pset2dataq1 please copy paste to excel Year L thousands K bi

pset2_data_q1: please copy paste to excel

Year	L (thousands)	K (billions, real $, 2005)	I (billions, real $, 2005)	k = K/L (real $, 2005)	i = I/L (real $, 2005)
1950	152271	6826.338432	369.4345807	44830.19375	2426.165066
1951	154878	6995.235062	383.4883425	45166.09888	2476.067243
1952	157553	7173.841433	338.1763527	45532.8774	2146.429155
1953	160184	7381.49867	348.9883052	46081.37311	2178.671435
1954	163026	7555.218298	329.8994359	46343.64026	2023.600137
1955	165931	7976.324833	415.9884247	48070.13055	2506.99643
1956	168903	8336.459548	419.6782467	49356.49188	2484.729381
1957	171984	8487.803227	397.720862	49352.28409	2312.545714
1958	174882	8555.638932	355.8817038	48922.35297	2034.981895
1959	177830	8790.518048	428.0261723	49432.14333	2406.940181
1960	180671	8985.496827	424.2847924	49734.02941	2348.383484
1961	183691	9231.395905	415.8468492	50255.02559	2263.838997
1962	186538	9503.792834	462.1760571	50948.29383	2477.650972
1963	189242	9730.412614	486.8933299	51417.82804	2572.860834
1964	191889	10092.128	521.9035935	52593.57231	2719.820279
1965	194303	10525.17692	593.4032833	54168.88528	3054.009888
1966	196560	11098.22305	640.9880883	56462.26624	3261.03016
1967	198712	11501.11295	609.0457021	57878.30102	3064.966897
1968	200706	12184.58573	641.46829	60708.62718	3196.059361
1969	202677	12709.19083	677.0855881	62706.62597	3340.712504
1970	205052	12974.24024	626.7220463	63272.92708	3056.40543
1971	207661	13544.53452	697.9203384	65224.25744	3360.863804
1972	209896	14485.17688	779.4548322	69011.20974	3713.528758
1973	211909	15672.97951	869.7353443	73960.896	4104.286955
1974	213854	16279.5363	813.3315941	76124.53495	3803.209639
1975	215973	16328.47183	685.8743259	75604.22752	3175.741069
1976	218035	17033.10606	822.7901603	78120.97168	3773.660928
1977	220239	18168.17833	957.0607401	82493.01135	4345.555238
1978	222585	19500.75005	1084.158416	87610.35132	4870.761353
1979	225055	20882.00676	1126.345376	92786.23787	5004.756064
1980	227726	21712.60078	1003.748613	95345.28681	4407.703172
1981	229966	22043.19192	1096.026807	95854.13461	4766.038489
1982	232188	21913.78947	933.3718328	94379.50914	4019.896949
1983	234307	22013.01845	979.6364773	93949.46994	4180.995349
1984	236348	23133.67634	1230.80012	97879.72116	5207.57578
1985	238466	24320.97087	1195.595687	101989.26	5013.694559
1986	240651	25382.7081	1186.106742	105475.1823	4928.74221
1987	242804	26287.09161	1212.093138	108264.6563	4992.064126
1988	245021	27308.68814	1226.488326	111454.48	5005.645746
1989	247342	28011.16977	1258.522972	113248.7397	5088.189521
1990	250132	27528.12703	1192.504259	110054.3994	4767.499796
1991	253493	26581.10754	1073.970037	104859.3355	4236.685184
1992	256894	26141.24887	1129.970078	101758.8923	4398.584935
1993	260255	26314.0315	1218.679689	101108.6492	4682.636987
1994	263436	27012.64148	1373.823117	102539.6737	5215.016615
1995	266557	27682.03002	1403.061224	103850.321	5263.644266
1996	269667	28534.92442	1492.634315	105815.4109	5535.101868
1997	272912	29819.05032	1642.362959	109262.5107	6017.921378
1998	276115	31826.52758	1766.790238	115265.4784	6398.747759
1999	279295	33727.24507	1891.82648	120758.4993	6773.578044
2000	282385	36310.95243	1999.165228	128586.6899	7079.573024
2001	285267	37435.23442	1833.314948	131228.7591	6426.663258
2002	288028	39290.85304	1787.924184	136413.3106	6207.46658
2003	290704	41546.2933	1838.150903	142916.1391	6323.101517
2004	293310	44905.25989	2034.308153	153098.2916	6935.693135
2005	295994	50372.109	2172.2	170179.4935	7338.66227

1. Exercise - You are given an Excel spreadsheet file, pset2.dataqi.xlsx. The file contains the U.S. annual time series data from 1950-2005 of per-capita investment i, -It/Lt, and per-capita capita stock kt -K:/Lt, measured in real dollar. We wish to calibrate the depreciation rate parameter, 6, in the Solow growth model. We have seen a similar calibration in class, where the parameter 1-a- 0.67 in the Cobb-Douglas production is inferred from the ratio of labor-income to GDP, averaged across time. We will look at per-capita variables, that is, per-capita capital stock is k; - Kt/Lt, and per-capita investment is it -It/Lt (a) Rearrange the per-capita capital accumulation equation kt+1 = (1-5) kit , so that only the parameter is on the left-hand-side. (b) Using the dataset given, construct the time series (k,+1 -k) /kt and it/k, from the data, then find the average values of each time serie - that is, the average growth rate of per-capita capital stock, and the average per-capita investment-to-capital stock ratio. (c) In light of your findings from part (a) and (b), what is the value of ?

