Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 16: Problem 6

Consider a linear probability model for whether employers offer a pension plan based on the percentage of workers belonging to a union, as well as other factors: \(\begin{aligned} \text {pension}=& \beta_{0}+\beta_{1} \text {percunion}+\beta_{2} \text {avgage}+\beta_{3} \text { avgeduc} \\\ &+\beta_{4} \text {percmale}+\beta_{5} \text {percmarr}+u_{1} \end{aligned}\) i. Why might percunion be jointly determined with pension? ii. Suppose that you can survey workers at firms and collect information on workers' families. Can you think of information that can be used to construct an IV for percunion? iii. How would you test whether your variable is at least a reasonable IV candidate for percunion?

Short Answer

Expert verified
"Percunion" might be jointly determined with "pension" due to simultaneity bias. Historical union strength can be used as an IV. Test IV for relevance and exogeneity.

Step by step solution

01

Understanding Joint Determination

Joint determination refers to the possibility that two variables may influence each other. In this context, "percunion" (percentage of unionized workers) and "pension" (whether a pension plan is offered) might be jointly determined because firms that offer pension plans may attract more unionized employees, and strong union representation may negotiate for pension benefits. Thus, there exists potential simultaneity bias in the regression model.
02

Identifying a Potential Instrument

To construct an Instrumental Variable (IV) for "percunion," one must find a variable that is correlated with "percunion" but not directly with "pension" except through "percunion." Information such as the historical strength of unions in the industry or region, government policies regarding unions, or parental union membership rates could serve as potential instruments, assuming these affect unionization but not directly the offering of pension plans.
03

Testing IV Validity

To test whether the selected variable is a reasonable IV for "percunion," you must check two main conditions: relevance and exogeneity. Relevance means the IV is correlated with "percunion"; you can use the first-stage regression method to test this. Exogeneity means that the IV is not correlated with the error term in the pension equation, which can be tested using tests like the over-identification test if multiple instruments are available.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Instrumental Variable
In regression analysis, a challenge often faced is when an independent variable is correlated with the error term, causing biased and inconsistent estimates. In such cases, we use an Instrumental Variable (IV). An IV helps to isolate the variation in the independent variable that is unrelated to the error term, thus avoiding bias. To be effective, the IV must satisfy two conditions:
  • Relevance: The IV must be correlated with the endogenous explanatory variable, meaning, it should have predictive power over our variable of interest, like 'percunion.'
  • Exogeneity: The IV must not be correlated with the error term, meaning it shouldn't affect the dependent variable, 'pension,' except through 'percunion.'
When selecting an IV, careful evaluation must be made to ensure these conditions are met. This ensures a more reliable estimate free from simultaneity bias.
Simultaneity Bias
Simultaneity bias occurs when two variables may simultaneously affect each other, causing regression estimators to be biased. In our model, 'percunion' and 'pension' might influence each other, leading to potential bias. For example, firms offering pension plans might attract more unionized employees, while strong unions may push for pension benefits.
This dual influence creates endogeneity, making it challenging to determine the causal relationship. Addressing simultaneity bias is crucial to obtain accurate and reliable regression results. Using tools like Instrumental Variables can help in isolating the causal effect of the primary intéressée variable, ensuring unbiased results.
First-Stage Regression
The first-stage regression is a crucial step in using Instrumental Variables. It involves regressing the endogenous variable, like 'percunion,' on the Instrumental Variable and other control variables. This step checks the relevance condition of the IV.
The goal is to establish a significant correlation between the IV and the endogenous variable. This ensures the IV can reliably predict 'percunion,' necessary for accurate estimation in the second stage, which determines the impact on 'pension.'
In a practical sense, first-stage regression helps in identifying whether the selected IV has enough explanatory power, making it an essential diagnostic tool in the IV approach.
Unionized Workers
Unionized workers are employees who are part of a labor union, an organization that represents their interests with employers, particularly regarding wages and benefits.
In the context of our model, the percentage of unionized employees, 'percunion,' could impact if a company offers pension benefits. Unions often have the power to negotiate better benefits for their members, including pension plans. Understanding the dynamics of unionized workers is vital in analyzing workplace policies and structures, especially in the labor market.
  • Unions might demand pension plans during negotiations
  • Companies with more union workers might need to offer pensions to attract such employees
Knowing the characteristics and strategies of unionized workers can provide insight into labor market behaviors.
Pension Benefits
Pension benefits are retirement plans provided by employers to support employees financially after retirement. They can take various forms, such as defined benefit plans or defined contribution plans.
Pensions are an essential aspect of employee compensation and can influence employment decisions. Offering pensions can make a firm more attractive to prospective employees and help retain current ones.
  • Pensions can affect a firm's labor costs and organizational decisions
  • They represent a significant bargaining point for unions in negotiations
  • Pensions can influence the overall job satisfaction and financial security of employees
Understanding pension benefits helps in evaluating labor market strategies and the economic implications for both employers and employees.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write a two-equation system in "supply and demand form," that is, with the same variable \(y_{t}\) (typically, "quantity") appearing on the left-hand side: $$\begin{aligned} &y_{1}=\alpha_{1} y_{2}+\beta_{1} z_{1}+u_{1}\\\ &y_{1}=\alpha_{2} y_{2}+\beta_{2} z_{2}+u_{2} \end{aligned}$$ i. If \(\alpha_{1}=0\) or \(\alpha_{2}=0,\) explain why a reduced form exists for \(y_{1}\). (Remember, a reduced form expresses \(y_{t}\) as a linear function of the exogenous variables and the structural errors.) If \(\alpha_{1} \neq 0\) and \(\alpha_{2}=0,\) find the reduced form for \(y_{2}\) ii. If \(\alpha_{1} \neq 0, \alpha_{2} \neq 0,\) and \(\alpha_{1} \neq \alpha_{2}\), find the reduced form for \(y_{1}\). Does \(y_{2}\) have a reduced form in this case? iii. Is the condition \(\alpha_{1} \neq \alpha_{2}\) likely to be met in supply and demand examples? Explain.

