what is hypothesis testing in econometrics

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What Is Econometrics?

Understanding econometrics.

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Econometrics: Definition, Models, and Methods

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Econometrics is the use of statistical and mathematical models to develop theories or test existing hypotheses in economics and to forecast future trends from historical data. It subjects real-world data to statistical trials and then compares the results against the theory being tested.

Depending on whether you are interested in testing an existing theory or in using existing data to develop a new hypothesis, econometrics can be subdivided into two major categories: theoretical and applied. Those who routinely engage in this practice are commonly known as econometricians.

Key Takeaways

• Econometrics is the use of statistical methods to develop theories or test existing hypotheses in economics or finance.
• Econometrics relies on techniques such as regression models and null hypothesis testing.
• Econometrics can also be used to try to forecast future economic or financial trends.
• As with other statistical tools, econometricians should be careful not to infer a causal relationship from statistical correlation.
• Some economists have criticized the field of econometrics for prioritizing statistical models over economic reasoning.

Investopedia / Michela Buttignol

Econometrics analyzes data using statistical methods in order to test or develop economic theory. These methods rely on statistical inferences to quantify and analyze economic theories by leveraging tools such as frequency distributions , probability, and probability distributions , statistical inference, correlation analysis, simple and multiple regression analysis, simultaneous equations models, and time series methods.

Econometrics was pioneered by Lawrence Klein , Ragnar Frisch, and Simon Kuznets . All three won the Nobel Prize in economics for their contributions. Today, it is used regularly among academics as well as practitioners such as Wall Street traders and analysts.

An example of the application of econometrics is to study the income effect using observable data. An economist may hypothesize that as a person increases their income, their spending will also increase.

If the data show that such an association is present, a regression analysis can then be conducted to understand the strength of the relationship between income and consumption and whether or not that relationship is statistically significant—that is, it appears to be unlikely that it is due to chance alone.

Methods of Econometrics

The first step to econometric methodology is to obtain and analyze a set of data and define a specific hypothesis that explains the nature and shape of the set. This data may be, for example, the historical prices for a stock index, observations collected from a survey of consumer finances, or unemployment and inflation rates in different countries.

If you are interested in the relationship between the annual price change of the S&P 500 and the unemployment rate, you'd collect both sets of data. Then, you might test the idea that higher unemployment leads to lower stock market prices. In this example, stock market price would be the dependent variable and the unemployment rate is the independent or explanatory variable.

The most common relationship is linear, meaning that any change in the explanatory variable will have a positive correlation with the dependent variable. This relationship could be explored with a simple regression model, which amounts to generating a best-fit line between the two sets of data and then testing to see how far each data point is, on average, from that line.

Note that you can have several explanatory variables in your analysis—for example, changes to GDP and inflation in addition to unemployment in explaining stock market prices. When more than one explanatory variable is used, it is referred to as multiple linear regression . This is the most commonly used tool in econometrics.

Some economists, including John Maynard Keynes , have criticized econometricians for their over-reliance on statistical correlations in lieu of economic thinking.

Different Regression Models

There are several different regression models that are optimized depending on the nature of the data being analyzed and the type of question being asked. The most common example is the ordinary least squares (OLS) regression, which can be conducted on several types of cross-sectional or time-series data. If you're interested in a binary (yes-no) outcome—for instance, how likely you are to be fired from a job based on your productivity—you might use a logistic regression or a probit model. Today, econometricians have hundreds of models at their disposal.

Econometrics is now conducted using statistical analysis software packages designed for these purposes, such as STATA, SPSS, or R. These software packages can also easily test for statistical significance to determine the likelihood that correlations might arise by chance. R-squared , t-tests ,  p-values , and null-hypothesis testing are all methods used by econometricians to evaluate the validity of their model results.

Limitations of Econometrics

Econometrics is sometimes criticized for relying too heavily on the interpretation of raw data without linking it to established economic theory or looking for causal mechanisms. It is crucial that the findings revealed in the data are able to be adequately explained by a theory, even if that means developing your own theory of the underlying processes.

Regression analysis also does not prove causation, and just because two data sets show an association, it may be spurious. For example, drowning deaths in swimming pools increase with GDP. Does a growing economy cause people to drown? This is unlikely, but perhaps more people buy pools when the economy is booming. Econometrics is largely concerned with correlation analysis, and it is important to remember that correlation does not equal causation.

What Are Estimators in Econometrics?

An estimator is a statistic that is used to estimate some fact or measurement about a larger population. Estimators are frequently used in situations where it is not practical to measure the entire population. For example, it is not possible to measure the exact employment rate at any specific time, but it is possible to estimate unemployment based on a randomly-chosen sample of the population.

What Is Autocorrelation in Econometrics?

Autocorrelation measures the relationships between a single variable at different time periods. For this reason, it is sometimes called lagged correlation or serial correlation, since it is used to measure how the past value of a certain variable might predict future values of the same variable. Autocorrelation is a useful tool for traders, especially in technical analysis.

