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\title{Determination of Domestic Prices of Milk and Wheat in Pakistan: Error in Estimation}
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             \author[1]{riaz  ahmed}

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\date{\small \em Received: 5 May 2012 Accepted: 4 June 2012 Published: 16 June 2012}

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\begin{abstract}
        


The domestic prices of traded goods in an open economy are a function of international prices and the levied tariff rates. The key question arising here is whether the domestic prices can be ?estimated? from the information on international prices and the tariff rates given that the later two independent variables are determined out of the system? Some authors have ?estimated? domestic prices from international prices and the tariff rates. However the estimation of domestic prices in such way has presented inaccurate estimates. Present study is an attempt to correct such failing in case of domestic prices of milk and wheat and strived to calculate instead of estimating the domestic prices in presence of two independently determined variables i.e. tariff rates and international prices.

\end{abstract}


\keywords{Domestic prices, Error in estimation, Credit goods.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
he domestic prices are determined from the information on international prices and the tariff rates. Since the price variations accounted for here are trade and tariff driven, it would be interesting to know how domestic prices of traded goods are determined in the local market when the tariff rates change. Pakistan, being an economically small developing country, plays the role of a price taker in the global trade sector. Thus in analogy with other small open economies, the determination of domestic prices of traded goods in Pakistan would look as follows:i wi i P =P (1+t )\textbf{(1)}\par
rate of tariff (which is also exogenously determined as it is fixed by the government). This is shown in the following set of equations.\par
) t ( \par
It can be inferred from equation (3) that given exogenous world price, the absolute change in the domestic price depends upon the international price times the tariff change. Taking log on both sides to linearize equation (3) we have;) t (1 dlnP dlnP i wi + = (4)\par
For simplicity reasons, here we would allow the relaxation of two strong assumptions. Firstly, there are unified products and one tariff line for imports of the same product for all countries. In this way, we are indeed relaxing the Armington assumption [Lloyd, J. P.  et al. (2006)] of differentiated products with respect to their various points of origin or production (countries). Secondly, it is further assumed that the goods have similar prices throughout the whole country. See Table \hyperref[tab_1]{1} for the summary of the percentage difference between the domestic prices of two goods in major cities of Pakistan 1 .\par
Here Pi and P wi are the domestic and world prices of the traded goods i respectively, and ti is the rate of tariff applied on traded goods. If the international price is exogenously determined, then the change in the local price would be established by the given change in the Though, in developing countries, this assumption may not hold in its entirety for a variety of reasons such as irregular market structures, information unevenness, etc. Nevertheless, in the case of Pakistan, owing to sea access and a relative good communication and transportation infrastructure, as well as developed markets in urban sectors, equation (  {\ref 4}) can be a reliable exercise to determine the absolute price changes caused by a change in tariff. 
\section[{II.}]{II.} 
\section[{Data}]{Data}\par
The main sources of data are FBS' (Federal Bureau of Statistics) book '50 years of Pakistan in Statistics' all volumes and FBS online statistics portal 2 ; online datasets of Federal Board of Revenue (FBR), Pakistan, a public sector organization formerly known as Central Board of Revenue responsible for collecting all types of tax revenues and framing national tariff policies \hyperref[b3]{3} ; Food and Agriculture Organization (FAO) online datasets. Due to the unavailability of straight forward data on tariff rates on the two goods, the appropriate data has been calculated from available statistics before using in the study. The detailed description on the calculation and quality of data used in the study is provided in the following paragraphs. Following paragraphs present the issues related to the quality and availability of the data used on the domestic and international prices of the two selected goods.\par
The data on the import tariff per ton on the two goods is not available in a straight forward fashion instead the information on total tariff revenue collected from various commodity groups is available from the Federal Board of Revenue (FBR) for the years from 1992 to 2005. Amongst, the provided selected commodity groups are fruits, nuts and vegetables; tea, coffee and spices; milk, butter and cheese; animal and vegetable oil; edible cereals and vegetables; tobacco; fuels and oils; sugar and confectionary; and meat, fish and other preparations. The two goods, wheat and milk, selected for the present study fall in "milk, butter and cheese" and "edible cereals and vegetables" groups. The tariff per ton on each commodity group is calculated by dividing the total yearly tariff revenue in PKR for 1992-2005 by the total import (C.I.F) quantity in tons of all varieties of goods in the respective commodity group. For example, the tariff per ton in PKR on the commodity group of milk, butter and cheese is calculated by dividing the total tariff revenue in PKR collected from the commodity group by the total sum of the import quantities in tons of milk, butter and cheese. See Table \hyperref[tab_5]{2} for summary of the information. Since milk and wheat are the most dominant traded goods in the above two groups therefore the calculated average commodity-wise tariffs may also apply to the individual goods.\par
