Import Demand Estimation of Two Commodities in the United States - Research Proposal Example

Import Demand Estimate Report Name of the student: Course Tittle: Name of the professor: Date Table of Contents Table of Contents 2 Abstract 3 1.0 Introduction 3 2.0 Findings and result 4 2.1 Country Demand Estimate 4 2.2 Pharmaceutical demand Estimate 5 2.3 Chemical product demand Estimate 6 3.0 Discussion 7 4.0 Application of the estimated equation and elasticity’s 10 4.1 Statistical significance of result 11 Appendices 12 Abstract This paper gives a report on import demand estimation of two commodities in United States. The commodities under study here are pharmaceutical product and chemical product. The analysis is done using excel on and regression on effect of income and price on demand of these two commodities are done. The result shows that price, income and demand are inversely related and there are price elasticities on demand of both pharmaceutical and chemical product. The finding also shows that income demand elasticities for the two products are also high. These findings are similar to the study done by Judge and Miller (2000) but contradict the findings of Frank and Atle (2009) on the import demand estimation of swordfish. 1.0 Introduction When investigating trade allocation, demand system is normally preferred and it has been used in a number of papers like Deffy et al, David and Krus among other literatures. In this discussion, we are going to base our estimation using Armirgton approach and the assumption to be used here is that goods from all sources have the ability to be separated from each other (Reed and Hallahan. 2005). Statistical surveys of consumer behavior do rarely collect information about price of specific individual commodity units. Consumer theory suggests that observed commodity prices should be identical in order for the household to make similar consumption decisions in the market. Though, econometric estimation of the consumer demand always requires that the demand function requires a substantial price variability of commodities price and without which the duality approach for demand estimation would be infeasible Unrealistic characteristics of traditional approach to demand function estimation is the absence of primal information which is presented by the first order necessary condition for utility maximization. More flexible functions like almost ideal demand system (AIDS) of Deaton and Muellbauer, the primal relations contribute independent information which exists only in a latent state (Reed and Hallahan. 2005). Therefore, the only efficient estimators of the demand functions require the utilization of the complete system of primal and dual relations. Using micro-economic theory, it is assumed that individual representative consumer behaves in such a way to maximize a well defined quasiconcave utility function which is subjected to a budget constrain (Sinha, 1997) The model we are going to use is as follows; Y = aXbZc Ln Qd = ln a + b ln X + c ln Z 2.0 Findings and result 2.1 Country Demand Estimate From the analysis and the out put of ln (income) and ln (price) the regression result are as shown below; Table 1.1: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .967a .935 .934 .20518 From the model summary in table 1.1 above, R is 96.7%; the correlation between Income and price of commodities R2 is 93.4%% of the variation in income is explained by the independent variables price of the commodities Std. Error is 20.518%; The Standard Error is the error you would expect between the predicted and actual dependent variable. Thus, 0.20518 means that the expected error for a demand price prediction is off by 20.518% In the coefficient table, the following result was found as shown in table 1.2 below; Table 1.2 Regression result   Coefficients Standard Error t Stat P-value Intercept -21.756 0.704 -30.924 9.34E-01 X Income 1.331 .045 29.458 .20518 X Price 0.428979259 0.389544754 1.10123228 