What Is Endogeneity in Econometrics?

An endogenous variable is a variable that is influenced by changes in another variable. Due to the complexity of economic systems, it is difficult to determine all of the subtle relationships between different factors, and some variables may be partially endogenous and partially exogenous. In econometric studies, the researchers must be careful to account for the possibility that the error term may be partially correlated with other variables.

Econometrics is a popular discipline that integrates statistical tools and modeling for economic data, and it is frequently used by policymakers to forecast the result of policy changes. Like with other statistical tools, there are many possibilities for error when econometric tools are used carelessly. Econometricians must be careful to justify their conclusions with sound reasoning as well as statistical inferences.

The Nobel Prize. " Simon Kuznets ."

The Nobel Prize. " Ragnar Frisch ."

The Nobel Prize. " Lawrence R. Klein ."

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Econometrics for Business Analytics

Chapter 7 hypothesis testing.

Hypothesis testing is the most important thing you learned in business statistics. It is the foundation of the statistical world.

Hypothesis testing tells us if the treatment effect we observed is statistically significant .

A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. Hypothesis testing refers to the formal procedures used by statisticians to accept or reject statistical hypotheses.

7.1 Statistical Hypotheses

The best way to determine whether a statistical hypothesis is true would be to examine the entire population. Since that is often impractical, researchers typically examine a random sample from the population. If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected.

There are two types of statistical hypotheses.

• Null hypothesis. The null hypothesis, denoted by Ho, is usually the hypothesis that sample observations result purely from chance.
• Alternative hypothesis. The alternative hypothesis, denoted by H1 or Ha, is the hypothesis that sample observations are influenced by some non-random cause.

7.2 Case Study: Birthweight and Smoking

There is a lot of evidence that smoking is bad for one’s health. What is less certain is the effect of smoking on birth-weight.

You might ask, “how is this hard to measure or why is it controversial?”

The issue is with reporting. If you are a pregnant mother, how honestly would you respond to the question of “Do you smoke?”

It is easy to see that mothers may lie about how much or even if they smoked while pregnant.

7.2.1 Load the Data

First, let’s load the data.

7.2.2 Difference in Birthweight by Smoking Status

Compare birth-weight by smoking status, we can see that smoker babies are smaller, but there is overlap.

7.2.3 Differences in Birthweight by Smoking Status

7.2.4 Differences in Birthweight by Smoking Status

How can we assess whether this difference is statistically significant?

Let’s compute a summary table

7.2.5 Differences in Birthweight by Smoking Status

The standard deviation is good to have, but to assess statistical significance we really want to have the standard error.

If we use a confidence interval around the sample means, there is less overlap between the two groups. \[\bar{x}\pm se*t_{\alpha /2} \]

7.2.6 T-test for Birthweight by Smoking Status

In this case study, we have been looking at a sample of mothers, some who smoke and some who do not. These are samples and not populations. Therefore, we need to use a two sample t-test.

This difference is looking quite significant. To run a two-sample t-test, we can simple use the t.test() function.

7.2.7 Interpreting Output

There are a few things from the output we can note.

First, is the p-value. The p-value tells us the likelihood that the null hypothesis (in this case no difference between groups) is true. For p-values less than 5 percent, we can reject the null hypothesis and state there is a statistically significant difference between the two groups.

The p-value in our t-test was 0.0070025, which is less than 1 percent so we can reject the null hypothesis.

Our study finds that birth weights are on average higher in the non-smoking group compared to the smoking group (t-statistic 2.73, p=0.007, 95 % CI [78.6, 489]g)

7.3 Standard Levels of significance

Levels of significance, \(\alpha\) , are commonly - \(\alpha\) = 0.10 is marginally significant - \(\alpha\) = 0.05 is significant - \(\alpha\) = 0.01 is very significant

We reject the null hypothesis \(H_0\) if the p-value \(< \alpha\) .

The significance level represents the probability of committing a Type I error that we are willing to accept. A Type I error is rejecting the null hypothesis when the null hypothesis is true.

7.4 Warning

7.4.1 can we accept the null hypothesis.

Some researchers say that a hypothesis test can have one of two outcomes: you accept the null hypothesis or you reject the null hypothesis. Many statisticians, however, take issue with the notion of “accepting the null hypothesis.” Instead, they say: you reject the null hypothesis or you fail to reject the null hypothesis.

Why the distinction between “acceptance” and “failure to reject?” Acceptance implies that the null hypothesis is true. Failure to reject implies that the data are not sufficiently persuasive for us to prefer the alternative hypothesis over the null hypothesis.

Think of it this way. In court, we say a person is either guilty or not guilty. We do not say the person is innocent. That is, we conclude that either there is enough evidence to say the person is guilty or there isn’t enough evidence (fail to reject).