This weeks homework is based on Fuchs-Schündeln and Hassan (2015) available here: http://www.hoover.org/sites/default/files/fuschs-schundeln-hassan-papernaturalexperimentsmacro_mar16.pdf.
Read the paper up until the end of the fiscal policy section (do not read the part on the determinants of economic growth). Then answer the following (strong hint: all of this material is examinable):
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## intersect, setdiff, setequal, union## Warning: package 'latex2exp' was built under R version 3.2.21. Draw a causal diagram, as in class. Include an outcome variable, a treatment variable, an observed confounding variable (control variable), an unobserved confounding variable, an instrumental variable, and a bad control variable.
2. If I want to estimate the (linear) causal relationship between the treatment variable and outcome variable under the assumption that there are no unobserved confounders, what linear regression model should I estimate?
A regression estimation of the linear causal relationship between a treatment variable and an outcome variable would take a form similar to the simple fiscal multiplier estimate introduced in this weekâs lecture slides (slides 59-61):
\[\bigtriangleup Y_(t + 1) = \alpha + \beta \bigtriangleup F_(t + 1) + \delta \bigtriangleup X_(t + 1) + \epsilon \]
Assuming a time-series data set, a more general form of this would be:
\[\bigtriangleup Y_(t + 1) = \beta_0 + \beta_1 \bigtriangleup X_(t + 1) + \beta_2 \bigtriangleup X_(t + 1) + \epsilon \]
where X is the treatment variable, Y is the outcome variable and Z is the control.
3. Suppose I am concerned that there are unobserved confounders that affect both the treatment and the outcome, and as such I cannot assume that the relationship between them is causal. How should I go about identifying the causal effect? If unobserved confounders affect both the treatment and outcome variables, the causal effect of the treatment will be distorted and over-estimated in a regression model. If a confounder is correlated with both treatment and outcome variables, the regression model will overestimate the relationship by attributing the mutual correlation of the variables of interest with the confounder, to the causal relationship between the two variables. This can be overcome by replacing the treatment variable with and instrumental variable. A well selected instrumental variable should not be correlated with the confounding variable and should only be correlated with the outcome variable by its relationship to the original treatment variable. Replacing the treatment variable with an instrumental variable therefore removes the distortion in the causal relationship created by the confounding variable. It does this by removing the relationship between the confounder and the treatment variable, allowing the causal effect of the treatment variable, through its instrument, to be measured.
4. Describe the two properties that an instrumental variable must have. What is the exclusion restriction? What is the relationship between an instrumental variable and a natural experiment? The instrumental variable must have two properties there are :1.The instrument must be correlated with the endogenous explanatory variables, conditional on the other covariates.2.The instrument cannot be correlated with the error term in the explanatory equation (conditional on the other covariates), that is, the instrument cannot suffer from the same problem as the original predicting variable. Instrumental variable estimation requires untestable exclusion restrictions. With policy effects on individual outcomes, there is typically a time interval between the moment the agent realizes that he may be exposed to the policy and the actual exposure. In such cases there is an incentive for the agent to acquire information on the value of the IV. This leads to violation of the exclusion restriction. The method of instrumental variables (IV) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered to every unit in a randomized experiment. The natural experiment is an empirical study in which individuals (or clusters of individuals) exposed to the experimental and control conditions are determined by nature or by other factors outside the control of the investigators, yet the process governing the exposures arguably resembles random assignment. Thus, natural experiments are observational studies and are not controlled in the traditional sense of a randomized experiment.
5. Divide the following between your teammates (put a name next to each submission, one paper each): describe two natural experiments that researchers have used to examine the permanent income hypothesis and two natural experiments used to examine the fiscal multiplier. You may need to read the original papers. What data do they use? What is the natural experiment? What are their exclusion restrictions? Do you believe their exclusion restrictions? What are their findings?
What data do they use? Hsieh studied data issued by the Alaskan Permanent Fund to determine the size of the dividend payments and its recipients. He uses data on Alaskan households from the consumer expenditure survey to review consumption.
What is the natural experiment? Each year, Alaskan residents receive a payment from the state’s permanent fund. This payment is relatively large, and can be perfectly anticipated. This marks it as a textbook natural experiment with which to test the validity of the permanent income hypothesis.
What are their exclusion restrictions? Given that income is the treatment variable and the annual payment is the instrumental variable, the impacts on consumption arises purely from the change in income.
Do you believe their exclusion restrictions? I believe the exclusion restriction is valid. It is highly unlikely that there is a causal relationship between the nature of the dividends and the decision making of its recipients.
What are their findings? Hsieh finds evidence to suggest that the households that received the payment smoothed their consumption in a way that is consistent with the permanent income hypothesis. However, Hsieh compared the results of his natural experiment with those of the Souleles paper, which analysed the effects on consumption of tax refunds. Souleles findings contradict those of Hsieh and the permanent income hypothesis, displaying far higher sensitivity to consumption. Hsieh concludes that this is evidence that households are more likely to smooth their consumption paths when the size of the income increase is greater, as in both examples the increase is forecastable and affected the same participants.