0.283872943 From the equation, Ln Qd = ln a + b ln X + c ln Z Therefore the estimated demand equation for the country will be; Qd =-21.75a+ 1.331X +0.429Z 2.2 Pharmaceutical demand Estimate The regression result for demand was done and the results are recorded in the table below; Table2.0 Regression out put Regression Statistics Multiple R 0.989316427 R Square 0.978746992 Adjusted R Square 0.976621691 Standard Error 0.191931332 Observations 23 From the model summary in table 2.0 above, R is 98.93%.7%; the correlation between Income and price of commodities R2 is 97.87%% of the variation in income is explained by the independent variables price of the commodities. Std. Error is 19.1931%; The Standard Error is the error you would expect between the predicted and actual dependent variable. Thus, 0.191931 means that the expected error for a demand price prediction is off by 19.1931% for pharmaceutical product. Table 2.1 Coefficient regression table   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -64.84983393 4.487935987 -14.4498 4.78E-12 -74.21150435 -55.48816351 X Price 5.466786571 0.273208464 20.00958 1.07016E-14 4.896883702 6.036689439 X Income 0.428979259 0.389544754 1.101232 0.283872943 -0.38359686 1.241555377 With demand equation of The estimated demand equation for pharmaceutical product will therefore be; Y = 64.85 +5.45P +0.43I 2.3 Chemical product demand Estimate The regression result for demand was done and the results are recorded in the table below; Table3.0: Regression out put Regression Statistics Multiple R 0.995531021 R Square 0.991082014 Adjusted R Square 0.990190215 Standard Error 0.08053085 Observations 23 From the model summary in table 3.0 above, R is 99.55%. The correlation between Income and price of commodities R2 is 99.11% of the variation in income is explained by the independent variables price of the commodities. Std. Error is 8.05%; The Standard Error is the error you would expect between the predicted and actual dependent variable. Thus, 8.05 meaning that the expected error for a demand price prediction is off by 8.05%; for pharmaceutical product Table 3.1 Coefficient regression table   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -30.09096808 1.883055239 -15.97986478 7.45062E-13 -34.01895248 -26.16298369 X Price 3.414290738 0.114633237 29.78447468 4.8314E-18 3.175169996 3.65341148 X Income 0.557303897 0.163445801 3.409716834 0.002778386 0.216361932 0.898245863 With demand equation of The estimated demand equation for chemical product will therefore be; Y =- 30.09 + 3.41P +0.557I 3.0 Discussion From the above result in table 2.0 and 3.0, there is price elastic of the commodities since a small change in price leads to change in quantity demanded i.e. For pharmaceutical product, a unit change in price lead change in Quantity demanded Y = 64.85 +5.45P and For chemical product Y =- 30.09 + 3.41P From the general equation; Ln Qd = ln a + b ln X + c ln Z Where demand of a commodity is being related to price and income, Ln Qd =-21.75a+ 1.331X Qd =-21.75a +0.429Z Which implies that a unit change in price lead to change in quantity demanded and the seam is true for income? For pharmaceutical product, The estimated demand equation for pharmaceutical product is; Y = -64.85 +5.45P +0.43I This gives a positive relationship of price and income on demand of a product If the income of consumer increases, it means that consumer can afford to buy more pharmaceutical products hence the demand for the product will increase as shown in the equation above since the consumer can afford bundles that he could not afford before. On the price effect, when price increases demand decreases and when price decreases demand increases thus there is inverse relationship between price of pharmaceutical commodities and there prices. This findings fulfills the law of demand which states that price of a normal goods is inversely related with its demand hence we can conclude that the pharmaceutical product is a