# Economics & Finance

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### Defining and Justifying the Least Squares Principle

When you need to estimate a sample regression function (SRF), the most common econometric method is the ordinary least squares (OLS) technique, which uses the least squares principle to fit a prespecified

### Estimating the Regression Function and the Residuals

The regression function is usually expressed mathematically in one of the following ways: basic notation, summation notation, or matrix notation. The Y

### Quadratic Functions Offer Flexibility in Econometrics

Because economic relationships are rarely linear, you may want to allow your econometric model to have some flexibility. With a quadratic function, you allow the effect of the independent variable

### Cubic Functions in Econometrics Are Good for Inflexion

With a cubic function, you allow the effect of the independent variable (X) on the dependent variable (Y) to change. As the value of X increases (or decreases), the impact of the dependent variable may

### In Econometrics, the Inverse Function Limits the Dependent Variable's Value

If you believe that the outcome (dependent variable) you’re modeling is likely to approach some value asymptotically (as X approaches zero or infinity), then an inverse function may be the way to go.

### The Linear-Log Model in Econometrics

If you use natural log values for your independent variables (X) and keep your dependent variable (Y) in its original scale, the econometric specification is called a

### How to Find Average Differences by Using a Dummy Variable

You should recall from your statistics course how to conduct the t-test to examine the differences in means between two groups. But what you may not know is that you can use dummy variables and regression

### The 2 Types of Multicollinearity

Multicollinearity arises when a linear relationship exists between two or more independent variables in a regression model. In practice, you rarely encounter perfect multicollinearity, but high multicollinearity

### Perfect Multicollinearity and Your Econometric Model

Getting a grasp on perfect multicollinearity, which is uncommon, is easier if you can picture an econometric model that uses two independent variables, such as the following:

### High Multicollinearity and Your Econometric Model

High multicollinearity results from a linear relationship between your independent variables with a high degree of correlation but aren’t completely deterministic

### How to Check for Heteroskedasticity by Examining Graphed Residuals

In econometrics, an informal way of checking for heteroskedasticity is with a graphical examination of the residuals. If you want to use graphs for an examination of heteroskedasticity, you first choose

### Test for Heteroskedasticity with the Goldfeld-Quandt Test

The Goldfeld-Quandt (GQ) test in econometrics begins by assuming that a defining point exists and can be used to differentiate the variance of the error term. Sample observations are divided into two groups

### Use the Park Test to Check for Heteroskedasticity

The Park test begins by assuming a specific model of the heteroskedastic process. Specifically, it assumes that the heteroskedasticity may be proportional to some power of an independent variable

### Patterns of Autocorrelation

Autocorrelation, also known as serial correlation,may exist in a regression model when the order of the observations in the data is relevant or important. In other words, with time-series

### 3 Main Linear Probability Model (LPM) Problems

Using the ordinary least squares (OLS) technique to estimate a model with a dummy dependent variable is known as creating a linear probability model, or LPM. LPMs aren’t perfect. Three specific problems

### Specifying Appropriate Nonlinear Functions: The Probit and Logit Models

If your outcome of interest is qualitative, you use a dummy dependent variable and estimate the probability that the outcome (Y = 1) occurs using your econometric model. Although OLS can be used to estimate

### Using Maximum Likelihood (ML) Estimation

Probit and logit functions are both nonlinear in parameters, so ordinary least squares (OLS) can’t be used to estimate the betas. Instead, you have to use a technique known as maximum likelihood

### Limited Dependent Variables in Econometrics

Limited dependent variables arise when some minimum threshold value must be reached before the values of the dependent variable are observed and/or when some maximum threshold value restricts the observed

### How to Estimate Seasonality Effects

Seasonality effects can be correlated with both your dependent and independent variables. In order to avoid confounding the seasonality effects with those of your independent variables, you need to explicitly

### How to Deseasonalize Time-Series Data

In many cases, seasonal patterns are removed from time-series data when they’re released on public databases. Data that has been stripped of its seasonal patterns is referred to as

### How to Use OLS for Seasonal Adjustments

The higher the frequency of an economic time series, the more likely it is to display seasonal patterns. For example, retail sales figures often exhibit a significant increase around the winter holidays

### Intercepts and/or Slopes That Change over Time

Unlike typical cross-section analysis, which imposes a static nature to your models, a pooled cross section allows you to incorporate a dynamic time element. You can do this with a pooled cross section

### Quantifying Qualitative Information for Econometric Models

Estimating an econometric model requires that all the information be quantified. In other words, numbers must be used to characterize both your quantitative and qualitative variables. Quantitative variables

### How to Create and Save STATA Databases

In order to begin doing any exploratory data analysis or econometric work, you need a dataset that can be opened by specialized econometric software such as those in STATA format

### The F Distribution in Econometrics

When studying economics, you probably used the Fdistribution in your statistics class to compare variances of two different normal distributions. In econometrics, you have a similar use for the