditures do not vary, the amount of income directed toward them can. For example, in an individual sense, the need for food qualifies as an autonomous expenditure, though the need can be fulfilled in a variety of manners, ranging from the use of food stamps to eating every meal at a five-star restaurant. Even though income level may affect how the need is met, the need itself does not change.

Governments and Autonomous Expenditures

The vast majority of government spending qualifies as autonomous expenditures. This is due to the fact that the spending often relates strongly to the efficient running of a nation, making some of the expenditures required in order to maintain minimum standards.

Factors Affecting Autonomous Expenditures

Technically, autonomous expenditures are not affected by external factors. In reality, however, several factors can affect autonomous expenditures. For example, interest rates have a significant effect on consumption in an economy. High interest rates can tamp down on consumption while low interest rates can spur it. In turn, this affects spending within an economy.

Trade policies between countries can also affect autonomous expenditures made by their citizens. If a producer of cheap goods imposes duties on exports, then it would have the effect of making finished products for outside geographies more expensive. Governments can also impose controls on an individual’s autonomous expenditures through taxes. If a basic household good is taxed and no substitutes are available, then the autonomous expenditure pertaining to it may decrease.

Examples of Autonomous Expenditure

Some of the spending classes that are considered independent of income levels, which can be counted as either individual income or taxation income, are government expenditures, investments, exports, and basic living expenses such as food and shelter.

What Is Analysis of Variance (ANOVA)?

Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.

The t- and z-test methods developed in the 20th century were used for statistical analysis until 1918, when Ronald Fisher created the analysis of variance method. ANOVA is also called the Fisher analysis of variance, and it is the extension of the t- and z-tests. The term became well-known in 1925, after appearing in Fisher’s book, “Statistical Methods for Research Workers.” It was employed in experimental psychology and later expanded to subjects that were more complex.

The Formula for ANOVA is:


$\begin{aligned} &\text{F} = \frac{ \text{MST} }{ \text{MSE} } \\ &\textbf{where:} \\ &\text{F} = \text{ANOVA coefficient} \\ &\text{MST} = \text{Mean sum of squares due to treatment} \\ &\text{MSE} = \text{Mean sum of squares due to error} \\ \end{aligned}$​F=MSEMST​where:F=ANOVA coefficientMST=Mean sum of squares due to treatmentMSE=Mean sum of squares due to error​

What Does the Analysis of Variance Reveal?

The ANOVA test is the initial step in analyzing factors that affect a given data set. Once the test is finished, an analyst performs additional testing on the methodical factors that measurably contribute to the data set’s inconsistency. The analyst utilizes the ANOVA test results in an f-test to generate additional data that aligns with the proposed regression models.

The ANOVA test allows a comparison of more than two groups at the same time to determine whether a relationship exists between them. The result of the ANOVA formula, the F statistic (also called the F-ratio), allows for the analysis of multiple groups of data to determine the variability between samples and within samples.

If no real difference exists between the tested groups, which is called the null hypothesis, the result of the ANOVA’s F-ratio statistic will be close to 1. The distribution of all possible values of the F statistic is the F-distribution. This is actually a group of distribution functions, with two characteristic numbers, called the numerator degrees of freedom and the denominator degrees of freedom.

Example of How to Use ANOVA

A researcher might, for example, test students from multiple colleges to see if students from one of the colleges consistently outperform students from the other colleges. In a business application, an R&D researcher might test two different processes of creating a product to see if one process is better than the other in terms of cost efficiency.

The type of ANOVA test used depends on a number of factors. It is applied when data needs to be experimental. Analysis of variance is employed if there is no access to statistical software resulting in computing ANOVA by hand. It is simple to use and best suited for small samples. With many experimental designs, the sample sizes have to be the same for the various factor level combinations.

ANOVA is helpful for testing three or more variables. It is similar to multiple two-sample t-tests. However, it results in fewer type I errors and is appropriate for a range of issues. ANOVA groups differences by comparing the means of each group and includes spreading out the variance into diverse sources. It is employed with subjects, test groups, between groups and within groups.

