The dataset for this question is contained in the table below. The variables are daily time-series of COVID-19 related measures in the United Kingdom for the period 11 March 202031 March 2020. In particular, the dataset contains the following variables:

- immobility: index measuring mobility restrictions, where 0 indicates average (unrestricted) mobility and 100 indicates 100% less mobilility than the average;

- cases: the natural logarithm of new daily COVID-19 cases;

- icu: the natural logarithm of total daily COVID-19 patients in the intensive care unit;

- deaths: the natural logarithm of new daily COVID-19 deaths.

Question 2: Use the data provided to compute the dynamic effects of mobility restrictions on new cases and ICU occupancy. In particular, investigate the following questions:

(a) Are there any identifiable equilibrium relationships between immobility and cases, immobility and icu, cases and icu, or all three together?

(b) If immobility is increased by 1 and maintained at the new level thereafter, what is the expected effect (all else constant) on cases (i) at the time of impact, (ii) 28 days after impact, (iii) 92 days after impact, (iv) in the long run?

(c) If immobility is increased by 1 and maintained at the new level thereafter, what is the expected effect (all else constant) on icu (i) at the time of impact, (ii) 28 days after impact, (iii) 92 days after impact, (iv) in the long run?

Please answer question 2 including all parts (a) through to (c) including all sub-sections.

date	immobility	cases	icu	deaths
11-Mar-20	0.407428566	4.75359	4.407936	0.922325
12-Mar-20	1.553824969	5.241747	4.543724	1.315709
13-Mar-20	3.033190503	5.690359	4.721432	1.694297
14-Mar-20	4.950250769	5.924256	5.005429	2.057554
15-Mar-20	7.40514975	6.150603	5.280732	2.403912
16-Mar-20	10.47418049	5.337538	5.534735	2.730532
17-Mar-20	14.19239042	6.395262	5.744767	3.033401
18-Mar-20	18.54158015	6.911747	5.926352	3.308926
19-Mar-20	23.46054899	6.853299	6.106998	3.561468
20-Mar-20	28.85292846	6.954639	6.276585	3.798098
21-Mar-20	34.58028068	7.31322	6.428541	4.02537
22-Mar-20	40.45883193	6.860664	6.56549	4.249442
23-Mar-20	46.26925027	7.24065	6.697083	4.476176
24-Mar-20	51.76754036	7.646354	6.822197	4.711237
25-Mar-20	56.71413539	7.633854	6.949806	4.958987
26-Mar-20	60.92663124	8.037866	7.079615	5.215243
27-Mar-20	64.30580037	8.345693	7.199619	5.4722
28-Mar-20	66.83506814	8.213382	7.320496	5.721973
29-Mar-20	68.57066995	8.170469	7.437484	5.956543
30-Mar-20	69.62350704	8.23244	7.549892	6.167749
31-Mar-20	70.1355534	8.372399	7.650014	6.347339