***USE STATA***

***All Data to answer the question are are provided ***

1-please provide screenshots from STATA where/when necessary

2- please provide a clear answer on each step as stipulated by the question

************************

Question: This lab is an exercise in specification: choosing the variables and the functional form. It also gives you experience in transforming and manipulating variables and conducting joint hypothesis tests in Stata. The dependent variable we will study is the price of a used farm tractor sold at auction in the United States.

Table 2.1 Variable Definitions for the Used Tractor Price Model

Variable	Description	Hypoth. Sign of Coef.
salepricei	price paid for the tractor i in dollars	n/a
Tractor Specifications:
horsepoweri	horsepower of the tractor i engine	+
agei	number of years since tractor i was manufactured	-
enghoursi	number of hours of use recorded on tractor i	-
dieseli	a dummy variable = 1 if tractor i runs on diesel fuel, 0 otherwise	+
fwdi	a dummy variable = 1 if tractor i has four-wheel drive, 0 otherwise	+
manuali	a dummy variable = 1 if tractor i transmission is manual, 0 otherwise	-
johndeerei	a dummy variable = 1 if tractor i is manufactured by John Deere, 0 otherwise	+
cabi	a dummy variable = 1 if tractor i has an enclosed cab, 0 otherwise	+
Time of year:
springi	a dummy variable = 1 if tractor i sold in April or May, 0 otherwise	?
summeri	a dummy variable = 1 if tractor i sold June-September, 0 otherwise	?
winteri	a dummy variable = 1 if tractor i sold December-March, 0 otherwise	?

Step 1: Estimate the Basic Model

As our basic model, let's estimate a variation of Diekmann's model using a more current dataset. Table 2.1 contains the definitions of the variables we'll need to attempt to replicate Diekmann's regression. The dependent variable is the price of a used farm tractor that was sold at auction in the United States between June 1, 2011 and May 31, 2012. The data are available in the file TRACTOR. Table 2.1 (below step 7) also has the hypothesized expected sign of the coefficient of each variable, given the underlying theory. Now:

a. Estimate an equation with the natural log of the sale price (saleprice) as the dependent variable using all of the independent variables in Table 2.1 except for cab. (Hints: Don't forget to generate lnsaleprice before you run your regression and make sure not to includecab as an independent variable.)

b. Take a look at your regression results. What is R^2 ? Does this seem reasonable? Explain your thinking.

c. Does any of your estimated coefficients have unexpected signs? If so, which ones?

d. Testthe coefficients of all your independent variables except for the seasonal dummies at the 5 percent significance level. For which coefficients can you reject the null hypothesis?

e. Carefully interpret the coefficient of John Deere. What does it mean in real-world terms?

f. What econometric problems (if any) appear to exist in the basic model?

Step 2: Consider a Polynomial Functional Form for Horsepower

Suppose you show the results of your basic model to a used tractor dealer who happened to take econometrics in college. He says that your results are promising, but he's found it very difficult to sell overpowered used tractors because these tractors waste fuel and provide no extra benefit to the buyer. He thinks that new tractor buyers don't make this mistake as often. He therefore suggests that it could be that as horsepower increases, the price increases, at least up to a point, but beyond that point, further increases in horsepower start to have a negative effect on price. You decide to take his advice and consider changing the functional form of horsepower to a polynomial.

a. Generate the new variable and run the new regression. Hypothesize the signs of the coefficients of horsepower and its square before you run the regression.

b. Run 5-percent t-tests on your hypotheses for the coefficients of horsepower and its square.

c. At what horsepower (to the nearest round number) does the value of a tractor reach an extreme (other things being equal)? Is the extreme a minimum or a maximum?

d. Which equation do you prefer between the basic equation and the polynomial equation? Why? (Be sure to cite evidence to support your choice.)

