Week 10

1. 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?

The linear regression model that should be used to estimate the casual relationship between a treatment variable and outcome variable is: Outcome= \(\beta0+ \beta1(treatment)+X\beta2+ \epsilon\) Where:

\(\beta0\) is the initial state of the outcome.

\(\beta1\) is the effect the treatment has on outcome

\(X\) is the control variables

\(\beta2\) is the effect of the control variables on the outcome variable

\(\epsilon\) is everything else/unobserved variables.

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?

Experiments in macroeconomics are not like other lab experiments with multiple variables affecting results making causal relationships hard to measure. These variables can be dealt with in a few different ways. Instrumental variables are the most common method used to measure effects of particular variables on the treatment variables. Instrumental variables must only inadvertently effect the outcome through the treatment variable. Other methods are fixed effect estimations, propensity score matching and regression discontinuity.

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?

An instrumental variable (IV) must be correlated with the endogenous explanatory variable being investigated. The IV cannot be correlated with the error term of the model.

Exclusion restrictions for an instrument are variables that impact the treatment assignment of a natural experiment but not the outcome that is conditional on the treatment assignment. For example when analysing fiscal multipliers it is important to instil an exclusion restriction for instrumental variables that affects growth in GDP only through its effects on fiscal measure being carried out.

Natural experiments are infamously difficult to perform because outside of science labs the world and its economies are messy and complex with huge amounts of variables effecting decisions. Inferring causality between two variables can then be seriously flawed and create questionable data. Instrumental variables are a handy way of inferring causality in natural experiments. Economists find a variable that effects the outcome of a policy only in how it effects the policy itself. You can then estimate the causal effect of a policy on the outcome by measuring the effect on a policy that is only attributable to the instrumental variable. You can then measure the strength of a causal relationship using this method and construct multiple causal relationships with multiple IVs.

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?

Permanent Income Hypothesis experiment:

Stephens and Unayama (2011) -

The Consumption Response to Seasonal Income: Evidence from Japanese Public Pension Benefits

Analysed by Declan Gleeson

In this study, Stephens and Unayama are examining a natural experiment in which Japanese pension reform resulted in the pension being paid once every two months from February 1990, as opposed to once every three months prior to February 1990. They then analyse the impact on spending on durables and nondurables, examining the timing of consumption in response to this anticipated seasonal income variation. They use data from the Japanese Income and Expenditure Survey (1986-1994), their sample size is 2503 retirees and employees prior to the pension reform, and 3595 retirees and employees following the pension reform. This paper rejects the Permanent Income Hypothesis, they find that there is a considerable impact of seasonal income variation on consumption. Non-durable consumption increases by 4% whilst non-durable consumption increases by 4% when the payment receipt is received.

Fuchs-Schundeln (2008)

German Reunification

Analysed by Marta Sisay

What data do they use? Fuchs-Schundeln (2008) uses German Reunification as a natural experiment that led to a large positive permanent income shock for East Germans. This natural experiment of German reunification is used to gain insights into the validity of the life cycle consumption model, and to analyze the relative importance of different saving motives What is the natural experiment? The experiment involved comparisons of the behaviour of a treatment group (East Germans) to a control group (West Germans), with different economic consequences for different birth cohorts. What are their exclusion restrictions? - excludes households whose head is retired

• drop households whose head serves an apprenticeship

• controlling for the potential self-selection on unobservables

Do you believe their exclusion restrictions?

What are their findings?

Although incomes of East Germans remained below those of West Germans, they increased substantially after reunification. Important for the predictions of the model, the East-West wealth ratio at reunification was very low, especially for older cohorts, also compared to the East-West income ratio. Examining empirical saving rates of East and West Germans after reunification from a large representative household survey, the paper finds three stylized features:

1. East Germans have higher saving rates than West Germans;

2. this East-West gap is increasing in age at reunification; that is, it is larger for older birth cohorts than for younger birth cohorts; and 

3. for every birth cohort, this gap is declining over time.

Taking the cohort-specific East and West German income processes after reunification, and the cohort-specific East-West wealth ratio at reunification from the data, the paper finds that a life cycle model that incorporates precautionary savings, retirement savings, and changing household composition over the life cycle can replicate these three features. The higher East German saving rates are a result of their low initial wealth levels, which leave them unprepared for the new economic environment.

The East-West difference in saving rates is especially large for older cohorts, because older cohorts of East Germans are least prepared for the new environment: their wealth position relative to their West German counterparts is especially low, and they have less time left over their working life to accumulate more wealth through higher saving rates.

Thus, the paper concludes that East Germans react according to the predictions of the life cycle model after the large shock of German Reunification, and that a precautionary saving motive is essential for replicating the data. German Reunification led to a permanent income change, and the income process has to be carefully calibrated to determine the optimal consumption change.

Fiscal Multiplier

Government Spending Multipliers in good times and Bad: Evidence from historical US data

Valerie Ramey & Sarah Zubairy (2014)

Analysed by Maxine Catchlove

What Data is Used?

The data used is US quarterly data from 1889-2013, they chose to use quarterly data over annual data because agents tend to respond so quickly to news about government spending and can change the economy rapidly. The study also uses historical series data of real GDP, GDP deflator, government purchases, federal government receipts, population, the unemployment rate, interest rates and defence laws. Post WW2 sample was based on published quarterly series while for earlier periods Gordon Krenn (2010) higher frequency series to interpolate existing annual series. This mostly consisted of proportional Denton procedure which resulted in a series of averages up to the annual series. Real GDP data was constructed from the Historical series data from 1889-1929 and NIPA data was used from 1929-present. Monthly outlay data from NBER Macrohistory database was also used to interlope government spending.

What is the experiment?

The authors are investigating the relationship between government spending multipliers and recessions. Recent conjecture has stated that multipliers are higher during recessions. The authors use instrumental variables 1- ‘level of slack’ and 2- interest rates near zero lower bound to gauge this causality. Slack, the measure of the quantity of unemployment services available, and lower bound interest rates can act as automatic stabilisers for an economy in recession by increasing government spending and confidence begins to fall and growth becomes negative. Although there is a causality relationship between these variables and government spending there is no direct relationship between them and the level of responsiveness during recession.

What is the Exclusion Restriction?

The exclusion restriction for this experiment is that neither instrumental variable can have a direct relationship to the elasticity of government spending multipliers. Both ‘level of slack’ and lower bound interest rates affect the level of government spending but indirectly effect the elasticity of multipliers during growth and recession. If this was just an investigation into weather these variables effect economic growth then they would violate an exclusion restriction of being exogenous to the independent variable as both are endogenous to economic growth as automatic stabilisers.

What are the Findings?

There is no evidence that multipliers differ by the amount of slack in the economy. This finding was robust to many alternative specifications Results were less clear for zero lower bound interest rates. For the whole sample there was no evidence for higher multipliers near zero lower bound. When WW2 was excluded though there was some higher multipliers during zero lower bound state but not enough to be statistically significant from the normal state. Cortrary to the recent conjecture government spending multipliers were not necessarily higher during recessions.