Table \hyperref[tab_2]{3} presents the real world tariff for some years acquired from the WTO online data sets on the two commodities \hyperref[b4]{4} . International prices are taken from the FAO online dataset and are presented in the following table 4. Source : Food and Agriculture Organization (FAO) online data set \hyperref[b5]{5} The domestic prices of selected goods are taken from FBS' 50 years of Pakistan in Statistics (from 1992 to 2005) \hyperref[b6]{6} and are the averages of the prices in major cities of Pakistan. The average variation in the domestic prices of goods across major cities of Pakistan is trivial so these prices can best reflect the domestic prices in Pakistan in general. See following Table \hyperref[tab_1]{1} above.\par
The domestic prices from 1997-2005 are taken from the statistical year book 2006 published by FBS. All prices have been taken in local currency (PKR) per ton. The calculated tariff per ton is then added to the international prices to determine the domestic prices. 
\section[{III.}]{III.} 
\section[{Failing}]{Failing}\par
The approach is based on the specifications of Porto (2003, 2006) to correct some of its methodological inaccuracies. Porto (2003) implicitly treated the import tariff rates as determined in the system which is against the fact that the trade policy of any country introduces the tariff rates on import of various commodities from prices on the international prices and the tariff rates. Resultantly, it produced estimated domestic prices which may not be accurate so cannot be relied for further policy making.\par
In present study this failing has been proved and suggested that the domestic prices can be computed instead of being estimated by exercising the simple addition of information on import tariff per ton to the international prices of the two goods. Following paragraphs show how the failings may be corrected and the calculated domestic prices reflect better approximation of domestic prices rather than the estimated domestic prices.\par
As an initial step, the domestic prices of wheat and milk are estimated using OLS Least Squares Method. Following section provides a detailed discussion on the regression methodology, functional form and the results.\par
IV. 
\section[{Regression}]{Regression}\par
The domestic prices of wheat and milk are estimated using real tariff rates available from WTO online dataset. The functional form of the regression equation is the natural log to linearize the price equation 3 to the form of equation 4. The regression results are significant and reliable as indicated from the large t-and f-values and their significance near to zero chance of error. Fairly large R2 indicates the overall satisfactory coverage of the regression analysis. (Table \hyperref[tab_5]{2}). \par
.37\par
Slightly large value of the constant indicates that there are some factors which affect the domestic prices of milk and wheat other than the tariff rates. However other values and the positive signs of the coefficients are in congruence with the expected and hypothesis.\par
The calculated domestic prices on average tariff rate are compared with the estimated domestic prices at average tariff rate and the calculated domestic prices at the real world tariff rate. \hyperref[b7]{7} The calculated prices at average tariff rate are found closer to the calculated domestic prices at real world tariff rate than the estimated domestic prices.\par
This indicates the methodological error in Porto (2003) 8 who took the estimated domestic prices instead of calculated prices. The Figure \hyperref[fig_1]{1} (wheat and milk estimated and calculated domestic prices) confirms that the average tariff rates calculated on various commodity groups are also applicable to the individual commodities selected in the study. out of the system. Porto (2003) estimated the domestic 
\section[{Wheat (PKR per ton) Milk (PKR per ton)}]{Wheat (PKR per ton) Milk (PKR per ton)}\par
Estimated domestic prices at calculated Tariff Calculated domestic prices at calculated Tariff Calculated domestic prices at real world tariff  The prices taken as an indicator of the domestic prices of milk and wheat are not the estimated ones instead they are the calculated ones obtained by adding the tariff per ton to the international prices.\par
V. 
\section[{Conclusion}]{Conclusion}\par
Estimating the domestic prices of traded goods in presence of international prices and tariff rates may not be a good approximation since the two independent variables are exogenous and determined out of the system. Therefore the failings in the past studies may be corrected by simply adding the international prices to tariff rates to determine the domestic prices of the goods. It has been attempted here to correct this flaw by using information on the prices and tariff rates of milk and wheat for Pakistan.\begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Fig. 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.08916083916083915\textwidth}P{0.427972027972028\textwidth}P{0.023776223776223775\textwidth}P{0.22587412587412586\textwidth}P{0.03566433566433567\textwidth}P{0.023776223776223775\textwidth}P{0.023776223776223775\textwidth}}
\tabcellsep 1992\tabcellsep 1994\tabcellsep 1996\tabcellsep 1998\tabcellsep 2000\tabcellsep 2004\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \%\tabcellsep \\
Wheat flour\tabcellsep \multicolumn{6}{l}{-0.244211 -0.7886 -0.5986 -1.9057 -0.2967 -0.2348538}\\
Milk\tabcellsep \multicolumn{2}{l}{-1.727605 -1.711}\tabcellsep \multicolumn{4}{l}{-1.2273 -1.1534 -1.2862 -0.7658772}\end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_2}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.32241379310344825\textwidth}P{0.2149425287356322\textwidth}P{0.31264367816091954\textwidth}}
Import (Tons) Total Revenue\tabcellsep Tariff per ton\tabcellsep Import (Tons) Total Revenue\\
(PKR)*\tabcellsep in PKR**\tabcellsep (PKR)\end{longtable} \par
 
