Here Are Some Examples of the Instrumental Variables Regression Model $\chi _ { m - k } ^ { 2 }$

question 42

Essay

Here are some examples of the instrumental variables regression model. In each case you are given the number of instruments and the J-statistic. Find the relevant value from the $\chi _ { m - k } ^ { 2 }$ distribution, using a 1% and 5% significance level, and make a decision whether or not to reject the null hypothesis.
(a)Y_i = β₀ + β₁X_1i + u_i, i = 1, ..., n; Z_1i, Z_2i are valid instruments, J = 2.58.
(b)Y_i = β₀ + β₁X_1i + β₂X_2i + β₃W_1i + u_i, i = 1, ..., n; Z_1i, Z_2i, Z_3i, Z_4i are valid instruments, J = 9.63.
(c)Y_i = β₀ + β₁X_1i + β₂W_1i + β₃W_2i + β₄W_3i + u_i, i = 1, ..., n; Z_1i, Z_2i, Z_3i, Z_4i are valid instruments, J = 11.86.

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Definitions:

Negative Framing Effect

A psychological phenomenon where people make decisions based on the presentation of negative outcomes rather than positive ones, even when both presentations convey the same information.

Smooth Consumption

A concept in economics where individuals prefer to have a stable consumption pattern over time, smoothing out the highs and lows in their spending and consumption.

Future Earnings

The expected amount of money an individual, business, or asset is anticipated to generate in the future.

Behavioral Economists

Specialists in economics focusing on how psychological, emotional, cultural, and social factors influence the economic decisions of individuals and institutions.