Econometrics: Bivariate population model

Hello I'm finally back from my extended break. I thought that we should start studying Econometrics.

Let's begin by analyzing a simple bivariate regression. Assume that this equation describes the relationship between two variables X and Y.

$Y= \beta_0 + \beta_1 \cdot X + \epsilon$

We say that Y is the dependent variable, whereas X is the independent variable. In other words, we assume that Y (the output) depends on X (the input). Epsilon is the error term, it represents other factors that affect Y.

The error term must be uncorrelated with the variable X so that we do not need to include them in our regression, and thus the coefficient of X (beta) should not change, even though Epsilon also determines Y.

beta-0 is the constant term. It tells us what would be Y if X=0.

beta-1 is the effect on Y if X changes by one unit.

To see this, assume X=education is a continuous function, let's take the derivative of Y=wage with respect to X:

$\frac{\partial Wage}{\partial educ }=\beta_1$

Thus, if education goes up by one unit, we should expect, on average, wage to go up by about beta-1.

Note that this principal can be extended to non-continuous functions as well.

To run this regression, all I need is set of (random) data with wage and the education for each participant in the dataset.

reg wage educ

The following line above is what you should use in order to run this bivariate regression in STATA.

We need one more condition in order to make sure that our bivariate model is correct:

$E[\epsilon|X]=E[\epsilon]=0$

This tells us that given X, the other factors are randomly distributed in the population, and thus does not bias the coefficient of X (beta-1).

Reference: Wooldridge, Jeffrey. Introductory Econometrics, 3rd edition. Thomson South-Western (2006). p 24-28.

Comments

Macroeconomics: multiplier and crowding out effects

Multiplier effect: whenever any of the components of AD increases, the increase in GDP will be greater than the initial increase in expenditures. The impact on GDP of a particular increase in spending depends on the proportion of the new income that is taken out of the system to the proportion that continues to circulate in the economy. The multiplier effect tells us the impact a particular change in one the components of AD will have on the total income (GDP). Let k denote the spending multiplier, which is a function of MPC and MPS. The larger the marginal propensity to consume, the larger the spending multiplier. Notice that the larger the MPC, the greater the impact a particular change in the spending variables will have on the nation's GDP. The crowding out effect: If government spending increases without an increase in taxes, the government must borrow funds from the private sector to finance its deficit, thereby increasing the interest rate. This increase in interest ...

Macroeconomics: different types of inflation and methods to stabilize inflation

Types of inflation: Demand pull inflation: caused by a rightward shift in the aggregate demand. The increased in consumption among consumers for a limited amount of goods forces prices to rise. When the economy is below full employment, an increase in AD does not drastically change the price level, since the economy is not fully using its resources (workers and machines) and can therefore easily increase production. When the economy is at full employment, an increase in AD causes a large increase in inflation, it becomes relatively more costly to increase production. Methods for reducing demand pull inflation: Contractionary fiscal policies: raising taxes or reducing the government spending, will put downward pressure on the aggregate demand, and thereby reduces its rightward shift. Contractionary monetary policies: Usually, the central bank is the entity that deals with inflation. It does so by increasing the federal funds rate through open market transaction, which decreas...

Microeconomics: Firms and cost in the short run

In Economics, the term short run refers to a time period where at least one variable of interest does not change . In our case, the short run for a firm is when at least one input (labor, land, capital) stays fixed. Usually land and capital are considered fixed in the short run. If an input is fixed during a period time, no matter how much the total product a firm produces, its cost stays the same. This cost is commonly known as fixed cost (FC). Examples of fixed costs: rent, property taxes, loan payments. Labor is often considered to be a part of the variable cost (VC) . Variable cost can be defined as the cost a firm has control over during the short run. Unlike fixed cost, variable cost increases (decreases) as a firm's total product increases (decreases). Examples of variable costs include: utility bills, wages, raw materials A firm's total cost (TC) is the sum of its variable and fixed costs. As you can see, the fixed cost...

Economics and Statistics

Search This Blog