ECON323 Lecture Notes - Lecture 1: Linear Probability Model, Null Hypothesis, Test Statistic

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pinkrabbit481

20 Oct 2017

School

University of Waterloo

Department

Economics

Course

ECON323

Professor

Emmanuelle Pierard

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Document Summary

Yi = + xi + zi + i. Yi = + xi + x 2 i + i. In the latter case, one cannot infer that a one unit change in x will a ect y by : if there is a one unit change in x, x2 will also change. By linear model, we mean that the model is linear in parameters , , , etc. In the case of the second model, the e ect of a one-unit change of. X on y will be + 2 x (which is equal to y. There will always be factors for which we cannot control that will be included in . Overall, the model will include k variables and 1 constant, which means that we will need to estimate k+1 parameters. athese notes are based on wooldridge, 2006. The ordinary least squares estimate are obtained by minimizing the sum of squared residuals, i. e. , by minimizing.

Related Questions

Suppose that the economy is given by:

C = c0 + c1(Y âT)

I = b0 + b1Y âb2i
with 0 < c1 < 1, 0 < b1 < 1, (c1 + b1) < 1, 0 < b2 < 1, and G, T are exogenous constants.

(a) Derive an expression for equilibrium output.

(b) Derive âY/âi, and invert this expression so that it is now âi/âY (hint: (3/2)â1 = (2/3). This is the IS curve we derived graphically in class. What is itâs sign? What is the eï¬ect on output of a small increase in the interest rate?

(c) What happens to the slope of the IS curve if b2 increases? What happens to the slope of the IS curve if (c1 + b1) increases? What is the economic intuition behind this?

(d) Using the expression for equilibrium output you derived in part b, derive âY/âG and âY/âT. What are the signs of these derivatives? How much does output change (and in what direction) if there is a
small increase in G? How much does output change (and in what direction) if there is a small increase in T? Now suppose equilibrium in the goods market is given by: Y (Y,i,G,T) (+,â,+,â) = C(Y,T +,â ) + I(Y,i +,â ) + G
(e) Derive âY/âi, and invert this expression so that it is now âi/âY (hint: (3/2)â1 = (2/3). This is the IS curve we derived graphically inclass. Whatisthesignofthisexpression? Whatdoesthesteepness of the slope of the IS curve depend on? How do the terms in this expression relate to the parameters b2,b1, and c1 in the IS curve you derived in part b?

(f) Through which channels does the interest rate aï¬ect output (i.e. what is the eï¬ects of changes in the interest rate on C, I, and G )? (Hint: To answer this question, you could take partial derivatives of C, I, and G with respect to i; or simply infer this from your answer to part a. )

ECON 3050

Q24. The coefficient of determination (r²) is calculated as 0.49, then the correlation coefficient:

Cannot be determined without the data

Should be - 0.70 or 0.70

Should be 0.

Neither of the above

Q25. A regression line is used for all of the following except one. Which one is not a valid use of a regression line?

To estimate the average value of Y at a specified value of X.

To predict the value of Y for an individual, given that individual's X-value.

To estimate the change in Y for a one-unit change in X.

To determine if a change in X causes a change in Y.

Q26. Which choice is not an appropriate description of YË in a regression equation?

Estimated response

Predicted response

Estimated average response

Observed response

Q27. Which of the following is the best way to determine whether or not there is a statistically significant linear relationship between two quantitative variables?

Compute a regression line from a sample and see if the sample slope is 0.

Compute the correlation coefficient and see if it is greater than 0.5 or less than â0.5.

Conduct a test of the null hypothesis that the population slope is 0.

Conduct a test of the null hypothesis that the population intercept is 0.

Q28. There is no relationship between variables unless the data points lie in a straight line.

True

False

Q29. The sample regression analysis

Is the same as the population regression line

Is used to estimate the population regression line

Shows the true relation between dependent and independent variables

None of the above.

Q30. In regression, a dependent variable is sometimes called a predictor variable.

True

False

Q31. In a linear regression equation of the form y = a + bx, the intercept shows

The amount that y changes when x changes by one unit

The amount that x changes when y changes by one unit

The value of y when x is zero

The value of x when y is zero.

Q32. In a linear regression equation of y = a + bx, the slope b shows

Y / b

X / b

Y / X

X / Y

yellowturtle964

Need help explaining PART C THANK YOU!

Suppose that two individuals, Jon and David, form a community and would like to construct a communal fort that would protect them from attacks. They both consume good X, a private good, and the protection of the fort, P. One unit of good X costs 1 unit of currency, and one unit of P costs 2 units of currency. Both Jon and David have an income of 100 and a utility function of the form:

U = log(X_i) + 2 Ã log(P_J + P_D)
The budget constraint for each is given by:
X_i + 2 Ã P_i = 100

(a) Find the amount of protection Jon will provide as a function of how much David provides, and explain why the relationship is the way it is.

(b) How much protection P will be privately provided in this case?

(c) Explain the economic intuition behind this amount, and compare it to the socially optimal amount without solving for the socially optimal amount.

HERE IS WHAT I DID SO FAR

A_ First you need to find the max utility, with is the utility and the budget constraint

U = log(X_i) + 2 Ã log(P_J + P_D) -> log(100-2PJ)+2log(PJ+PD)

Next you will need to differentiate the logarithim to get PJ

- 2 2

----------- + ----------------- = 0

100-2PJ PJ + PD

which we cal solve to generate

3PJ = 100 - PD

This can also be applied to PD

3PD = 100 - PJ

Using the substitute method we can find that (PJ = X; PD = Y)

3x = 100 - Y -> Y = -3x + 100

3(-3x + 100) = 100 - x

-9x + 300 = 100 - x

-8x = -200

x = 25

Which means that Y = 25

PJ = 25, PD = 25

25 +25 = 50

ECON323 Lecture Notes - Lecture 1: Linear Probability Model, Null Hypothesis, Test Statistic

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