Step 3: Add a Potential Omitted Variable to Your Step 3 Model

As you're leaving the used tractor lot, you happen to notice that quite a few of the tractors have enclosed cabs. Since such a cab would come in handy in bad weather, you have a sudden sinking feeling that you might have an omitted variable! To test this, you find the data for cab (also in TRACTOR). Now:

a. Add cab to the model you preferred in Step 3, part d, and re-estimate the equation.

b. Use our four specification criteria to decide whether cab belongs in the equation. (Hint: Write out specific answers for all four criteria and then justify your conclusion.)

Step 4: Joint Hypothesis Testing

Go back to the basic model of Step 2, and test at the 5-percent level the joint hypothesis that the time of year of the sale has no effect on the price of the tractors:

a. What is the omitted condition in this seasonal model?

b. Carefully write out your null and alternative hypotheses.

c. Estimate your constrained equation (that is, without the seasonal dummies)

d. Run the appropriate F-test at the 5-percent level. Calculate F and look up the appropriate critical F-value.

e. What's your conclusion? Do used tractor prices have a seasonal pattern?

Step 5: Consider a Slope Dummy That Interacts Diesel with Use

It is well known that diesel engines tend to be more durable than gasoline engines. That fact raises the question of whether an additional hour of use affects the value of a diesel tractor differently than for a gasoline tractor. Generate the variable you need to test that hypothesis, add this variable to the basic model of Step 2, estimate the revised slope dummy model, and test the appropriate slope dummy hypothesis at the 5-percent level. What is your t-value? Can you reject the null hypothesis?

Step 6: Interpreting Coefficients in Different Specifications

Replace age in the Step 4 model with the natural log of age. Refer to this specification as S1.

a. State the precise meaning of the coefficient on lnage.

b. What is the effect of an additional 1 hour of use on the price of a used tractor?

Step 7: Excluding a Variable

How does the coefficient on lnage in the S1 specification change if you run it without enghours? Why does this happen? Explain. Does this violate a classical assumption? How do you know? Briefly explain.