A simple model to determine the effectiveness of condom usage on reducing sexually transmitted diseases among sexually active high school students is $$\text { in frate }=\beta_{0}+\beta_{1} \text { conuse }+\beta_{2} \text { percmale }+\beta_{3} \text { avginc }+\beta_{4} \text { city }+u_{1},$$ where in frate \(=\) the percentage of sexually active students who have contracted venereal disease. conuse \(=\) the percentage of boys who claim to use condoms regularly. avginc = average family income. city = a dummy variable indicating whether a school is in a city. The model is at the school level. i. Interpreting the preceding equation in a causal, ceteris paribus fashion, what should be the sign of \(\beta_{1} ?\) ii. Why might infrate and conuse be jointly determined? iii. If condom usage increases with the rate of venereal disease, so that \(\gamma_{1}>0\) in the equation conuse \(=\gamma_{0}+\gamma_{1}\) in frate \(+\) other factors what is the likely bias in estimating \(\beta_{1}\) by OLS? iv. Let condis be a binary variable equal to unity if a school has a program to distribute condoms. Explain how this can be used to estimate \(\beta_{1}\) (and the other betas) by IV. What do we have to assume about condis in each equation?

Let corn denote per capita consumption of corn in bushels at the county level, let price be the price per bushel of corn, let income denote per capita county income, and let rainfall be inches of rainfall during the last corn-growing season. The following simultaneous equations model imposes the equilibrium condition that sunply equals demand: $$\begin{array}{l} \text {corn}=\alpha_{1} \text { price }+\beta_{1} \text {income}+u_{1} \\ \text {corn}=\alpha_{2} \text { price }+\beta_{2} \text { rain fall }+\gamma_{2} \text { rain } f a l l^{2}+u_{2} \end{array}$$ Which is the supply equation, and which is the demand equation? Explain.

Suppose that annual earnings and alcohol consumption are determined by the SEM $$\begin{aligned} \log (\text {earnings}) &=\beta_{0}+\beta_{1} \text { alcohol }+\beta_{2} e d u c+u_{1} \\ \text { alcohol} &=\gamma_{0}+\gamma_{1} \log (\text {earnings})+\gamma_{2} e d u c+\gamma_{3} \log (\text {price})+u_{2} \end{aligned}$$ where price is a local price index for alcohol, which includes state and local taxes. Assume that \(e d u c\) and price are exogenous. If \(\beta_{1}, \beta_{2}, \gamma_{1}, \gamma_{2},\) and \(\gamma_{3}\) are all different from zero, which equation is identified? How would you estimate that equation?

How big is the effect of per-student school expenditures on local housing values? Let \(H P R I C E\) be the median housing price in a school district and let \(E X P E N D\) be per-student expenditures. Using panel data for the years \(1992,1994,\) and \(1996,\) we postulate the model $$\begin{aligned} l H P R I C E_{i t}=& \theta_{t}+\beta_{1} l E X P E N D_{i t}+\beta_{2} l P O L I C E_{i t}+\beta_{3} l M E D I N C_{i t} \\ &+\beta_{4} P R O P T A X_{i t}+a_{i 1}+u_{i t 1} \end{aligned}$$ where \(P O L I C E_{i t}\) is per capita police expenditures, \(M E D I N C_{i t}\) is median income, and \(P R O P T A X_{i t}\) is the property tax rate; \(l\) denotes natural logarithm. Expenditures and housing price are simultaneously determined because the value of homes directly affects the revenues available for funding schools. Suppose that, in \(1994,\) the way schools were funded was drastically changed: rather than being raised by local property taxes, school funding was largely determined at the state level. Let ISTATEALLiti denote the log of the state allocation for district \(i\) in year \(t,\) which is exogenous in the preceding equation, once we control for expenditures and a district fixed effect. How would you estimate the \(\beta_{j}\) ?
See all solutions

Recommended explanations on History Textbooks

Modern Britain

Read Explanation

Cold War

Read Explanation

European History

Read Explanation

Classical Studies

Read Explanation

Spread of Islam

Read Explanation

The Mughal Empire

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free