One-Way ANOVA Versus Two-Way ANOVA

There are two main types of ANOVA: one-way (or unidirectional) and two-way. There also variations of ANOVA. For example, MANOVA (multivariate ANOVA) differs from ANOVA as the former tests for multiple dependent variables simultaneously while the latter assesses only one dependent variable at a time. One-way or two-way refers to the number of independent variables in your analysis of variance test. A one-way ANOVA evaluates the impact of a sole factor on a sole response variable. It determines whether all the samples are the same. The one-way ANOVA is used to determine whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

A two-way ANOVA is an extension of the one-way ANOVA. With a one-way, you have one independent variable affecting a dependent variable. With a two-way ANOVA, there are two independents. For example, a two-way ANOVA allows a company to compare worker productivity based on two independent variables, such as salary and skill set. It is utilized to observe the interaction between the two factors and tests the effect of two factors at the same time.

What Is the Addition Rule for Probabilities?

The addition rule for probabilities describes two formulas, one for the probability for either of two mutually exclusive events happening and the other for the probability of two non-mutually exclusive events happening.

The first formula is just the sum of the probabilities of the two events. The second formula is the sum of the probabilities of the two events minus the probability that both will occur.

The Formulas for the Addition Rules for Probabilities Is

Mathematically, the probability of two mutually exclusive events is denoted by:


$P(Y \text{ or } Z) = P(Y)+P(Z)$P(Y or Z)=P(Y)+P(Z)

Mathematically, the probability of two non-mutually exclusive events is denoted by:


$P(Y \text{ or } Z) = P(Y) + P(Z) – P(Y \text{ and } Z)$P(Y or Z)=P(Y)+P(Z)−P(Y and Z)

What Does the Addition Rule for Probabilities Tell You?

To illustrate the first rule in the addition rule for probabilities, consider a die with six sides and the chances of rolling either a 3 or a 6. Since the chances of rolling a 3 are 1 in 6 and the chances of rolling a 6 are also 1 in 6, the chance of rolling either a 3 or a 6 is:

1/6 + 1/6 = 2/6 = 1/3

To illustrate the second rule, consider a class in which there are 9 boys and 11 girls. At the end of the term, 5 girls and 4 boys receive a grade of B. If a student is selected by chance, what are the odds that the student will be either a girl or a B student? Since the chances of selecting a girl are 11 in 20, the chances of selecting a B student are 9 in 20 and the chances of selecting a girl who is a B student are 5/20, the chances of picking a girl or a B student are:

11/20 + 9/20 – 5/20 =15/20 = 3/4

In reality, the two rules simplify to just one rule, the second one. That’s because in the first case, the probability of two mutually exclusive events both happening is 0. In the example with the die, it’s impossible to roll both a 3 and a 6 on one roll of a single die. So the two events are mutually exclusive.

Mutual Exclusivity

Mutually exclusive is a statistical term describing two or more events that cannot coincide. It is commonly used to describe a situation where the occurrence of one outcome supersedes the other.  For a basic example, consider the rolling of dice. You cannot roll both a five and a three simultaneously on a single die. Furthermore, getting a three on an initial roll has no impact on whether or not a subsequent roll yields a five. All rolls of a die are independent events.

What Is an Anomaly?

In economics and finance, an anomaly is when the actual result under a given set of assumptions is different from the expected result predicted by a model. An anomaly provides evidence that a given assumption or model does not hold up in practice. The model can either be a relatively new or older model.

Understanding Anomalies

In finance, two common types of anomalies are market anomalies and pricing anomalies. Market anomalies are distortions in returns that contradict the efficient market hypothesis (EMH). Pricing anomalies are when something—for example, a stock—is priced differently than how a model predicts it will be priced.

Common market anomalies include the small-cap effect and the January effect. The small-cap effect refers to the small company effect, where smaller companies tend to outperform larger ones over time. The January effect refers to the tendency of stocks to return much more in the month of January than in others.