***Data from TRACTOR.xls***

saleprice	horsepower	age	enghours	diesel	fwd	manual	johndeere	cab	spring	summer	winter
200000	491	2	1148	1	1	1	1	1	1	0	0
183500	270	3	467	1	1	1	1	1	0	0	0
162500	215	5	1511	1	1	1	1	1	0	0	0
135000	205	2	128	1	1	0	0	1	0	0	1
122100	235	2	1620	1	1	0	0	1	1	0	0
120000	510	7	5038	1	1	1	0	1	0	1	0
117500	333	5	2825	1	1	1	0	1	0	0	1
110000	275	4	1360	1	1	1	0	1	1	0	0
109000	221	6	1003	1	1	0	0	1	0	0	0
105000	275	4	1227	1	1	1	0	1	1	0	0
101250	221	4	1250	1	1	1	0	1	0	0	1
96000	215	7	2221	1	1	0	0	1	0	0	0
95000	535	5	7297	1	1	1	0	1	0	0	1
74600	180	8	4257	1	1	0	0	1	0	0	0
65600	225	18	5624	1	1	1	1	1	1	0	0
58600	190	7	2699	1	1	1	0	1	0	0	1
48700	350	18	4985	1	1	1	1	1	0	0	1
48000	240	9	7056	1	1	1	0	1	1	0	0
47000	105	5	1650	1	1	1	1	1	0	0	0
46000	100	6	2872	1	1	0	0	1	0	1	0
45500	350	19	6131	1	1	1	0	1	0	0	0
45000	105	5	513	1	1	0	0	1	1	0	0
43100	145	17	3800	1	1	1	0	1	0	0	0
42750	187	29	3918	1	1	1	0	1	1	0	0
42500	95	5	460	1	1	0	0	1	0	0	0
42400	225	15	7595	1	1	1	0	1	0	0	0
41700	210	19	4990	1	1	0	0	1	0	0	0
41700	125	7	391	1	1	0	0	1	0	1	0
41100	210	18	7300	1	0	1	0	1	0	1	0
41100	95	5	300	1	1	1	0	1	1	0	0
39800	235	14	7750	1	1	1	0	1	1	0	0
37200	175	9	6390	1	1	1	0	1	0	1	0
36900	210	18	9224	1	1	0	0	1	1	0	0
36500	100	8	3517	1	1	0	0	1	0	1	0
36100	105	4	784	1	1	1	0	0	0	0	0
36000	95	5	2417	1	1	0	0	1	0	0	1
35600	215	18	6849	1	1	1	0	1	0	1	0
35100	78	4	78	1	1	0	0	1	0	0	1
35000	93	7	636	1	1	1	0	1	1	0	0
34400	150	17	9000	1	1	1	1	1	0	0	1
34400	85	16	1251	1	1	1	1	0	0	0	1
33900	91	6	26	1	1	0	0	1	0	0	0
33000	300	18	8975	1	1	1	1	1	0	1	0
33000	81	5	430	1	1	1	1	1	0	0	0
33000	80	5	271	1	0	0	0	1	0	0	1
32600	68	4	85	1	1	1	0	1	0	0	1
32500	95	7	2757	1	0	0	0	1	0	0	0
32000	65	4	410	1	1	0	0	1	1	0	0
31500	99	4	325	1	1	1	0	1	1	0	0
30100	360	18	8230	1	1	1	0	1	1	0	0
28800	99	17	4512	1	1	1	1	1	1	0	0
28400	200	25	2595	1	1	1	0	1	1	0	0
28200	110	13	4497	1	1	1	0	1	1	0	0
27900	85	8	1400	1	0	0	0	1	0	0	1
27500	120	11	721	1	1	0	0	1	0	0	0
27100	335	25	11685	1	1	1	0	1	0	0	0
27000	180	30	6400	1	0	1	0	1	0	0	1
27000	98	3	178	1	1	1	0	0	1	0	0
25100	95	5	2360	1	1	1	0	1	1	0	0
25100	90	6	1757	1	1	1	0	1	1	0	0
24800	325	23	9067	1	1	1	0	1	1	0	0
24250	150	14	9037	1	1	1	0	1	1	0	0
24100	50	4	9	1	1	1	0	0	0	1	0
23750	145	18	7194	1	1	1	0	1	0	0	0
22800	96	21	1010	1	1	1	0	1	1	0	0
