Chapter 15 - Estimating dynamic causal effects

# Chapter 15 - Estimating dynamic causal effects - Estimation...

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23-1 Estimation of Dynamic Causal Effects (SW Chapter 15) A dynamic causal effect is the effect on Y of a change in X over time. For example: The effect of an increase in cigarette taxes on cigarette consumption this year, next year, in 5 years; The effect of a change in the Fed Funds rate on inflation, this month, in 6 months, and 1 year; The effect of a freeze in Florida on the price of orange juice concentrate in 1 month, 2 months, 3 months…

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23-2 The Orange Juice Data (SW Section 15.1) Data Monthly, Jan. 1950 – Dec. 2000 ( T = 612) Price = price of frozen OJ (a sub-component of the producer price index; US Bureau of Labor Statistics) %ChgP = percentage change in price at an annual rate, so %ChgP t = 1200 Δ ln( Price t ) FDD = number of freezing degree-days during the month, recorded in Orlando FL o Example: If November has 2 days with low temp < 32 o , one at 30 o and at 25 o , then FDD Nov = 2 + 7 = 9
23-3

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Initial OJ regression n % t ChgP = -.40 + .47 FDD t (.22) (.13) Statistically significant positive relation More/deeper freezes, price goes up Standard errors: not the usual – heteroskedasticity and autocorrelation-consistent ( HAC ) SE’s – more on this later But what is the effect of FDD over time? 23-4
23-5 Dynamic Causal Effects (SW Section 15.2) Example : What is the effect of fertilizer on tomato yield? An ideal randomized controlled experiment Fertilize some plots, not others (random assignment) Measure yield over time over repeated harvests – to estimate causal effect of fertilizer on: o Yield in year 1 of expt o Yield in year 2, etc. The result (in a large expt) is the causal effect of fertilizer on yield k years later.

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23-6 In time series applications, we can’t conduct this ideal randomized controlled experiment: We only have one US OJ market …. We can’t randomly assign FDD to different replicates of the US OJ market (?) We can’t measure the average (across “subjects”) outcome at different times – only one “subject” So we can’t estimate the causal effect at different times using the differences estimator
23-7 An alternative thought experiment: Randomly give the same subject different treatments ( FDD t ) at different times Measure the outcome variable (% ChgP t ) The “population” of subjects consists of the same subject (OJ market) but at different dates If the “different subjects” are drawn from the same distribution – that is, if Y t ,X t are stationary – then the dynamic causal effect can be deduced by OLS regression of Y t on lagged values of X t . This estimator (regression of Y t on X t and lags of X t ) s called the distributed lag estimator.

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23-8 Dynamic causal effects and the distributed lag model The distributed lag model is: Y t = β 0 + 1 X t + … + p X t r + u t 1 = impact effect of change in X = effect of change in X t on Y t , holding past X t constant 2 = 1-period dynamic multiplier = effect of change in X t –1 on Y t , holding constant X t , X t –2 , X t –3 ,… 3 = 2-period dynamic multiplier (etc.)= effect of change in X t –2 on Y t
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Chapter 15 - Estimating dynamic causal effects - Estimation...

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