Econometrics-Basic Theory

Assignment A

1.    Explain briefly the difference between a sharp and a fuzzy discontinuity design (you do not need to explain how estimation would proceed in each case; just describe the kind of situation that would give rise to a sharp RDD and a fuzzy one).    

2.    Given the model Yi= β0+ β1X1i+ β2X2i + β3X3i +ui, where you know that E[ui|X]=0, imagine that you estimate instead the “incomplete” model Yi= β0+ β1X1i  +u*i. Under what conditions will the OLS estimator of β1 be inconsistent?

    

3.    Could you test that the instruments (Z1i, Z2i y Z3i) are exogenous? If your answer is yes, how would you do it? If not, why?

4.    How could you check whether the instruments are weak? Explain.    

5.    You want to estimate whether there is a relationship between gender and smoking at your university. You collect data for a random sample of 200 students and run a linear probability model, a probit model and a logit model, where the dependent variable is a binary indicator for whether an individual smokes, and the main explanatory variable is a dummy variable indicating males (you also include other controls such as age). Your estimated coefficients are 0.084 in the LMP, 0.688 in the probit model, and 0.389 in the logit model. In spite of these large differences, all three models yield similar estimates of the marginal effect of gender on the probability of smoking. How can this be?    

6.    What is meant by marginalization and conditioning in the process of model reduction within the dynamic modeling tradition?

7.    Define the term’s weak stationarity, Integrated of order one and uniform mixing. How would you asses the stationarity of a variable X.    

8.    When  does  non-stationary data  not  give  rise to  the problems  of  a spurious regression.

Assignment B

Case Detail:  
In “The Power of Political Voice: Women's Political Representation and Crime in India”, Lakshmi Iyer and her coauthors study the effect of political representation among under-represented social groups on crimes committed against members of the disadvantaged group. In particular, they study the impact of increased female representation in local governments on crimes against women in India.

1.    Do you expect the “true” causal effect of interest to be positive, negative, or about zero? Why?

2.    Suppose that they collected (observational) data across different Indian municipalities in a given year (say, 2005) on the fraction of women in the local council and the annual number of crimes against women (normalized by population). They could then run an OLS regression where crime would be the dependent variable and the  fraction of women the main explanatory variable. Do you think a simple OLS regression with no additional regressors would answer the causal question of interest? Explain why such an OLS estimate would be biased, and in which direction you think the bias would go.

3.    Describe one variable that should be included in the regression and explain why.

Assignment C

Question No.  1    Marks - 10
A qualitative forecast    
 
Options    
Predicts the quality of a new product.    
predicts the direction, but not the magnitude, of change in a variable.    
is a forecast that is classified on a numerical scale from 1 (poor quality) to 10 (perfect quality).    
is a forecast that is based on econometric methods.

Question No.  2    Marks - 10
Which of the following is not a qualitative forecasting technique?    
 
Options    
Surveys of consumer expenditure plans    
Perspectives of foreign advisory councils    
Consumer intention polling    
Time-series analysis    

Question No.  3    Marks - 10
The first step in time-series analysis is to    
 
Options    
perform preliminary regression calculations.    
calculate a moving average.    
plot the data on a graph.    
identify relevant correlated variables.

Question No.  4    Marks - 10
Forecasts are referred to as naive if they    
 
Options    
are based only on past values of the variable.    
are short-term forecasts.    
are long-term forecasts    
generally result in incorrect forecasts.

Question No.  5    Marks - 10
Time-series analysis is based on the assumption that    
 
Options    
random error terms are normally distributed.    
there are dependable correlations between the variable to be forecast and other independent variables.    
past patterns in the variable to be forecast will continue unchanged into the future.    
the data do not exhibit a trend.    

Question No.  6    Marks - 10
Which of the following is not one of the four types of variation that is estimated in time-series analysis?    
 
Options    
Predictable    
Trend    
Cyclical    
Irregular

Question No.  7    Marks - 10

The cyclical component of time-series data is usually estimated using    
 
Options    
linear regression analysis.    
moving averages.    
exponential smoothing.    
qualitative methods.

Question No.  8    Marks - 10
In time-series analysis, which source of variation can be estimated by the ratio-to-trend method?    
 