22500	95	20	5439	1	0	1	0	1	0	0	0
22000	50	8	689	1	1	1	0	1	1	0	0
21100	97	27	5350	1	1	1	0	1	0	1	0
21000	95	8	680	1	1	0	0	1	1	0	0
20900	62	5	399	1	1	0	0	0	0	1	0
20700	133	28	3042	1	1	1	0	1	0	0	0
20100	130	17	9467	1	1	0	0	1	1	0	0
20000	106	21	4769	1	1	1	0	1	0	0	1
19500	98	24	2670	1	1	1	0	1	0	0	1
19500	94	23	9573	1	1	1	0	1	0	0	0
19400	105	10	3924	1	1	0	0	1	0	1	0
19100	335	25	7200	1	1	1	0	1	0	1	0
18700	78	6	1145	1	0	0	0	1	0	0	1
18600	100	23	13869	1	1	1	0	1	0	0	0
18500	90	19	9008	1	1	1	0	1	0	1	0
18250	105	7	1935	1	1	1	0	1	0	1	0
18000	90	17	5020	1	1	1	0	1	0	0	0
18000	75	11	3900	1	0	1	0	1	0	1	0
18000	65	2	5	1	1	1	0	0	0	0	0
17700	86	23	4914	1	1	1	0	1	0	0	0
17500	325	21	9392	1	1	1	0	1	1	0	0
17500	154	26	5400	1	0	1	0	1	0	0	1
17500	52	5	673	1	1	1	0	1	0	1	0
17250	108	22	6300	1	1	1	0	1	0	0	0
17250	75	4	350	1	0	1	1	0	0	0	0
17100	116	28	3458	1	1	1	0	1	1	0	0
17100	90	22	5922	1	1	0	0	1	0	0	0
17000	138	31	6441	1	0	1	0	1	1	0	0
17000	105	11	105	1	1	1	0	1	0	0	0
16750	100	21	8837	1	1	1	0	1	0	1	0
16600	100	22	7811	1	0	1	0	1	0	0	0
16500	86	23	8452	1	1	1	0	1	0	0	0
16300	140	22	5316	1	0	1	0	1	1	0	0
16100	105	23	1800	1	0	1	0	1	0	1	0
16100	87	24	6559	1	0	1	0	1	1	0	0
16000	90	9	2582	1	1	1	0	0	0	0	0
16000	52	8	293	1	1	1	0	1	0	1	0
15900	70	3	243	1	0	0	0	0	0	0	0
15700	85	28	3736	1	0	1	1	1	0	0	1
15200	50	4	10	1	1	1	0	0	0	0	1
15100	105	32	6424	1	0	1	0	1	0	1	0
15100	47	8	2500	1	1	1	0	1	0	1	0
15000	90	9	90	1	1	1	0	1	0	0	0
15000	52	13	710	1	1	1	0	1	0	0	0
14900	74	13	2484	1	0	1	0	1	0	1	0
14800	90	16	1540	1	1	1	0	1	0	0	0
14750	90	12	6337	1	1	1	0	1	0	0	0
14100	73	12	1586	1	1	0	0	1	0	0	0
14000	355	18	17543	1	1	1	0	1	0	1	0
14000	230	32	4380	1	1	1	0	1	1	0	0
14000	105	7	2452	1	1	1	0	0	0	0	0
14000	32	6	931	1	1	1	0	0	0	0	1
13900	108	22	5796	1	1	1	0	1	0	0	0
13750	131	33	4122	1	0	1	0	1	0	0	0
13500	205	2	128	1	1	1	0	1	0	0	1
13500	100	27	5200	1	0	1	0	1	0	1	0
13500	82	27	5100	1	0	1	0	1	1	0	0
13500	48	7	270	1	1	1	0	0	0	1	0
13500	29	5	395	1	1	1	0	0	0	0	0
13250	76	5	2220	1	0	0	0	0	0	0	0
13000	54	6	948	1	1	1	0	0	0	0	0
13000	30	15	850	1	1	1	0	0	0	0	1
12700	48	5	1176	1	1	1	0	1	0	0	0
12600	76	5	2379	1	0	0	0	0	0	0	0
12600	70	7	3500	1	1	1	0	1	1	0	0
12500	45	5	727	1	1	0	0	0	1	0	0
12500	42	13	3805	1	1	1	0	1	0	0	0
12400	35	5	304	1	1	1	0	0	1	0	0
12300	45	6	165	1	0	0	0	0	0	0	1