normal good. In chemical product, following the general demand equation is given by Ln Qd = ln a + b ln X + c ln Z Qd= -30.09 + 3.41P +0.557I This gives a positive relationship of price and income on demand of a product If the income of consumer increases, it means that consumer can afford to buy more chemical products hence the demand for the product will increase as shown in the equation above since the consumer can afford bundles that he could not afford before. On the price effect, when price increases demand decreases and when price decreases demand increases thus there is inverse relationship between price of chemical commodities and there prices. This findings fulfills the law of demand which states that price of a normal goods is inversely related with its demand hence we can conclude that the chemical product is a normal good. In conclusion, all the two products (Pharmaceutical and chemical) products are normal goods in United States since they obey law of demand. 4.0 Application of the estimated equation and elasticity’s Demand equation estimation and elasticity is very crucial component for market analysis and study of consumer behavior under different economic environments. As the price elasticity of demand measures the responsiveness of quantity demanded of a good to a change in its price, the traders and business people can use this to measure how consumers will react to the price changes in case a product manager wants to implement changes in price. It also measures the percentage change in quantity demanded divided by the percentage change in price hence the marketing manager will actually know the actual change which will take place when they implement price change and in turn advise the production departments accordingly. The income elasticity of demand measures the responsiveness of quantity demanded of a good to a change in income. Thus business people will actually knows how the quantity of chemical and pharmaceutical products will respond to increase or decrease in income of the consumers hence they will put necessary measures to avert demand shortage and excess demand hence they will be able to maintain market demand equilibrium. It also measures the percentage change in quantity demanded divided by the percentage change in income thus business community will adjust their production to meet changes of income of the consumers. 4.1 Statistical significance of result From the regression statistics data of pharmaceutical product in table 2.0 R2 is 0.991082014which is greater than P-Value of 0.05 that is 0.991082014>0.05 hence change in price and income affect demand of pharmaceutical product. In the case of regression statistics data for chemical product in table 3.0 R2 is 0.978746992 which is greater than P-Value of 0.05 that is 0.978746992 >0.05 hence change in price and income affect demand of pharmaceutical product. T-statistics for pharmaceutical product as shown in table 2.1 above is 20.01 for price and 1.10 for income; both are greater than critical value p thus 20.01>1.07016E-14 and 1.10>0.283872943 respectively hence they are statistically significance. In a study by Frank and Atle (2009) in investigating the import demand of swordfish in United States, mixed findings were found. In their findings, they found that the price elasticities are negatives while the income demand elasticities were positive. This result are opposite of our findings since all our price and demand elasticities for both product were positive and both the R2 and T-statistics were positive something which is different with which contradict with the Frank and Atle findings though both commodities are necessities. A more restricted function approach was used to produce and derive a demand equation for chemical product by Judge and Miller (2000), they produce similar result though in their findings, they found that R2 is not statistically significance hence their conclusion contradict our conclusion that price demand of