1 consider an economy a where debt to dgp equals 100 of gdp...

1. Consider an economy A where:  Debt-to-DGP equals 100% of GDP  The primary deficit is 4% of GDP  The normal growth is 3%  The real interest rate is 3%. a) Confirm that by reducing the primary deficit to 1% for 10 years will produce a debt-to-GDP ratio of 110% in 10 years. Thereafter, what value of the primary deficit will be required to maintain the debt-to-GDP ratio at 110%? b) Continuing with part-a, suppose that policy makers wait five years before changing fiscal policy. For five years the deficit remains at 4% of GDP. What is the debt-to-GDP ratio in 5 years? Assume that after 5 years the policy makers decide to reduce the debt-to-GDP ratio to 100% by year-10. In years 6 through 10, what constant value of the primary deficit will produce a debt-to-GDP ratio of 100% at the end of year 10? c) Suppose that policy makers carry out the policy in part (b). If these policies reduce the growth rate of output down to 2 per cent in years 6 through 10, how will this affect the size of the reduction in the primary deficit required to achieve a debt-to-GDP ratio of 100% in 10 years. d) Suppose that policy makers carry out the policy in part (b). If these policies reduce the growth rate of output down to 1 per cent in years 6 through 10, how will this affect the size of the reduction in the primary deficit required to achieve a debt-to-GDP ratio of 100% in 10 years. Which policy – the one in part (a) or part (b) – do you think is more dangerous to the stability of the economy?

Transcript

00:01 Here we have a multi -part question about the congressional budget office and growth predictions for the period 2011 to 2021 based on the three economic scenarios shown here.

00:13 So we can see we have growth, the debt -to -gdp ratio, and the federal deficit.

00:19 Those are the three variables, and that's the question that is being asked of us in part a.

00:25 So as we look at growth, we see that there are three scenarios for growth, and each scenario is going to have an association with a certain debt -to -gdp ratio and federal deficit.

00:43 So what we're going to do first is use some technology.

00:47 We'll use a graphing calculator in my case to find the regression line for predicting the debt -to -gdp ratio for the debt -to -gdp ratio.

00:55 From the growth rate.

00:56 So that means that you can enter the growth rates in a list, and you can enter the debt to gdp ratio in another list.

01:08 You can then use linear regression.

01:11 I did this on a ti 84.

01:13 So i set up linear regression using l1 and l2.

01:18 And once i did that, it gave me the results over here on the right that says, a, which is my constant, is 129, and b, which is my slope, negative 19 .1.

01:34 So how do we use that information to write the regression line? well, remember, we're predicting the gdp ratio.

01:43 So we'll call that ratio hat, and that is equal to the constant that we saw right over here, constant, and our constant is going to be added to the slope times our variable.

02:01 But look at the slope.

02:02 It's negative.

02:03 So i'm going to write negative minus 19 .1.

02:07 And that is times the growth rate.

02:10 So instead of using x and y hat, we can use growth and ratio hat to make this a little more descriptive equation.

02:19 Okay.

02:19 Next thing, let's interpret the slope and the y intercept of what we have done.

02:24 So the slope interpretation tells us for every 1 % increase in our growth variable, the ratio is going to decrease by 19 .1%.

02:49 It's a negative slope, so it will decrease.

02:52 So every time growth increases by 1%, the ratio decreases by 19 .1%.

02:59 How would we interpret the y intercept? well, that means if we have 0 % growth.

03:09 So if our input variable, our explanatory variable is zero, that means that our ratio would be approximately 129%.

03:20 So ratio is 129%.

03:27 All right, let's move on to the next part.

03:31 And that asks us to estimate the 2021 debt to gdp ratio given two different growth rates, 2 % than 4%.

03:41 So remember we have a regression equation here.

03:46 Ratio hat equals 129 minus 19 .1 times growth.

03:53 So we want to calculate this one growth is 2 and also one growth is 4.

04:04 So all we'll do is replace growth with two and then four.

04:09 Notice, you can notice that i'm not writing the percent signs in my list one and list two.

04:16 We just have to remember at the end that the values that we get are in terms of percent.

04:21 So for example, i get 91 when we input 2 percent growth rate.

04:27 And remember that 91 translates to a 91 percent debt to gdp ratio.

04:32 Similarly here, if we have 53 for our result, if the growth rate is 4%, that's going to translate to about 53 % debt to gdp ratio.

04:45 And then in the next part e, we're working backwards.

04:49 What growth rate could we expect if the ratio in 2021 is 90 %? well, that means that the ratio is 90%.

04:57 And we have 129 minus 19 .1 times the growth.

05:06 And that means we want to solve for the, let's do it this way, solve for the growth...

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