12100	136	30	5148	1	0	1	0	1	0	1	0
12100	41	17	1785	1	1	1	0	0	0	1	0
12000	80	14	7622	1	0	1	0	1	1	0	0
12000	75	14	3000	1	0	1	0	0	0	0	1
12000	45	3	22	1	0	1	1	0	0	0	1
11600	29	9	29	0	1	0	0	0	0	0	0
11500	55	10	291	1	1	1	0	1	0	0	0
11400	30	7	208	0	0	0	0	0	0	0	0
11250	75	9	755	1	0	0	0	0	0	0	0
11000	90	16	17020	1	1	1	0	1	0	0	0
11000	80	7	1625	1	0	1	0	0	0	1	0
10800	27	4	63	1	1	1	1	0	0	0	0
10700	35	11	1388	1	1	0	0	0	0	1	0
10600	165	31	6155	1	0	1	0	1	0	1	0
10600	163	31	9438	1	0	1	0	1	1	0	0
10600	23	6	1301	1	1	0	0	0	1	0	0
10500	50	11	1722	1	1	0	0	0	1	0	0
10500	28	11	732	1	1	0	1	0	0	0	1
10500	24	11	1392	0	1	0	0	0	0	0	1
10250	46	17	1021	1	0	1	0	1	0	1	0
10100	52	4	20	0	0	0	0	0	0	0	1
10000	100	19	3091	1	1	1	0	0	0	1	0
10000	98	26	2785	1	1	1	0	1	0	0	0
10000	90	7	209	1	0	1	0	1	0	0	0
10000	85	27	3800	1	0	1	1	0	1	0	0
10000	80	11	2964	1	1	1	0	1	0	1	0
10000	75	12	3730	1	0	1	0	1	0	0	0
10000	72	13	1347	0	0	0	0	0	0	0	1
10000	62	10	608	1	0	1	0	1	0	1	0
10000	44	10	4484	0	1	0	1	0	0	1	0
10000	21	7	883	1	0	0	0	0	0	0	0
9900	85	24	8604	1	0	1	1	0	0	0	0
9800	66	21	3772	1	0	0	0	1	0	0	0
9800	26	4	56	1	1	0	0	0	0	0	0
9750	52	7	2350	1	1	0	0	0	0	1	0
9600	85	25	6228	1	0	0	0	0	0	0	0
9600	52	4	27	1	0	0	0	0	0	0	0
9600	48	4	48	1	0	0	0	0	0	0	1
9500	85	15	3477	1	0	1	0	0	1	0	0
9500	21	18	259	1	1	1	0	0	0	0	0
9300	187	31	4788	1	0	1	0	1	0	0	0
9200	140	32	4690	1	0	1	0	1	0	0	1
9200	88	24	5870	1	0	1	1	0	0	1	0
9200	75	27	9001	1	0	1	1	0	0	0	0
9100	150	32	12370	1	0	1	0	1	0	1	0
9100	120	22	4300	1	0	1	1	0	0	1	0
9100	50	24	1391	1	1	1	0	0	0	0	0
9100	48	5	228	0	0	0	0	0	0	1	0
9100	25	12	1031	1	1	0	0	0	0	0	0
9000	163	30	9042	1	0	1	0	1	0	0	0
9000	58	8	888	1	0	1	0	0	1	0	0
9000	52	11	633	1	1	1	0	0	0	1	0
9000	46	6	171	1	1	1	0	0	1	0	0
9000	32	4	55	1	1	0	0	0	0	0	0
9000	28	3	1	1	1	0	0	0	0	1	0
8800	90	22	9470	1	0	1	0	1	0	0	0
8800	50	7	203	0	0	0	1	0	0	0	0
8700	45	11	128	1	0	1	0	0	1	0	0
8600	130	33	8975	1	0	1	0	1	0	0	0
8600	76	19	4500	1	0	0	0	0	1	0	0
8600	21	11	557	1	1	0	0	0	0	1	0
8500	52	7	2019	1	1	1	0	0	0	1	0
8100	90	32	6600	1	0	1	0	1	0	0	0
8000	80	6	2348	1	1	0	0	0	0	1	0
8000	66	18	1157	1	0	1	0	1	0	0	0
8000	62	12	1489	1	0	1	0	1	0	0	0
8000	35	16	1290	1	1	0	0	0	0	0	0
8000	33	6	2348	1	1	0	0	0	0	1	0
8000	27	9	807	1	1	1	1	0	0	0	1
7900	111	33	9264	1	0	1	1	1	1	0	0
7900	75	16	9320	1	1	1	1	1	1	0	0