imported chemical are elastic. The excel findings and excel regression analysis for the study are given in the table below for the two products. Appendices Table 4.0 Pharmaceutical data translation Year Pharmaceutical   MC P I LN (MC) LN (P) LN (I) 1980 803131456 5796400 0.501684 20.50403 15.57275 -0.68978 1990 2539952128 7962600 0.726797 21.65541 15.89027 -0.31911 1991 3092085760 7941800 0.742867 21.85211 15.88765 -0.29724 1992 3860722944 8212200 0.741459 22.07412 15.92113 -0.29914 1993 4198334976 8448100 0.712757 22.15795 15.94945 -0.33861 1994 4755057664 8795700 0.74455 22.28247 15.98977 -0.29498 1995 5605342208 9019900 0.791217 22.44699 16.01494 -0.23418 1996 7150377984 9361400 0.787687 22.69043 16.05211 -0.23865 1997 8819066880 9783200 0.770313 22.90018 16.09618 -0.26096 1998 10982181888 10213800 0.746806 23.11954 16.13925 -0.29195 1999 13649302528 10711100 0.750624 23.33695 16.18679 -0.28685 2000 14855222626 11158100 0.70046 23.42162 16.22768 -0.35602 2001 18753075200 11280100 0.673296 23.65462 16.23855 -0.39557 2002 24873689088 11486300 0.676463 23.93708 16.25667 -0.39088 2003 31739336704 11779500 0.738884 24.18082 16.28187 -0.30261 2004 35371215175 12189400 0.786403 24.28916 16.31608 -0.24029 2005 39322558305 12564300 0.754133 24.39506 16.34637 -0.28219 2006 46222000000 12898400 0.817533 24.55672 16.37261 -0.20146 2007 53954000000 13144400 0.923393 24.7114 16.39151 -0.0797 2008 59868000000 13097200 0.982215 24.81541 16.38791 -0.01794 2009 60157000000 12690000 0.940885 24.82022 16.35632 -0.06093 2010 65563000000 12992000 0.977282 24.90628 16.37984 -0.02298 2011 69912000000 13225900 1.017357 24.9705 16.39769 0.017208 Table 5.0: Chemical data translation Year Chemicals   MC P I LN (MC) LN (P) LN (I) 1980 8957200000 5796400 0.50168 22.91572352 15.57275 -0.68978 1990 23663534080 7962600 0.7268 23.88720105 15.89027 -0.31911 1991 25248696320 7941800 0.74287 23.95204036 15.88765 -0.29724 1992 28886255616 8212200 0.74146 24.08663173 15.92113 -0.29914 1993 30483341312 8448100 0.71276 24.14044618 15.94945 -0.33861 1994 35442466816 8795700 0.74455 24.29117657 15.98977 -0.29498 1995 42101796864 9019900 0.79122 24.46335626 16.01494 -0.23418 1996 46608261120 9361400 0.78769 24.56504364 16.05211 -0.23865 1997 52103991296 9783200 0.77031 24.67650739 16.09618 -0.26096 1998 56423194624 10213800 0.74681 24.75614616 16.13925 -0.29195 1999 64095137792 10711100 0.75062 24.88363434 16.18679 -0.28685 2000 75826339737 11158100 0.70046 25.05171156 16.22768 -0.35602 2001 81173225472 11280100 0.6733 25.11985129 16.23855 -0.39557 2002 88375001088 11486300 0.67646 25.20485497 16.25667 -0.39088 2003 103846354944 11779500 0.73888 25.36617829 16.28187 -0.30261 2004 116099777305 12189400 0.7864 25.47771581 16.31608 -0.24029 2005 131987791887 12564300 0.75413 25.60597527 16.34637 -0.28219 2006 146576000000 12898400 0.81753 25.7108099 16.37261 -0.20146 2007 159162000000 13144400 0.92339 25.79318839 16.39151 -0.0797 2008 180913000000 13097200 0.98222 25.92128209 16.38791 -0.01794 2009 153956000000 12690000 0.94089 25.75993268 16.35632 -0.06093 2010 177010000000 12992000 0.97728 25.89947207 16.37984 -0.02298 2011 202081000000 13225900 1.01736 26.03193444 16.39769 0.017208 Table 6.0: Country price Income data country code country currency unit year rgdpna (Income) pl_m (Prices) LN Income LN (P) USA United States US Dollar 1950 1,979,348.96 0.09890 14.49827854 -2.3136 USA United States US Dollar 1951 2,132,525.90 0.10697 14.5728177 -2.23521 USA United States US Dollar 1952 2,214,200.42 0.10960 14.61040191 -2.21096 USA United States US Dollar 1953 2,316,120.74 0.11319 14.65540425 -2.17866 USA United States US Dollar 1954 2,301,504.21 0.11594 14.64907347 -2.15465 USA United States US Dollar 1955 2,467,223.63 0.11580 14.71860404 -2.15587 USA United States US Dollar 1956 2,516,011.24 0.11966 14.73818536 -2.12308 USA United States US Dollar 1957 2,566,576.34 0.12131 14.7580834 -2.10942 USA United States US Dollar 1958 2,543,466.34 0.12265 14.74903841 -2.09845 