Anomalies also often occur with respect to asset pricing models, in particular, the capital asset pricing model (CAPM). Although the CAPM was derived by using innovative assumptions and theories, it often does a poor job of predicting stock returns. The numerous market anomalies that were observed after the formation of the CAPM helped form the basis for those wishing to disprove the model. Although the model may not hold up in empirical and practical tests, it still does hold some utility.

Anomalies tend to be few and far between. In fact, once anomalies become publicly known, they tend to quickly disappear as arbitragers seek out and eliminate any such opportunity from occurring again.

Types of Market Anomalies

In financial markets, any opportunity to earn excess profits undermines the assumptions of market efficiency, which states that prices already reflect all relevant information and so cannot be arbitraged.

January Effect

The January effect is a rather well-known anomaly. According to the January effect, stocks that underperformed in the fourth quarter of the prior year tend to outperform the markets in January. The reason for the January effect is so logical that it is almost hard to call it an anomaly. Investors will often look to jettison underperforming stocks late in the year so that they can use their losses to offset capital gains taxes (or to take the small deduction that the IRS allows if there is a net capital loss for the year). Many people call this event tax-loss harvesting.

As selling pressure is sometimes independent of the company’s actual fundamentals or valuation, this “tax selling” can push these stocks to levels where they become attractive to buyers in January.

Likewise, investors will often avoid buying underperforming stocks in the fourth quarter and wait until January to avoid getting caught up in the tax-loss selling. As a result, there is excess selling pressure before January and excess buying pressure after Jan. 1, leading to this effect.

September Effect

The September effect refers to historically weak stock market returns for the month of September. There is a statistical case for the September effect depending on the period analyzed, but much of the theory is anecdotal. It is generally believed that investors return from summer vacation in September ready to lock in gains as well as tax losses before the end of the year.

There is also a belief that individual investors liquidate stocks going into September to offset schooling costs for children. As with many other calendar effects, the September effect is considered a historical quirk in the data rather than an effect with any causal relationship. 

Days of the Week Anomalies

Efficient market supporters hate the “Days of the Week” anomaly because it not only appears to be true, but it also makes no sense. Research has shown that stocks tend to move more on Fridays than Mondays and that there is a bias toward positive market performance on Fridays. It is not a huge discrepancy, but it is a persistent one.

The Monday effect is a theory which states that returns on the stock market on Mondays will follow the prevailing trend from the previous Friday. Therefore, if the market was up on Friday, it should continue through the weekend and, come Monday, resume its rise. The Monday effect is also known as the “weekend effect.”

On a fundamental level, there is no particular reason that this should be true. Some psychological factors could be at work. Perhaps an end-of-week optimism permeates the market as traders and investors look forward to the weekend. Alternatively, perhaps the weekend gives investors a chance to catch up on their reading, stew and fret about the market, and develop pessimism going into Monday.

Superstitious Indicators

Aside from calendar anomalies, there are some non-market signals that some people believe will accurately indicate the direction of the market. Here is a short list of superstitious market indicators:

• The Super Bowl Indicator: When a team from the old American Football League wins the game, the market will close lower for the year. When an old National Football League team wins, the market will end the year higher. Silly as it may seem, the Super Bowl indicator was correct almost three-quarters of the time over a 53-year period ending in 2021. However, the indicator has one limitation: It contains no allowance for an expansion-team victory!
• The Hemline Indicator: The market rises and falls with the length of skirts. Sometimes this indicator is referred to as the “bare knees, bull market” theory. To its merit, the hemline indicator was accurate in 1987, when designers switched from miniskirts to floor-length skirts just before the market crashed. A similar change also took place in 1929, but many argue as to which came first, the crash or the hemline shifts.
• The Aspirin Indicator: Stock prices and aspirin production are inversely related. This indicator suggests that when the market is rising, fewer people need aspirin to heal market-induced headaches. Lower aspirin sales should indicate a rising market.