Solution

1) K(t+1) = (1-d)K(t) + i(t)

K(t+1) - i(t)= (1-d)K(t)

(K(t+1) - i(t))/K(t)= 1-d

d = 1 - (K(t+1) - i(t))/K(t)

d = (K(t) - K(t+1))/K(t) + i(t)/K(t)

2) https://www.scribd.com/document/369827098/Book1

or  

Average (K(t+1) - K(t))/K(t) = 0.000136233

Average i(t)/ k(t) = 0.000978953

3) d = -0.000136233 + 0.000978953 = 0.00084272

Year	L (thousands)	K (billions, real $, 2005)	I (billions, real $, 2005)	k = K/L (real $, 2005)	i = I/L (real $, 2005)	(K(t+1)-K(t))/K(t)	i(t)/K(t)
1950	152271	6826.338	369.4346	44830.19	2426.165		0.054119
1951	154878	6995.235	383.4883	45166.1	2476.067	0.007492832	0.054821
1952	157553	7173.841	338.1764	45532.88	2146.429	0.00812066	0.04714
1953	160184	7381.499	348.9883	46081.37	2178.671	0.012046146	0.047279
1954	163026	7555.218	329.8994	46343.64	2023.6	0.005691392	0.043665
1955	165931	7976.325	415.9884	48070.13	2506.996	0.037254093	0.052153
1956	168903	8336.46	419.6782	49356.49	2484.729	0.026760096	0.050343
1957	171984	8487.803	397.7209	49352.28	2312.546	-8.5253E-05	0.046858
1958	174882	8555.639	355.8817	48922.35	2034.982	-0.008711474	0.041596
1959	177830	8790.518	428.0262	49432.14	2406.94	0.010420397	0.048692
1960	180671	8985.497	424.2848	49734.03	2348.383	0.006107081	0.047219
1961	183691	9231.396	415.8468	50255.03	2263.839	0.010475648	0.045047
1962	186538	9503.793	462.1761	50948.29	2477.651	0.013795003	0.048631
1963	189242	9730.413	486.8933	51417.83	2572.861	0.009215897	0.050038
1964	191889	10092.13	521.9036	52593.57	2719.82	0.022866471	0.051714
1965	194303	10525.18	593.4033	54168.89	3054.01	0.029952576	0.056379
1966	196560	11098.22	640.9881	56462.27	3261.03	0.042337607	0.057756
1967	198712	11501.11	609.0457	57878.3	3064.967	0.025079312	0.052955
1968	200706	12184.59	641.4683	60708.63	3196.059	0.048901335	0.052646
1969	202677	12709.19	677.0856	62706.63	3340.713	0.032911283	0.053275
1970	205052	12974.24	626.722	63272.93	3056.405	0.009030961	0.048305
1971	207661	13544.53	697.9203	65224.26	3360.864	0.030839894	0.051528
1972	209896	14485.18	779.4548	69011.21	3713.529	0.058060489	0.053811
1973	211909	15672.98	869.7353	73960.9	4104.287	0.071722931	0.055493
1974	213854	16279.54	813.3316	76124.53	3803.21	0.029253823	0.04996
1975	215973	16328.47	685.8743	75604.23	3175.741	-0.006834951	0.042005
1976	218035	17033.11	822.7902	78120.97	3773.661	0.033288405	0.048305
1977	220239	18168.18	957.0607	82493.01	4345.555	0.055964993	0.052678
1978	222585	19500.75	1084.158	87610.35	4870.761	0.062033618	0.055596
1979	225055	20882.01	1126.345	92786.24	5004.756	0.059078482	0.053939
1980	227726	21712.6	1003.749	95345.29	4407.703	0.027580048	0.046229
1981	229966	22043.19	1096.027	95854.13	4766.038	0.005336895	0.049722
1982	232188	21913.79	933.3718	94379.51	4019.897	-0.015384057	0.042593
1983	234307	22013.02	979.6365	93949.47	4180.995	-0.004556489	0.044503
1984	236348	23133.68	1230.8	97879.72	5207.576	0.041833671	0.053204
1985	238466	24320.97	1195.596	101989.3	5013.695	0.0419856	0.049159
1986	240651	25382.71	1186.107	105475.2	4928.742	0.034179308	0.046729
1987	242804	26287.09	1212.093	108264.7	4992.064	0.026446733	0.04611
1988	245021	27308.69	1226.488	111454.5	5005.646	0.029463204	0.044912
1989	247342	28011.17	1258.523	113248.7	5088.19	0.016098588	0.044929
1990	250132	27528.13	1192.504	110054.4	4767.5	-0.028206409	0.043319
1991	253493	26581.11	1073.97	104859.3	4236.685	-0.047204509	0.040404
1992	256894	26141.25	1129.97	101758.9	4398.585	-0.029567641	0.043226
1993	260255	26314.03	1218.68	101108.6	4682.637	-0.006390037	0.046313
1994	263436	27012.64	1373.823	102539.7	5215.017	0.014153334	0.050859
1995	266557	27682.03	1403.061	103850.3	5263.644	0.012781856	0.050685
1996	269667	28534.92	1492.634	105815.4	5535.102	0.018922329	0.052309
1997	272912	29819.05	1642.363	109262.5	6017.921	0.032576538	0.055078
1998	276115	31826.53	1766.79	115265.5	6398.748	0.054940781	0.055513
1999	279295	33727.25	1891.826	120758.5	6773.578	0.047655386	0.056092
2000	282385	36310.95	1999.165	128586.7	7079.573	0.064825173	0.055057
2001	285267	37435.23	1833.315	131228.8	6426.663	0.020546988	0.048973
2002	288028	39290.85	1787.924	136413.3	6207.467	0.039507739	0.045505
2003	290704	41546.29	1838.151	142916.1	6323.102	0.047670044	0.044243
2004	293310	44905.26	2034.308	153098.3	6935.693	0.071245645	0.045302
2005	295994	50372.11	2172.2	170179.5	7338.662	0.111570167	0.043123