Options    
Cyclical    
Trend    
Seasonal    
Irregular

Question No.  9    Marks - 10
If regression analysis is used to estimate the linear relationship between the natural logarithm of the variable to be forecast and time, then the slope estimate is equal to    
 
Options    
the linear trend.    
the natural logarithm of the rate of growth.    
the natural logarithm of one plus the rate of growth.    
the natural logarithm of the square root of the rate of growth.

Question No.  10    Marks - 10
The use of a smoothing technique is appropriate when    
 
Options    
random behavior is the primary source of variation.    
seasonality is present.    
data exhibit a strong trend.    
all of the above are correct.    

Question No.  11    Marks - 10
The greatest smoothing effect is obtained by using    
 
Options    
a moving average based on a small number of periods.    
exponential smoothing with a small weight value.    
the root-mean-square error.    
the barometric method.

Question No.  12    Marks - 10
The root-mean-square error is a measure of    
 
Options    
sample size.    
moving average periods.    
exponential smoothing.    
forecast accuracy.

Question No.  13    Marks - 10
Barometric methods are used to forecast    
 
Options    
seasonal variation.    
secular trend.    
cyclical variation.    
irregular variation.

Question No.  14    Marks - 10
A leading indicator is a measure that usually    
 
Options    
changes at the same time and in the same direction as the general economy.    
responds to a change in the general economy after a time lag.    
changes in the same direction as the general economy before the general economy changes
has all of the properties listed above.

Question No.  15    Marks - 10
If 3 of the leading indicators move up, 2 move down, and the remaining 6 are constant, then the diffusion index is    
 
Options    
3/6 = 50%    
3/11 = 27%    
5/11 = 45%    
6/11 = 55%

Question No.  16    Marks - 10
A single-equation econometric model of the demand for a product is a ________ equation in which the quantity demanded of the product is an ________ variable.    
 
Options    
structural, exogenous    
structural, endogenous    
definitional, exogenous    
definitional, endogenous    

Question No.  17    Marks - 10
A reduced form equation expresses    
 
Options    
an exogenous variable as a function of endogenous variables.    
an endogenous variable as a function of exogenous variables.    
an exogenous variable as a function of both endogenous and exogenous variables.    
an endogenous variable as a function of both exogenous and endogenous variables.

Question No.  18    Marks - 10
Trend projection is an example of which kind of forecasting?    
 
Options    
Qualitative    
Time-series    
Barometric    
Econometric

Question No.  19    Marks - 10
Turning points in the level of economic activity can be forecast by using    
 
Options    
Time-series analysis    
Exponential smoothing    
Barometric methods    
Moving average

Question No.  20    Marks - 10
Econometric forecasts require    
 
Options    
accurate estimates of the coefficients of structural equations.    
forecasts of future values of exogenous variables.    
appropriate theoretical models.    
all of the above.

Question No.  21    Marks - 10
Which of the following is an example of a capital input?    
 
Options    
Money.    
Shares of stock.    
Long-term bonds.    
A hammer.

Question No.  22    Marks - 10
Which of the following is an example of an intermediate product?    
 
Options    
A personal computer.    
A barrel of crude oil.    
A sports car.    
A house.

Question No.  23    Marks - 10
Which of the following is an assumption associated with the definition of a production function?    
 
Options    
Technology remains constant.    
Both inputs and outputs are measured in monetary units.    
The function shows the maximum level of output possible with a given combination of inputs.    
All units of the inputs are homogeneous.

Question No.  24    Marks - 10
The marginal product of labor is equal to    
 
Options    
the additional labor required to produce one more unit of output.    
average product when average product is at a minimum.    
the additional output produced by hiring one more unit of labor.    
the slope of a ray drawn from the origin to a point on the total product curve.    

Question No.  25    Marks - 10
The average product of labor is equal to    
 
Options    
the additional labor required to produce one more unit of output.    
marginal product when average product is at a minimum.    
the additional output produced by hiring one more unit of labor.    
the slope of a ray drawn from the origin to a point on the total product curve.

Question No.  26    Marks - 10
The output elasticity of labor is    
 
Options    
equal to one at the level of output where average product is at a maximum.    
the percentage change in labor required to produce one more unit of output.    
equal to the ratio of total product to the quantity of labor employed.    
a measure of the percentage change in output that can result when the quantity of labor is held constant.