\caption{\label{tab_3}Milk, Butter and Cheese Edible prep. Cereals and vegetables}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.2645408163265306\textwidth}P{0.3165816326530612\textwidth}P{0.26887755102040817\textwidth}}
Years\tabcellsep Wheat\tabcellsep Milk\\
1992\tabcellsep 7951\tabcellsep 3649\\
1993\tabcellsep 9008\tabcellsep 4036\\
1994\tabcellsep 10256\tabcellsep 4674\\
1995\tabcellsep 11280\tabcellsep 4720\\
1996\tabcellsep 12428\tabcellsep 6004\\
1997\tabcellsep 13595\tabcellsep 7408\\
1998\tabcellsep 14953\tabcellsep 7231\\
1999\tabcellsep 15620\tabcellsep 7694\\
2000\tabcellsep 15906\tabcellsep 8244\\
2001\tabcellsep 16057\tabcellsep 7871\\
2002\tabcellsep 16525\tabcellsep 8825\\
2003\tabcellsep 16525\tabcellsep 9150\\
2004\tabcellsep 16800\tabcellsep 10696\\
2005\tabcellsep 17000\tabcellsep 11126\end{longtable} \par
 
\caption{\label{tab_4}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.054255319148936165\textwidth}P{0.14106382978723403\textwidth}P{0.08319148936170213\textwidth}P{0.1627659574468085\textwidth}P{0.08319148936170213\textwidth}P{0.14829787234042552\textwidth}P{0.0976595744680851\textwidth}P{0.05063829787234043\textwidth}P{0.02893617021276596\textwidth}}
\tabcellsep \multicolumn{2}{l}{Coefficients}\tabcellsep \multicolumn{2}{l}{Standard Error}\tabcellsep T\tabcellsep \tabcellsep F\tabcellsep R 2\\
\tabcellsep \multicolumn{2}{l}{Constant International}\tabcellsep \multicolumn{2}{l}{Constant International}\tabcellsep \multicolumn{2}{l}{Constant International}\tabcellsep \\
\tabcellsep \tabcellsep price and\tabcellsep \tabcellsep price and\tabcellsep \tabcellsep price and\tabcellsep \\
\tabcellsep \tabcellsep Tariff\tabcellsep \tabcellsep Tariff\tabcellsep \tabcellsep Tariff\tabcellsep \\
\multicolumn{2}{l}{Wheat 3.942}\tabcellsep .608\tabcellsep .678\tabcellsep .080\tabcellsep 5.812\tabcellsep 7.579\tabcellsep 57.445\tabcellsep 0.827\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep (0.000)\tabcellsep (0.000)\tabcellsep (0.000)\\
Milk\tabcellsep 6.096\tabcellsep .361\tabcellsep 1.362\tabcellsep .136\tabcellsep 4.477\tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep (\tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_5}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_6}Table 5}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.14053333333333332\textwidth}P{0.15186666666666668\textwidth}P{0.15413333333333334\textwidth}P{0.07593333333333334\textwidth}P{0.16433333333333333\textwidth}P{0.1632\textwidth}}
Wheat\tabcellsep \tabcellsep \tabcellsep Milk\tabcellsep \tabcellsep \\
Estimated\tabcellsep Calculated Prices\tabcellsep Calculated Prices\tabcellsep Estimated\tabcellsep Calculated\tabcellsep Calculated\\
