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.

Causal Diagram

Treatment Variable - creates the causal effect of the outcome within the experiment

Instrumental Variable - used to estimate the causal relationship when controlled experiment is not feasable, only seen to influence the treatment variable

Observed Variable - factors that may influence the treatment as well as the outcome directly

Unobserved Variable - factors influencing the research not accounted for

Bad Control Variable - errors creating biased estimates

Outcome - Result of all factors

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?

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, then there aren’t any additional variables except for the controlled variable affecting both the policy/treatment and the outcome and Ordinary Least Squares regression should be estimated

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?

To identify the causal effect when there are unobserved confounders controls need to be found that can limit the bias. This can be done through randomisation of the instrumental variable which affects the treatment variable only.

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 two properties that an instrument variable must have are: 1) It only impact outcome through policy 2) uncorrelated with the errors The exclusion restriction means the instrument should not directly affect the outcome. The relationship between an instrument variable and a natural experiment is that natural experiments are generally speaking the most common and available way in which macroeconomist can analyse the effects of policy in which the instrumental variables within are critical to than analyse. Unlike microeconomics field and laboratory experiments are generally unaffordable and/or immoral to test such theories.

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?

Edward Southerington

The Response of Expenditures to Anticipated Income Changes: Panel Data Estimates

By Martin Browning and M. Dolores Collado (2001)

What data do they use?

The data used in this natural experiment is the Encuesta Continua de Presupuestos Familiares (ECPF). This is a data set which gives information on a detailed set of expenditures as well as demographics, incomes and labour force status for more than four quarters, specifically five to eight quarters for each household from the first quarter of 1985 to the fourth quarter of 1995. Only households headed by a married couple in which the husband was in full-time employment and the wife was out of the labor force were included.

What is the natural experiment?

The natural experiment is that in Spain at the time there was two distinct types of payment schemes. Those whom received twelve equal monthly payments over the year and those whom received higher payments in the months of July and December. In testing the Permanent Income Hypothesis the two distinct groups were compared for seasonal consumption patterns. To satisfy the hypothesis there should be no difference in consumption growth between the two groups.

What are their exclusion restrictions? Do you believe their exclusion restrictions?

The exclusion restriction is that the payment scheme is randomly allocated amongst the population and there isn’t significant difference between the two groups in terms of traditions, income, job classification or age, which each would have their own individual effects on the outcome. Without more knowledge on the framework of the Spanish employment sector their exclusion restrictions could be plausible with t values between 1 and 2 in relation to the uneven payment group being older households and home-owning households and there being no partial correlation with the other variables discussed. However I believe it is unlikely that the dual payment structure is evenly balanced across all relevant variables. Taking into account the findings however it does seem to be supported.

What are their findings?

They found that the growth patterns of both groups resembled each other, thereby not rejecting the null hypothesis derived from the Permanent Income Hypothesis .

Nick Russell

Estimating Local Fiscal Multipliers

J. Serrato, P. Wingender, 2014.

Describe the natural experiment.

In an attempt to measure the causal impact of government spending on the economy, Serrato and Wingender isolate the fact that federal spending programs are dependent on the local population. They use the Census as a measure for population in the years which it occurs (every 10 years). They find that in the years between the Censuses, there is variation in the population due to error in the administration data to estimate the population. They find that this variation in population estimation tools lead to variation in billions of dollars of federal spending in local areas.

What data do they use?

The data used for population is from the 1970, 1980, 1990 and 2000 US Censuses, as well as the administrative data sources used by the U.S. Census Bureau of tax data, medicare information, school enrolment and automobile registration data to formulate population levels between the census years. This led to large spikes in population growth in the 1980 and 2000 Census estimates as well as negative growth in the 1990 Census, suggesting the administrative sources were not entirely accurate. The data on federal spending came from the Consolidated Federal Funds Reports, published by the Census Bureau, which discusses where federal spending was present down to a city level.

What is the natural experiment?

The natural experiment in this paper is the extent of the variation within the population estimates of the years between the Census and the population data from the Census, with the instrument used being the error in the Census Bureau’s estimates in population. This is compared to the change in federal spending when it receives the decennial Census information.

What are their exclusion restrictions?

Their exclusion restriction is that the Census shock will only influence local economic growth through the impact on federal spending.

Do you believe their exclusion restrictions?

It is fairly likely that the major change in local economic growth is the amount of Federal spending into an area, however a greater or lesser population within a local area will influence the economic output in the area due to the output of these members of the population. Should there be a large increase in population, there will be greater economic output from these workers, however there will also be a greater level of economic spending from the Federal government. As a result, the exclusion restriction will be the main, but not sole reason for economic output of an area.

What are their findings?

They find that there is a negative of positive Federal spending shock dependant on the shock of the population, being either positive or negative. This is found to take between 1 and 2 years to take effect, with the Federal spending shock coming in to play years after the Census has be completed due to the processing time of the census.

Sumitro Sumitro

Souleles 1999

Describe natural experiments that researchers have used to examine the permanent income hypothesis. 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?

This paper describes about the definition of natural experiment and permanent income hypothesis and its example that Souleles examined.

Natural experiment is an experiment in which the independent variable is not artificially manipulated, but rather changes naturally in terms of its level or presence, so that these alterations can be used to monitor its effect and attempt to determine its impact upon a dependent variable. To simply put, it can be worded in a straightforward manner as an experiment that runs naturally without the intervention of the investigator but allows the researchers to observe and identify the changes that manipulate the results of the interest of observation.

Permanent income hypothesis is a theory of consumer spending which states that people will spend money at a level consistent with their expected long term average income. According to this theory, People tend to save their money when current income is higher than anticipated level of permanent income, in order to guard against future declines in income. It is important to note that this particular hypothesis does not accommodate to conditions where individuals has doubt or limited expectation to their expected long term average income.

In the year of 1999, Souleles released an article with the name of “The response of Household Consumption to Income Tax Refunds” that discussed about permanent income hypothesis under the natural experiment of Income tax refunds over the year of 1980 to 1990 coupled with other variables that act as complements of the experiment. Within 4,121 observations on households receiving refunds with head aged 24 to 64, Souleles found that the total refunds greatly increases from year 1980 to 1990 according to the IRS and CEX data which can be tied to average disbursement attempted by the households concluding that there is excess sensitivity in the response of households’ consumption to their income tax refunds. It is assumed that Souleles’ exclusion restriction is quite robust although it is not in all parts to be guaranteed. Souleles (1999) found that Nondurable consumption of constrained households increased at the time of refund receipt, far more than for unconstrained households moreover the durable expenditures by the unconstrained also responded substantially; and the response of nondurables extended later into the year, after refund receipt. Standard models of durables or self-control themselves are limited in capability into explaining the response in durables by the unconstrained because liquid households could have brought their durables before receiving their refunds. There was also some evidence of unreasonable response to larger refunds, counter to some views of mental accounts. Instrumenting for refunds were also found to lessen the power of the excess sensitivity test (p.956).