Question No.  27    Marks - 10
The point of inflection on the total product curve corresponds to the level of output where    
 
Options    
Stage II of production begins.    
average product is at a maximum.    
average product is at a maximum.    
All of the above are correct.

Question No.  28    Marks - 10
The law of diminishing returns    
 
Options    
is reflected in the negatively sloped portion of the marginal product curve.    
is the result of specialization and division of labor.    
applies in both the short run and the long run    
All of the above are correct.

Question No.  29    Marks - 10
Stage II of production begins at the point    
 
Options    
of inflection of the total product curve.    
where average and marginal product are equal.    
where total product is at a maximum.    
where marginal product is at a maximum.

Question No.  30    Marks - 10
The marginal revenue product of labor for a firm    
 
Options    
will increase if the price of the firm's output increases.    
is the firm's demand curve for labor.    
will decrease if the firm hires more labor.    
All of the above are correct.

Question No.  31    Marks - 10
An isoquant that is    
 
Options    
further from the origin represents greater output.    
flatter represents the trade-offs between inputs that are poor substitutes.    
negatively sloped represents input combinations associated with Stage I of production.    
All of the above are correct.    

Question No.  32    Marks - 10
The absolute value of the slope of a convex isoquant    
 
Options    
is equal to the marginal rate of technical substitution.    
is equal to the ratio of the marginal products of the two inputs.    
decreases from left to right.    
All of the above are correct.    

Question No.  33    Marks - 10
The combination of inputs is optimal    
 
Options    
at points of tangency between isoquants and isocosts.    
if the marginal revenue product is equal to the marginal resource cost for all inputs
if the marginal rate of technical substitution between every pair of inputs is equal to the ratio of the prices of those inputs.    
All of the above are correct.    

Question No.  34    Marks - 10
An isocost line will be shifted further away from the origin    
 
Options    
if the prices of both inputs increase.    
if total cost increases.    
if there is an advance in technology.    
All of the above are correct.

Question No.  35    Marks - 10
If isoquants are plotted on a graph with capital measured on the vertical axis and labor on the horizontal axis, then an increase in the wage rate will cause the isocost line    
 
Options    
to become steeper and the optimal quantity of labor will decrease.    
to become steeper and the optimal quantity of labor will increase.    
to become flatter and the optimal quantity of labor will decrease.    
to become flatter and the optimal quantity of labor will increase.

Question No.  36    Marks - 10
A line that connects all points where the marginal rate of technical substitution is equal to the ratio of input prices is called the    
 
Options    
input demand curve.    
total product curve.    
expansion path.    
isocost line.

Question No.  37    Marks - 10
Suppose that three isoquants that represent 10, 20, and 30 units of output are plotted on a graph and a straight line is drawn from the origin through the isoquants. If the portion of the line between the isoquants that represent 10 and 20 units of output is longer than the portion of the line between the isoquants that represent 20 and 30 units of output, then the firm represented by these isoquants    
 
Options    
has engaged in product innovation.    
is experiencing increasing returns to scale.    
is experiencing decreasing returns to scale.    
will maximize profits by producing 10 units of output.

Question No.  38    Marks - 10
If the output elasticities of all inputs used by a firm are summed together, then the total    
 
Options    
will be greater than one if returns to scale are decreasing.    
will be equal to one if returns to scale are constant.    
will be less than one if returns to scale are increasing.    
All of the above are correct.

Question No.  39    Marks - 10
Which of the following is not a characteristic of production technologies that can be described by the Cobb-Douglas production function?    
 
Options    
The marginal product of an input divided by the average product of that input is constant.
The exponents will sum to one if returns to scale are constant.    
Linear regression can be used to estimate the parameters of the function.    
All of the above are characteristics of the Cobb-Douglas production function.

Question No.  40    Marks - 10
If the marginal product of labor is 2, the marginal product of capital is 4, the wage rate is $3, the rental price of capital is $6, and the price of output is $1.50, then the firm should    
 
Options    
Increase output by hiring more labor, more capital, or both.    
Hold output constant, but hire more labor and less capital.    
Decrease output by reducing the quantity of capital, reducing the number of units of labor, or both.    
None of the above is correct.