7900	44	18	1275	1	0	1	0	0	0	0	0
7800	162	30	8486	1	1	1	0	1	0	0	0
7600	25	12	981	1	1	0	0	0	0	1	0
7550	26	12	916	1	1	0	1	0	1	0	0
7500	40	11	273	1	1	1	0	0	0	0	0
7500	28	7	970	1	1	0	0	0	0	0	0
7400	217	29	7500	1	0	1	0	1	0	0	0
7400	95	17	3900	1	0	1	0	0	0	1	0
7400	28	15	1370	1	0	0	0	0	0	0	0
7300	105	33	6453	1	0	1	0	1	0	0	1
7300	99	22	18744	1	0	1	0	1	0	0	1
7300	72	23	4527	1	0	1	0	0	0	1	0
7000	162	31	6170	1	0	1	0	1	0	0	0
7000	44	10	681	1	1	1	0	0	0	0	0
7000	22	7	159	1	1	0	0	0	0	1	0
6750	24	4	140	1	1	0	0	0	0	1	0
6700	45	11	750	1	0	0	0	0	0	1	0
6600	50	33	4647	1	0	1	1	0	1	0	0
6500	62	28	1201	1	0	1	0	0	0	1	0
6500	33	11	1409	1	1	1	0	0	1	0	0
6400	217	27	5716	1	0	1	0	1	1	0	0
6400	85	29	5336	1	1	1	1	0	0	1	0
6300	195	33	3955	1	0	1	0	1	0	1	0
6200	27	12	1712	0	1	1	1	0	0	0	1
6100	61	30	2457	1	0	1	0	0	0	0	0
6100	53	27	550	1	0	1	0	0	0	1	0
6000	52	30	5125	1	0	1	0	0	0	0	1
6000	20	15	578	0	0	0	0	0	0	0	1
5600	122	33	5521	1	0	1	0	1	0	1	0
5600	27	29	938	0	0	0	0	0	0	0	0
5500	65	32	877	1	0	1	0	0	0	0	0
5500	33	33	1681	1	0	1	1	1	0	0	0
5400	20	15	3939	0	1	1	1	0	0	0	1
5300	38	15	1493	1	0	0	0	0	0	1	0
5250	90	31	6859	1	0	1	0	1	1	0	0
5100	86	33	9479	1	0	1	0	1	1	0	0
5100	41	27	609	0	0	1	0	0	0	1	0
5000	80	5	300	1	1	1	0	1	0	0	1
5000	48	5	286	1	1	1	0	0	1	0	0
5000	32	23	4028	1	1	1	0	0	1	0	0
4800	45	11	2860	0	0	0	0	0	0	0	0
4700	122	33	5188	1	0	1	0	1	0	0	1
4700	26	13	1257	0	0	0	1	0	0	0	0
4600	16	27	1310	0	0	0	1	0	0	0	1
4500	60	23	4617	0	0	0	0	0	0	0	0
4500	27	20	2376	1	0	1	0	0	0	0	0
4250	45	26	3084	1	0	1	0	0	0	1	0
4250	38	17	713	1	0	1	0	0	0	0	0
4200	30	5	757	1	0	1	0	0	0	0	1
4100	64	31	3750	1	0	1	0	0	0	0	1
4000	55	21	8283	1	0	1	0	0	0	0	0
4000	50	33	9872	0	0	1	1	0	0	0	0
3800	51	21	8332	1	0	1	0	0	0	0	0
3800	20	20	2227	1	1	0	0	0	1	0	0
3750	70	32	10734	0	0	0	1	0	0	1	0
3500	65	30	4078	1	0	1	0	0	0	0	1
3500	56	27	7200	1	0	1	0	0	0	0	0
3500	45	29	2319	1	0	1	0	0	0	0	1
3300	28	30	3530	1	0	0	1	0	0	0	0
3000	63	31	9543	1	0	1	0	0	0	0	1
3000	61	26	6483	1	0	1	0	0	0	0	0
3000	36	28	2277	0	1	1	0	0	0	0	0
3000	22	28	10611	0	0	0	1	0	1	0	0
3000	19	10	1737	0	0	0	0	0	1	0	0
2800	22	33	1228	1	0	1	1	0	0	0	0
2600	47	14	1350	1	0	1	0	0	1	0	0
2250	24	28	1390	0	0	0	0	0	0	1	0
1750	55	18	5325	1	0	1	0	0	0	1	0
1650	25	33	1140	0	0	0	0	0	0	0	0
1600	18	25	3351	0	0	0	0	0	1	0	0
1500	32	19	6833	1	0	1	0	0	0	0	0