Prices\tabcellsep at average Tariff\tabcellsep at actual tariff\tabcellsep Prices\tabcellsep Prices at\tabcellsep Prices at\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep average Tariff\tabcellsep actual tariff\\
1992\tabcellsep 2303.19\tabcellsep 5710.44\tabcellsep \tabcellsep 18198.05\tabcellsep 15372.38\\
1993\tabcellsep 2512.14\tabcellsep 6020.14\tabcellsep \tabcellsep 11549.63\tabcellsep 13043.77\\
1994\tabcellsep 2564.06\tabcellsep 6095.50\tabcellsep \tabcellsep 29086.18\tabcellsep 18210.46\\
1995\tabcellsep 2835.30\tabcellsep 6479.90\tabcellsep \tabcellsep 14966.69\tabcellsep 14324.13\\
1996\tabcellsep 4274.04\tabcellsep 8317.06\tabcellsep \tabcellsep 13760.75\tabcellsep 13895.92\\
1997\tabcellsep 3874.86\tabcellsep 7835.60\tabcellsep \tabcellsep 16228.91\tabcellsep 14749.33\\
1998\tabcellsep 3237.58\tabcellsep 7024.46\tabcellsep \tabcellsep 17524.88\tabcellsep 15164.46\\
1999 2893.62\tabcellsep 3054.84\tabcellsep 6780.59\tabcellsep 21909.05\tabcellsep 18106.10\tabcellsep 15344.27\\
2000 3417.45\tabcellsep 3874.23\tabcellsep 7834.82\tabcellsep 47965.89\tabcellsep 38503.78\tabcellsep 20152.62\\
2001 4885.09\tabcellsep 7657.62\tabcellsep 11857.50\tabcellsep 25368.37\tabcellsep 22506.73\tabcellsep 16599.05\\
2002 7216.55\tabcellsep 7751.85\tabcellsep 11946.03\tabcellsep 28339.09\tabcellsep 27072.45\tabcellsep 17744.49\\
2003\tabcellsep 10189.22\tabcellsep 14107.03\tabcellsep \tabcellsep 44670.53\tabcellsep 21263.79\\
2004 9040.87\tabcellsep 13416.13\tabcellsep 16676.47\tabcellsep 31543.21\tabcellsep 29771.98\tabcellsep 18364.43\\
2005 8798.66\tabcellsep 8592.59\tabcellsep 12718.04\tabcellsep 36635.98\tabcellsep 34835.70\tabcellsep 19436.73\end{longtable} \par
 
\caption{\label{tab_7}Table 6 :}\end{figure}
 			\footnote{Major cities are: Karachi (Port city), Lahore, Sialkot, Rawalpindi, Peshawar, Quetta, Islamabad.} 			\footnote{Global Journal of Management and Business Research Volume XII Issue XI Version I} 			\footnote{© 2012 Global Journals Inc. (US) July} 			\footnote{http://tariffdata.wto.org/ReportersAndProducts.aspx\hyperref[b5]{5} Real world tariff rates (in percentage) are available from WTO online dataset for 1999-2002 and 2004-2005 on some goods. These tariff rates on various goods are used as a benchmark to verify the reliability and accuracy of the average calculated tariff.\hyperref[b6]{6} Volume IV. Pp. 477-503.} 			\footnote{Global Journal of Management and Business Research Volume XII Issue XI Version I 2012 © 2012 Global Journals Inc. (US) July} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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