USA United States US Dollar 1959 2,725,876.35 0.12679 14.81830053 -2.06523 USA United States US Dollar 1960 2,793,428.13 0.12364 14.84278012 -2.09038 USA United States US Dollar 1961 2,858,510.91 0.12813 14.86581139 -2.05473 USA United States US Dollar 1962 3,031,736.19 0.13297 14.92464601 -2.01766 USA United States US Dollar 1963 3,164,272.14 0.13477 14.96743361 -2.00416 USA United States US Dollar 1964 3,347,373.18 0.13984 15.02368647 -1.96722 USA United States US Dollar 1965 3,562,275.16 0.14600 15.08590999 -1.92414 USA United States US Dollar 1966 3,794,460.14 0.15223 15.1490527 -1.88238 USA United States US Dollar 1967 3,890,356.01 0.15770 15.17401123 -1.84707 USA United States US Dollar 1968 4,078,691.38 0.16327 15.22128676 -1.81237 USA United States US Dollar 1969 4,205,400.82 0.17193 15.25188017 -1.76068 USA United States US Dollar 1970 4,213,400.00 0.17699 15.25378048 -1.73167 USA United States US Dollar 1971 4,359,100.00 0.19025 15.28777617 -1.65941 USA United States US Dollar 1972 4,599,800.00 0.20751 15.34152338 -1.57256 USA United States US Dollar 1973 4,871,700.00 0.23371 15.39895351 -1.45367 USA United States US Dollar 1974 4,846,400.00 0.27884 15.39374672 -1.27712 USA United States US Dollar 1975 4,836,900.00 0.30383 15.39178458 -1.19129 USA United States US Dollar 1976 5,099,000.00 0.31802 15.444555 -1.14564 USA United States US Dollar 1977 5,335,500.00 0.35135 15.48989316 -1.04598 USA United States US Dollar 1978 5,635,700.00 0.38640 15.54463192 -0.95088 USA United States US Dollar 1979 5,813,100.00 0.43490 15.57562455 -0.83265 USA United States US Dollar 1980 5,796,400.00 0.50168 15.57274759 -0.68978 USA United States US Dollar 1981 5,943,700.00 0.53381 15.59784239 -0.62772 USA United States US Dollar 1982 5,826,000.00 0.53233 15.57784122 -0.6305 USA United States US Dollar 1983 6,089,100.00 0.52938 15.62201085 -0.63604 USA United States US Dollar 1984 6,527,200.00 0.52722 15.69148862 -0.64015 USA United States US Dollar 1985 6,795,600.00 0.49786 15.7317859 -0.69743 USA United States US Dollar 1986 7,028,500.00 0.55375 15.76548387 -0.59105 USA United States US Dollar 1987 7,251,100.00 0.61002 15.79666374 -0.49426 USA United States US Dollar 1988 7,548,400.00 0.65837 15.83684618 -0.41799 USA United States US Dollar 1989 7,817,500.00 0.69054 15.87187537 -0.37028 USA United States US Dollar 1990 7,962,600.00 0.72680 15.89026614 -0.31911 USA United States US Dollar 1991 7,941,800.00 0.74287 15.88765051 -0.29724 USA United States US Dollar 1992 8,212,200.00 0.74146 15.92113141 -0.29914 USA United States US Dollar 1993 8,448,100.00 0.71276 15.94945212 -0.33861 USA United States US Dollar 1994 8,795,700.00 0.74455 15.98977352 -0.29498 USA United States US Dollar 1995 9,019,900.00 0.79122 16.01494381 -0.23418 USA United States US Dollar 1996 9,361,400.00 0.78769 16.05210541 -0.23865 USA United States US Dollar 1997 9,783,200.00 0.77031 16.09617719 -0.26096 USA United States US Dollar 1998 10,213,800.00 0.74681 16.13925031 -0.29195 USA United States US Dollar 1999 10,711,100.00 0.75062 16.18679114 -0.28685 USA United States US Dollar 2000 11,158,100.00 0.70046 16.22767625 -0.35602 USA United States US Dollar 2001 11,280,100.00 0.67330 16.23855067 -0.39557 USA United States US Dollar 2002 11,486,300.00 0.67646 16.25666558 -0.39088 USA United States US Dollar 2003 11,779,500.00 0.73888 16.28187129 -0.30261 USA United States US Dollar 2004 12,189,400.00 0.78640 16.31607728 -0.24029 USA United States US Dollar 2005 12,564,300.00 0.75413 16.34637002 -0.28219 USA United States US Dollar 2006 12,898,400.00 0.81753 16.37261383 -0.20146 USA United States US Dollar 2007 13,144,400.00 0.92339 16.39150637 -0.0797 USA United States US Dollar 2008 13,097,200.00 0.98222 16.38790902 -0.01794 USA United States US Dollar 2009 12,690,000.00 0.94089 16.35632484 -0.06093 USA United States US Dollar 2010 12,992,000.00 0.97728 16.37984434 -0.02298 USA United States US Dollar 2011 13,225,900.00 1.01736 16.39768759 0.017208 Read More